origin 15 : a kaleidoscope of color

8/7/2019 Origin 15 : A Kaleidoscope of Color

1/30

Of particular interest in our study of the universe is the existence of Great Walls and the GreatAttractor. Thought to be extremely long, yet thin, alignments of galaxies, clusters of galaxies andsuperclusters, assembled by large quantities of dark matter, it is thought that they might representa geometric structure congruent with the infalling strings from the superverse into the black holewe are within. These also represent topological defects left over from the early universe, earlyconnections still maintained, perhaps reflected in ancient black hole wormhole tunnelentanglements that still link distant parts of the universe which were once adjacent (and still are inother layers.) This reflects the universe's existence as a quantum particle, subject to quantumnonlocality. They expand in length as the universe expands, but remain narrow in width andheight. The parallel string-like timelines of the Hopf Fibration universe we are within may alsorepresent different states of the Universal string we reside upon (time proceeds lengthwise downthe string and space-time is any given point upon it.) The different timeline fibers of the HopfFibration are actually all one universal string that loops around from big bounce to big bounce(see image.) This is also reflected in the one dimensional mobius strip, which is our universe onits very basic level, expanding to torus and later to hypersphere (the 4th dimension being time.)The twist of the mobius and the center of the torus and the hypersphere are where the big bangoccurred. Since time is the fourth dimension of the hypersphere or glome, we exist on its threedimensional surface, all equidistant from the center, which is where the big bang and bouncesoccur. It's quite interesting and no accident that the volume of a torus and the surface area of thehypersphere are the same, just like how the Hopf Fibration looks very much like a torus. This

should give you an idea of why our universe can exist in all these shapes all across its timelines(remember that all times exist simultaneously.) As mentioned in Origin 12, this is the regionwhich flips from black hole to white hole as polarity reverses between the different members ofthe quadverse and we are either expanding or contracting, and either accumulating dark energyor dark matter in a higher ratio to the other. The reason the Great Wall and Great Attractor wereassembled so quickly is precisely because the universe is cyclical and information for theirassemblage isn't lost, but maintained in the cosmic DNA of the universe, which was impartedupon it by the superverse. This is why it is a fractal representative of the superverse and theomniverse, as this cosmic DNA gets passed down to all baby universes/quadverses. The otherreason why this happened with such rapidity is that dark matter, only influenced by gravity, canproceed at faster than c speeds, and therefore experiences negative time (it is actually matterfrom the antiverse, just like our matter is their dark matter and experiences negative time there).The transfer and conversion of matter to dark matter in both directions is what ultimately causes

the balanced cyclical nature of the quadverse, as this transference occurs between the universeand the antiverse, and the mirrorverse and the antimirroverse. This brings to bear the AharanovEffect, and the future postselects the past on the macro level, just as is the case on the quantumlevel. Bolstering this idea is the recent possible discovery of the sterile neutrino, which alsoexperiences time in both directions, because the only force which impacts it is gravity, whichexists in all dimensions, in a looping form (just like time), unlike the other forces, which are limitedstrings.

If, as mentioned in Origin 13, our universe evolved from 1D to 2D to 3D and will one day reach4D, the question then becomes what will be the nature of this fourth dimension? Will it be aninternally manufactured dimension, like the other three spatial dimensions, or will it behyperspace, from the omniverse? I believe it will be the latter. Why? Because 3D space isstable, and once our universe expands to the extent needed to create the fourth dimension, it will

be so cold that it will reach the below absolute zero temps needed to interface with theomniverse. This, in turn, will cause explosive inflation (inflation phase 2), which will expand theuniverse within the omniverse, until it reaches the Cauchy Horizon of the black hole we residewithin, and then it will bounce back just as explosively, and contraction will begin. In inflationphase 2, no alternate timelines will be manufactured, unlike the first inflation, because when theuniverse was 2D there was no gravitation. In 3D space, we have gravitation, so that will keepnew emergent timelines from forming. The situation will be the reverse for the antiverse; whenwe go from 3D to 4D space and reach inflation phase 2, hit the Cauchy Horizon and contracttowards our next big bounce with converging timelines, it will be big bouncing and reachinginflation phase 1 and creating the parallel timelines in 2+1, just prior to phase transitioning to 3+1


2/30


3/30

well chapter one was written about a year ago and in it I mention a theory called technicolor, fromwhich I theorized that our dimensions and mass emerged from... instead of the Higgs Bosonwhich is what conventional physics has assumed.... I just think technicolor makes much moresense and is a much more elegant theory, and it is a structure of reality based on color theory

well basically I analogized the three primary colors to the three spatial dimensions and time asthe background.... and then you can also construct three negative spatial dimensions which arethe represented by the complementary primary colors and a similar complementary timedimensionRed Green Blue RGB are the additive primariesthe complementary subtractive primaries arecyan magenta and yellowblack and white represent time and complementary time. The complementary dimensions makeup the antiverse and the antimirrorverse.

it just occurred to me how three dimensions of space are so similar to the three primary colorsand how time could be similar to the background upon which it was built. Note that in QCD, colorcharge effect becomes nil outside of the particle..... thus, anyone in the superverse would not seeour dimensions (they have their own dimensions that arise from their own cosmic color charge),but on the inside, we are subject to them and perceive them as dimensions.

well there are two possibilitiesone is just two dimensionswhich would be a particle and its complementaryif youve seen a color wheel, you know its the color opposite to it on the color wheelthe other possibility is 3 particles, in which case you have the primary colorseach color represents one third of the charge of the particlethe colors correspond to color chargeyou have to imagine it as a rubber band.... within the rubber band they can move freelybut once they reach the edge and start trying to get out, the rubber band becomes tightand pushes them back in

it is how I also picture the universe.... with gravity taking the place of this force on a universal

scale and the dimensions taking the place of color charge. Once the universe expands to thecauchy horizon, it "bounces back." Notice the fractal representation of quantum lattice and spinnetworks-- this shows that cosmic DNA replicates itself in the baby universe and thus they aremade in the image of the omniverse itself.

This also works with Calabi-Yau manifolds, which are six dimensional, as each manifold would beconstructed of the three additive primary spatial dimensions plus the three subtractive primaryspatial dimensions.

This is the first step towards a gravity-strong force unification, to match electro-weak unification....so instead of 4 forces, we'd have 2 x 2 (just like the quadverse arrangement..... more fractality!)

Universes with additional dimensions can be created based on this framework by adding inresonances or higher and lower energy versions that exist on higher or lower energy levels.... likethe electron, muon and tauon, for example. Universes with the same dimensions, like paralleltimeverses and mirrorverses can also exist on different energy levels.

The renowned Kip Thorne has created a solution to the geometry of two colliding black holeswhich looks suspiciously like the Hopf Fibration and E8, as well as the toroidal model of the


4/30

universe. It is therefore theorized that baby universes can be created when two black holescollide and merge, resulting in a warping of space and time that creates the shape of the babyuniverse that lies within. The physical properties and laws of the universe are determined by thespin, charge, cosmic color charge (aka dimensions, which may also arise from infalling quarkgluon plasma and cosmic strings) and other properties of the parent black holes as well as theresults of the collision. Both parent black holes provide cosmic DNA which goes into producingthe baby universe. The fractal representation of this also resembles the structure of largegalaxies, therefore it is also theorized that these baby universes are produced at the core of thesegalaxies where the supermassive blackhole exists, during the quasar active stage of its life cycle.As mentioned above, this also shows how quantum lattice and spin networks are replicatedthroughout the omniverse, as cosmic DNA and gravity mold not only the structures withinuniverses, but the omniverse itself.

The interesting thing about the quantum mirror analogy is it reminds me of the "FunhouseMirrors" analogy I used in describing parallel time universes-- basically, they are multiple imagesof the same thing, distorted by various gravitational effects. But they are really reflections of thesame universe in superpositional states with itself.

Physicists discover new way to visualize warped space and timeApril 11th, 2011 in Physics / General Physics

Enlarge

Two doughnut-shaped vortexes ejected by a pulsating black hole. Also shown at the center aretwo red and two blue vortex lines attached to the hole, which will be ejected as a third doughnut-shaped vortex in the next pulsation. Credit: The Caltech/Cornell SXS Collaboration

(PhysOrg.com) -- When black holes slam into each other, the surrounding space and time surgeand undulate like a heaving sea during a storm. This warping of space and time is so complicatedthat physicists haven't been able to understand the details of what goes on -- until now.

"We've found ways to visualize warped space-time like never before," says Kip Thorne, FeynmanProfessor of Theoretical Physics, Emeritus, at the California Institute of Technology (Caltech).

By combining theory with computer simulations, Thorne and his colleagues at Caltech, CornellUniversity, and the National Institute for Theoretical Physics in South Africa have developedconceptual tools they've dubbed tendex lines and vortex lines.

Using these tools, they have discovered that black-hole collisions can produce vortex lines thatform a doughnut-shaped pattern, flying away from the merged black hole like smoke rings. Theresearchers also found that these bundles of vortex linescalled vortexescan spiral out of theblack hole like water from a rotating sprinkler.

The researchers explain tendex and vortex linesand their implications for black holesin a

paper that's published online on April 11 in the journal Physical Review Letters.

