Chierici, R

Cossutti, F

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DELPHI Collaboration DELPHI 2001-112 PROG 24326 July, 2001Event reweighting to account for DPAR.ChiericiCERN, CH-1211 Geneve, Switzerland.F. CossuttiINFN, Sezione di Trieste, Via A. Valerio 2, IT-34127 Trieste, Italy.AbstractThis note reports about the way it is possible to reweight four-fermion (4-f) eventsin order to account for the O(α) radiative corrections implemented in double poleapproximation (DPA). The recommended choice for the DELPHI users is describedand commented. This work is based on the new codes implementing DPA developedin the frame of the 2000 LEP2 Montecarlo workshop.1 IntroductionOne of the successes of the LEP2 MC workshop [1] has been the introduction of newcodes, able to calculate O(α) correction to 4-f processes in the so-called Double-PoleApproximation (DPA), allowing a substantial improvement of the theoretical accuracyon total and differential cross-sections. This approach consists of an expansion of the4-fermion matrix elements around the W poles, keeping only the first term. The numberof contributing diagrams is thus enormously reduced, and it is possible to calculate thefull radiative corrections for this subset only. This procedure has the big advantage ofbeing gauge invariant, but is exact only at the resonances (i.e. for CC03 physics).The codes which can be used for generating unweighted events and that include DPAare essentially two: RacoonWW [2] and YFSWW [3]. The features of these codes and adetailed comparison at distribution level which shows the necessity of taking into accountthese new calculation in a Montecarlo generation for precision measurements at LEP2 aredescribed elsewhere [4]. Our aim, here, is to determine how to concile the generation of4-f samples and WW samples with DPA in.In what follows we will describe the possible solutions to this question and the choicemade by DELPHI, providing practical ways to include the DPA through an event reweight-ing.2 DPA and four-fermion2.1 interfacing the twoBy construction the DPA approach to radiative corrections is valid only for the signal,represented by the CC03 diagrams. The prediction of DPA calculations in regions of thephase space which are not WW -like are therefore expected to be wrong and, in general,not to be trusted. This means that it is not possible to simply use a DPA code for thewhole 4-f physics generation. The best solution is to use then two generators, each of thetwo optimised for its own sector, and then match them.The first indication on how the matching might be done comes from a decompositionof the new 4-f amplitude (4f ′) as:|4f ′|2 = |4f |2 − |CC03|2 + |CC03DPA|2 = |4f − CC03|2 + Int. + |CC03DPA|2 (1)where |CC03| is the CC03 matrix element in the so-called Improved Born Approximation(IBA), i.e. already including radiative corrections like Initial State Radiation (ISR) andCoulomb corrections, whereas Int. indicates the interference term between CC03 andthe rest. A possible matching is therefore realised by using a pure 4-f generator for the|4f − CC03| part and a DPA generator for |CC03DPA|. In doing this one can eitherneglect the interference term or include it in the pure 4-f part in the generation. Both ofthese possibilities have undesired drawbacks; the first one introduces a systematic effectdue to neglecting the interference, particularly evident for final states of the CC20 classwhich can lead to important systematic contributions; the second one implies that manyevents will result with negative weights in the generation because of the presence of thedestructive interference term, which is rather awkward to be taken into account in theanalyses.1An elegant way out to the problem of interfacing DPA with a full 4-f generation comesfrom the event reweighting. There are two ways of doing this:• 4f reweighting: consists in generating DPA CC03 events and reweighting them toaccount for the 4-f background contributions. This approach has the disadvantageof being totally inefficient (and therefore not precise) in certain regions of the phasespace, particularly the non-CC03 like.• DPA reweighting: consists in generating 4-f events and reweight them to accountfor the DPA correction in the CC03 part only. This is the approach chosen byDELPHI which will be explained with more details in the next subsections.2.2 DPA event reweightingThe weight to be used to account for DPA in 4-f events can be evaluated as a ratio ofmatrix elements. Using the same notation of identity (1) the weight is written as:w =|4f ′|2|4f |2=|4f |2 − |CC03|2 + |CC03DPA|2|4f |2= 1−|CC03|2|4f |2(1−|CC03DPA|2|CC03|2)(2)In this reweighting procedure the interference term is included, although computed usingCC03 as given by IBA. Relation (2) can be re-written in a more concise form as:|4f ′|2 = |CC03|2(1 + δ4f + δDPA) (3)where:δ4f =|4f |2|CC03|2− 1 ; δDPA =|CC03DPA|2|CC03|2− 1 (4)This represents the so-called additive approach to the DPA reweighting. In this formu-lation the new 4-f matrix element results from the CC03 one with the addition of twocorrections, one accounting for the presence of extra diagrams due to the 4-f backgroundand the other for the radiative corrections.In the literature, also the so-called multiplicative approach can be found, where:|4f ′|2 = |CC03|2(1 + δ4f )(1 + δDPA) = |4f |2(1 + δDPA) (5)The multiplicative approach is convenient for reweighting already generated 4-f events,for which it is impossible to recalculate δ4f . The error of this approach, compared to theadditive one, is of the order of δ4fδDPA. Such