high p t hadron collider physics

FNAL Academic Lectures - May, 2006 1

High PHigh PTT Hadron Collider Physics Hadron Collider PhysicsHigh PHigh PTT Hadron Collider Physics Hadron Collider Physics

Outline

• 1 - The Standard Model and EWSB

• 2 - Collider Physics

• 3 - Tevatron Physics• QCD• b and t Production• EW Production and D-Y


Backup TextBackup TextBackup TextBackup Text


UnitsUnitsUnitsUnits

Recall that coupling constants indicate the strength of the interaction and characterize a

particular force. For example, electromagnetism has a coupling constant which is the electron

charge, e and a “fine structure” constant ce 4/2 that is dimensionless. The

electromagnetic potential energy is rereVrU /)()( 2 and V(r) is the electromagnetic

potential. The dimensions of e2 are then energy times length, 2[ ] [ ( ) ]e U r r , the same as those of

c . Thus, in the units we adopt, 1c , e is also dimensionless. With ~ 1/137, we find e ~

0.303. Coupling constants for the two other forces, the strong and the weak, will be indicated by

gi, and the corresponding fine structure constants by i with i = s, W.

The units for cross section, , which we will use are barns (1 barn = 10-24 cm2). Note that 2 2( ) 0.4c GeV mb where 27 21 10mb cm . The units used in COMPHEP are pb = 10-12 b for

cross section and GeV for energy units. As an example, at a center of mass, C.M., energy, s ,

of 1 TeV = 1000 GeV, in the absence of dynamics and coupling constants, a cross section scale

of s/1~ ~ 400 pb is expected simply by dimensional arguments.


Tools NeededTools NeededTools NeededTools NeededWe will extensively use a single computational tool, COMPHEP. The aim was to expand a

slightly formal academic presentation to a more interactive mode for the student, giving “hands

on” experience. The plan was that the student would work the examples and then be fully

enabled to do problems on her own. COMPHEP runs on the Windows platform, which was why

it was chosen since the aim was to provide maximum applicability of the tool. A LINUX version

is also available for students using that operating system

The COMPHEP program is freeware. We have taken the approach of first working through the

algebra. That way, the reader can make a “back of the envelope” calculation of the desired quantity.

Then she can use COMPHEP for a more detailed examination of the question. The use and description

of COMPHEP is explained in detail. A web address where the executable code (zipped) and a users

manual are available. The author has also posted these items: http://uscms.fnal.gov/uscms/dgreen.

Freeware to unzip files can be found at http://www.winzip.com/ and http://www.pkware.com/.

(will use both during lecture demonstrations)

( Google them all – also Ghostview and Acrobat reader )


COMPHEP – Models and ParticlesCOMPHEP – Models and ParticlesCOMPHEP – Models and ParticlesCOMPHEP – Models and Particles

Can edit the couplings – e.g. ggH

Use SM Feynman gauge

Watch for LOCK


COMPHEP - ProcessCOMPHEP - ProcessCOMPHEP - ProcessCOMPHEP - Process

1-> 2,3

1-> 2,3,4

1,2 ->3,4

1,2 ->3,4,5

1,2-> 3,4,5,6 (slow)

*x options

No 2 -> 1


COMPHEP –Simpson, BRCOMPHEP –Simpson, BRCOMPHEP –Simpson, BRCOMPHEP –Simpson, BR

Find simple 2->2. Graphs (with menu)

Results can be written in .txt files

Several PDF, p and pbar,

Check stability of results


COMPHEP - CutsCOMPHEP - CutsCOMPHEP - CutsCOMPHEP - Cuts

May be needed to avoid poles or to simulate experimental cuts, e.g. rapidtiy or mass or Pt.


COMPHEP - CutsCOMPHEP - CutsCOMPHEP - CutsCOMPHEP - Cuts


COMPHEP - VegasCOMPHEP - VegasCOMPHEP - VegasCOMPHEP - Vegas

Full matrix element calculation – interference. Watch chisq approach 1. Setup plots, draw them and write them.


