lecture 1 the particle content of the standard model has fully...

1

A. Goshaw SM Course 2017

Lecture 1 August 29, 2017 TheparticlecontentoftheStandardModelhasfully

beendirectlyandunambiguouslyobserved!

21897

1937

1975

1968

1974

1994 1968

1955

1977

1956

1962

2000

19791900

1983 1983

2012

2


mHc2 = 125.09 + 0.21 GeV

 Quarks are point particles

 down to ~ 10-4 fm

 The Higgs boson   was discovered in 2012

 H -> γ γ

 It took over a century of experimental work to discover all the particles in the SM.

3


Outline for Today

Standard Model introduction Ø  What it predicts Ø  What it excludes Ø  What are possible extensions Ingredients of the Standard Model Ø  The SM elementary particle spectrum Ø  Input parameters obtained from experiment

Course introduction Ø  Structure and goals Ø  Course content

Reading: the text Chapter 1 Choice of units …

4


General information Ø  The lectures define the course content and are meant to be self-contained. Ø  Text book: An Introduction to the Standard Model of Particle Physics by Cottingham and Greenwood (2nd edition): useful supplementary reading.

Ø  Communications about the course will use the web site: http://phy.duke.edu/~goshaw/846/SM/

§  Work the problem assignments

Course work (yours and mine) Ø  Lectures on Tuesday and Thursday Ø  Your participation

§  Prepare a research paper on a topic that interests you

Course Structure

§  Attend lectures

5


Course Goals Goals

Ø  Understand the Standard Model’s structure and predictions Ø  Study successes Ø  Discuss limitations Ø  Explore speculative extensions of the “SM” Ø  Watch developments from on-going experiments

Approach Ø  Develop the tools for making testable SM predictions Ø  Develop the Standard Model theory from symmetry principles Ø  Show where experiment enters to “patch-up” the theory Ø  Learn how the SM is tested by experiments Ø  Compare the SM predictions to measurements

(… but this is not a quantum field theory course, and we will not emphasize the technical details of matrix element calculations.) ( … and we will have to gloss over many of the challenging experimental techniques.)

6

A. Goshaw SM Course 2017Course Content (part 1)

●  Overview of the Standard Model ➤  Theoretical assumptions and experimental parameters ➤  Our approach to building the SM ➤  Extending the reach of the “SM”

●  Describe how the Standard Model is tested ➤  Measurements of particle interaction and decay rates ➤  Calculation of particle interaction and decay rates

●  Review of some basics ➤  Relativistic kinematics and phase space ➤  Conservation laws and symmetry principles

7

A. Goshaw SM Course 2017 Course Content (part 2)

●  The Standard Model with one generation SM1.0 ➤  Electroweak and QCD theory with zero mass particles ➤  Addition of electroweak symmetry breaking è particle masses ➤  Introduction of parity violation è left-handed EWK doublets

●  The Standard Model with more generations SM2.0 and SM3.0 ➤  The strange and charm quarks: quark mixing ➤  The bottom and top quarks: CP violation

●  Limitations of the Standard Model BSM1.0 ➤  Future directions in theory and experiment

●  Speculative extensions of the Standard Model SM3.0++

➤  Addition of neutrino mass and mixing ➤  A possible candidate for dark mattter

8


Standard Model Introduction

9


Overview of the Standard Model What it includes

The Standard Model is a relativistic quantum field theory in which the dynamics is generated from the assumption of local gauge symmetries.

It is renormalizable, meaning that divergences appearing in certain calculations can be absorbed into parameters such as masses and coupling strengths.

It encompasses the electromagnetic and weak interactions in a unified electroweak theory [the Weinberg-Salem Model: SUL(2)xUY(1) ].

The strong interaction is included as a separate self contained theory called Quantum Chromdynamics: SUC(3) .

Given the input parameters and fundamental particle spectra, the Standard Model makes specific predictions for the structure of composite systems such as nucleons, nuclei, and atoms, and their interactions such as collisions or decays.

