Using the SANC system we study the one-loop electroweak standard model
prediction, including virtual and real photon emissions, for the decays of
on-shell vector and scalar bosons B --> f anti-f (gamma), where B is a vector
boson, Z or W, or a Standard Model Higgs. The complete one-loop corrections and
exact photon emission matrix element are taken into account. For the
phase-space integration, the Monte Carlo technique is used. For Z decay the QED
part of the calculation is first cross-checked with the exact one-loop QED
prediction of KORALZ. For Higgs boson and W decays, a comparison is made with
the approximate QED calculation of PHOTOS Monte Carlo. This provides a useful
element for the evaluation of the theoretical uncertainty of PHOTOS, very
interesting for its application in ongoing LEP2 and future LC and LHC
phenomenology.Comment: Submitted to Acta Physica Polonica. 9 pages, 6 figure

Andonov, A.

Jadach, S.

Nanava, G.

Was, Z.

English

arXiv

Using the SANC system we study the one-loop electroweak standard model prediction, including virtual and real photon emissions, for the decays of on-shell vector and scalar bosons B --> f anti-f (gamma), where B is a vector boson, Z or W, or a Standard Model Higgs. The complete one-loop corrections and exact photon emission matrix element are taken into account. For the phase-space integration, the Monte Carlo technique is used. For Z decay the QED part of the calculation is first cross-checked with the exact one-loop QED prediction of KORALZ. For Higgs boson and W decays, a comparison is made with the approximate QED calculation of PHOTOS Monte Carlo. This provides a useful element for the evaluation of the theoretical uncertainty of PHOTOS, very interesting for its application in ongoing LEP2 and future LC and LHC phenomenology.Using the SANC system we study the one-loop electroweak standard model prediction, including virtual and real photon emissions, for the decays of on-shell vector and scalar bosons B --> f anti-f (gamma), where B is a vector boson, Z or W, or a Standard Model Higgs. The complete one-loop corrections and exact photon emission matrix element are taken into account. For the phase-space integration, the Monte Carlo technique is used. For Z decay the QED part of the calculation is first cross-checked with the exact one-loop QED prediction of KORALZ. For Higgs boson and W decays, a comparison is made with the approximate QED calculation of PHOTOS Monte Carlo. This provides a useful element for the evaluation of the theoretical uncertainty of PHOTOS, very interesting for its application in ongoing LEP2 and future LC and LHC phenomenology

