The theoretical accuracy of the program TOPAZ0 in the large-angle Bhabha
channel is estimated. The physical error associated with the full Bhabha cross
section and its forward and backward components separately is given for some
event selections and several energy points of interest for LEP1 physics, both
for the $s$ and non-$s$ contributions to the cross section.Comment: 8 pages, LaTeX, six tables, no figure

Beenakker

Fulvio Piccinini

Guido Montagna

Oreste Nicrosini

Physics Letters B

English

arXiv

Crossref

On large-angle Bhabha scattering at LEP

Estimate of the theoretical accuracy of the program TOPAZ0, used at LEP, in the large-angle Bhabha channel

MONTAGNA, GUIDO

Nicrosini Oreste

Piccinini Fulvio

Archivio Istituzionale della Ricerca - Università degli Studi di Pavia

The theoretical accuracy of the program TOPAZ0 in the large-angle Bhabha channel is estimated. The physical error associated with the full Bhabha cross section and its forward and backward components separately is given for some event selections and several energy points of interest for LEP1 physics, both for the $s$ and non-$s$ contributions to the cross section

Montagna, G

Nicrosini, O

Piccinini, Fulvio

CERN Document Server

FNT/T-99/05On Large-Angle Bhabha Scattering at LEPGuido MONTAGNAa,b, Oreste NICROSINIb,a and Fulvio PICCININIb,aa Dipartimento di Fisica Nucleare e Teorica, Universita di Pavia,Via A. Bassi 6, 27100, Pavia, Italyb INFN, Sezione di Pavia, Via A. Bassi 6, 27100, Pavia, ItalyAbstractThe theoretical accuracy of the program TOPAZ0 in the large-angle Bhabhachannel is estimated. The physical error associated with the full Bhabha crosssection and its forward and backward components separately is given for someevent selections and several energy points of interest for LEP1 physics, bothfor the s and non-s contributions to the cross section.E-mail:montagna@pv.infn.itnicrosini@pv.infn.itpiccinini@pv.infn.itFNT/T-99/05April 19, 1999One of the open issues of precision physics at LEP is the determination of theaccuracy of the theoretical predictions for the large-angle Bhabha scattering crosssection. At present, several computer codes developed for large-angle Bhabha scat-tering studies can be found in the literature, ranging from semi-analytical to trulyMonte Carlo ones. A detailed account of them has been presented in refs. [1, 2]. Inparticular, in ref. [1] several comparisons have been performed, both for \academic"and realistic event selections (ES’s), both for LEP1 and LEP2 energies.After the publication of ref. [1], a new analysis concerning specically two codes,namely ALIBABA [3] and TOPAZ0 [4], has been performed [5], where a very detailedcomparison between the two programs is developed and the estimate of the theoreticalerror associated with their predictions is given. If, on the one hand, the comparisonis very careful, on the other hand the study is, in the opinion of the authors of thepresent note, lacking for the following aspects: it considers, as the main source ofinformation on large-angle Bhabha observables, only ALIBABA and TOPAZ0; it isbased on a comparison for a \bare" ES, which is far from being realistic, and ignoresmore realistic ES’s such as the ones considered in ref. [1]; it does not fully exploitthe detailed comparisons for s-channel annihilation processes, that can be found inthe literature [6] and give valuable pieces of information on a signicant part of thefull Bhabha cross section; it considers only centre of mass energies around the Z0resonance, leaving aside LEP2 energies, from which additional information can beextracted concerning the accuracy of the non-s component of the full Bhabha crosssection; it addresses the problem of assigning a theoretical