A Particle Physics Tourwith CompHEP

Jeffrey D. Richman

April 26, 2006

Outline Outline Introduction

Getting, installing, and running CompHEP; references

Using CompHEP; particle content in SM and SUSY; limitations of CompHEP; exclusive vs. inclusive processes; intermediate states

“Observables” in particle physics: decay rates, cross sections,…

Z-boson, t-quark, and Higgs decay in the SM

Compton Scattering

Muon decay and radiative corrections; b-quark decay

e+ e- scattering

Structure functions

pp and pp interactions: production of dijets, t-quarks, t t H

Conclusions

A Tour of Particle Physics with CompHEP

ee μμ ν ν− −→

ee μμ ν ν γ− −→

eb ce ν−→,e e Zγ μ μ+ − + −→ →

,e e Z bbγ+ − → →

e e W W+ − + −+ → +

e e Z Z+ −+ → +

, ,H qq

W W ZZ+ −

→

→

t bW +→2 bodyZ → e eγ γ− −+ → +

g g g g+ → +g g t t Hq q t t Hg g t t b b

+ → + ++ → + +

+ → + + +

g g t tq q t t+ → ++ → +

Each one of these processes has a story to tell and could be investigatedin much more depth…we will just scratch the surface.

e e μν ν μ− −+ → +

Getting CompHEP and Other GeneratorsCompHEP is a tool for calculating observables for particle processes, both scattering and decays

developed at Moscow State Universitypowerful, simple and fast to use, but has significant limitationsa good tool for learning particle physicsCompHEP home page: http://theory.sinp.msu.ru/compheplatest version is comphep-4.4.3 (25/05/2004)documentation: hep-ph/9908288, hep-ph/0403113.

Comprehensive set of links to other Monte Carlo generators for hadron-colliderphysics

http://www.ippp.dur.ac.uk/montecarlo/BSMLes Houches Guidebook to Monte Carlo Generators for Hadron Physics (hep-ph/0403045)

Note: all figures in this talk were made by the author using CompHEP,FeynDraw, ROOT,…

Installation for LinuxInstallation of CompHEP

download archive file (comphep-4.4.3.tgz) to your directory

/home/richman/CompHEPSource

tar xzvf comphep-4.4.3.tgz

creates directory with name comphep-4.4.3

cd comphep-4.4.3

./configureNote: the configure script looks for CERNLIB. You may need to change the CERNLIB environment variable to point to the appropriate directory. CERNLIB is needed only for SUSY models.

make

make setup WDIR=/home/richman/MyCompHEPWorkDir

Running CompHEP

cd ~/MyCompHEPWorkDir

./comphep &

CompHEP Model Selection

Particle Content of CompHEP: Standard Model

Can constrain possible intermediate-state particles; can beuseful in reducing execution time when there are many possibleFeynman diagrams and some have negligible amplitudes.

CompHEP Standard Model Parameters

Also a separate menu of constraints, such as CKM unitarity relations.

Particle Content of CompHEP: Minimal SUSY

Some useful features of CompHEPYou can restrict/specify the particles that enter in the intermediate state

CompHEP provides a menu of structure functions, including the CTEQ6 series, which can be used to help compute pp scattering processes.

You can apply cuts before computing cross sections; sometimes this is necessary to remove divergences.

You can write out “events.”

CompHEP can peform calculations in various SUSY models; this requires CERNLIB.

CompHEP Limitations No hadronic bound states (mesons, baryons) and no hadronization of quarks and gluons into jets

No loop/box diagrams

All processes are averaged over allowed initial-state spin polarizations and summed over final-state polarizations.

No neutrino oscillations

CompHEP can be used to compute quasi-inclusive processes (e.g., H 2*x), but it is awkward to perform truly inclusive calculations.

u

u

d

d

HW+

W-

tH

tNo, No No

Yes

Procedure for computing results1. Specify decay or scattering process2. View Diagrams; can write Latex code; can Delete selected

diagrams; Exit (escape key)3. Square Diagrams (can View and escape)4. Symbolic calculation5. Write results6. C code7. C-Compiler (hit return in separate window after complete)8. Go to new window for numerical calculations9. Select subprocess if applicable10. Define cuts if desired11. Vegas (or Simpson if applicable)12. Set distributions and ranges if desired13. Integrate (Χ2<1 for numerically consistent results)14. View distributions15. Generate events if desired

“Observables” in CompHEPCompHEP allows us to compute the main “observables” that can be predicted by theories of particle physics.