error is negligibly small in the signal region,i.e. for CC03 where δ4f is virtually zero. However, outside this region, the magnitudeof the error cannot be predicted since δDPA can be arbitrarily wrong and δ4f large. It istherefore dangerous to use such approach for 4-f analyses.2.3 The DELPHI approachThe DELPHI approach to DPA reweighting makes use of the additive scheme describedin the previous section. The advantage of writing the DPA weight w in terms of theidentity (2), is that it can be conveniently decomposed as a product of terms dependingonly upon two ratios, namely |CC03|2/|4f |2 and |CC03DPA|2/|CC03|2. The first term2can be calculated event by event with an IBA 4-f generator given the matrix elements ofsubsets of diagrams, whereas the second can be determined from an output of YFSWW.The YFSWW generator, used as a rewighter, returns the value |CC03DPA|2/|CC03K−C|2,i.e. the DPA matrix element with respect to the CC03 one which already includes theCoulomb screening via the Khoze-Chapovski correction [5]. The desired ratio can bedetermined by multiplying this output by |CC03K−C|2/|CC03|2, which gives a very smallsmearing to the weight distribution of the order of a few permill.Figure 1 shows the distributions of these matrix element ratios for 670K 4-f chargedcurrent events generated with the WPHACT [8] generator. In the upper left-hand plotthe CC03 weight is shown; the peak at zero is due to the non-CC03 part of the sample,basically composed by single W events. Interference effects introduce events with weightlarger than 1. The DPA weight, relative to CC03 with Khoze-Chapovski, is shown in theupper right-hand figure for all 4-f events. The lower figure is the derived DPA weight to4-f ; the average value of the distribution gives the total cross-section reduction inducedby DPA. The peak at 1 represents the contribution of the non-CC03 part for which|CC03|2/|4f |2 ≈ 0A question might arise about the conceptual correctness of the DPA weight calculationinside YFSWW, where the input number of photons from a 4-f event without real radia-tion from W is different from the one of events where such radiation is calculated. Anywaythe YFSWW group has shown in [6] that the reweighting procedure of 4-f KoralW [7]events in the additive scheme correctly reproduces the main differential distributions ofCC03 obtained with YFSWW alone, thus demonstrating the robustness of the approach.It is important to note again that in (2) the |CC03| matrix element is evaluated asgiven by IBA, and therefore already accounts for part of the radiation. In the ratio|CC03|2/|4f |2, the standard ISR factorises and therefore which radiator function is usedfor the generation of 4-f events is not a crucial issue. This is also true for the matrixelements ratio DPA/IBA, since it is calculated in YFSWW by using the same ISR imple-mentation via the YFS exponentiation. However, in order to have a consistent 4-f+n-γphase space coverage in all the parts of the DPA weight, it is convenient to use the sameISR implementation in both terms. This guarantees the use of the same kinematics usedfor the generation in the determination of the DPA/IBA ratio. This is the reason why inDELPHI it is preferred to use, where possible, the YFS exponentiation for ISR in the 4-fgeneration, realised by interfacing the KoralW implementation with the WPHACT 4-fgenerator.Both the ratios of relation (2) needed for calculating the DPA event weight can now bedirectly determined from the information contained in the extra comment lines of the sim-ulation banks. All relevant matrix elements and both ratios |CC03DPA|2/|CC03K−C|2,|CC03K−C|2/|CC03|2 are now stored there, and can be retrieved by using the routineWPHDST, in /afs/cern.ch/delphi/tasks/generators/wphact/wphdst.car. An exam-ple on how to use it can be found in the subroutine REAWPH, contained in the same file.The decoding of the simulation banks and the calculation of the DPA weight is alreadyimplemented in the W physics common code and saved in the simulation block of thentuple. The explanation of the common WW ntuple structure can be found in [9].3Figure 1: Distributions of the CC03 relative weights (upper left), the DPA to CC03 withK-C relative weight (upper right) and the global DPA weight (lower) from WPHACT 4-fsimulated samples.3 ConclusionsIn this note we briefly reported about the ways in which it is possible to account for themost recent calculations of O(α) EW radiative corrections in a coherent 4-f event genera-tion. Advantages and disadvantages of the different approaches have been illustrated and4the DELPHI choice, summarised in relation (2), presented. This work is also intended asa reference for the DELPHI users.References[1] E. Accomando et al., Four-Fermion Production in Electron-Positron Collisions, in Re-port of the Working Groups on precision calculations for LEP2 physics (ed. S. Jadachet al.) CERN 2000-009 (2000).[2] A. Denner et al., Phys. Lett. B475 (2000) 127.[3] S. Jadach et al., hep-ph/0007012;S. Jadach et al., hep-ph/0103163.[4] R. Chierici and F. Cossutti, DELPHI 2001-111 PHYS 898.[5] A.P. Chapovsky and V.A. Khoze, Eur. Phys. J. C9 (1999), 449.[6] S. Jadach, W. Placzek, M. Skrzypek, B. F. L. Ward and Z. Was, CERN-TH/2001-040.[7] S. Jadach, W. Placzek, M. Skrzypek and Z. Was, Comput. Phys. Commun. 94 (1996),216.[8] E. Accomando and A. Ballestrero, Comput. Phys. Commun. 99 (1997), 270.[9] http://delphiwww.cern.ch/teams/measurements/delwww/ww4f/Welcome.html, fol-lowing the link Analysis and Standard tools and Code.5

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