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A Particle Physics Tour with CompHEP
Jeffrey D. Richman

April 26, 2006


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
Z 2 body

t bW

+

+ e- + e

-

- e - e
-



- e - e
e+ + e- W + + W e+ + e- Z + Z
-

b ce -

e

e + e- +

-

e+e- , Z + e + e - , Z bb
g+gt+t +H q+q t+t +H g + g t+ t +b+b

g+gg+g

g+gt+t q+q t+t

H qq , W +W - , ZZ

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


Getting CompHEP and Other Generators
CompHEP is a tool for calculating observables for particle processes, both scattering and decays developed at Moscow State University powerful, simple and fast to use, but has significant limitations a good tool for learning particle physics CompHEP home page: http://theory.sinp.msu.ru/comphep latest 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-collider physics http://www.ippp.dur.ac.uk/montecarlo/BSM Les Houches Guidebook to Monte Carlo Generators for Hadron Physics (hepph/0403045)

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


Installation for Linux
Installation 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 ./configure
Note: 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 be useful in reducing execution time when there are many possible Feynman 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 CompHEP
You 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.

t t
No, No No

u
H

d
W+
H

Wd
Yes

u


Procedure for computing results
1. Specify decay or scattering process 2. View Diagrams; can write Latex code; can Delete selected diagrams; Exit (escape key) 3. Square Diagrams (can View and escape) 4. Symbolic calculation 5. Write results 6. C code 7. C-Compiler (hit return in separate window after complete) 8. Go to new window for numerical calculations 9. Select subprocess if applicable 10. Define cuts if desired 11. Vegas (or Simpson if applicable) 12. Set distributions and ranges if desired 13. Integrate (2<1 for numerically consistent results) 14. View distributions 15. Generate events if desired


"Observables" in CompHEP
CompHEP 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 Rates
The total decay rate () 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 Exponential decay law: number of surviving particles
m

N (t ) = N 0e
decays sec

- t /

= N 0e

- t

=


f =1



f

Normally write in energy units:

Decays/sec summed over all distinguishable final states f
-23

( ) ( Energy

)

65.8 MeV 10 =

s


Observables: Decay Rates
Branching fractions (Bf)

1=


f =1

m



f


4

=


f =1
f

m

B

f

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

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

(2 ) d f = M 2M

2

d n ( P; p1 , ..., pn )

p1 p2
n n

sum of amplitudes for specified final state

p3
d 3 pi (2 )3 ( 2 Ei )

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

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

d n ( P; p1 , ..., pn ) = 4 ( P -

p )
i =1 i i =1


Initial states, intermediate states, and final states
f = final state
source

M M

f1

f2

· 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!


CompHEP: Z 2*x subprocesses

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


CompHEP Diagrams for Z 2*x
These diagrams are distinct subprocesses: no interference.

Note: kinematically forbidden diagram.

in CompHEP menus, is l

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


Examples
CompHEP results for Z 2*x

CompHEP results for t 2*x



t

65.8 MeV â 10-23 s 1.55 GeV

4.4 â 10

-25

s

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


SM Higgs Decay H 2*x


Observables: Scattering Cross Sections
The scattering cross section () 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...

p
-

If interaction is short range, and particle has finite extent, then the cross section roughly corresponds to the geometric area of the particle. If interaction is long range, and/or particle has no finite extent, the cross section does not correspond to a geometrical area.

e

1 barn = 10

-24

cm

2


pp and pp cross sections
pp cross sections (LHC)

hep-ex/9901018

100 mb

109 evts s

-1



tot

100 mb 80 mb 20 mb

inelastic elastic



(1.2 â 10-13 cm)2 A2 / 3 1024 barn / cm 30 mb (pp )

2 ( NN ) rnucleus (1.2 fm A1 / 3 )

Geometric cross section (very naÎve)

2
2

Huge range of cross sections! 14 TeV


Observables: Scattering Cross Sections
N (t ) = N 0e
=
-x/

1 = n

scattering from a fixed target with n = #scattering objects/volume
-1 nucl int (Fe) = n ( 25 cm

)

-1

N

interactions

(

dt L ( t )
(2 )
4

)

colliding-beam experiment L(t)=instantaneous luminosity (cm-2s-1) L(t ) = N1 N 2nB f
A

d f =

2 4 ( p1 p2 ) 2 - m12m2
f ,2

M

2 f

d n ( p1 + p2 ; p3 , ..., pn + 2 )

M f = M f ,1 + M

+ ...

d n ( P; p1 , ..., pn ) = 4 ( P -

p )
i =1 i i =1

n

n

d 3 pi (2 )3 (2 Ei )


+ e-

+ e- (Compton Scattering)
6 â 1011 pb

2 2 s 1 = ln 2 + s me 2

KN

( + e + e ) =
- -

2 (1 - v ) 4v
2 me v 3

3 1 + v 2v (1 + 2v ) â + (v + 2v - 2) ln - 1+ v 1- v (1 + v )2 2

2 s - me v= 2 s + me

Thomson scattering
2

8 2 8 = v0 2 3me

1 ( 137 )

2

(1973 â 10-6 MeV 10-8 cm) 3(0.511 MeV) 2

0.67 â 10

-24

cm

2


Muon decay: a prototype low-energy weak decay
W-mediated b-quark transitions have several key features in common with muon decay.

i

-g
-



2 + ( q q / M W ) 2 q 2 - MW

g

e

-



g



1 2

e

(1 - 5 )



q m
2



2

M

2 W

Very strong dependence of decay rate on mass!