These are two spiral-shaped vortexes (yellow) of whirling space sticking out of a black hole, andthe vortex lines (red curves) that form the vortexes. Credit: The Caltech/Cornell SXSCollaborationTendex and vortex lines describe the gravitational forces caused by warped space-time. They areanalogous to the electric and magnetic field lines that describe electric and magnetic forces.


5/30

Tendex lines describe the stretching force that warped space-time exerts on everything itencounters. "Tendex lines sticking out of the moon raise the tides on the earth's oceans," saysDavid Nichols, the Caltech graduate student who coined the term "tendex." The stretching forceof these lines would rip apart an astronaut who falls into a black hole.

Vortex lines, on the other hand, describe the twisting of space. If an astronaut's body is alignedwith a vortex line, she gets wrung like a wet towel.

When many tendex lines are bunched together, they create a region of strong stretching called atendex. Similarly, a bundle of vortex lines creates a whirling region of space called a vortex."Anything that falls into a vortex gets spun around and around," says Dr. Robert Owen of CornellUniversity, the lead author of the paper.

Tendex and vortex lines provide a powerful new way to understand black holes, gravity, and thenature of the universe. "Using these tools, we can now make much better sense of thetremendous amount of data that's produced in our computer simulations," says Dr. Mark Scheel,a senior researcher at Caltech and leader of the team's simulation work.

Using computer simulations, the researchers have discovered that two spinning black holescrashing into each other produce several vortexes and several tendexes. If the collision is head-

on, the merged hole ejects vortexes as doughnut-shaped regions of whirling space, and it ejectstendexes as doughnut-shaped regions of stretching. But if the black holes spiral in toward eachother before merging, their vortexes and tendexes spiral out of the merged hole. In either casedoughnut or spiralthe outward-moving vortexes and tendexes become gravitational wavesthekinds of waves that the Caltech-led Laser Interferometer Gravitational-Wave Observatory (LIGO)seeks to detect.

"With these tendexes and vortexes, we may be able to much more easily predict the waveformsof the gravitational waves that LIGO is searching for," says Yanbei Chen, associate professor ofphysics at Caltech and the leader of the team's theoretical efforts.

Additionally, tendexes and vortexes have allowed the researchers to solve the mystery behind thegravitational kick of a merged black hole at the center of a galaxy. In 2007, a team at the

University of Texas in Brownsville, led by Professor Manuela Campanelli, used computersimulations to discover that colliding black holes can produce a directed burst of gravitationalwaves that causes the merged black hole to recoillike a rifle firing a bullet. The recoil is sostrong that it can throw the merged hole out of its galaxy. But nobody understood how thisdirected burst of gravitational waves is produced.

Now, equipped with their new tools, Thorne's team has found the answer. On one side of theblack hole, the gravitational waves from the spiraling vortexes add together with the waves fromthe spiraling tendexes. On the other side, the vortex and tendex waves cancel each other out.The result is a burst of waves in one direction, causing the merged hole to recoil.

"Though we've developed these tools for black-hole collisions, they can be applied whereverspace-time is warped," says Dr. Geoffrey Lovelace, a member of the team from Cornell. "For

instance, I expect that people will apply vortex and tendex lines to cosmology, to black holesripping stars apart, and to the singularities that live inside black holes. They'll become standardtools throughout general relativity."

The team is already preparing multiple follow-up papers with new results. "I've never beforecoauthored a paper where essentially everything is new," says Thorne, who has authoredhundreds of articles. "But that's the case here."

More information: Physical Review Letters paper: "Frame-dragging vortexes and tidal tendexesattached to colliding black holes: Visualizing the curvature of spacetime"


6/30

Provided by California Institute of Technology

"Physicists discover new way to visualize warped space and time." April 11th, 2011.http://www.physorg.com/news/2011-04-physicists-visualize-warped-space.html

Atom and its quantum mirror imageApril 5, 2011 By Florian Aigner

Enlarge

Towards the mirror or away from the mirror? Physicists create atoms in quantum superpositionstates.

A team of physicists experimentally produces quantum-superpositions, simply using a mirror.Standing in front of a mirror, we can easily tell apart ourselves from our mirror image. The mirrordoes not affect our motion in any way. For quantum particles, this is much more complicated. In aspectacular experiment in the labs of the Heidelberg University, a group of physicists from

Heidelberg Unversity, together with colleagues at TU Munich and TU Vienna extended agedanken experiment by Einstein and managed to blur the distinction between a particle and itsmirror image. The results of this experiment have now been published in the journal NaturePhysics.

Emitted Light, Recoiling Atom

When an atom emits light (i.e. a photon) into a particular direction, it recoils in the oppositedirection. If the photon is measured, the motion of the atom is known too. The scientists placedatoms very closely to a mirror. In this case, there are two possible paths for any photon travellingto the observer: it could have been emitted directly into the direction of the observer, or it couldhave travelled into the opposite direction and then been reflected in the mirror. If there is no wayof distinguishing between these two scenarios, the motion of the atom is not determined, the

atom moves in a superposition of both paths.

If the distance between the atom and the mirror is very small, it is physically impossible todistinguish between these two paths, Jiri Tomkovic, PhD student at Heidelberg explains. Theparticle and its mirror image cannot be clearly separated any more. The atom moves towards themirror and away from the mirror at the same time. This may sound paradoxical and it is certainlyimpossible in classical phyiscs for macroscopic objects, but in quantum physics, suchsuperpositions are a well-known phenomenon. This uncertainty about the state of the atom doesnot mean that the measurement lacks precision, Jrg Schmiedmayer (TU Vienna) emphasizes.It is a fundamental property of quantum physics: The particle is in both of the two possible statessimultaneousely, it is in a superposition. In the experiment the two motional states of the atom one moving towards the mirror and the other moving away from the mirror are then combinedusing Bragg diffraction from a grating made of laser light. Observing interference it can be directly

shown that the atom has indeed been traveling both paths at once.On Different Paths at the Same Time

This is reminiscent of the famous double-slit experiment, in which a particle hits a plate with twoslits and passes through both slits simultaneously, due to its wave-like quantum mechanicalproperties. Einstein already discussed that this can only be possible if there is no way todetermine which path the particle actually chose, not even precise measurements of any tinyrecoil of the double slit plate itself. As soon as there even a theoretically possible way ofdetermining the path of the particle, the quantum superposition breaks down. In our case, thephotons play a role similar to the double slit, Markus Oberthaler (Heidelberg University) explains.


7/30

If the light can, in principle, tell us about the motion of the atom, then the motion isunambiguously determined. Only when it is fundamentally undecidable, the atom can be in asuperposition state, combining both possibilities. And this fundamental undecidability isguaranteed by the mirror which takes up the photon momentum.

Quantum Effect Using Only a Mirror

Probing under which conditions such quantum-superpositions can be created has become veryimportant in quantum physics. Jrg Schmiedmayer and Markus Obertaler came up with the ideafor this experiment already a few years ago. The fascinating thing about this experiment, thescientists say, is the possibility of creating a quantum superposition state, using only a mirror,without any external fields. In a very simple and natural way the distinction between the particleand its mirror image becomes blurred, without complicated operations carried out by theexperimenter.

Provided by Vienna University of Technology

http://www.physorg.com/news/2011-04-atom-quantum-mirror-image.html

http://www.newscient...true&print=true

Home |Physics& Math |Space | News |Back to articleMystery signal at Fermilab hints at 'technicolour' force

* 19:46 07 April 2011 by Amanda Gefter* For similar stories, visit the Quantum World and The Large Hadron Collider Topic Guides

Hints of new physics at the Tevatron (Image: Fermilab)

Hints of new physics at the Tevatron (Image: Fermilab)

1 more image

The physics world is buzzing with news of an unexpected sighting at Fermilab's Tevatron colliderin Illinois a glimpse of an unidentified particle that, should it prove to be real, will radically alterphysicists' prevailing ideas about how nature works and how particles get their mass.

The candidate particle may not belong to the standard model of particle physics, physicists' besttheory for how particles and forces interact. Instead, some say it might be the first hint of a newforce of nature, called technicolour, which would resolve some problems with the standard modelbut would leave others unanswered.

The observation was made by Fermilab's CDF experiment, which smashes together protons andantiprotons 2 million times every second. The data, collected over a span of eight years, looks atcollisions that produce a W boson, the carrier of the weak nuclear force, and a pair of jets ofsubatomic particles called quarks.

Physicists predicted that the number of these events producing a W boson and a pair of jets would fall off as the mass of the jet pair increased. But the CDF data showed something strange(see graph): a bump in the number of events when the mass of the jet pair was about 145 GeV.Just a fluke?

That suggests that the additional jet pairs were produced by a new particle weighing about 145GeV. "We expected to see a smooth shape that decreases for increasing values of the mass,"says CDF team member Pierluigi Catastini of Harvard University in Cambridge, Massachusetts."Instead we observe an excess of events concentrated in one region, and it seems to be a bump


8/30

the typical signature of a particle."