CERN Document Server

CERN-TH/2002-315Comparison of SANC with KORALZ and PHOTOSA. Andonova, S. Jadachb, G. Nanavaa and Z. Wa¸sb;ca Lab. of Nuclear Problems, JINR, RU-141980 Dubna, Russiab Institute of Nuclear Physics, ul. Radzikowskiego 152, PL-31-342 Cracow, Polandc CERN, Theory Division, CH-1211 Geneva 23, SwitzerlandAbstractUsing the SANC system we study the one-loop electroweak standard model pre-diction, including virtual and real photon emissions, for the decays of on-shell vectorand scalar bosons B → f f¯(γ), where B is a vector boson, Z or W , or a StandardModel Higgs. The complete one-loop corrections and exact photon emission matrixelement are taken into account. For the phase-space integration, the Monte Carlotechnique is used. For Z decay the QED part of the calculation is first cross-checkedwith the exact one-loop QED prediction of KORALZ. For Higgs boson and W decays, acomparison is made with the approximate QED calculation of PHOTOS Monte Carlo.This provides a useful element for the evaluation of the theoretical uncertainty ofPHOTOS, very interesting for its application in ongoing LEP2 and future LC andLHC phenomenology.Submitted to Acta Physica PolonicaWork supported in part by the European Union 5-th Framework under contract HPRN-CT-2000-00149,Polish State Committee for Scientific Research (KBN) grant 2 P03B 001 22, NATO grant PST.CLG.977751and INTAS Mo 00-00313.1 IntroductionThe SANC project of Ref. [1] has several purposes. The intermediate goal is to summarizeand consolidate the eort of the last three decades in calculating Standard Model radiativecorrections for LEP, in a well organized calculational environment for future reference.However, it is aimed not only at training young researchers and students, but at someremaining calculational projects for LEP as well.SANC provides an Internet-oriented, graphic interface platform, which is meant to serveas a starting point for longer term research eorts in the area of the higher order (multi-loop) calculations within the SM and beyond, for the experiments at future high energycolliders. An important lesson from the LEP experiments [2] is that the desirable wayof providing theoretical predictions is in the form of Monte Carlo event generators. Thisaspect has been taken into account in the development of SANC from an early stage of itsdevelopment.The currently available version of SANC can construct one-loop spin amplitudes for thedecays of the gauge bosons W and Z and Higgs boson H . All of the Born and one-loop-corrected spin amplitudes are generated interactively from scratch1 by SANC with the helpof the algebraic package Form3 [4] in the form of Fortran77 source codes, and are thenused in the MC generation/intgration part of the package. For the moment, SANC featuressingle real photon emission, in the calculations of the total rate and decay spectra of theB → f f(γ) process. The complete spin polarization density matrix of the decaying bosonis taken into account as well.The integration, with the Monte Carlo method, over the three (two)-body nal stateis done without any approximation (in particular small mass approximation is not used).The program provides MC events with constant weight (unweighted events). The wholesystem is, therefore, fairly self-contained and complete2.It is of the utmost importance for such a new system to precisely reproduce knownresults. Concerning virtual corrections, comparisons were performed with the calculationsof refs. [5,6]. The precise comparisons with the FeynArt package [7] were made in [9,8,10]as well.Our paper is organized as follows: in the next section we describe in detail the set ofobservables chosen for tests and the input parameter set-ups for comparisons SANC withKORALZ [11] and SANC PHOTOS [12]. Section 3 is devoted to a discussion of SANC technicalreliability in the domain of QED bremsstrahlung. To this end, comparisons with KORALZand leading-log distributions from PHOTOS are collected. Section 4 describes comparisonsof SANC with PHOTOS, focusing on the non-leading contributions in W and H decays andon the relevant discussion of PHOTOS physical uncertainties. The summary in section 5closes the paper.1The form2 codes related to the review of ref. [3] were exploited at the early stage of the SANCdevelopment.2That is why it may be valuable for teaching and training.12 Initialization set-ups for SANC , KORALZ and PHOTOSrunsIn the following sections we compare predictions from the programs SANC, KORALZ andPHOTOS. It is essential that the initialization be identical in all cases and close to thephysical reality; in particular the following options are set in the three programs:• In SANC we switch o the EW part of the radiative corrections. The soft photonlimit is kept at 0.005 of the decaying particle mass.• In KORALZ we switch to the O() mode of operation (no exponentiation) with nalstate bremsstrahlung only. We set the CMS energy equal to the Z mass. The s-channel γ exchange is switched o and the soft photon limit is kept at 0.01 of the\beam energy".