LPAIR A Generator for Lepton Pair Pro duction

Authors SP Baranov PNLeb edev Physical Institute Moscow USSR

O Dunger Deutsches Elektronen Synchrotron Hamburg Germany

H Sho oshtari MaxPlanck Institut fur Physik Munc hen Germany

JAM Vermaseren NIKHEFH Amsterdam the Netherlands

This manual is derived from the publication in It contains up to date information on

the LPAIR program version and some information sp ecic to the H collab oration

Last up date May Dirk Homann DESYFH

Program summary

Title of the program LPAIR

Computer SGI originally developp ed on IBM

Programming language FORTRAN

Numb er of program lines

Other programs used PDFLIB for parton distributions

AXOHS for phase space integration

JETSET for hadronic state evolution

Hroutines from HGEN HMCUTIL HUTIL HNDB

FPACK SHIFT and BOS for le access and data handling

CERNLIB

Keywords QED twophoton pro cesses MonteCarlo simulation

Nature of physical problem electromagnetic pro duction of lepton pairs

in twophoton interactions at high energies

Metho d of solution MonteCarlo event generation

Restrictions Other than twophoton diagrams are not considered

Typical running time ms p er event min for VEGAS

on IBM ES

Intro duction

The program LPAIR is a MonteCarlo generator devoted to the pro cess of electromagnetic

pro duction of lepton pairs in leptonlepton leptonhadron or hadronhadron interactions

via the twophoton pro cess as is shown in g ab

p1 p3 e- e- e- e- }

p6 µ- µ- p4 p}7 µ+ µ+

p2 }p5

p p

a b c

Figure

a b Feynman diagrams of the twophoton mechanism of fermion pair production

c The kinematics of the process as it is considered in the program

The main feature of pro cesses is their multip eripheral structure in which there are

two photons in the tchannel This is resp onsible for the large cross sections and also for

the very strong gauge cancellations in the matrix element Most of the cross section is

found at very small values of jtj for b oth photons This can cause severe problems for a

numerical integration program Another problem concerns the evaluation of the matrix

element of the pro cess The cancellations b etween the various terms can b e so bad that

even the bit accuracy of a CDC computer will not suce It was therefore necessary

to use a dierent form for the matrix element

LPAIR is based on a numerically stable formula for the matrix element of the two

photon pro duction of a pair of fermions in which the b eam particles can have arbitrary

structure functions This formula has b een obtained using a new metho d of formulating

the matrix element to avoid gauge cancellations The explicit description of this metho d

is presented in

It should b e noted that the twophoton diagrams are not the only ones that contribute

to the sp ecied nal state but extra diagrams typically contribute on the level of of

the twophoton diagrams or are of imp ortance only in an easily recognizable corner of the

phase space So their contribution can b e rather easily separated or estimated with the

help of some other programs

The kinematics of the twophoton reaction is written as a pro cess like in g c

All the essential twophoton physics prop erties can b e describ ed in this kinematics in

dep endently of the particle contents of the systems denoted by the vectors p p or p

3 4 5

each may represent more than one particle In the vertex p p elastic and inelastic

1 3

interactions are considered in the program

2 2 2 2 2 2

The basic kinematical variables are M p M p and M p the masses

3 3 4 4 5 5

2 2

squared of the nal state systems t q and t q the momenta squared of the

1 2

1 2

2

virtual photons s p p p p q q p q p q and the angles cos

2 4 5 1 2 1 2 1 2 2 1

and of the pro duced leptons p and p in their centreofmass cm system This choice

6 7

of kinematical variables is adjusted to the metho d mentioned ab ove of formulating the

matrix element in a numerically stable form

1 1

Since the dierential cross section b ehaves roughly like t t by changing the in

1 2

tegrals over t and t into integrals over log t and log t the integrand is not so

1 2 1 2

strongly p eaked anymore After this the integration routine VEGAS is used The combi

nation of VEGAS with a reformulation of phase space yields a go o d event generator We

do not consider here the principles of VEGAS since they are describ ed elsewhere

The contents of the program

The routines which the program consists of may b e divided into two classes those

essential for the physics and others concerning the inputoutput handling Below the

task of each of them is explained

Routines essential for the physics of the pro cess

Fx the function to b e integrated which returns the value of the weight of an

event including the matrix element of the pro cess all the kinematical factors and