Intriguing as it sounds, there is a 1 in 1000 chance that the bump is simply a statistical fluke.Those odds make it a so-called three-sigma result, falling short of the gold standard for adiscovery five sigma, or a 1 in a million chance of error. "I've seen three-sigma effects comeand go," says Kenneth Lane of Boston University in Massachusetts. Still, physicists are 99.9 percent sure it is not a fluke, so they are understandably anxious to pin down the particle's identity.

Most agree that the mysterious particle is not the long-sought Higgs boson, believed by many toendow particles with mass. "It's definitely not a Higgs-like object," says Rob Roser, a CDFspokesperson at Fermilab. If it were, the bump in the data would be 300 times smaller. What'smore, a Higgs particle should most often decay into bottom quarks, which do not seem to makean appearance in the Fermilab data.Fifth force

"There's no version of a Higgs in any model that I know of where the production rate would bethis large," says Lane. "It has to be something else." And Lane is confident that he knows exactlywhat it is.

Just over 20 years ago, Lane, along with Fermilab physicist Estia Eichten, predicted that

experiments would see just such a signal. Lane and Eichten were working on a theory known astechnicolour, which proposes the existence of a fifth fundamental force in addition to the fouralready known: gravity, electromagnetism, and the strong and weak nuclear forces. Technicolouris very similar to the strong force, which binds quarks together in the nuclei of atoms, only itoperates at much higher energies. It is also able to give particles their mass rendering theHiggs boson unnecessary.The new force comes with a zoo of new particles. Lane and Eichten's model predicted that atechnicolour particle called a technirho would often decay into a W boson and another particlecalled a technipion.

In a new paper, Lane, Eichten and Fermilab physicist Adam Martin suggest that a technipion witha mass of about 160 GeV could be the mysterious particle producing the two jets. "If this is real, Ithink people will give up on the idea of looking for the Higgs and begin exploring this rich world of

new particles," Lane says.Future tests

But if technicolour is correct, it would not be able to resolve all the questions left unanswered bythe standard model. For example, physicists believe that at the high energies found in the earlyuniverse, the fundamental forces of nature were unified into a single superforce. Supersymmetry,physicists' leading contender for a theory beyond the standard model, paves a way for the forcesto unite at high energies, but technicolour does not.

Figuring out which theory if either is right means combing through more heaps of data todetermine if the new signal is real. Budget constraints mean the Tevatron will shut down this year,but fortunately the CDF team, which made the find, is already "sitting on almost twice the datathat went into this analysis", says Roser. "Over the coming months we will redo the analysis with

double the data."

Meanwhile, DZero, Fermilab's other detector, will analyse its own data to provide independentcorroboration or refutation of the bump. And at CERN's Large Hadron Collider near Geneva,Switzerland, physicists will soon collect enough data to perform their own search. In their paper,Lane and his colleagues suggest ways to look for other techniparticles.

"I haven't been sleeping very well for the past six months," says Lane, who found out about thebump long before the team went public with the result. "If this is what we think it is, it's a wholenew world beyond quarks and leptons. It'll be great! And if it's not, it's not."


9/30

Journal reference: arxiv.org/abs/1104.0699

Invariant Mass Distribution of Jet Pairs Produced in Association with a W boson in ppbarCollisions at sqrt(s) = 1.96 TeVCDF Collaboration, T. Aaltonen, et al(Submitted on 4 Apr 2011)We report a study of the invariant mass distribution of jet pairs produced in association with a Wboson using data collected with the CDF detector which correspond to an integrated luminosity of4.3 fb^-1. The observed distribution has an excess in the 120-160 GeV/c^2 mass range which isnot described by current theoretical predictions within the statistical and systematic uncertainties.In this letter we report studies of the properties of this excess. Comments: 8 pages, 2figuresSubjects: High Energy Physics - Experiment (hep-ex)Report number: FERMILAB-PUB-11-164-ECite as: arXiv:1104.0699v1 [hep-ex]

Submission historyFrom: Alberto Annovi [view email][v1] Mon, 4 Apr 2011 22:08:31 GMT (119kb,D)

http://en.wikipedia....icolor_(physics)

Technicolor theories are models of physics beyond the standard model that address electroweaksymmetry breaking, the mechanism through which elementary particles acquire masses. Earlytechnicolor theories were modelled on quantum chromodynamics (QCD), the "color" theory of thestrong nuclear force, which inspired their name.

Instead of introducing elementary Higgs bosons, technicolor models hide electroweak symmetryand generate masses for the W and Z bosons through the dynamics of new gauge interactions.Although asymptotically free at very high energies, these interactions must become strong andconfining (and hence unobservable) at lower energies that have been experimentally probed.This dynamical approach is natural and avoids the hierarchy problem of the Standard Model.[1]

In order to produce quark and lepton masses, technicolor has to be "extended" by additionalgauge interactions. Particularly when modelled on QCD, extended technicolor is challenged byexperimental constraints on flavor-changing neutral current and precision electroweakmeasurements. It is not known what is the extended technicolor dynamics.

Much technicolor research focuses on exploring strongly-interacting gauge theories other thanQCD, in order to evade some of these challenges. A particularly active framework is "walking"technicolor, which exhibits nearly-conformal behavior caused by an infrared fixed point withstrength just above that necessary for spontaneous chiral symmetry breaking. Whether walkingcan occur and lead to agreement with precision electroweak measurements is being studiedthrough non-perturbative lattice simulations.[2]

Experiments at the Large Hadron Collider are expected to discover the mechanism responsiblefor electroweak symmetry breaking, and will be critical for determining whether the technicolorframework provides the correct description of nature.

Contents [hide]1 Introduction2 Early technicolor3 Extended technicolor4 Walking technicolor


10/30

4.1 Top quark mass5 Minimal Walking Models6 Technicolor on the lattice7 Technicolor phenomenology7.1 Precision electroweak tests7.2 Hadron collider phenomenology7.3 Dark matter8 See also9 References

[edit]Introduction

The mechanism for the breaking of electroweak gauge symmetry in the Standard Model ofelementary particle interactions remains unknown. The breaking must be spontaneous, meaningthat the underlying theory manifests the symmetry exactly (the gauge-boson fields are masslessin the equations of motion), but the solutions (the ground state and the excited states) do not. Inparticular, the physical W and Z gauge bosons become massive. This phenomenon, in which theW and Z bosons also acquire an extra polarization state, is called the "Higgs mechanism".Despite the precise agreement of the electroweak theory with experiment at energies accessible

so far, the necessary ingredients for the symmetry breaking remain hidden, yet to be revealed athigher energies.

The simplest mechanism of electroweak symmetry breaking introduces a single complex field andpredicts the existence of the Higgs boson. Typically, the Higgs boson is "unnatural" in the sensethat quantum mechanical fluctuations produce corrections to its mass that lift it to such highvalues that it cannot play the role for which it was introduced. Unless the Standard Model breaksdown at energies less than a few TeV, the Higgs mass can be kept small only by a delicate fine-tuning of parameters.

Technicolor avoids this problem by hypothesizing a new gauge interaction coupled to newmassless fermions. This interaction is asymptotically free at very high energies and becomesstrong and confining as the energy decreases to the electroweak scale of roughly 250 GeV.

These strong forces spontaneously break the massless fermions' chiral symmetries, some ofwhich are weakly gauged as part of the Standard Model. This is the dynamical version of theHiggs mechanism. The electroweak gauge symmetry is thus broken, producing masses for the Wand Z bosons.

The new strong interaction leads to a host of new composite, short-lived particles at energiesaccessible at the Large Hadron Collider (LHC). This framework is natural because there are noelementary Higgs bosons and, hence, no fine-tuning of parameters. Quark and lepton massesalso break the electroweak gauge symmetries, so they, too, must arise spontaneously. Amechanism for incorporating this feature is known as extended technicolor. Technicolor andextended technicolor face a number of phenomenological challenges. Some of them can beaddressed within a class of theories known as walking technicolor.[edit]

Early technicolor

Technicolor is the name given to the theory of electroweak symmetry breaking by new stronggauge-interactions whose characteristic energy scale TC is the weak scale itself, TC FEW 246 GeV. The guiding principle of technicolor is "naturalness": basic physicalphenomena should not require fine-tuning of the parameters in the Lagrangian thatdescribes them. What constitutes fine-tuning is to some extent a subjective matter,but a theory with elementary scalar particles typically is very finely tuned (unless it issupersymmetric). The quadratic divergence in the scalar's mass requires adjustmentsof a part in , where Mbare is the cutoff of the theory, the energy scale at which the


11/30

theory changes in some essential way. In the standard electroweak model with Mbare 1015 GeV (the grand-unification mass scale), and with the Higgs boson massMphysical = 100500 GeV, the mass is tuned to at least a part in 1025.

By contrast, a natural theory of electroweak symmetry breaking is an asymptotically-free gauge theory with fermions as the only matter fields. The technicolor gauge

group GTC is often assumed to be SU(NTC). Based on analogy with quantumchromodynamics (QCD), it is assumed that there are one or more doublets ofmassless Dirac "technifermions" transforming vectorially under the same complexrepresentation of GTC, TiL,R = (Ui,Di)L,R, i = 1,2, ,Nf/2. Thus, there is a chiralsymmetry of these fermions, e.g., SU(Nf)L SU(Nf)R, if they all transform accordingthe same complex representation of GTC. Continuing the analogy with QCD, therunning gauge coupling TC() triggers spontaneous chiral symmetry breaking, thetechnifermions acquire a dynamical mass, and a number of massless Goldstonebosons result. If the technifermions transform under [SU(2) U(1)]EW as left-handeddoublets and right-handed singlets, three linear combinations of these Goldstonebosons couple to three of the electroweak gauge currents.