Decay rates of particles (and lifetimes)

Scattering cross sections

Differential distributions for both scattering and decays processes

Decay rates and asymmetries as a function of a parameter

Note that none of these quantities is directly measured with a detector!

charged particles ionization in detector voltages/charges

neutral particles generate EM or hadronic showers…

energy loss, multiple scattering, Cerenkov radiation, radiation damage,…

Particle interactions with the detector or not simulated by CompHEP, but they form the fundamental basis of our measurements!

Observables: Decay RatesObservables: Decay RatesThe total decay rate (Γ) of a particle measures • the strength, range of the interactions governing the decay processes• the number of accessible final states that the particle can decay into• for a given final state, the possible effects of interference among

different amplitudes

/0 0( ) t tN t N e N eτ− −Γ= =

Exponential decay law: number of surviving particles

1

m

ff =

Γ = Γ∑ Decays/sec summedover all distinguishable final states f

Normally write Γ in energy units:

( )decays ( ) Energysec

⎛ ⎞Γ → Γ⎜ ⎟⎝ ⎠

-2365.8 MeV 10 sτ ⋅= ≅Γ Γ

Observables: Decay RatesObservables: Decay Rates

1 1

1m m

ff

f f

B= =

Γ= =

Γ∑ ∑

Branching fractions (Bf)

4 2

1(2 ) ( ; ,..., )2f f n nd d P p p

Mπ

Γ = ΦM

34

1 31 1

( ; ,..., ) ( )(2 ) (2 )

n ni

n n ii i i

d pd P p p P pE

δπ= =

Φ = −∑ ∏

sum of amplitudes for specified final state

phase space factor: integrate it over kinematicconfigurations consistent with (E,p) conservation

1p

2p3p

Each mode i corresponds to a distinguishable set of final-state particles and is called a “subprocess” in CompHEP.

1 2 ...f f f= + +M M M

Differential decay rate for mode i (in diff. region of phase space)

Initial states, intermediate states, and final states

source

• Sum the rate over final states (they are distinguishable)• Sum the amplitudes over intermediate states (they are not

distinguishable)• Average the resulting rate over possible initial states• Interference pattern allows us to infer that there is more than one

intermediate state!

1fM

2fM

final statef =

CompHEP: Z 2*x subprocesses

Each subprocess corresponds to a distinguishable final state; we need to add the rates forthe subprocesses, not the amplitudes.

CompHEP Diagrams for Z 2*x

in CompHEP menus, τ is l

Left out Z W+W- diagram, also kinematically forbidden.

These diagrams are distinct subprocesses: no interference.

Note: kinematically forbidden diagram.

Examples

-23 2565.8 MeV 10 s 4.4 10 s

1.55 GeVtτ−×

×

CompHEP results for Z 2*x

CompHEP results for t 2*x

The top quark decays before it has time to form a hadronic bound state!

SM Higgs Decay H 2*x

Observables: Scattering Cross SectionsObservables: Scattering Cross SectionsThe scattering cross section (σ) of two particles measures • the strength and range of the interactions governing the scattering

processes• the number of accessible final states that the particles can scatter into• for a given final state, the possible effects of interference among

different amplitudes

imagine a particle coming directly at you…If interaction is short range, and particle has finite extent, then the cross section roughly corresponds to the geometric area of the particle.

p

If interaction is long range, and/or particle has no finiteextent, the cross section does not correspond to a geometrical area.e−

24 21 barn = 10 cm−

pp and pp cross sections

pp cross sections (LHC)100 mbtotσ

20 mbelasticσ

100 mb

14 TeV

9 -110 evts s

( ) 2 1/ 3 2(1.2 fm )nucleusNN r Aσ π π≈ ≈13 2 2 / 3 24 2(1.2 10 cm) 10 barn / cm

30 mb ( )A

ppπ −≈ × ⋅ ⋅

≈

hep-ex/9901018

80 mbinelasticσ

Geometric cross section (very naïve)

Huge range of cross sections!

Observables: Scattering Cross SectionsObservables: Scattering Cross Sections

34

1 31 1

( ; ,..., ) ( )(2 ) (2 )

n ni

n n ii i i

d pd P p p P pE

δπ= =

Φ = −∑ ∏

,1 ,2 ...f f f= + +M M M

4 2

1 2 3 22 2 21 2 1 2

(2 ) ( ; ,..., )4 ( )

f f n nd d p p p pp p m m

πσ += Φ +⋅ −

M

/0( ) xN t N e λ−= 1

nλ

σ=

( )interactions ( )N dt L t σ= ⋅∫

scattering from a fixed target withn = #scattering objects/volume

colliding-beam experimentL(t)=instantaneous luminosity

(cm-2s-1)

( ) 1-1nucl int (Fe) 25 cmnλ σ −= ≈

1 2( ) BN N n fL tA

=

γ + e- γ + e- (Compton Scattering)