10


Overview of the Standard Model What it includes

There are certain computational difficulties Ø  Some calculations are very difficult and limit the predictive power Ø  A great deal of theory effort goes into the improvement of the precisions of SM predictions

However there are no violations of the Standard Model‘ in the domain where it has currently been quantitatively tested. [ see latter discussion of SM3.0++ ]

There is now a mechanism for electroweak symmetry breaking [the fact that the W and Z boson masses are not zero]. This was imposed “by hand” into the Standard Model in 1964 and led to the prediction of a scalar particle [the Higgs boson] that was observed in 2012.

11


Overview of the Standard Model What it lacks

It is special relativity quantum field theory, not a general relativity quantum field theory, and therefore has a major structural defect. The Standard Model does not include the gravitational force.

The Standard Model does not unify the electroweak and strong force

The usual Standard Model contains no candidate for “dark matter” as observed from astrophysics measurements. [ see latter discussion in SM3.0++ ]

The Standard Model contains no explanation for the “dark energy” observed from astrophysics measurements.

13


Rotational Curves of Galaxies

• Outer rim of galaxies is seen to rotate faster than expected from Newtonian mechanics

• there is more mass than is seen interacting

Dark Matter

12


Overview of the Standard Model Possible Extensions

There are many proposed extensions of the Standard Model

Supersymmetry: imposes a symmetry between fermions and bosons §  For every quark (spin 1/2) there is a squark (spin 0) §  For a photon (spin 1) there is a photino (spin 1/2), etc

Technicolor: postulates a new super-strong interaction §  Predicts new force carriers (gauge bosons) §  Predicts cross-breeds between quarks and leptons (leptoquarks)

§  No super-partners have been observed

§  No new gauge bosons or leptoquarks have been observed

13


Overview of the Standard Model Possible Extensions

Grand-unified theories (GUTS): postulate that the Standard Model symmetry groups are subgroups of a larger symmetry group, thus unifying the strong and electroweak forces [SU(5) SO(10), etc.]

§  Predicts more quarks and leptons §  Predicts baryon number violation (proton decay)

Preons: postulating that quarks and leptons are composite §  Predict extended structure of quarks and leptons

String theories: postulate that the elementary particles are string, not points §  Needs 10 space time dimensions (6 “compactified”)

§  No such phenomena have been observed

§  Scattering experiments observe no such structure

§  No evidence for additional dimensions has been observed

14


Required inputs to the Standard Model

Let’s survey the required inputs to the Standard Model.

What must be supplied by sampling Nature with experiments?

The best answer would be “nothing” . That is, one might hope that the theory contained enough internal constraints to be completely predictive without requiring any experimental input.

This is far from true for the Standard Model.

We will show that in order to be predictive the SM requires 19 measured parameters (26 with massive neutrinos).

These parameters are the “genetic code” of our universe when viewed from the perspective of the SM.

15


Ingredients of the

Standard Model

16


The number of distinct fundamental particles included in the Standard Model:

24 + 24 + 12 + 1 = 61 .

Particle content of the SM

But the number of independent masses is not so large because:

quarks + leptons

anti-quarks + anti-leptons

gauge bosons

Higgs boson

Ø  QFT with CPT invariance requires: M(particle) = M(antiparticle)

Ø  QCD structure requires: M(qr) = M(qg) = M(qb)

17


Input parameters required by the Standard Model

What numbers must be measured from experiment to make the SM completely predictive?

Here is the list:

Constants of QFT: c = 299,792,458 m/s (defined, sets standard of length) h = 6.58211915(56) MeV s

Constants of the Standard Model: 1. Masses 2. Coupling constants 3. Quark and neutrino mixing parameters 4. QCD CP violating parameter

18

A. Goshaw SM Course 20171. Input masses

 3 charged lepton masses  me mµ mτ

 6 quark masses  mu md ms mc mb mt

3 boson masses  mW mZ mH

 And now 3 neutrino masses  ν1 ν2 ν3

19


 top quark

  Z  W

 ... νe νµ ντ e µ τ u d s c b

 photons  gluons

 Photons  gluons

 = 0

A very strange mass spectrum …

  H

 Observed mass pattern  of SM particles

20


Measured Fermion Masses

Leptons Mc2 Electron 0.511 MeV Muon 0.106 GeV Tau 1.78 GeV ν < 2 eV

Ø  At least 2 neutrino masses non zero based upon observed neutrino mixing.