In 1973 Jackiw and Johnson[3] and Cornwall and Norton[4] studied the possibility thata (non-vectorial) gauge interaction of fermions can break itself; i.e., is strong enoughto form a Goldstone boson coupled to the gauge current. Using Abelian gaugemodels, they showed that, if such a Goldstone boson is formed, it is "eaten" by theHiggs mechanism, becoming the longitudinal component of the now massive gaugeboson. Technically, the polarization function (p2) appearing in the gauge bosonpropagator, = (p p/p2 - g)/[p2(1 g2 (p2))] develops a pole at p2 = 0 withresidue F2, the square of the Goldstone boson's decay constant, and the gaugeboson acquires mass M g F. In 1973, Weinstein[5] showed that compositeGoldstone bosons whose constituent fermions transform in the standard way underSU(2) U(1) generate the weak boson masses

This standard-model relation is achieved with elementary Higgs bosons inelectroweak doublets; it is verified experimentally to better than 1%. Here, g and gare SU(2) and U(1) gauge couplings and tanW = g/g defines the weak mixing angle.

The important idea of a new strong gauge interaction of massless fermions at theelectroweak scale FEW driving the spontaneous breakdown of its global chiralsymmetry, of which an SU(2) U(1) subgroup is weakly gauged, was first proposedin 1979 by S. Weinberg[6] and L. Susskind.[7] This "technicolor" mechanism isnatural in that no fine-tuning of parameters is necessary.[edit]Extended technicolor

Elementary Higgs bosons perform another important task. In the Standard Model,quarks and leptons are necessarily massless because they transform under SU(2)

U(1) as left-handed doublets and right-handed singlets. The Higgs doublet couples tothese fermions. When it develops its vacuum expectation value, it transmits thiselectroweak breaking to the quarks and leptons, giving them their observed masses.(In general, electroweak-eigenstate fermions are not mass eigenstates, so thisprocess also induces the mixing matrices observed in charged-current weakinteractions.)

In technicolor, something else must generate the quark and lepton masses. The onlynatural possibility, one avoiding the introduction of elementary scalars, is to enlarge


12/30

GTC to allow technifermions to couple to quarks and leptons. This coupling is inducedby gauge bosons of the enlarged group. The picture, then, is that there is a large"extended technicolor" (ETC) gauge group GETC GTC in which technifermions,quarks, and leptons live in the same representations. At one or more high scalesETC, GETC is broken down to GTC, and quarks and leptons emerge as the TC-singletfermions. When TC() becomes strong at scale TC FEW, the fermionic

condensate forms. (The condensate is the vacuum expectation value of thetechnifermion bilinear . The estimate here is based on naive dimensional analysis ofthe quark condensate in QCD, expected to be correct as an order of magnitude.)Then, the transitions can proceed through the technifermion's dynamical mass bythe emission and reabsorption of ETC bosons whose masses METC gETC ETC aremuch greater than TC. The quarks and leptons develop masses given approximatelyby

Here, is the technifermion condensate renormalized at the ETC boson mass scale,

where m() is the anomalous dimension of the technifermion bilinear at the scale .The second estimate in Eq. (2) depends on the assumption that, as happens in QCD,TC() becomes weak not far above TC, so that the anomalous dimension m of issmall there. Extended technicolor was introduced in 1979 by Dimopoulos andSusskind,[8] and by Eichten and Lane.[9] For a quark of mass mq 1 GeV, and withTC 250 GeV, one estimates ETC 15 TeV. Therefore, assuming that , METC willbe at least this large.

In addition to the ETC proposal for quark and lepton masses, Eichten and Laneobserved that the size of the ETC representations required to generate all quark andlepton masses suggests that there will be more than one electroweak doublet oftechnifermions.[9] If so, there will be more (spontaneously broken) chiral symmetriesand therefore more Goldstone bosons than are eaten by the Higgs mechanism. Thesemust acquire mass by virtue of the fact that the extra chiral symmetries are alsoexplicitly broken, by the standard-model interactions and the ETC interactions. These"pseudo-Goldstone bosons" are called technipions, T. An application of Dashen'stheorem[10] gives for the ETC contribution to their mass

The second approximation in Eq. (4) assumes that . For FEW TC 250 GeV andETC 15 TeV, this contribution to MT is about 50 GeV. Since ETC interactionsgenerate and the coupling of technipions to quark and lepton pairs, one expects thecouplings to be Higgs-like; i.e., roughly proportional to the masses of the quarks andleptons. This means that technipions are expected to decay to the heaviest andpairs allowed.

Perhaps the most important restriction on the ETC framework for quark massgeneration is that ETC interactions are likely to induce flavor-changing neutralcurrent processes such as e , KL e, and | S| = 2 and | B| = 2 interactionsthat induce and mixing.[9] The reason is that the algebra of the ETC currentsinvolved in generation imply and ETC currents which, when written in terms offermion mass eigenstates, have no reason to conserve flavor. The strongestconstraint comes from requiring that ETC interactions mediating mixing contributeless than the Standard Model. This implies an effective ETC greater than 1000 TeV.


13/30

The actual ETC may be reduced somewhat if CKM-like mixing angle factors arepresent. If these interactions are CP-violating, as they well may be, the constraintfrom the -parameter is that the effective ETC > 104 TeV. Such huge ETC massscales imply tiny quark and lepton masses and ETC contributions to MT of at most afew GeV, in conflict with LEP searches for T at the Z0.

Extended technicolor is a very ambitious proposal, requiring that quark and leptonmasses and mixing angles arise from experimentally accessible interactions. If thereexists a successful model, it would not only predict the masses and mixings of quarksand leptons (and technipions), it would explain why there are three families of each:they are the ones that fit into the ETC representations of q, and T. It should not besurprising that the construction of a successful model has proven to be very difficult.[edit]Walking technicolor

Since quark and lepton masses are proportional to the bilinear technifermioncondensate divided by the ETC mass scale squared, their tiny values can be avoidedif the condensate is enhanced above the weak-TC estimate in Eq. (2), .

During the 1980s, several dynamical mechanisms were advanced to do this. In 1981Holdom suggested that, if the TC() evolves to a nontrivial fixed point in theultraviolet, with a large positive anomalous dimension m for , realistic quark andlepton masses could arise with ETC large enough to suppress ETC-induced mixing.[11] However, no example of a nontrivial ultraviolet fixed point in a four-dimensionalgauge theory has been constructed. In 1985 Holdom analyzed a technicolor theory inwhich a slowly varying TC() was envisioned.[12] His focus was to separate thechiral breaking and confinement scales, but he also noted that such a theory couldenhance and thus allow the ETC scale to be raised. In 1986 Akiba and Yanagida alsoconsidered enhancing quark and lepton masses, by simply assuming that TC isconstant and strong all the way up to the ETC scale.[13] In the same year Yamawaki,Bando and Matumoto again imagined an ultraviolet fixed point in a non-asymptotically free theory to enhance the technifermion condensate.[14]

In 1986 Appelquist, Karabali and Wijewardhana discussed the enhancement offermion masses in an asymptotically free technicolor theory with a slowly running, orwalking, gauge coupling.[15] The slowness arose from the screening effect of alarge number of technifermions, with the analysis carried out through two-loopperturbation theory. In 1987 Appelquist and Wijewardhana explored this walkingscenario further.[16] They took the analysis to three loops, noted that the walkingcan lead to a power law enhancement of the technifermion condensate, andestimated the resultant quark, lepton, and technipion masses. The condensateenhancement arises because the associated technifermion mass decreases slowly,roughly linearly, as a function of its renormalization scale. This corresponds to thecondensate anomalous dimension m in Eq. (3) approaching unity (see below).[17]

In the 1990s, the idea emerged more clearly that walking is naturally described by

asymptotically free gauge theories dominated in the infrared by an approximatefixed point. Unlike the speculative proposal of ultraviolet fixed points, fixed points inthe infrared are known to exist in asymptotically free theories, arising at two loops inthe beta function providing that the fermion count Nf is large enough. This has beenknown since the first two-loop computation in 1974 by Caswell.[18] If Nf is close tothe value at which asymptotic freedom is lost, the resultant infrared fixed point isweak, of parametric order , and reliably accessible in perturbation theory. This weak-coupling limit was explored by Banks and Zaks in 1982.[19]


14/30

The fixed-point coupling IR becomes stronger as Nf is reduced from . Below somecritical value Nfc the coupling becomes strong enough (> SB) to breakspontaneously the massless technifermions' chiral symmetry. Since the analysismust typically go beyond two-loop perturbation theory, the definition of the runningcoupling TC(), its fixed point value IR, and the strength SB necessary for chiralsymmetry breaking depend on the particular renormalization scheme adopted. For ;

i.e., for Nf just below Nfc, the evolution of TC() is governed by the infrared fixedpoint and it will evolve slowly (walk) for a range of momenta above the breakingscale TC. To overcome the -suppression of the masses of first and secondgeneration quarks involved in mixing, this range must extend almost to their ETCscale, of . Cohen and Georgi argued that m = 1 is the signal of spontaneous chiralsymmetry breaking, i.e., that m( SB) = 1.[17] Therefore, in the walking-TCregion, m 1 and, from Eqs. (2) and (3), the light quark masses are enhancedapproximately by METC/TC.