2 32

2 3 2

(1 ) 4 1 2 (1 2 )( ) ( 2 2) ln1 1 (1 )e

v v v v ve e v vm v v v v

πασ γ γ− − ⎡ ⎤− + +⎛ ⎞+ → + = × + + − −⎜ ⎟⎢ ⎥+ − +⎝ ⎠⎣ ⎦2

2e

e

s mvs m−

=+

( )2 6 -8 22 124 2137

2 2

8 (1973 10 MeV 10 cm)80 0.67 10 cm3 3(0.511 MeV)e

vm

ππασ−

−× ⋅→ ⇒ → = ×

116 10 pb×

Thomson scattering

2

2

2 1ln2KN

e

ss mπασ

⎡ ⎤⎛ ⎞= +⎢ ⎥⎜ ⎟

⎝ ⎠⎣ ⎦

W-mediated b-quark transitions have several key features in common with muon decay.

Very strong dependence of decay rate on mass!

MuonMuon decay: a prototype lowdecay: a prototype low--energy weak decayenergy weak decay

μ−

e−

eνμνg

g

2 53 4 2

3 (1 8 8 12 ln )192

FG mx x x x xμ

πΓ = ⋅ − + − − 2

2emx

mμ

≡

2

282F

W

G gM

≡

(ignoring QED radiative corrections)

152 (1 )μγ γ−

2

2 2

( / )W

W

g q q Miq M

μν μ ν− +−

2 2 2Wq m Mμ≤

Mass dependence of weak decay ratesMass dependence of weak decay rates(correcting for CKM elements)(correcting for CKM elements)

π −

μ−

K −

D−τ −

B−

μμ Decay Rate and DistributionsDecay Rate and Distributions

Electron energy spectrum

coupling is V, A comb.

(excludes T,S,P)

19( ) (3.05 10 ) GeV ee μμ ν ν− − −Γ → = ×

6 2.16 10 stot

τ −⇒ = ≅ ×Γ

2 52

3 (3 2 ) 962

F

e

G md x xdx

Exm

μ

μ

πΓ= −

≡

μ Decay with Radiative Corrections

γ energy spectrum: Eγ>10 MeV

21

( )

(5.0 10 ) GeV 10 MeV

ee

E

μ

γ

μ ν ν γ− −

−

Γ →

= ×>

( )1.7%

( )e

e

ee

μ

μ

μ ν ν γμ ν ν

− −

− −

Γ →Γ →

b-quark decay in CompHEPElectron energy spectrum in b c e ν

Used to measure Vcb, mb, and mc…a long story!

e+e- Scattering

M.M. Kado and C.G. Tully, Ann. Rev. Nucl. Part. Phys., Vol 52 (2002)

PDG 2005

Cross section vs. CM energy for e+e- bb

Interfering amplitudes

Cross section vs. CM energy for e+e- μ+μ-

Distribution of cosθbetween μ- and e-

Angular asymmetry vs. CM energy

Measurement was done at theTevatron too! (hep-ex/0106047)

e+e- μ+ μ- angular distribution and forward-backward asymmetry

e+e- b b angular distribution and forward-backward asymmetry

Distribution of cosθbetween b and e-

Angular asymmetry vs. CM energy

Cross section vs. CM energy for e+e- W+W-

e+ + e- W+ + W-

Angular Distributions and Asymmetry for Angular Distributions and Asymmetry for ee++ee-- WW++WW--

W- tends to go in e- direction

e+ + e- Z + Z

CompHEPCompHEP Diagrams for Diagrams for ee++ee-- WW++WW--ZZ

pp Scattering Cross Sections

PYTHIA6.205/PHOJET1.12 predictions for cross sections at sqrt(s)=14 TeV

)119/5.101( mbtotσ)4.34/2.22( mbelasσ

)5.84/3.79( mbinelasσ)68/2.55( mbmbσ

)5.16/1.24( mbdiffσ)4.1(~ mbcdσ

)1.4/8.9( mbddσ

)11/3.14( mbsdσ

from talk by A. Sobol at US CMS meeting, April 7, 2006:

q,g

q,g

p

p

p

pNon-Diffractive event

Exchange of color triplets, octets

• exponential suppression of rapidity gaps(gaps filled by color exchange in hadronization)

P,R

P,R

p

pp

p

Diffractive (central)event

Exchange of color singlets: Reggeons, Pomerons• rapidity gaps• momentum loss of the leading protons

43−>Δη

1.005.0 −<Δ

=ppξ

ηΔ

ηΔ

Diffraction: events topologiesDiffraction: events topologies

7 April, 2006 US-CMS Collaboration Meeting A.Sobol

0 10-10 η

ϕ

0p

p

p

pP

elastic scattering

p

p0 10-10 η

ϕ

0

non-diffractive ev.