• In PHOTOS we switch o the double bremsstrahlung corrections but we keep inter-ference eects. The soft/hard photon limit is kept at 0.005 of the decaying particlemass. For the generation of the Born-level two-body decays, we use the Monte Carlogeneration from SANC.To visualize the dierences (or the agreement) between the calculations, we choosea certain class of (pseudo-)observables, more precisely the one-dimensional distributions,which are quite similar to the one used in the rst tests of PHOTOS reported in [13]. Tovisualize the usually small dierences, we plot ratios of the predictions from two programsrather than the distributions themselves.List of observables:• -A- Photon energy in the decaying particle rest frame: this observable is sensitivemainly to the leading-log (i.e. collinear) non-infrared (i.e. not soft) component ofthe distributions.• -B- Energy of the final state charged particle: as in the previous case this observableis sensitive mainly to the leading-log (i.e. collinear) non-infrared (i.e. not soft)component of the distributions.• -C- Angle of the photon with respect to one of the charged final state particles: thisobservable is sensitive mainly to the non-collinear (i.e. non-leading-log) but soft(i.e. infrared) component of the distributions.• -D- Acollinearity angle of the final state charged particles: this observable is sensitivemainly to the non-collinear (i.e. non-leading-log) and non-soft (i.e. non-infrared)component of the distributions.23 Technical tests of SANCLet us rst cross check SANC predictions in the case of Z → +− decay and for the realphoton emission with KORALZ. The corresponding part of the KORALZ code, essentiallyan improved emulation of the MC program MUSTRAL [14], was thorougly tested over twodecades and is an excellent candidate for the benchmark test for SANC matrix-elementand phase-space generation. It can be noted that the phase-space parametrization of thesingle photon emission in SANC, although developed independently, is essentially the sameas in KORALB [15{17].As we can see from gs. 1 and 2 the level of the agreement for all distributions ofthe types A, B, C and D is satisfactory, at the level of better than 0.5% (or at the levelof statistical error). We have checked that the O() FSR correction to the total decayrate calculated as a dierence of SANC results, with FSR on and o, agrees well with thestandard factor 1+34 = 1:001743. In fact we get 1:001733±2:8×10−5. The agreementis thus better than 10−4. We can thus conclude that SANC is “commissioned” for the Zdecay.0 10 20 30 400.970.980.9911.011.021.03Ratio , GeVγE)γ(-µ+µ→ZRatio = SANC/KORALZ0 10 20 30 400.970.980.9911.011.021.03Ratio , GeV-µE)γ(-µ+µ→ZRatio = SANC/KORALZFigure 1: Comparisons (ratios) of the SANC and KORALZ predictions for the Z decay.Observables A and B: ratios of the photon energy (left-hand side) and muon energy (right-hand side) distributions from the two programs. The dominant contribution is of leading-log (collinear) nature.In the case of the W and Higgs decay we rely on the comparison with PHOTOS. Due tothe incomplete one-loop QED in PHOTOS we cannot, in priciple, expect the agreement forthe decay distributions A, B to be better than the order of 1 lnm2B=m2 ' 7%. We see ing. 3 for Higgs boson decay and in g. 5 for W decay, that this is indeed the case. In fact,the agreement is much better in the case of the Higgs boson decay. In gs. 4 and 6 we see3-1 -0.5 0 0.5 10.970.980.9911.011.021.03→Z )γ(-µ+µRatioRatio = SANC/KORALZγθcos-1 -0.5 0 0.5 10.90.9511.051.1acolθcosRatio)γ(-µ+µ→ZRatio = SANC/KORALZFigure 2: Comparisons (ratios) of the SANC and KORALZ predictions for the Z decay.Observables C and D: ratios of the photon angle with respect to − (left-hand side) and−+ acollinearity (right-hand side) distributions from the two programs. The dominantcontribution is of infrared non-leading-log nature for the left-hand side plot, and non-infrared non-leading-log nature for the right-hand side one.the angular distributions of the photon with respect to the charged fermion (observable C).Here, in principle, the agreement should not be worse than 1 lnmB=Eminγ ' 20% for thephoton emitted in directions far from the charged particle and 1lnm2B=m2 ln mB=Eminγ '1.4% for directions close to the charged particle. This is indeed the case.4 Physical uncertainties of PHOTOS in W and H decayIn the case of testing H and W decays, the comparisons of PHOTOS with the \matrix-element" type calculations were never accounted for in a well documented way. Thefollowing discussion will give us a chance systematically evaluate uncertainties of PHOTOSfor these two decays.In the case of the Linear Collider studies and many scenarios for new physics, thecross section for the production of the Higgs boson can be quite large. In the case ofsophisticated observables, the reconstruction of the reference frames of the intermediatestates requires good control of the bremsstrahlung corrections. Our comparison showsthat, in the case of the Higgs boson decay, the approximation used in PHOTOS works muchbetter than could be expected from its design principles. In fact it provides results dicultto distinguish from the \matrix-element" ones in the case of all observables A to D (gs.3 and 4).40 20 40 600.960.9811.021.04 , GeVγERatio)γ(-µ+µ→HRatio = SANC/PHOTOS0 20 40 600.90.9511.051.1)γ(-µ+µ→HRatio , GeV-µERatio = SANC/PHOTOSFigure 3: Comparisons (ratios) of the SANC and PHOTOS predictions for the H decay.Observables A and B: ratios of the photon energy (left-hand side) and muon energy (right-hand side) distributions from the two programs. The dominant contribution is of leading-log (collinear) nature.At LEP2, the production and decay of W pairs is now