COMPHEP - DecaysCOMPHEP - DecaysCOMPHEP - DecaysCOMPHEP - Decays

Strictly tree level. Does not do “loops” or “box” diagrams.

Explore this very useful tool. If there are problems bring them to the class and we’ll try to fix them.


1 - The SM and EWSB1 - The SM and EWSB1 - The SM and EWSB1 - The SM and EWSB

• 1.1 The Energy Frontier

• 1.2 The Particles of the SM

• 1.3 Gauge Boson Masses and Couplings

• 1.4 Electroweak Unification

• 1.5 The Higgs Mechanism for Bosons and Fermions

• 1.6 Higgs Interactions and Decays


Higgs boson

t quark

b quark

s quark

ISR

Tevatron

SPEAR

SppS

TRISTAN

LEPII

CESR

Prin-Stan

Accelerators

electron

hadron

W, Z bosons

c quark

LHC

PEP

SLC

1960 1970 1980 1990 2000

Starting Year2010

10-1

100

101

102

103

104

Con

stit

uent

CM

Ene

rgy

(GeV

)

Historically HEP has advanced with machines that increase the available C.M. energy. The LHC is designed to cover the allowed Higgs mass range. Colliders give maximum C.M. energy.

The Energy The Energy FrontierFrontier


The Standard Model of Elementary The Standard Model of Elementary Particle PhysicsParticle Physics

The Standard Model of Elementary The Standard Model of Elementary Particle PhysicsParticle Physics

• Matter consists of half integral spin fermions. The strongly interacting fermions are called quarks. The fermions with electroweak interactions are called leptons. The uncharged leptons are called neutrinos.

• The forces are carried by integral spin bosons. The strong force is carried by 8 gluons (g), the electromagnetic force by the photon (), and the weak interaction by the W+ Zo and W-. The g and are massless, while the W and Z have ~ 80 and 91 GeV mass respectively.

J = 1 g,, W+,Zo,W- Force Carriers

J = 1/2

u

d

c

s

t

b

e

e

Q/e=

2/3

-1/3

1

0

Quarks

Leptons

J = 0 H


Gravity – Hail and FarewellGravity – Hail and FarewellGravity – Hail and FarewellGravity – Hail and Farewell

UG(r) = GNM2/r, depends on mass in comparison to the electrical energy UEM(r) = e2/r. The

quantity GN is Newton’s gravitational constant. The fine structure constants of the forces

appearing in the SM, such as electromagnetism, where 137/1~4/2 ce , are dimensionless

and mass independent. The gravitational analogue, 2 / 4Gr NG M c , is not.

Ignore gravity. However, gravity is a precursor gauge theory which is non-Abelian. The gauge quanta are “charged” non-linearity. The gravity field carries energy, or mass. Therefore, “gravity gravitates”. This is also true of the strong force (gluons are colored) and the weak force (W,Z carry weak charge). The photon is the only gauge boson which is uncharged.


How do the Z and W acquire mass and not How do the Z and W acquire mass and not the photon?the photon?

How do the Z and W acquire mass and not How do the Z and W acquire mass and not the photon?the photon?

Gravity - Physics is the same in any local general coordinate system --> metric tensor or spin 2 massless graviton coupled universally to mass = GN.

Electromagnetism - Physics is the same regardless of wave function phase assigned at each local point --> massless, spin = 1, photon field with universal coupling = e

These are “gauge theories” where local invariance implies massless quanta and specifies a universal ( GN, e ) coupling of the field to matter.

Strong interactions are mediated by massless “gluons” universally coupled to the “color charge” of quarks = gs.

Weak interactions are mediated by massive W+,Z,W- universally coupled to quarks and leptons. gWsinW = e. How does this “spontaneous electroweak symmetry breaking” occur? (Higgs mechanism)


Lepton Colliders - LEPLepton Colliders - LEPLepton Colliders - LEPLepton Colliders - LEP

Z peak

L and R leptons have different couplings to the Z. There is Z-photon interference which leads to a F/B asymmetry. A way to measure the Weinberg angle. gW measured from muon decay.