The idea that TC() walks for a large range of momenta when IR lies just above SB was suggested by Lane and Ramana.[20] They made an explicit model, discussedthe walking that ensued, and used it in their discussion of walking technicolorphenomenology at hadron colliders. This idea was developed in some detail byAppelquist, Terning and Wijewardhana.[21] Combining a perturbative computation ofthe infrared fixed point with an approximation of SB based on the Schwinger-Dyson equation, they estimated the critical value Nfc and explored the resultantelectroweak physics. Since the 1990s, most discussions of walking technicolor are inthe framework of theories assumed to be dominated in the infrared by anapproximate fixed point. Various models have been explored, some with thetechnifermions in the fundamental representation of the gauge group and someemploying higher representations.[22][23][24]

The possibility that the technicolor condensate can be enhanced beyond thatdiscussed in the walking literature, has also been considered recently by Luty andOkui under the name "conformal technicolor".[25] They envision an infrared stablefixed point, but with a very large anomalous dimension for the operator . It remainsto be seen whether this can be realized, for example, in the class of theoriescurrently being examined using lattice techniques.[edit]Top quark mass

The walking enhancement described above may be insufficient to generate themeasured top quark mass, even for an ETC scale as low as a few TeV. However, thisproblem could be addressed if the effective four-technifermion coupling resultingfrom ETC gauge boson exchange is strong and tuned just above a critical value.[26]The analysis of this strong-ETC possibility is that of a NambuJonaLasinio model withan additional (technicolor) gauge interaction. The technifermion masses are smallcompared to the ETC scale (the cutoff on the effective theory), but nearly constantout to this scale, leading to a large top quark mass. No fully realistic ETC theory forall quark masses has yet been developed incorporating these ideas. A related study

was carried out by Miransky and Yamawaki.[27] A problem with this approach is thatit involves some degree of parameter fine-tuning, in conflict with technicolorsguiding principle of naturalness.

Finally, it should be noted that there is a large body of closely related work in whichETC does not generate mt. These are the top quark condensate,[28] topcolor andtop-color-assisted technicolor models,[29] in which new strong interactions areascribed to the top quark and other third-generation fermions. As with the strong-ETCscenario described above, all these proposals involve a considerable degree of fine-


15/30

tuning of gauge couplings.[edit]Minimal Walking Models

In 2004 Francesco Sannino and Kimmo Tuominen proposed technicolor models withtechnifermions in higher-dimensional representations of the technicolor gauge group.

[23] They argued that these more "minimal" models required fewer flavors oftechnifermions in order to exhibit walking behavior, making it easier to pass precisionelectroweak tests.

For example, SU(2) and SU(3) gauge theories may exhibit walking with as few as twoDirac flavors of fermions in the adjoint or two-index symmetric representation. Incontrast, at least eight flavors of fermions in the fundamental representation of SU(3)(and possibly SU(2) as well) are required to reach the near-conformal regime.[24]

These results continue to be investigated by various methods, including latticesimulations discussed below, which have confirmed the near-conformal dynamics ofthese minimal walking models. The first comprehensive effective Lagrangian forminimal walking models, featuring a light composite Higgs, spin-one states, tree-levelunitarity, and consistency with phenomenological constraints was constructed in2007 by Foadi, Frandsen, Ryttov and Sannino.[30][edit]Technicolor on the lattice

Lattice gauge theory is a non-perturbative method applicable to strongly-interactingtechnicolor theories, allowing first-principles exploration of walking and conformaldynamics. In 2007, Catterall and Sannino used lattice gauge theory to study SU(2)gauge theories with two flavors of Dirac fermions in the symmetric representation,[31] finding evidence of conformality that has been confirmed by subsequent studies.[32]

As of 2010, the situation for SU(3) gauge theory with fermions in the fundamentalrepresentation is not as clear-cut. In 2007, Appelquist, Fleming and Neil reportedevidence that a non-trivial infrared fixed point develops in such theories when thereare twelve flavors, but not when there are eight.[33] While some subsequent studiesconfirmed these results, others reported different conclusions, depending on thelattice methods used, and there is not yet consensus.[34]

Further lattice studies exploring these issues, as well as considering theconsequences of these theories for precision electroweak measurements, areunderway by several research groups.[35][edit]Technicolor phenomenology

Any framework for physics beyond the Standard Model must conform with precisionmeasurements of the electroweak parameters. Its consequences for physics at

existing and future high-energy hadron colliders, and for the dark matter of theuniverse must also be explored.[edit]Precision electroweak tests

In 1990, the phenomenological parameters S, T, and U were introduced by Peskinand Takeuchi to quantify contributions to electroweak radiative corrections fromphysics beyond the Standard Model.[36] They have a simple relation to theparameters of the electroweak chiral Lagrangian.[37][38] The Peskin-Takeuchi


16/30

analysis was based on the general formalism for weak radiative correctionsdeveloped by Kennedy, Lynn, Peskin and Stuart,[39] and alternate formulations alsoexist.[40]

The S, T, and U-parameters describe corrections to the electroweak gauge bosonpropagators from physics Beyond the Standard Model. They can be written in terms

of polarization functions of electroweak currents and their spectral representation asfollows:

where only new, beyond-standard-model physics is included. The quantities arecalculated relative to a minimal Standard Model with some chosen reference mass ofthe Higgs boson, taken to range from the experimental lower bound of 117 GeV to1000 GeV where its width becomes very large.[41] For these parameters to describethe dominant corrections to the Standard Model, the mass scale of the new physicsmust be much greater than MW and MZ, and the coupling of quarks and leptons tothe new particles must be suppressed relative to their coupling to the gauge bosons.This is the case with technicolor, so long as the lightest technivector mesons, T andaT, are heavier than 200300 GeV. The S-parameter is sensitive to all new physics atthe TeV scale, while T is a measure of weak-isospin breaking effects. The U-parameter is generally not useful; most new-physics theories, including technicolortheories, give negligible contributions to it.

The S and T-parameters are determined by global fit to experimental data includingZ-pole data from LEP at CERN, top quark and W-mass measurements at Fermilab,and measured levels of atomic parity violation. The resultant bounds on theseparameters are given in the Review of Particle Properties.[41] Assuming U = 0, the Sand T parameters are small and, in fact, consistent with zero:

where the central value corresponds to a Higgs mass of 117 GeV and the correctionto the central value when the Higgs mass is increased to 300 GeV is given inparentheses. These values place tight restrictions on beyond-standard-modeltheorieswhen the relevant corrections can be reliably computed.

The S parameter estimated in QCD-like technicolor theories is significantly greaterthan the experimentally-allowed value.[36][40] The computation was done assumingthat the spectral integral for S is dominated by the lightest T and aT resonances, orby scaling effective Lagrangian parameters from QCD. In walking technicolor,however, the physics at the TeV scale and beyond must be quite different from thatof QCD-like theories. In particular, the vector and axial-vector spectral functionscannot be dominated by just the lowest-lying resonances.[42] It is unknown whetherhigher energy contributions to are a tower of identifiable T and aT states or asmooth continuum. It has been conjectured that T and aT partners could be more

nearly degenerate in walking theories (approximate parity doubling), reducing theircontribution to S.[43] Lattice calculations are underway or planned to test theseideas and obtain reliable estimates of S in walking theories.[2][44]

The restriction on the T-parameter poses a problem for the generation of the top-quark mass in the ETC framework. The enhancement from walking can allow theassociated ETC scale to be as large as a few TeV,[21] butsince the ETC interactionsmust be strongly weak-isospin breaking to allow for the large top-bottom masssplittingthe contribution to the T parameter,[45] as well as the rate for the decay ,


17/30

[46] could be too large.[edit]Hadron collider phenomenology

Early studies generally assumed the existence of just one electroweak doublet oftechnifermions, or one techni-family including one doublet each of color-triplet

techniquarks and color-singlet technileptons.[47] In the minimal, one-doublet model,three Goldstone bosons (technipions, T) have decay constant F = FEW = 246 GeVand are eaten by the electroweak gauge bosons. The most accessible collider signalis the production through annihilation in a hadron collider of spin-one , and theirsubsequent decay into a pair of longitudinally-polarized weak bosons, and . At anexpected mass of 1.52.0 TeV and width of 300400 GeV, such T's would be difficultto discover at the LHC. A one-family model has a large number of physicaltechnipions, with F = FEW/4 = 123 GeV.[48] There is a collection of correspondinglylower-mass color-singlet and octet technivectors decaying into technipion pairs. TheT's are expected to decay to the heaviest possible quark and lepton pairs. Despitetheir lower masses, the T's are wider than in the minimal model and thebackgrounds to the T decays are likely to be insurmountable at a hadron collider.