the cut restrictions X is an array of random numb ers used to select a random

p oint inside the phase space

PICKIN describ es the kinematics of the pro cess p p p p p in terms of

1 2 3 4 5

Lorentzinvariant variables Fills common blo cks to b e used in PERIPP essential

for the evaluation of the matrix element

ORIENT calculates energies and momenta of the st nd rd th and th

particle in the overall cm frame

GAMGAM describ es the kinematics of a decay p p p and calculates

4 6 7

the energies and momenta of the th and the th particle in the cm frame

PERIPP contains the expression of the matrix element squared for the pro cess

under consideration It returns the value of the pro duct of the formfactors or struc

ture functions and the matrix element squared Its two arguments dene whether

the upp er and lower photon vertices are taken to b e elastic structureless like

in the electron or single quark case elastic with nontrivial form factor like

proton inelastic with the structure functions of

MAPW MAPXQ MAPMX MAPT MAPT MAPLA redene the variables

of integration in order to avoid the strong p eaking of the integrand

Service input and output routines

The program has b een interfaced to H software The most imp ortant nonstandard

routines are the following

GMUPA main steering routine for the generation of ep events Called by

HGEN

GMUBEG prepares the event generator Calls VEGAS and SETGEN

GMUGNA reconsiders the generated events and rejects some of them with a

denite probability in order to pro duce unweighted events

User dened parameters

These parameters are transmitted to the program via the steering card ie BOS bank

GMUP

AXOHS parameters

Keyword Default Explanations

IBEG the starting step of the program

times to run a completely new job

to use the grid pro duced by VEGAS from a previous run

to use the VEGAS grid and the information ab out the

weights of events pro duced by SETGEN in a previous run

IEND the concluding step of the program

to estimate the crosssection only

to save SETGEN information for further runs

times to pro duce a complete output event to b e stored

PRVG Print parameter from VEGAS

NTRT Strategy parameter NTREAT from VEGAS

NCVG Numb er of events for VEGAS to p erform the integration

ITVG Numb er of iterations for VEGAS

NCSG Numb er of events in each bin for SETGEN

Beam particle and interaction parameters

INPP rst incoming particle momentum in GeV c default

PMOD rst incoming particle typ e and kind of interaction

electron for tests

proton elastic default

proton inelastic with structure functions

proton inelastic with structure functions for

2 2

M GeV Q GeV

x

proton inelastic in parton mo del only valence quarks

proton inelastic in parton mo del only sea quarks

proton inelastic in parton mo del valence and sea quarks

GPDF author group co de for structure function default

PDFlibparameter NGROUP cf PDFLIB for details

SPDF set co de for structure function default

PDFlibparameter NSET cf PDFLIB for details

QPDF choice of scattered quark avour default

up down updown strange charm b ottom

INPE second incoming particle momentum in GeV c default

EMOD second incoming particle typ e

electron default

p ositron

proton elastic for tests

PAIR particle co de of pro duced leptons

+

e e

+

default

+

MPDF Obsolete overrides selections via SPDFGPDF

choice of proton structure function via the outdated interface

parameter PMODE of PDFlib

Backward compatibility of the default structure function From version

on the obsolete interface to PDFlib via the MPDF LPAIR PMODE PDFlib pa

rameter has b een abandoned The previous versions and b elow default value for

MPDFPMODE corresp onds to GPDFSPDF GRV HO from However

we made the choice to take the recommended successor set GRV HO by default in the

newer versions

Cut parameters

Keyword Default Explanations

MCUT No cuts at all for the total cross section

Vermaserens hyp othetical detector cuts see

Cut with the following parameters for b oth leptons

Cut with the following parameters for one lepton only

THMX of lepton in degrees

max

THMN of lepton in degrees

min

ECUT minimal energy of lepton in GeV

PTCT minimal transverse momentum of lepton in GeV

2 2

QMN minimal Q at the proton side in GeV

2 2

QMX maximal Q at the proton side in GeV

for PMOD only

MXMN minimal inv mass of the hadronic system in GeV

MXMX maximal inv mass of the hadronic system in GeV

References

S P Baranov et al LPAIR A Generator for Lepton Pair Pro duction Physics at

HERA Pro ceedings of the Workshop Octob er pp

J A M Vermaseren Nucl Phys B

G P Lepage J Comp Phys

S Stein et al Phys Rev D

A Suri and D R Yennie Ann of Phys

F W Brasse et al DESY

H PlothowBesch PDFLIB Nucleon Pion and Photon Parton Density Functions

and Calculations Users Manual Version CERNPPE Software do cumen

s

tation W

H standards unpublished