Field TheoryField TheoryField TheoryField Theory

2 2 2,E P M P P M

2( ) M

To describe quantum fields we will use for fermion (J = ½) fields, for scalar (J = 0)

fields, and for vector (J = 1) gauge fields in this text. For masses, m is used for fermions and

M for bosons.

2

( )( ) ( )( )

~ ( ) ,I

D D

g g

P

by AeP

ieAD

ggggggg, ZWWWW , WWWWZZWWZWWWW ,,,

Classical Special Relativity

Lagrangian density, P is an operator

Classical gauge replacement

Quantum gauge replacement


WW in e+e- CollisionsWW in e+e- CollisionsWW in e+e- CollisionsWW in e+e- Collisions

Test of self-coupling of vector bosons. There are s channel Z and photon diagrams, and t channel neutrino exchange. Test of VVV couplings.

In COMPHEP play with the Breit-Wigner option as s dependence of the cross section depends crucially on the W width – i.e. technique to measure W width..


Simpson –Angular DistSimpson –Angular DistSimpson –Angular DistSimpson –Angular Dist

Cross section without neutrino exchange in the t channel. Note divergent C.M. energy dependence – voilates unitarity.


WW Cross Section at LEPWW Cross Section at LEPWW Cross Section at LEPWW Cross Section at LEP

COMPHEP point shown. Proof that the WWZ triple gauge boson coupling is needed and that there are interfering amplitudes that themselves violate initarity.


WWWW at LEP at LEPWWWW at LEP at LEP

Probe of quartic couplings.

LEP data confirms SM

WWAA, WWZA

Cross section in COMPHEP with all final state bosons having Pt > 5 GeV is 0.36 pb


ZZ at LEPZZ at LEPZZ at LEPZZ at LEP

SM has only the single Feynman diagram. There are no relevant triple or quartic couplings – in the SM. Use the data to set limits on couplings beyond the SM.


e+e- Cross Sectionse+e- Cross Sectionse+e- Cross Sectionse+e- Cross Sections

WW, ZZ, and WW are seen at LEPII. At even higher C.M. energies, WWZ and ZZZ are produced - indicating triple and quartic V couplings. New channels open up at the proposed ILC.

Try a few (red dots) processes yourself…..


ILC Process - ExampleILC Process - ExampleILC Process - ExampleILC Process - Example

Cross section ~ 1 fb at 500 GeV in COMPHEP. Approximate agreement with full calculation.


The Higgs Boson PostulatedThe Higgs Boson PostulatedThe Higgs Boson PostulatedThe Higgs Boson Postulated

422 ||||)( V

2/22

~ ( ) ( )V

4~)( V

Potential Lagrangian density

Minimum at a non-zero vev “cosmological term”

This is Landau-Ginzberg superconductivity – much too simple?


How the W and Z get their MassHow the W and Z get their MassHow the W and Z get their MassHow the W and Z get their Mass

Covariant derivative contains gauge fields W,Z. Suppose an additional scaler field exists and has a vacuum expectation value. Quartic couplings give mass to the W and Z, as required by the data [ V(r) ~e(exp(-r/)/r) - weak at large r, strength e at small r].

2 2 2 2 2 22 1 2

( )( ) ( )( )

0~

( )( ) ~ / 2 ( ) / 2 (0)W W Z Z

D D

D D g g g e

WWZ

W

MggM

gM

M

cos/2/

2/

0

22

21

2


Numerical W, Z Mass PredictionNumerical W, Z Mass PredictionNumerical W, Z Mass PredictionNumerical W, Z Mass Prediction

The masses for the W and Z are specified by the coupling constants. G comes from beta decays or muon decay.