This picture changed with the advent of walking technicolor. A walking gaugecoupling occurs if SB lies just below the IR fixed point value IR, which requireseither a large number of electroweak doublets in the fundamental representation ofthe gauge group, e.g., or a few doublets in higher-dimensional TC representations.[22][49] In the latter case, the constraints on ETC representations generally implyother technifermions in the fundamental representation as well.[9][20] In either case,there are technipions T with decay constant . This implies so that the lightesttechnivectors accessible at the LHCT, T, aT (with IG JPC = 1+ 1, 0 1, 11++)have masses well below a TeV. The class of theories with manytechnifermions and thus is called low-scale technicolor.[50]

A second consequence of walking technicolor concerns the decays of the spin-onetechnihadrons. Since technipion masses (see Eq. (4)), walking enhances them muchmore than it does other technihadron masses. Thus, it is very likely that the lightestMT < 2MT and that the two and three-T decay channels of the light technivectorsare closed.[22] This further implies that these technivectors are very narrow. Theirmost probable two-body channels are , WL WL, T and WL. The coupling of thelightest technivectors to WL is proportional to F/FEW.[51] Thus, all their decay ratesare suppressed by powers of or the fine-structure constant, giving total widths of afew GeV (for T) to a few tenths of a GeV (for T and T).

A more speculative consequence of walking technicolor is motivated by considerationof its contribution to the S-parameter. As noted above, the usual assumptions madeto estimate STC are invalid in a walking theory. In particular, the spectral integralsused to evaluate STC cannot be dominated by just the lowest-lying T and aT and, ifSTC is to be small, the masses and weak-current couplings of the T and aT could bemore nearly equal than they are in QCD.

Low-scale technicolor phenomenology, including the possibility of a more parity-doubled spectrum, has been developed into a set of rules and decay amplitudes.[51]An April 2011 announcement of an excess in jet pairs produced in association with aW boson measured at the Tevatron[52] has been interpreted by Eichten, Lane andMartin as a possible signal of the technipion of low-scale technicolor.[53]

The general scheme of low-scale technicolor makes little sense if the limit on ispushed past about 700 GeV. The LHC should be able to discover it or rule it out.


18/30

Searches there involving decays to technipions and thence to heavy quark jets arehampered by backgrounds from production; its rate is 100 times larger than that atthe Tevatron. Consequently, the discovery of low-scale technicolor at the LHC relieson all-leptonic final-state channels with favorable signal-to-background ratios: , and .[54][edit]

Dark matter

Technicolor theories naturally contain dark matter candidates. Almost certainly,models can be built in which the lowest-lying technibaryon, a technicolor-singletbound state of technifermions, is stable enough to survive the evolution of theuniverse.[41][55] If the technicolor theory is low-scale (), the baryon's mass shouldbe no more than 12 TeV. If not, it could be much heavier. The technibaryon must beelectrically neutral and satisfy constraints on its abundance. Given the limits on spin-independent dark-matter-nucleon cross sections from dark-matter searchexperiments ( for the masses of interest[56]), it may have to be electroweak neutral(weak isospin I = 0) as well. These considerations suggest that the "old" technicolordark matter candidates may be difficult to produce at the LHC.

A different class of technicolor dark matter candidates light enough to be accessibleat the LHC was introduced by Francesco Sannino and his collaborators.[57] Thesestates are pseudo Goldstone bosons possessing a global charge that makes themstable against decay.

TopcolorFrom Wikipedia, the free encyclopedia

In theoretical physics, Topcolor is a model of dynamical electroweak symmetrybreaking in which the top quark and anti-top quark form a top quark condensate andact effectively like the Higgs boson. This is analogous to the phenomenon ofsuperconductivity.

Topcolor naturally involves an extension of the standard model color gauge group toa product group SU(3)xSU(3)xSU(3)x... One of the gauge groups contains the top andbottom quarks, and has a sufficiently large coupling constant to cause thecondensate to form. The topcolor model thus anticipates the idea of dimensionaldeconstruction and extra space dimensions, as well as the large mass of the topquark. Topcolor, and its prediction of "topgluons," will be tested in comingexperiments at the Large Hadron Collider at CERN.

Topcolor rescues the Technicolor model from some of its difficulties in a schemedubbed "Topcolor-assisted Technicolor."

In particle physics, the top quark condensate theory is an alternative to the Standard

Model in which a fundamental scalar Higgs field is replaced by a composite fieldcomposed of the top quark and its antiquark. These are bound by a four-fermioninteraction, analogous to Cooper pairs in a BCS superconductor and nucleons in theNambu-Jona-Lasinio model. The top quark condenses because its measured mass isapproximately 173 GeV (comparable to the electroweak scale), and so its Yukawacoupling is of order unity, yielding the possibility of strong coupling dynamics.

http://en.wikipedia.org/wiki/Color_confinement


19/30

Color confinementFrom Wikipedia, the free encyclopedia

The color force favors confinement because at a certain range it is more energeticallyfavorable to create a quark-antiquark pair than to continue to elongate the color fluxtube. This is analoguous to the behavior of an elongated rubber-band.

Color confinement, often simply called confinement, is the physics phenomenon thatcolor charged particles (such as quarks) cannot be isolated singularly, and thereforecannot be directly observed.[1] Quarks, by default, clump together to form groups, orhadrons. The two types of hadrons are the mesons (one quark, one antiquark) andthe baryons (three quarks). The constituent quarks in a group cannot be separatedfrom their parent hadron, and this is why quarks can never be studied or observed inany more direct way than at a hadron level.[2]Contents [hide]1 Origin2 Models exhibiting confinement3 See also4 References5 External links

[edit]Origin

The reasons for quark confinement are somewhat complicated; no analytic proofexists that quantum chromodynamics should be confining, but intuitively,confinement is due to the force-carrying gluons having color charge. As any twoelectrically-charged particles separate, the electric fields between them diminishquickly, allowing (for example) electrons to become unbound from atomic nuclei.However, as two quarks separate, the gluon fields form narrow tubes (or strings) ofcolor charge, which tend to bring the quarks together as though they were some kindof rubber band. This is quite different in behavior from electrical charge. Because ofthis behavior, the color force experienced by the quarks in the direction to hold themtogether, remains constant, regardless of their distance from each other.[3][4]

The color force between quarks is large, even on a macroscopic scale, being on theorder of 100,000 newtons.[citation needed] As discussed above, it is constant, anddoes not decrease with increasing distance after a certain point has been passed.

When two quarks become separated, as happens in particle accelerator collisions, atsome point it is more energetically favorable for a new quarkantiquark pair tospontaneously appear, than to allow the tube to extend further. As a result of this,when quarks are produced in particle accelerators, instead of seeing the individualquarks in detectors, scientists see "jets" of many color-neutral particles (mesons andbaryons), clustered together. This process is called hadronization, fragmentation, orstring breaking, and is one of the least understood processes in particle physics.

The confining phase is usually defined by the behavior of the action of the Wilsonloop, which is simply the path in spacetime traced out by a quarkantiquark paircreated at one point and annihilated at another point. In a non-confining theory, theaction of such a loop is proportional to its perimeter. However, in a confining theory,the action of the loop is instead proportional to its area. Since the area will beproportional to the separation of the quarkantiquark pair, free quarks aresuppressed. Mesons are allowed in such a picture, since a loop containing anotherloop in the opposite direction will have only a small area between the two loops.[edit]


20/30

Models exhibiting confinement

Besides QCD in 4D, another model which exhibits confinement is the Schwingermodel.[citation needed] Compact Abelian gauge theories also exhibit confinement in2 and 3 spacetime dimensions.[citation needed] Confinement has recently beenfound in elementary excitations of magnetic systems called spinons.[5]

[edit]See alsoQuantum chromodynamicsAsymptotic freedomDeconfining phaseQuantum mechanicsParticle physicsFundamental forceDual superconducting model

http://en.wikipedia.org/wiki/Dual_superconducting_model

In the theory of quantum chromodynamics, dual superconductor models attempt toexplain confinement of quarks in terms of an electromagnetic dual theory ofsuperconductivity.

In an electromagnetic dual theory the roles of electric and magnetic fields areinterchanged. The BCS theory of superconductivity explains superconductivity as theresult of the condensation electric chargers to cooper pairs. In a dual superconductoran analogous effect occurs through the condensation of magnetic charges (alsocalled magnetic monopoles). In ordinary electromagnetic theory, no monopoles havebeen shown to exist. However, in quantum chromodynamics the theory of colourcharge which explains the strong interaction between quarks the colour chargescan be view as (non-abelian) analogues of electric charges and correspondingmagnetic monopoles are known to exist. Dual superconductor models posit thatcondensation of these magnetic monopoles in a superconductive state explainscolour confinement the phenomenon that only neutrally coloured bound states areobserved at low energies.