being combined for all fourLEP2 experiments, and uncertainties due to bremsstrahlung in W decay are important.PHOTOS is part of one of the main programs (YFSWW3) used in the LEP2 analysis of theW -pair data. Our tests will provide an estimate of the size of the uncertainties, due to useof PHOTOS. If they turn out to be sizeable, the improvements will need to be implementedeither into the PHOTOS algorithm or by other means.In gs. 5 and 6, we see that up to leading order, the distributions agree with the\matrix element" results provided by SANC. There is, however, no exceptionally goodagreement observed in the previous case of H decay.This point requires further study, before planning improvements of PHOTOS. In par-ticular, a comparison of PHOTOS with another available matrix-element calculation of → e(γ), e.g. from TAUOLA [18], should also be repeated to check if a pattern ofdiscrepancy similar to that for W decay is observed. The W channel is of importance forsome studies [19] of LHC Higgs discovery potential as well, see also [20].5 SummaryWe have successfully tested SANC versus KORALZ in case of the Z decay. In this way wehave veried the technical correctness of SANC, e.g. its phase-space generation and QEDcorrection amplitudes.5-1 -0.5 0 0.5 10.90.9511.051.1γθcosRatio)γ(-µ+µ→HRatio = SANC/PHOTOS-1 -0.5 0 0.5 10.70.80.911.11.21.3acolθcosRatio)γ(-µ+µ→HRatio = SANC/PHOTOSFigure 4: Comparisons (ratios) of the SANC and PHOTOS predictions for the H decay.Observables C and D: ratios of the photon angle with respect to − (left-hand side) and−+ acollinearity (right-hand side) distributions from the two programs. The dominantcontribution is of infrared non-leading-log nature for the left-hand side plot, and non-infrared non-leading-log nature for the right-hand side one.In case of W and H decays, we have checked that SANC agrees with the leading orderQED calculation provided by the PHOTOS Monte Carlo. These comparisons allow usto evaluate the size of missing non-leading terms in PHOTOS. In the case of H decays,we have found that PHOTOS results are exceptionally good { dierences with SANC areindistinguishable from zero and below 1% everywhere. In the case of W decay, PHOTOSpredictions are within 7% for the end parts of the spectra aected by the leading-logcorrections and within 20% for the angular part of the distributions, where the infrared-induced logarithm dominates over non-infrared non-leading terms only. The dierencesare up to 40% in the phase-space regions where only non-leading corrections contributeto the matrix element. We can conclude that results from all three programs for all fourobservables agree within the expected precision ranges.AcknowledgementsThe authors would like to thank D. Bardin and B.F.L. Ward for useful discussions.60 10 20 30 400.60.70.80.911.11.21.3Ratio , GeVγE)γ(ν-µ→-WRatio = SANC/PHOTOS0 10 20 30 400.60.70.80.911.11.21.3Ratio , GeV-µE)γ(ν-µ→-WRatio = SANC/PHOTOSFigure 5: Comparisons (ratios) of the SANC and PHOTOS predictions for the W decay.Observables A and B: ratios of the photon energy (left-hand side) and muon energy (right-hand side) distributions from the two programs. The dominant contribution is of leading-log (collinear) nature.References[1] D. Bardin et al., \Project SANC (former CalcPHEP): Support of analyticand numeric calculations for experiments at colliders", CERN-TH/2002-245,hep-ph/0209297, to be published in ICHEP2002 Proceedings;D. Bardin et al., \Project CalcPHEP: Calculus for precision high energy physics",hep-ph/0202004, CAAP-2001 Proceedings, Dubna 2001.[2] M. Kobel et al., \Two Fermion Working Group Collaboration", hep-ph/0007180.[3] D. Y. Bardin and G. Passarino, The standard model in the making: Precision studyof the electroweak interactions (Clarendon Oxford, UK, 1999), 685 p.[4] J. A. M. Vermaseren, \New features of FORM", math-ph/0010025.[5] D. Bardin et al., Comput. Phys. Commun. 133 (2001) 229, hep-ph/9908433.[6] G. Montagna, O. Nicrosini, F. Piccinini and G. Passarino, Comput. Phys. Commun.117 (1999) 278, hep-ph/9804211.[7] J. Kublbeck, M. Bohm and A. Denner, Comput. Phys. Commun. 60 (1990) 165;T. Hahn and M. Perez-Victoria, Comput. Phys. Commun. 118 (1999) 153,hep-ph/9807565;7-1 -0.5 0 0.5 10.60.70.80.911.11.21.3Ratioγθcos)γ(ν-µ→-WRatio = SANC/PHOTOS-1 -0.5 0 0.5 10.50.60.70.80.911.11.21.31.4Ratioacolθcos)γ(ν-µ→-WRatio = SANC/PHOTOSFigure 6: Comparisons (ratios) of the SANC and PHOTOS predictions for the W decay.Observables C and D: ratios of the photon angle with respect to − (left-hand side) and−+ acollinearity (right-hand side) distributions from the two programs. 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Commun. 79 (1994) 291.[13] E. Barberio, B. van Eijk and Z. Was, Comput. Phys. Commun. 66 (1991) 115.[14] F.A. Berends, R. Kleiss and S. Jadach, Comput. Phys. Commun. 29 (1983) 185.8[15] S. Jadach and Z. Was, Comput. Phys. Commun. 64 (1991) 267.[16] S. Jadach and Z. Was, Comput. Phys. Commun. 36 (1985) 191.[17] S. Jadach and Z. Was, Acta Phys. Polon. B15 (1984) 1151.[18] M. Je_zabek, Z. Was, S. Jadach and J.H. Ku¨hn, Comput. Phys. Commun. 70 (1992)69.[19] E. Richter-Was, Z. Phys. C 61 (1994) 323.[20] ATLAS collaboration, \ ATLAS Detector and Physics Performance Technical DesignReport", CERN/LHCC/99-15, vol. 2, p. 674{735.9

Comparison of SANC with KORALZ and PHOTOS

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