Event Generators for Bhabha Scattering Conveners S Jadach and O Nicrosini Working Group H Anlauf A Arbuzov M Bigi H Burkhardt M Cacciari M Cao H Czy zM Dallavalle J Field F Filthaut F Jegerlehner E Kuraev G Montagna T Ohl B Pietrzyk F Piccinini W Placzek E Remiddi M Skrzyp ek L Trentadue B F L Ward Z W as Contents Introduction Smallangle Bhabha scattering Sensitivity of LEP observables to luminosity Higher order photonic corrections at LEP and LEP Light pairs and other small contributions Vacuum p olarization Brief characteristics of the programscalculati ons Exp erimental event selection and theory uncertainty in luminosity measure ments hep-ph/9602393 26 Feb 1996 Reference event selections Comparison of exp onentiated and orderbyorder calculations Dep endence on energy and acollinearity cuts WideWide NarrowNarrow versus WideNarrow acceptance Multiple photon radiation Summary Comparisons of event generators for smallangle Bhabha scattering Event selections First order technical precision Beyond rst order physical precision Asymmetric and very narrow event selections Z and vacuum p olarizatio n included The total theoretical error for smallangle Bhabha scattering Largeangle Bhabha scattering Physics On Z p eak LEP Far o Z p eak LEP Shortwriteups of the programs BHAGEN BHAGENE BHLUMI BHWIDE NLLBHA SABSPV UNIBAB Conclusions and outlo ok Introduction The main goals of the Bhabha working group are to make an inventory of all the available Monte Carlo MC event generators for smallangle SABH and largeangle LABH Bhabha pro cesses at LEP and LEP and to improve our understanding of their theoretical uncertain ties through systematic comparisons of the MC event generators developed indep endently among themselves and with other nonMC programs The presented activity is of course an obvious continuation of the previous workshops on LEP physics In the b eginning of the present workshop the theoretical uncertainty at LEP for the SABH pro cess was typically estimated as and for the LABH pro cess was estimated at level at Z p eak and on the wings of the Z resonance There were no estimates sp ecic to LEP We shall concentrate on the comparison of all the presently available theoretical calculations published and unpublished This will b e done for several kinds of event selection ES dened as a set of exp erimental cuts and apparatus acceptances starting from ESs unrealistic but useful for some studies oriented towards the QED matrix element and ending on ESs very close to the exp erimental ones Let us add a few comments to clarify our priorities and to set the prop er p ersp ective for our work In spite of the considerable eort of several theoretical groups at present the theoretical error on the smallangle Bhabha cross section dominates the luminosity error at LEP This inhibits from taking full advantage of the high exp erimental precision of the nal LEP data for precision tests of the Standard Mo del As a consequence the reduction of the theoretical error in the SABH pro cess at LEP is the biggest challenge and was the main ob jective of our working group The precision requirements of LEP are lower than those of LEP The total cross section of W pair pro duction will b e measured with to precision at b est so it is sucient to keep the theoretical uncertainty of the SABH pro cess at the level Furthermore at LEP the detectors and exp erimental techniques for measuring the SABH pro cess are almost the same as for LEP Radiative corrections to the SABH cross section dep end on the center of mass energy but smo othly moreover in the smallangle regime the center of mass energy is not so imp ortant from the p oint of view of the physics involved we are always faced with a tchannel photonexchange dominated pro cess hence improving the small angle Bhabha generators for LEP is generally a sucient condition for improving them also for LEP The only subtle p oint concerns the error estimate a error at LEP do es not guarantee such a small error also at LEP so that an additional analysis has to b e p erformed For the LABH pro cess the nal LEP data analysis requires a theoretical uncertainty of the co des used to b e at the level The LABH pro cess at LEP is not of ma jor interest and we think that a precision of the order of is enough Nevertheless the physics of the LABH pro cess at LEP is signicantly dierent from LEP dierent Feynman diagrams rise to imp ortance so p erforming additional study for the LABH pro cess at LEP is a new nontrivial 1 Actually the main dierence is that due to machine background radiation the internal part of luminosity detectors may b e obscured by sp ecial masks We shall discuss the impact of such mo dication on the theoretical errors This asp ect was brought to our attention by B Blo chDevaux during our WG meeting in January work In view of the ab ove our strategy was to do all the work for the SABH and the LABH pro cesses rst for LEP exp erimental conditions and to supplement it with all necessary workdiscussion which would assure control of the precision at the level sucient for LEP exp eriments This practically means that all the numerical comparisons were done for LEP and rep eated for LEP or in rare cases a convincing argument was given that it is not nec essary sometimes numerical results for LEP were obtained but are not shown in full form b ecause they were trivially identical to those for LEP We include in our rep ort two main parts one part on the SABH pro cess and a second one on the LABH pro cess with the cases of LEP and LEP discussed in parallel These two pro cesses are governed by dierent physics ie dominated by dierent Feynman diagrams Also the theoretical precision requirements in calculating SABH and LABH cross sections are dierent by a factor of veten These two parts are followed by a section including short descriptions of all the involved Monte Carlo MC event generators or other co des and a nal section on conclusions and outlo ok Smallangle Bhabha scattering Smallangle Bhabha SABH scattering is used at LEP and LEP to measure the accelerator luminosity The LEP exp eriments have reached in a systematic uncertainty of b etter than in selecting luminosity Bhabha events see Ref and Refs On the theory side QED calculations have still an uncertainty larger than in determining the Bhabha cross section in the detector acceptance which is caused mostly by the nonexistence of a Monte Carlo program including complete O nexttoleading terms Actually there exist O calculations with complete nexttoleading contributions which claim a precision of the order of but they can not b e used in a straightforward way b ecause they are not implemented in the Monte Carlo event generators The size of the O contributions dep ends not only on the angular range covered by the detector and on the electron energy cuto but also on crucial exp erimental asp ects such as the sensitivity to soft photons or such as the electron cluster size This means that the main interest is in the theoretical predictions for the Bhabha pro cess including as many higher order radiative corrections at it is necessary to reach a precision of in a form of a Monte Carlo event generator Monte Carlo event generators are very p owerful to ols b ecause they are able to provide a theoretical prediction cross sections and any kind of distribution for arbitrary ESs However event generators are dicult to construct and what is even more serious they are very dicult to test one has to have at least two of them to compare with one another for a wide range of 2 The radiative LABH pro cess is an imp ortant background to other pro cesses like pair pro duction + W W ee new physics like SUSY pro cesses and so on but a detailed analysis of these items go es b eyond the aims of the present study ESs For the SABH pro cess the task of comparing various Monte Carlo event generators was the main goal of the Bhabha Working Group There were only a few comparisons of indep endently developed Monte Carlo event generators for the SABH pro cess in the past A few examples can b e found in Ref However we shall include in the comparisons results from nonMonte Carlo calculations as well They are usually limited to certain sp ecial primitive ESs Nevertheless they provide additional valuable crosschecks What shall we learn from these comparisons The calculations from various Monte Carlo event generators will of course dier The dierences have to b e understo o d In a certain class of the comparisons the underlying QED matrix element will b e the same and in that case the dierences will b e only due to numerical eects The results from two or more computer programs will dier due to rounding errors programming bugs numerical