error to the full Bhabhacross section both for ALIBABA and TOPAZ0, but the error for the non-s part of theBhabha cross section is given for ALIBABA only; moreover no information is givenconcerning the forward and backward components of the cross section itself.ps (GeV) 88.45 89.45 90.20 91.19 91.30 91.95 93.00 93.70σT (pb) 457.08 644.86 912.06 1185.70 1164.82 873.50 476.64 351.80σTs (pb) 172.94 331.55 590.93 994.27 998.32 820.80 461.49 329.61σTns (pb) 284.14 313.31 321.13 191.43 166.50 52.70 15.15 22.19σAns (pb) 284.11 312.69 320.71 192.66 166.93 55.27 16.88 23.82δσTs (pb) 0.2 0.3 0.6 1.0 1.0 0.8 0.5 0.3δσTns (pb) 2.8 3.1 3.2 1.9 1.7 2.6 1.7 1.6δσ/σ (%) 0.7 0.5 0.4 0.2 0.2 0.4 0.5 0.5Table 1: Estimate of the theoretical error of TOPAZ0 for the full Bhabha cross sectionat 10◦ maximum acollinearity. σT , σTs and σTns are the full, s and non-s part of theTOPAZ0 cross section. σAns is the non-s part of the ALIBABA cross section. δσTs andδσTns are the absolute theoretical error of the s and non-s parts of the TOPAZ0 crosssection, as obtained according to the procedure given in the text. δσ/σ is the totalrelative error.The aim of the present study is to critically analyze as much as possible of the2ps (GeV) 88.45 89.45 90.20 91.19 91.30 91.95 93.00 93.70σT (pb) 485.17 674.89 945.00 1221.13 1200.16 905.25 503.79 377.59σTs (pb) 176.31 336.84 599.25 1007.03 1011.10 831.43 468.16 334.94σTns (pb) 308.86 338.05 345.75 214.10 189.06 73.82 35.63 42.65σAns (pb) 306.62 335.47 343.44 212.36 187.84 73.86 35.16 42.48δσTs (pb) 0.2 0.3 0.6 1.0 1.0 0.8 0.5 0.3δσTns (pb) 3.1 3.4 3.5 2.1 1.9 0.7 0.5 0.4δσ/σ 0.7 0.5 0.4 0.3 0.2 0.2 0.2 0.2Table 2: The same as tab. 1 at 25◦ maximum acollinearity.available literature on large-angle Bhabha scattering, in order to give a reliable es-timate of the theoretical error associated with TOPAZ0, both for full cross sectionsand for the forward and backward components, both for the s and non-s parts. Thenumerical results presented in the following are obtained mostly by elaborating onthe ALIBABA and TOPAZ0 predictions shown in ref. [5].Let us consider rst the problem of assigning a theoretical error to the full s + tBhabha cross section. It can be decomposed into s and non-s contributions. As faras the s part is concerned, TOPAZ0 includes exact O(α) electroweak corrections plusall the relevant and presently under control higher order contributions. From severaltuned comparisons discussed in recent literature [6], one can see that the overalldierence between TOPAZ0 and ZFITTER [7] is at the scale of 0.01% for s channelQED convoluted cross sections, for both extrapolated and realistic set up. Whilefor completely inclusive s-channel cross sections, or for s-channel cross sections withan s′ cut, TOPAZ0 includes O(α3L3) and O(α2L) hard photon corrections accordingto ref. [8], these are not taken into account for s-channel processes with angularacceptance cuts and, in particular, for the s part of the full Bhabha cross section.When taking into account the theoretical error due to neglecting them, and the onedue to other minor sources such as the approximate treatment of additional lightpairs, one can conclude that the overall theoretical error of the s part of the Bhabhacross section in TOPAZ0 is 0.1%. In setting the theoretical error for the s part,no information coming from ALIBABA is considered, because it is known that thecode is not accurate for s-channel processes at the 0.1% level [1, 4] as, for instance,TOPAZ0 and ZFITTER are. As far as the non-s part is concerned, the theoreticalerror of TOPAZ0 is dominated by missing O(α) non-logarithmic QED corrections,that on the contrary are present in ALIBABA. A way of estimating such an error is toconsider the comparisons