Qualitatively, confinement in dual superconductor models can be understood as aresult of the dual to the Meissner effect. The Meissner effect says that asuperconducting metal will try to expel magnetic field lines from its interior. If amagnetic field is forced to run through the superconductor, the field lines arecompressed in magnetic flux tubes. In a dual superconductor the roles of magneticand electric fields are exchanged and the Meissner effect tries to expel electric fieldlines. Quarks and antiquarks carry opposite colour charges, and for a quarkantiquarkpair 'electric' field lines run from the quark to the antiquark. If the quarkantiquarkpair are immersed in a dual superconductor, then the electric field lines getcompressed to a flux tube. The energy associated to the tube is proportional to itslength, and the potential energy of the quarkantiquark is proportional to their

separation. A quarkantiquark will therefore always bind regardless of theirseparation, which explains why no unbound quarks are ever found.[note 1]

Dual superconductors are described by (a dual to) the LandauGinzburg model, whichis equivalent to the Abelian Higgs model.

The dual superconductor model is motivated by several observations in calculationsusing lattice gauge theory. The model, however, also has some shortcomings. Inparticular, although it confines coloured quarks, it fails to confine colour of some


21/30

gluons, allowing coloured bound states at energies observable in particle colliders.

http://en.wikipedia.org/wiki/Lattice_gauge_theory

In physics, lattice gauge theory is the study of gauge theories on a spacetime thathas been discretized into a lattice. Gauge theories are important in particle physics,

and include the prevailing theories of elementary particles: quantumelectrodynamics, quantum chromodynamics (QCD) and the Standard Model. Non-perturbative gauge theory calculations in continuous spacetime formally involveevaluating an infinite-dimensional path integral, which is computationally intractable.By working on a discrete spacetime, the path integral becomes finite-dimensional,and can be evaluated by stochastic simulation techniques such as the Monte Carlomethod. When the size of the lattice is taken infinitely large and its sitesinfinitesimally close to each other, the continuum gauge theory is recoveredintuitively. A mathematical proof of this fact is lacking.Contents [hide]1 Basics2 YangMills action3 Measurements4 Other applications5 See also6 Further reading7 External links8 References

[edit]Basics

In lattice gauge theory, the spacetime is Wick rotated into Euclidean space anddiscretized into a lattice with sites separated by distance a and connected by links. Inthe most commonly-considered cases, such as lattice QCD, fermion fields are definedat lattice sites (which leads to fermion doubling), while the gauge fields are definedon the links. That is, an element U of the compact Lie group G is assigned to eachlink. Hence to simulate QCD, with Lie group SU(3), there is a 33 special unitary matrixdefined on each link. The link is assigned an orientation, with the inverse element correspondingto the same link with the opposite orientation.[edit]YangMills action

The YangMills action is written on the lattice using Wilson loops (named after Kenneth G.Wilson), so that the limit formally reproduces the original continuum action.[1] Given a faithfulirreducible representation of G, the lattice Yang-Mills action is the sum over all latticesites of the (real component of the) trace over the n links e1, ..., en in the Wilsonloop,

Here, is the character. If is a real (or pseudoreal) representation, taking the real

component is redundant, because even if the orientation of a Wilson loop is flipped,its contribution to the action remains unchanged.

There are many possible lattice Yang-Mills actions, depending on which Wilson loopsare used in the action. The simplest "Wilson action" uses only the 11 Wilson loop, anddiffers from the continuum action by "lattice artifacts" proportional to the small lattice spacing a.By using more complicated Wilson loops to construct "improved actions", lattice artifacts can bereduced to be proportional to a2, making computations more accurate.[edit]


22/30

Measurements

Quantities such as particle masses are stochastically calculated using techniques such as theMonte Carlo method. Gauge field configurations are generated with probabilities proportional to e S, where S is the lattice action and is related to the lattice spacing a. Thequantity of interest is calculated for each configuration, and averaged. Calculations

are often repeated at different lattice spacings a so that the result can beextrapolated to the continuum, .

Such calculations are often extremely computationally intensive, and can require theuse of the largest available supercomputers. To reduce the computational burden,the so-called quenched approximation can be used, in which the fermionic fields aretreated as non-dynamic "frozen" variables. While this was common in early latticeQCD calculations, "dynamical" fermions are now standard.[2] These simulationstypically utilize algorithms based upon molecular dynamics or microcanonicalensemble algorithms.[3][4][edit]Other applications

Originally, solvable two-dimensional lattice gauge theories had already beenintroduced in 1971 as models with interesting statistical properties by the theoristFranz Wegner, who worked in the field of phase transitions.[5]

Lattice gauge theory has been shown to be exactly dual to spin foam modelsprovided that only 11 Wilson loops appear in the action.[edit]See alsoHamiltonian lattice gauge theoryLattice field theoryLattice QCDQuantum triviality

http://en.wikipedia.org/wiki/Lattice_QCD

Lattice QCD is a well-established non-perturbative approach to solving the quantumchromodynamics (QCD) theory of quarks and gluons. It is a lattice gauge theory formulated on agrid or lattice of points in space and time.

Analytic or perturbative solutions in low-energy QCD are hard or impossible due to the highlynonlinear nature of the strong force. This formulation of QCD in discrete rather than continuousspacetime naturally introduces a momentum cut off at the order 1/a, where a is the latticespacing, which regularizes the theory. As a result lattice QCD is mathematically well-defined.Most importantly, lattice QCD provides a framework for investigation of non-perturbativephenomena such as confinement and quark-gluon plasma formation, which are intractable bymeans of analytic field theories.

In lattice QCD, fields representing quarks are defined at lattice sites (which leads to fermiondoubling), while the gluon fields are defined on the links connecting neighboring sites. Thisapproximation approaches continuum QCD as the spacing between lattice sites is reduced tozero. Because the computational cost of numerical simulations can increase dramatically as thelattice spacing decreases, results are often extrapolated to a = 0 by repeated calculations atdifferent lattice spacings a that are large enough to be tractable.

Numerical lattice QCD calculations using Monte Carlo methods can be extremely computationallyintensive, requiring the use of the largest available supercomputers. To reduce the computationalburden, the so-called quenched approximation can be used, in which the quark fields are treated


23/30

as non-dynamic "frozen" variables. While this was common in early lattice QCD calculations,"dynamical" fermions are now standard.[1] These simulations typically utilize algorithms basedupon molecular dynamics or microcanonical ensemble algorithms.[2][3]

At present, lattice QCD is primarily applicable at low densities where the numerical sign problemdoes not interfere with calculations. Lattice QCD predicts that confined quarks will becomereleased to quark-gluon plasma around energies of 170 MeV. Monte Carlo methods are free fromthe sign problem when applied to the case of QCD with gauge group SU(2) (QC2D).

Lattice QCD has already made successful contact with many experiments. For example the massof the proton has been determined theoretically with an error of less than 2 percent.[4]

Lattice QCD has also been used as a benchmark for high-performance computing, an approachoriginally developed in the context of the IBM Blue Gene supercomputer.Contents [hide]1 Techniques1.1 Monte-Carlo simulations1.2 Fermions on the lattice1.3 Lattice perturbation theory2 See also3 Notes

4 Further reading5 External links

[edit]Techniques[edit]Monte-Carlo simulationsA frame from a Monte-Carlo simulation illustrating the typical four-dimensional structure of gluon-field configurations used in describing the vacuum properties of QCD.

Monte-Carlo is a method to pseudo-randomly sample a large space of variables. The importancesampling technique used to select the gauge configurations in the Monte-Carlo simulation

imposes the use of Euclidean time, by a Wick rotation of space-time.

In lattice Monte-Carlo simulations the aim is to calculate correlation functions. This is done byexplicitly calculating the action, using field configurations which are chosen according to thedistribution function, which depends on the action and the fields. Usually one starts with thegauge bosons part and gauge-fermion interaction part of the action to calculate the gaugeconfigurations, and then uses the simulated gauge configurations to calculate hadronicpropagators and correlation functions.[edit]Fermions on the lattice

Lattice QCD is a way to solve the theory exactly from first principles, without any assumptions, tothe desired precision. However, in practice the calculation power is limited, which requires a

smart use of the available resources. One needs to choose an action which gives the bestphysical description of the system, with minimum errors, using the available computational power.The limited computer resources force one to use physical constants which are different from theirtrue physical values:The lattice discretization means a finite lattice spacing and size, which do not exist in thecontinuous and infinite space-time. In addition to the automatic error introduced by this, thelimited resources force the use of smaller physical lattices and larger lattice spacing than wantedin order to minimize errors.Another unphysical quantity is the quark masses. Quark masses are steadily going down, but to-date (2010) they are typically too high with respect to the real value.


24/30

In order to compensate for the errors one improves the lattice action in various ways, to minimizemainly finite spacing errors.[edit]Lattice perturbation theory

The lattice was initially introduced by Wilson as a framework for studying strongly coupledtheories, such as QCD, non-perturbatively. it was found to be a regularization also suitable forperturbative calculations. Perturbation theory involves an expansion in the coupling constant, andis well-justified in high-energy QCD where the coupling constant is small, while it fails completelywhen the coupling is large and higher order corrections are larger than lower orders in theperturbative series. In this region non-perturbative methods, such as Monte-Carlo sampling of thecorrelation function, are necessary.