2 2 5 2

2

/ 2 / 8 , 10

/ / 2

2 / 4 , 174

W W

W W

G g M G GeV

M g

G GeV

2

2

sin ~ 0.231, ~ 28.7 , sin 0.481

~ 1/137, / sin ~ 1/ 31.6, ~ 0.63

oW W W

W W Wg

/ 2 ~ 80

/ cos ~ 91W W

Z W W

M g GeV

M M GeV


Higgs Decays to BosonsHiggs Decays to BosonsHiggs Decays to BosonsHiggs Decays to Bosons

Field excitations ==> interactions with gauge bosons VVH, VVHH, VVV, VVVV

2( ) / ~ ( /16)( / )H W H WH WW M M M

Higgs couples to mass. Photons and gluons are massless to preserve gauge symmetry unbroken. Thus there is no direct gluon or photon coupling.

2 2 2 2 22 1 2

0

( )( ) ( ) / 2 ( )( ) / 2

H

H W W H Z ZD D g g g

Using the Higgs potential, V(), expanding about the minimum at , and

identifying the mass term in as 2H H HM , we find that the mass is,

.2462 GeVM H Since is an arbitrary dimensionless coupling, there is no

prediction for the Higgs mass in the SM.

, ~ gW2 <>[ W W H ] ~ gWMW [ W W H ].


ZZH Coupling and ILC ProductionZZH Coupling and ILC ProductionZZH Coupling and ILC ProductionZZH Coupling and ILC Production

ILC at 500 GeV C.M. Higgs production by off shell Z production followed by H radiation, Z* ->Z+H.


Higgs Coupling to FermionsHiggs Coupling to FermionsHiggs Coupling to FermionsHiggs Coupling to Fermions

~ [ ]f L Rg

],[][~ ff mg

2/)/(

]/2[

WfWf

WWfff

Mmgg

gMggm

•The fermions are left handed weak doublets and right handed singlets. A mass term in the Lagrangian, is then not a weak singlet as is required.

•A Higgs weak doublet is needed, with Yukawa coupling,

Yukawa

Mass from Dirac Lagrangian density

Fermion weak coupling constant

( )m

( )L R R Lm


Higgs Decay to FermionsHiggs Decay to FermionsHiggs Decay to FermionsHiggs Decay to Fermions

• The threshold factor is for P wave, 2l+1 since scalar decay into fermion pairs occurs in P wave due to the intrinsic parity of fermion pairs.

• The Higgs is poorly coupled to normal (light) matter

• gt ~ gW (mt/ MW)/2 ~ 1.0, so top is strongly coupled to the Higgs.

2 3( ) / ~ (3 /8)( / )H W f WH qq M m M


The Higgs Decay WidthThe Higgs Decay WidthThe Higgs Decay WidthThe Higgs Decay Width

The Higgs decay width, scales as MH

3. Thus at low mass, the detector defines the effective resonant width and hence the time needed to discover a resonant enhancement. At high masses, the weak interactions become strong and /M ~ 1.


Higgs Width - WW + ZZHiggs Width - WW + ZZHiggs Width - WW + ZZHiggs Width - WW + ZZ

Higgs decays to V V have widths ~ M3

Try this as a

COMPHEP

example


Higgs Width Below ZZ ThresholdHiggs Width Below ZZ ThresholdHiggs Width Below ZZ ThresholdHiggs Width Below ZZ Threshold

Below ZZ threshold, decays can occur in the tails of the Breit Wigner Z resonance, with ~ 2.5 GeV, M ~ 91 GeV. This compares to the width to the heaviest quark, b at a Higgs mass of ~ 150 GeV. Means that W*W is an LHC strategy.


Early LHC Data TakingEarly LHC Data TakingEarly LHC Data TakingEarly LHC Data Taking

• We have seen that the Higgs couples to mass. Thus, the cross section for production from gluons or u, d quarks is expected to be small.

• Therefore, it is a good strategy to prepare for LHC discoveries by establishing credibility. The SM predictions , extrapolated from the Tevatron, should first be validated by the LHC experimenters.


Vector Bosons and Forces Vector Bosons and Forces Vector Bosons and Forces Vector Bosons and Forces

The 4 forces appear to be of much different strength and range. We will see that this view is largely a misperception.

high p t hadron collider physics

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