between TOPAZ0 and BHWIDE [9] performed in ref. [1] atLEP2 energies. Actually, in the LEP2 energy regime Bhabha scattering is essentiallya t-channel dominated process. Since BHWIDE contains exact O(α) QED correctionsfor the s and non-s contributions to the cross section, such a comparison sets the sizeof the missing non-log contributions in the non-s part of the TOPAZ0 cross section,which is at the 1% level. In order to be as much as conservative as possible, and3not to loose the information contained in ALIBABA for the non-s contributions, areliable recipe for setting the theoretical error of TOPAZ0 for the non-s part of theBhabha cross section is to take it as the maximum between 1% of the non-s part ofthe cross section and the absolute deviation from ALIBABA.ps (GeV) 88.45 89.45 90.20 91.19 91.30 91.95 93.00 93.70σTF (pb) 67.43 142.90 272.98 497.33 503.20 430.39 253.36 184.99σTB (pb) 105.51 188.65 317.95 496.94 495.12 390.41 208.13 144.62δσTF (pb) 0.1 0.1 0.3 0.5 0.5 0.4 0.3 0.2δσTB (pb) 0.1 0.2 0.3 0.5 0.5 0.4 0.2 0.1Table 3: Estimate of the absolute theoretical error of TOPAZ0 for the s part ofthe Bhabha cross section at 10◦ maximum acollinearity, for the forward (σTF ) andbackward (σTB) components separately.By following the above recipe for the estimate of the theoretical error of TOPAZ0for the full Bhabha cross section, tables 1 and 2 follow. As already stated, thenumerical results shown are elaborated from ref. [5], where all the details of the ESand input parameters adopted can be found.The estimate of the theoretical error for the F+B cross section given in tabs. 1and 2 refers to a BARE ES. Anyway, it is worth considering also the results of thecomparison between BHWIDE and TOPAZ0 shown in ref. [1] for the LEP1 energyrange, for both BARE and CALO ES’s. Actually, it is known that ALIBABA doesnot contain the bulk of the O(α2L) corrections, while BHWIDE and TOPAZ0 do,by virtue of their factorized formulation [4, 5, 8, 9]. Such missing corrections are, forinstance, responsible of part of the theoretical error of ALIBABA, that above the Zpeak for s channel processes can be of the order of several 0.1%. When consideringthe comparison between BHWIDE and TOPAZ0 for LEP1 energies, one realizes thatthe dierence between the two programs for a realistic CALO ES is generally smallerthan the errors quoted above1. Hence, the estimate of the theoretical error of tabs. 1and 2 has to be considered as a conservative one, and has its origin in the fact thatthe recipe adopted aims at using as much information as possible, and in particularthe piece of information given by ALIBABA. In the light of the above comments, theerror estimate of tabs. 1 and 2 can be considered as a conservative error estimate alsofor CALO ES’s. Less conservative error estimates for the full Bhabha cross sectioncan be found in refs. [2] and [9].Besides a reliable estimate of the theoretical error for the full s + t Bhabha crosssection, it is also interesting to give the forward (F) and backward (B) parts of1The authors of BHWIDE consider the program as more reliable for realistic ES’s (CALO) ratherthan for BARE ones [9].4ps (GeV) 88.45 89.45 90.20 91.19 91.30 91.95 93.00 93.70σTF (pb) 68.45 144.77 276.34 503.31 509.24 435.67 256.72 187.62σTB (pb) 107.86 192.07 322.91 503.72 501.86 395.76 211.44 147.32δσTF (pb) 0.1 0.1 0.3 0.5 0.5 0.4 0.3 0.2δσTB (pb) 0.1 0.2 0.3 0.5 0.5 0.4 0.2 0.2Table 4: The same as tab. 3 at 25◦ maximum acollinearity.ps (GeV) 88.45 89.45 90.20 91.19 91.30 91.95 93.00 93.70σTF (pb) 262.77 289.51 296.69 177.69 154.80 50.39 15.90 22.36σTB (pb) 21.37 23.80 24.44 13.74 11.70 2.31 -0.75 -0.17σA1F (pb) 263.16 289.26 296.64 179.00 155.58 52.42 17.38 23.90σA1B (pb) 20.95 23.43 24.07 13.66 11.35 2.85 -0.50 -0.08σA2F (pb) 263.54 289.95 296.74 179.00 156.06 52.79 17.91 23.88σA2B (pb) 21.06 23.26 23.95 14.76 11.85 2.24 -0.27 -0.051σF (pb) 0.39 0.25 0.05 1.31 0.78 2.03 1.48 1.541σB (pb) 0.42 0.37 0.37 0.08 0.35 0.54 0.25 0.092σF (pb) 0.77 0.44 0.05 1.31 1.26 2.40 2.01 1.522σB (pb) 0.31 0.54 0.49 1.02 0.15 0.07 0.48 0.12δσTF (pb) 2.6 2.9 3.0 1.8 1.5 2.4 2.0 1.5δσTB (pb) 0.4 0.5 0.5 1.0 0.4 0.5 0.5 0.1Table 5: Estimate of the absolute theoretical error of TOPAZ0 for the non-s partof the Bhabha cross section at 10◦ maximum acollinearity, for the forward (σTF ) andbackward (σTB) components separately. The apices A1 and A2 refer to the resultsof ALIBABA according to the procedures described in the text.  are the absolutedierences between ALIBABA and TOPAZ0.the cross section, together with their theoretical error, for both the s and non-scomponents. For the program TOPAZ0, the rst part of the task can be accomplishedby solving the systemσ = σF + σB,σAFB = σF − σB, (1)where σ and AFB are the cross section and the forward-backward asymmetry, respec-tively, even if TOPAZ0 has been designed for computing cross sections and asym-metries directly. For the second part, i.e. assigning a theoretical error to the F/Bcomponents, one should notice that a naive error propagation can lead to articiallyoverestimated errors. Hence, in the following an alternative procedure is proposed.First of all, by using the s components of cross section and asymmetry as quotedin ref. [5] one can compute the s components of the forward and backward crosssections. Since in general the s component of the F/B asymmetry is small, one can5ps (GeV) 88.45 89.45 90.20 91.19 91.30 91.95 93.00 93.70σTF (pb) 285.84 312.6 319.62 198.9 175.87 70.14 35.08 41.50σTB (pb) 23.02 25.45 26.13 15.20 13.19 3.68 0.55 1.15σA1F (pb) 283.82 310.17 317.71 197.09 174.52 70.09 34.54 41.22σA1B (pb) 22.80 25.30 25.73 15.27 13.32 3.77 0.62 1.26σA2F (pb) 284.18 310.87 317.24 197.64 173.84 69.91 34.80 40.86σA2B (pb) 22.67 24.98 25.59 16.14 13.20 3.43 0.94 1.201σF (pb) 2.02 2.43 1.91 1.81 1.35 0.05 0.54 0.281σB (pb) 0.22 0.15 0.40 0.07 0.13 0.09 0.07 0.112σF (pb) 1.66 1.73 2.38 1.26 2.03 0.23 0.28 0.642σB (pb) 0.35 0.47 0.54 0.94 0.01 0.25 0.39 0.05δσTF (pb) 2.9 3.1 3.2 2.0 2.0 0.7 0.5 0.6δσTB (pb) 0.4 0.5 0.5 0.9 0.1 0.3 0.4 0.1Table 6: The same as tab. 5 at 25◦ maximum acollinearity.attribute to the F/B components of the s-channel cross section the same theoreticalerror as the one attributed to the integrated s-channel cross section, namely 0.1%.From this recipe, tabs. 3 and 4 follow.For the non-s component of the cross section, it should be still desirable to exploitthe information provided by ALIBABA. To this aim, it has to be noticed that twoprocedures can be followed. The rst one consists in solving the system above asdone for TOPAZ0 (ALIBABA1). The second one consists in computing directly theF/B components of the cross section, both for the full and s parts (ALIBABA2).For the rst procedure, the results of ref. [5] have been used. For the second one,ALIBABA has been re-run with high numerical precision in order to neglect theintegration error. The theoretical error to be attributed to the non-s part of the F/Bcross section, similarly to what has been done for the F+B cross section, has thenbeen dened as the maximum among the 1% of the corresponding cross section andthe absolute deviation from ALIBABA1 and ALIBABA2. By following the recipehere described, tabs. 5 and 6 follow.Two technical comments are in order here. The rst one is that the recipe adoptedfor the estimate of the non-s theoretical error is sensible, since in some energy pointsthe error is xed to be 1% of the corresponding cross section (typically in the regionbelow the Z peak), whereas in other ones it is xed by one of the absolute dierences(typically in the region at and above the Z peak, where the F/B components arenumerically small). The second comment concerns the fact that in reconstructing thefull theoretical error of the F+B cross section by adding its F/B components fromtabs. 