Lattice perturbation theory can also provide results for condensed matter theory. One can use thelattice to represent the real atomic crystal. In this case the lattice spacing is a real physical value,and not an artifact of the calculation which has to be removed, and a quantum field theory can beformulated and solved on the physical lattice.[edit]See also

Lattice field theoryLattice gauge theoryQCD matterQCD sum rules

http://en.wikipedia.org/wiki/Hamiltonian_lattice_gauge_theory

In physics, Hamiltonian lattice gauge theory is a calculational approach to gauge theory and aspecial case of lattice gauge theory in which the space is discretized but time is not. TheHamiltonian is then re-expressed as a function of degrees of freedom defined on a d-dimensionallattice.

Following Wilson, the spatial components of the vector potential are replaced with Wilson lines

over the edges, but the time component is associated with the vertices. However, the temporalgauge is often employed, setting the electric potential to zero. The eigenvalues of the Wilson lineoperators U(e) (where e is the (oriented) edge in question) take on values on the Lie group G. It isassumed that G is compact, otherwise we run into many problems. The conjugate operator toU(e) is the electric field E(e) whose eigenvalues take on values in the Lie algebra . TheHamiltonian receives contributions coming from the plaquettes (the magnetic contribution) andcontributions coming from the edges (the electric contribution).

Hamiltonian lattice gauge theory is exactly dual to a theory of spin networks. This involves usingthe Peter-Weyl theorem. In the spin network basis, the spin network states are eigenstates of theoperator Tr[E(e)2].

http://en.wikipedia.org/wiki/Asymptotic_freedom

In physics, asymptotic freedom is a property of some gauge theories that causes interactionsbetween particles to become arbitrarily weak at energy scales that become arbitrarily large, or,equivalently, at length scales that become arbitrarily small (at the shortest distances).

Asymptotic freedom is a feature of quantum chromodynamics (QCD), the quantum field theory ofthe nuclear interaction between quarks and gluons, the fundamental constituents of nuclearmatter. Quarks interact weakly at high energies, allowing perturbative calculations by DGLAP ofcross sections in deep inelastic processes of particle physics; and strongly at low energies,preventing the unbinding of baryons (like protons or neutrons with three quarks) or mesons (like


25/30

pions with two quarks), the composite particles of nuclear matter.

Asymptotic freedom was discovered by Frank Wilczek, David Gross, and David Politzer who in2004 shared the Nobel Prize in physics.Contents [hide]1 Discovery2 Screening and antiscreening3 Calculating asymptotic freedom4 See also5 References

[edit]Discovery

Asymptotic freedom was discovered in 1973 by David Gross and Frank Wilczek, and by DavidPolitzer. Although these authors were the first to understand the physical relevance to the stronginteractions, in 1969 Iosif Khriplovich discovered asymptotic freedom in the SU(2) gauge theoryas a mathematical curiosity, and Gerardus 't Hooft in 1972 also noted the effect but did notpublish. For their discovery, Gross, Wilczek and Politzer were awarded the Nobel Prize in Physicsin 2004.

The discovery was instrumental in rehabilitating quantum field theory. Prior to 1973, manytheorists suspected that field theory was fundamentally inconsistent because the interactionsbecome infinitely strong at short-distances. This phenomenon is usually called a Landau pole,and it defines the smallest length scale that a theory can describe. This problem was discoveredin field theories of interacting scalars and spinors, including quantum electrodynamics, andLehman positivity led many to suspect that it is unavoidable. Asymptotically free theories becomeweak at short distances, there is no Landau pole, and these quantum field theories are believedto be completely consistent down to any length scale.

While the Standard Model is not entirely asymptotically free, in practice the Landau pole can onlybe a problem when thinking about the strong interactions. The other interactions are so weak thatany inconsistency can only arise at distances shorter than the Planck length, where a field theorydescription is inadequate anyway.

[edit]Screening and antiscreeningCharge screening in QED

The variation in a physical coupling constant under changes of scale can be understoodqualitatively as coming from the action of the field on virtual particles carrying the relevant charge.The Landau pole behavior of quantum electrodynamics (QED, related to quantum triviality) is aconsequence of screening by virtual charged particle-antiparticle pairs, such as electron-positronpairs, in the vacuum. In the vicinity of a charge, the vacuum becomes polarized: virtual particlesof opposing charge are attracted to the charge, and virtual particles of like charge are repelled.The net effect is to partially cancel out the field at any finite distance. Getting closer and closer tothe central charge, one sees less and less of the effect of the vacuum, and the effective charge

increases.

In QCD the same thing happens with virtual quark-antiquark pairs; they tend to screen the colorcharge. However, QCD has an additional wrinkle: its force-carrying particles, the gluons,themselves carry color charge, and in a different manner. Each gluon carries both a color chargeand an anti-color magnetic moment. The net effect of polarization of virtual gluons in the vacuumis not to screen the field, but to augment it and affect its color. This is sometimes calledantiscreening. Getting closer to a quark diminishes the antiscreening effect of the surroundingvirtual gluons, so the contribution of this effect would be to weaken the effective charge withdecreasing distance.


26/30

Since the virtual quarks and the virtual gluons contribute opposite effects, which effect wins outdepends on the number of different kinds, or flavors, of quark. For standard QCD with threecolors, as long as there are no more than 16 flavors of quark (not counting the antiquarksseparately), antiscreening prevails and the theory is asymptotically free. In fact, there are only 6known quark flavors.[edit]Calculating asymptotic freedom

Asymptotic freedom can be derived by calculating the beta-function describing the variation of thetheory's coupling constant under the renormalization group. For sufficiently short distances orlarge exchanges of momentum (which probe short-distance behavior, roughly because of theinverse relation between a quantum's momentum and De Broglie wavelength), an asymptoticallyfree theory is amenable to perturbation theory calculations using Feynman diagrams. Suchsituations are therefore more theoretically tractable than the long-distance, strong-couplingbehavior also often present in such theories, which is thought to produce confinement.

Calculating the beta-function is a matter of evaluating Feynman diagrams contributing to theinteraction of a quark emitting or absorbing a gluon. In non-abelian gauge theories such as QCD,the existence of asymptotic freedom depends on the gauge group and number of flavors of

interacting particles. To lowest nontrivial order, the beta-function in an SU(N) gauge theory with nfkinds of quark-like particle is

where is the theory's equivalent of the fine-structure constant, g2 / (4) in the unitsfavored by particle physicists. If this function is negative, the theory is asymptoticallyfree. For SU(3), the color charge gauge group of QCD, the theory is thereforeasymptotically free if there are 16 or fewer flavors of quarks.

For SU(3) N = 3, and 1 < 0 gives

http://en.wikipedia.org/wiki/Anomalous_scaling_dimension

In theoretical physics, by anomaly one usually means that the symmetry remainsbroken when the symmetry-breaking factor goes to zero. When the symmetry whichis broken is scale invariance, then true power laws usually cannot be found fromdimensional reasoning like in turbulence or quantum field theory. In the latter, theanomalous scaling dimension of an operator is the contribution of quantummechanics to the classical scaling dimension of that operator.

The classical scaling dimension of an operator O is determined by dimensionalanalysis from the Lagrangian (in 4 spacetime dimensions this means dimension 1 forelementary bosonic fields including the vector potentials, 3/2 for elementaryfermionic fields etc.). However if one computes the correlator of two operators of thistype, one often finds logarithmic divergences arising from one-loop Feynmandiagrams. The expansion in the coupling constant has the schematic form

where g is a coupling constant, 0 is the classical dimension, and is an ultravioletcutoff (the maximal allowed energy in the loop integrals). A is a constant thatappears in the loop diagrams. The expression above may be viewed as a Taylorexpansion of the full quantum dimension.

The term g2A is the anomalous scaling dimension while is the full dimension.


27/30

Conformal field theories are typically strongly coupled and the full dimension cannotbe easily calculated by Taylor expansions. The full dimensions in this case are oftencalled critical exponents. These operators describe conformal bound states with acontinuous mass spectrum.

In particular, 2 = d 2 + for the critical exponent for a scalar operator. We

have an anomalous scaling dimension when 0.

An anomalous scaling dimension indicates a scale dependent wavefunctionrenormalization.

Anomalous scaling appears also in classical physics.

http://www.scientificamerican.com/article.cfm?id=the-amazing-disappearing-neutrino

The Amazing Disappearing Antineutrino

A revised calculation suggests that around 3% of particles have gone missing from nuclearreactor experiments.

| April 1, 2011 | 10

*

By Eugenie Samuel Reich of Nature magazine

Neutrinos have long perplexed physicists with their uncanny ability to evade detection, with asmany as two-thirds of the ghostly particles apparently going missing en route from the Sun toEarth. Now a refined version of an old calculation is causing a stir by suggesting that researchershave also systematically underestimated the number of the particles' antimatter partners--antineutrinos--produced by nuclear reactor experiments.

The deficit could be caused by the antineutrinos turning into so-called 'sterile antineutrinos', whichcan't be directly detected, and which would be clear evidence for effects beyond the standardmodel of particle physics.

In the 1960s, physicist Ray Davis, working deep underground in the Homestake gold mine inSouth Dakota, found that the flux of solar neutrinos hitting Earth was a third of that predicted bycalculations of the nuclear reactions in the Sun by theorist John Bahcall. Davis later received aNobel prize for his contributions to neutrino astrophysics. That puzzle was consider

origin 15 : a kaleidoscope of color

Documents