Ø  The lepton masses can be measured

directly as they propagate as free particles

Quarks Mc2

up ~ 2 MeV down ~ 5 MeV strange ~ 104 MeV charm ~ 1.27 GeV beauty ~ 4.20 GeV top 175 GeV

Ø  The “current” quark masses that appear in the QCD Lagrangian are quoted. The quarks are bound in color singlet hadrons (except for the top quark) and the masses must be deduced indirectly.

21


Measured Boson Masses

 H à Z Z*   à e+ e- µ+ µ-

●  The gauge boson masses are zero except for: MWc2 = 80.40 GeV MZc2 = 91.19 GeV

●  The Higgs boson has now been observed with a mass: MHc2 = 125.1 GeV

16

HÆZZ*Æ4l VBF event arXiv:1708.02810ATLAS-CONF-2017-043

2e2μ,m4l=129 GeV,m12=91 GeV, m34=29 GeV, mjj= 2 TeV, Δηjj=6.4

• Selection: 4 lepton (e,μ), lowest/4th electron ET>7 GeV, muon pT> 5 GeV, m12/m34 consistent with Z/Z*

• 8% acceptance increasing by lowering muon pT to 5GeV from 6GeV compared to RUN-1

• ttbar, Z+jets and WZ (15.7% of bkg): estimated with data driven methods, others from MC

22


 2 coupling constants  αe(Q~0) αs(Q=mZ)

There are two independent coupling “constants” (not really constant). These must be measured at some energy scale that is convenient for making a precise measurement

2. Input coupling strengths

23


Measured Coupling Strengths

 αs(Q = MZ)  = 0.118 + 0.002

●  The electromagnetic coupling strength is measured to high precision from atomic physics experiments. αe(Q~0) = 1/137.036… (precision 1 part in 108) αs(Q = MZ) = 1/128 (slow evolution with Q2) ●  The strong coupling constant is measured to a precision of about 2%. It has a rapid evolution at low Q2 slowing at high Q2.

 energy Q of gluon probe  αs(Q = MZ)

 αs(Q )

24


 4 quark ewk mixing parameters   θ1 θ2 θ3 δ

The unitary mixing matrix that projects out quark electroweak eigenstates from the d, s and b mass eigenstates is paramaterized by three angles and one complex phase

These are expressed in a variety of ways and it can be confusing when reading the literature. We will study this in detail latter.

The phase angle δ is a source of CP violation in the SM , and is relevant to the cosmological separation of matter from antimatter.

3. Quark mixing parameters

 The Cabbibo-Kobayashi-Maskawa (CKM) mixing matrix.

25


 4 neutrino mixing parameters   θ’1 θ’2 θ’3 δ’

The unitary mixing matrix that projects out neutrino flavor eigenstates (νe νµ ντ ) from the mass eigenstates (ν1 ν2 ν3) is paramaterized by three angles and one complex phase for Dirac neutrinos.

As for quark mixing, the phase angle δ’ is a source of CP violation, and could be relevant to the cosmological separation of matter from antimatter.

3. Neutrino mixing parameters

 The Pontecorvo-Maki-Nakagawa-Sakate (PMNS) mixing matrix.

26


There is one “hidden” parameter in the Standard Model

In the development of the QCD Lagrangian, a constant appears (ΛQCD) that is not fixed by the theory. A “natural” value of this parameter would generate phenomena that are not observed.

Ø  large CP violation in the strong interaction (none is observed) Ø  an electric dipole moment of the neutron. (experiment finds < 10-25 e cm)

●  So experiment forces a very small value of this parameter and it is generally just set == 0 in the SM. We will come back to this issue when we study QCD dynamics.