3{6, for the s and non-s parts, one obtains values that are equal or slightlylarger than the ones obtained directly in tabs. 1 and 2, as expected. Of course, thesame remarks concerning the conservativeness of the error estimate for the F+B crosssection apply to the F/B components separately, also.6The present results correspond to an angular acceptance of 40◦{140◦ for the scat-tered electron. Since the sharing between the s and non-s component of the crosssection depends on the angular acceptance, the above estimate of the theoretical errorcan be considered valid for the presently adopted angular cuts; anyway, an importantchange in the angular cuts would require a reanalysis of the situation, bearing inmind that for larger/narrower angular acceptances the total error can be expected toincrease/decrease, respectively.To summarize, the estimate of the theoretical error of the Bhabha cross sectionderived in the present letter is based upon the following pieces of information: tunedcomparisons between TOPAZ0 and ZFITTER for s-channel observables [6]; estimateof missing higher-order QED corrections [8]; comparisons between BHWIDE andTOPAZ0 for the full Bhabha cross section in the LEP1 and LEP2 energy range [1];comparisons between ALIBABA and TOPAZ0 for the non-s part of the cross section.The present paper updates the existing literature for the theoretical error of the fullF+B Bhabha cross section [5], and improves it by providing additional informationon the theoretical uncertainty to be associated to the F/B components of the s/non-sparts of the Bhabha cross section.Acknowledgements The authors are indebted with Marta Calvi and GiampieroPassarino for stimulating discussions on the subject.References[1] S. Jadach, O. Nicrosini et al., \Event Generators for Bhabha Scattering", inPhysics at LEP2, G. Altarelli, T. Sjo¨strand and F. Zwirner, eds., CERN Report96-01 (Geneva, 1996), vol. 2, p. 229.[2] G. Montagna, O. Nicrosini and F. Piccinini, \Precision Physics at LEP", Rivistadel Nuovo Cimento 21 n. 9 (1998) 1; hep-ph/9802302.[3] W. Beenakker, F. Berends and S.C. van der Mark, Nucl. Phys. B349 (1991) 323.[4] G. Montagna, O. Nicrosini, G. Passarino F. Piccinini and R. Pittau, Com-put. Phys. Commun. 76 (1993) 328, Nucl. Phys. B401 (1993 ) 3;G. Montagna, O. Nicrosini, G. Passarino and F. Piccinini, TOPAZ0 version 2.0,in Comput. Phys. Commun. 93 (1996) 120;TOPAZ0 version 4.0, in Comput. Phys. Commun. 117 (1999) 278.[5] W. Beenakker and G. Passarino, Phys. Lett. B425 (1998) 199.[6] D. Bardin, M. Gru¨newald and G. Passarino, Precision Calculation Project Report,hep-ph/9902452;D. Bardin et al., \Electroweak Working Group Report", in Precision Calculations7for the Z resonance, D. Bardin, W. Hollik and G. Passarino, eds., CERN Report95-03 (Geneva, 1995), p. 7, hep-ph/9709229.[7] D. Bardin et al., Z. Phys. C44 (1989) 493; Comput. Phys. Commun. 59(1990) 303; Nucl. Phys. B351 (1991) 1; Phys. Lett. B255 (1991) 290; CERN-TH 6443/92.[8] G. Montagna, O. Nicrosini and F. Piccinini, Phys. Lett. B406 (1997) 243;Phys. Lett. B385 (1996) 348;S. Jadach, M. Skrzypek, B. Pietrzyk, LAPP-EXP-99-01.[9] S. Jadach, W. P laczek and B.F.L. Ward, Phys. Lett. B390 (1997) 298;W. P laczek, S. Jadach, M. Melles, B.F.L. Ward and S.A. Yost, CERN-TH/99-07,UTHEP-98-01, hep-ph/9903381.8

On Large-Angle Bhabha Scattering at LEP

On Large-Angle Bhabha Scattering at LEP

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