=

2 GF m


3

5

GF g2 2 2 8M W
2 me x 2 m

192

(1 - 8 x + 8 x - x - 12 x ln x )
3 4 2

(ignoring QED radiative corrections)

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

B

-


K
-

-

D

-



-



-


Decay Rate and Distributions
( - e - e ) = (3.05 â 10
= 2.16 â 10
tot -6

-19

) GeV

s

Electron energy spectrum coupling is V, A comb. (excludes T,S,P)
25 d GF m 2 = x (3 - 2x) 3 dx 96 2E x e m


Decay with Radiative Corrections

energy spectrum: E>10 MeV

( - e - e ) = (5.0 â 10-21 ) GeV E > 10 MeV

( - e - e ) ( e e )
- -

1.7%


b-quark decay in CompHEP
Electron energy spectrum in b ce

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


e+e- Scattering

PDG 2005 M.M. Kado and C.G. Tully, Ann. Rev. Nucl. Part. Phys., Vol 52 (2002)


Cross section vs. CM energy for e+e-

bb

Interfering amplitudes



Cross section vs. CM energy for e+e-

+

-


e+e

-

+ - angular distribution and forward-backward asymmetry Distribution of cos between - and e-

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

Angular asymmetry vs. CM energy


e+e

-

bb angular distribution and forward-backward asymmetry

Distribution of cos between 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 e+e- W+WW- tends to go in e- direction


e+ + e- Z + Z


CompHEP Diagrams for e+e- W+W-Z


pp Scattering Cross Sections
from talk by A. Sobol at US CMS meeting, April 7, 2006:
PYTHIA6.205/PHOJET1.12 predictions for cross sections at sqrt(s)=14 TeV



tot

elas

( 22 . 2 / 34 . 4 mb ) ( 79 . 3 / 84 . 5 mb )

(101 . 5 / 119 mb )





mb

( 55 . 2 / 68 mb )



inelas

sd

(14 . 3 / 11 mb )



diff

( 24 . 1 / 16 . 5 mb )



dd cd

( 9 . 8 / 4 . 1mb ) (~ 1 . 4 mb )

p q,g p q,g

p p
Non-Diffractive event

p P,R
Diffractive (central) event

p p

P,R

p

Exchange of color triplets, octets · exponential suppression of rapidity gaps
(gaps filled by color exchange in hadronization)

Exchange of color singlets: Reggeons, Pomerons > 3 - 4 · rapidity gaps · momentum loss of the leading protons

=

p < 0.05 - 0.1 p


Diffraction: events topologies

from talk by A. Sobol, US CMS meeting, April 7, 2006
RP ~30 mb p CMS RP T1/T2 p

p p

P

p p


0 -10

elastic scattering

0

10



p p p p p p p p
P


0 -10

non-diffractive ev.

"soft"
~ 60 mb

"hard"
~ 6 mb

0

10

P

p


0 -10

single diffraction ~ 12 mb
0 10

~ 2 mb p





double diffraction
0 -10

P


~ 6 mb central diffraction
0 10

~ 1 mb



p p

0 -10 0 10

~ 1 mb


~ 7 nb p

p

7 April, 2006

US-CMS Collaboration Meeting

A.Sobol


CompHEP: p + p Scattering


Proton Structure Functions
f i ( x, q )
2

e e
sea
-

-

q

2

valence quarks

u u d

u

Prob to find a parton of type i carrying a fraction of the proton's longitudinal momentum x=piL/pL Cannot be calculated from 1st principles: extracted from data.


Structure functions from Durham HEP Database CTEQ6L MRST2002NLO

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


Structure functions (Durham HEP database)
CTEQ6L Q 2 = 100 GeV
2
2 CTEQ6L Q = 500 GeV 2

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

( pp[GG ] GG ) 5 â 107 pb 0.05 mb

LHC


p+p

G + G at 14 TeV
M(G1,G2) initial state

(G3) initial state


Pt (G3)

Pt (G3)


p+p

t+t
CompHEP at
Process

s = 2.0 TeV

(pb)
6.88 1.28 0.53 0.014 8.7

uu t t
dd t t

gg t t uu t t
Total

mt = 174.3 GeV


· Are measurements in different final states consistent with each other and with theory?
Dilepton NEW
(L=360pb-1)

Evelyn Thomson talk at PANIC 2005

Top Pair Production Rate
D0 Run 2 Preliminary

10.1±2.2±1.3±0.6

(p p tt) (pb)

2/dof=4.3/5
Oct 30, 2000 HEPAP Meeting

CDF Run 2 Preliminary Combined Cross Section vs Tevatron Preliminary Combined Top Mass


p+p

t+t+H

· At the LHC, the mode with best sensitivity for a low-mass Higgs particle appears to be H . · 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
s = 14 TeV

t+t+H

mH = 115 GeV

Process
gg t tH

(pb)
0.647 0.074 0.045 0.885

uu t tH
dd t tH
Total (gg+2uu+2dd)

Challenge: Backgrounds from pp ttgg and pp ttbb

( gg t tgg ) 400 pb
( gg t tbb ) 6 pb
pt (b jets) > 20 GeV)
pt ( g jets) > 20 GeV),
jets

< 3, cos jj < 0.7

Background cross sections should not be taken too literally...


Conclusions
CompHEP 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 Scales
Band gap of silicon: 1.12 eV

Binding energy of H-atom (n=1): 13.6 eV Binding energy per nucleon in typical nucleus: 8 MeV Mass of proton (940 MeV) and neutron (940 MeV) Mass of b quark: 4.6 GeV Masses of W (80 GeV) and Z (91 GeV) Mass of t quark: 174 GeV Vacuum expectation value of Higgs field Planck mass:


p+p scattering cross section from PDG


Higgs Branching Fractions