4. QCD CP violation

27


Finding the SM’s input parameters

●  A detailed summary of all measured parameters, and a discussion of the formalism of the Standard Model and other theories can be found in a HEP “bible” prepared by a Particle Data Group. You can access this at : http://pdg.lbl.gov/

pdgLive - Interactive Listings Summary Tables Reviews, Tables, Plots (2016) Particle Listings

Previous Editions (& Errata) 1957-2016

Errata in current edition Figures in reviews Mirror Sites

Physical Constants Astrophysical Constants Atomic & Nuclear Properties Astrophysics & Cosmology

The Review of Particle Physics (2017)C. Patrignani et al. (Particle Data Group), Chin. Phys. C, 40, 100001 (2016) and 2017 update.

Search

Order: Book & BookletDownload or Print: Book, Booklet, Website, Figures & more

PDG Outreach

Particle Adventure & Apps CPEP Charts History book

Non-PDG Resources

Funded by:

US DOE, CERN, MEXT (Japan), IHEP-CAS (China), INFN (Italy),MINECO (Spain), IHEP (Russia)

All pages © 2017 Regents of the University of California

About PDG PDG Authors PDG Citation Contact Us

HEP Papers Databases & Info Institutions & People

Particle Data Group - 2017 Review http://pdg.lbl.gov/

1 of 1 6/26/17, 4:40 AM

28


SUMMARY

 Standard Model  M(neutrino) = 0

12 masses + 2 coupling strengths

+ 4 quark EWK mixing parameters + ΛQCD = 19 parameters

Comments: 1. These 19 parameters must be determined from experiment. 2. Small variations of some of these parameters from those in “our” universe result in a dramatically different predictions. For example few % variations in the coupling strengths result in the prediction that nuclei would be unstable.


29


SUMMARY

 Standard Model  M(neutrino) > 0

15 masses + 2 coupling strengths

+ 8 EWK mixing parameters + ΛQCD = 26 parameters

The simplest way to capture this in the Standard Model, would be to add the 3 neutrino masses plus 4 EWK mixing parameters.


30


Units and conventions

31


Units using the SI (mks) system

As in any branch of science, the first barrier to carrying out quantitative calculations is to understand the units being used.

We will use the Standard International system of units, but scale them to be more convenient for the description of elementary particles and their interactions.

Ø  Length 1 fermi (fm) = 10-15 m ( the size of a proton is ~ 1 fm) Ø  Area 1 barn (b) = 10-28 m2

( typical cross sections are in mb, µb, nb, pb)

Ø  Energy 1 eV = 1.60x10-19 J ( typical energies MeV, GeV, TeV)

Ø  Mass Mc2 in GeV

Ø  Momentum pc in GeV

32


Some handy conversion factors Ø  c = 3.00 x 1023 fm/s Ø  h = 6.58 x 10-25 GeV s Ø  h c = 0.197 GeV fm Ø  (h c)2 = 0.389 GeV2 mb

All these units are “SI-based” as they ultimately refer to the the standards of length, mass and time to be the meter, kilogram and second.

Units using the SI (mks) system

It is tempting to choose units that would make some of the fundamental constants ( c and h ) equal a more reasonable number.

33


Often SM calculations are done using “natural units” where h = c = 1 . When this is done the constants h and c will not appear explicitly in the final equation.

Natural units

To get a numerical prediction you have to re-insert h and c By dimensional analysis, this is always unambiguous.

Note that with this convention all physical quantities ( mass, length, time, cross section …) can be expressed in terms of powers of energy (say GeV). The SM is referred to as a “dimension 4” theory since in natural units the Lagrangian density has units GeV4

34


Natural units (an example)

A theory calculation is done using “natural” units. The results are: cross section = 0.86 GeV-2 lifetime = 540 GeV-1 particle size = 2.1 GeV-1

To convert these to standard SI mks units simply multiply by the required combinations of h and c (see page 33).

cross section = 0.86 GeV-2 (h c )2 = 0.86 GeV-2 (0.389 GeV2 mb) = 0.33 mb

lifetime = 540 GeV-1 (h ) = 540 GeV-1 (6.58x10-25 GeV s) = 3.55 x 10-22 s

particle size = 2.1 GeV-1 (h c) = 2.1 GeV-1 (0.197 GeV fm) = 0.41 fm

35


End Lecture 1

Lecture 2

Space-time symmetries and relativistic kinematics

lecture 1 the particle content of the standard model has fully...

Documents