0 10-10 η

ϕ

0p

p

pP

single diffraction

0 10-10η

ϕ

0p

pP

double diffraction

0 10-10 η

ϕ

0p

p

p

pP

central diffraction

~30 mb

~ 60 mb

~ 12 mb

~ 6 mb

~ 1 mb

p

p

p

ppT1/T2

RP RPCMS

“soft”

~ 6 mb

~ 2 mb

~ 1 mb

~ 7 nb

“hard”

from talk by A. Sobol, US CMS meeting, April 7, 2006

CompHEP: p + p Scattering

Proton Structure Functions

e−

e−

uud

u

2( , )if x q

2q

Prob to find a parton of type i carrying a fraction of the proton’s longitudinal momentum x=pi

L/pL

Cannot be calculated from 1st principles: extracted from data.

valence quarks

sea

Structure functions from Durham HEP Structure functions from Durham HEP DatabaseDatabase

http://durpdg.dur.ac.uk/HEPDATA

CTEQ6L MRST2002NLO

Structure functions (Durham HEP database)CTEQ6L CTEQ6L2 2100 GeVQ = 2 2500 GeVQ =

http://durpdg.dur.ac.uk/HEPDATA

p + p G + G at 14 TeV

Apply cut before computing cross section: pt(G)> 35 GeV

p + p G + G at 14 TeV

7( [ ] ) 5 10 pb 0.05 mbpp GG GGσ → × LHC

p + p G + G at 14 TeV

M(G1,G2) initial state

η(G3) initial state

Pt (G3)

Pt (G3)

p + p t + t

0.014

8.7Total

0.53

1.28

6.88

Process (pb)σ

uu tt→

dd tt→

gg tt→

uu tt→

2.0 TeVs =CompHEP at

174.3 GeVtm =

Oct 30, 2000 HEPAP Meeting

Top Pair Production Rate• Are measurements in different

final states consistent with each other and with theory?

Χ2/dof=4.3/5

D0 Run 2 Preliminary

CDF Run 2 PreliminaryCombined Cross Section

vsTevatron Preliminary Combined Top Mass

(pb))ttpσ(p →

10.1±2.2±1.3±0.6Dilepton NEW(L=360pb-1)

Evelyn Thomson talk at PANIC 2005

p + p t + t + H

• At the LHC, the mode with best sensitivity for a low-mass Higgs particle appears to be H γγ.

• By looking for the Higgs in association with t quarks, we might be able to see H bb, which would be the dominant decay mode.

(Also have production from initial-state quarks.)

Signal cross section vs. m(H)

p + p t + t + H

0.885Total (gg+2uu+2dd)

0.045

0.074

0.647

(pb)σProcessProcess

gg ttH→

uu ttH→

dd ttH→

115 GeVHm =

Challenge: Backgroundsfrom pp ttgg and pp ttbb

( ) 400 pbgg ttggσ → ≈jets jj( jets) 20 GeV), 3, cosθ 0.7tp g η> < <

14 TeVs =

( ) 6 pbgg ttbbσ → ≈( jets) 20 GeV)tp b > Background cross sections should not be taken too literally…

ConclusionsCompHEP is very fast and easy. It can provide a quick look at the overall situation for a physics analysis at the LHC.

It seems to be fairly reliable for electroweak processes.

Strong interaction processes and corrections are complicated, especially the identification of jets with partons. Predictions based on CompHEP alone—without jet fragmentation– must be treated with a lot of caution!

Next step: understand how CompHEP events can be given to Pythia to treat the jet fragmentation.

Extra Slides

Energy ScalesEnergy Scales

Band gap of silicon: 1.12 Band gap of silicon: 1.12 eVeV

Binding energy of HBinding energy of H--atom (n=1): 13.6 atom (n=1): 13.6 eVeV

Binding energy per nucleon in typical nucleus: 8 Binding energy per nucleon in typical nucleus: 8 MeVMeV

Mass of proton (940 Mass of proton (940 MeVMeV) and neutron (940 ) and neutron (940 MeVMeV))

Mass of b quark: 4.6 Mass of b quark: 4.6 GeVGeV

Masses of W (80 Masses of W (80 GeVGeV) and Z (91 ) and Z (91 GeVGeV))

Mass of t quark: 174 Mass of t quark: 174 GeVGeV

Vacuum expectation value of Higgs fieldVacuum expectation value of Higgs field

Planck mass: Planck mass:

p+p scattering cross section from PDG

Higgs Branching FractionsHiggs Branching Fractions