We present the new Coherent Exclusive Exponentiation (CEEX), in comparison to
the older Exclusive Exponentiation (EEX) and the semi-analytical Inclusive
Exponentiation (IEX), for the process e+e- -> f-bar f + n(gamma),
f=mu,tau,d,u,s,c,b, with validity for centre of mass energies from tau lepton
threshold to 1 TeV. We analyse 2f numerical results at the Z-peak, 189 GeV and
500 GeV. We also present precision calculations of the signal processes e+e- ->
4f in which the double resonant W+W- intermediate state occurs using our
YFSWW3-1.14 MC. Sample 4f Monte Carlo data are explicitly illustrated in
comparison to the literature at LEP2 energies. These comparisons show that a TU
for the signal process cross section of 0.4 percent is valid for the LEP2 200
GeV energy. LC energy results are also shown.Comment: 5 pages, 4 figures, Presented at ICHEP200

Jadach, S.

Płaczek, W.

Skrzypek, M.

Ward, B. F. L.

Was, Z.

English

arXiv

We present the new Coherent Exclusive Exponentiation (CEEX), in comparison to the older Exclusive Exponentiation (EEX) and the semi-analytical Inclusive Exponentiation (IEX), for the process e+e- -> f-bar f + n(gamma), f=mu,tau,d,u,s,c,b, with validity for centre of mass energies from tau lepton threshold to 1 TeV. We analyse 2f numerical results at the Z-peak, 189 GeV and 500 GeV. We also present precision calculations of the signal processes e+e- -> 4f in which the double resonant W+W- intermediate state occurs using our YFSWW3-1.14 MC. Sample 4f Monte Carlo data are explicitly illustrated in comparison to the literature at LEP2 energies. These comparisons show that a TU for the signal process cross section of 0.4 percent is valid for the LEP2 200 GeV energy. LC energy results are also shown.We present the new Coherent Exclusive Exponentiation (CEEX), in comparison to the older Exclusive Exponentiation (EEX) and the semi-analytical Inclusive Exponentiation (IEX), for the process e+e- -> f-bar f + n(gamma), f=mu,tau,d,u,s,c,b, with validity for centre of mass energies from tau lepton threshold to 1 TeV. We analyse 2f numerical results at the Z-peak, 189 GeV and 500 GeV. We also present precision calculations of the signal processes e+e- -> 4f in which the double resonant W+W- intermediate state occurs using our YFSWW3-1.14 MC. Sample 4f Monte Carlo data are explicitly illustrated in comparison to the literature at LEP2 energies. These comparisons show that a TU for the signal process cross section of 0.4 percent is valid for the LEP2 200 GeV energy. LC energy results are also shown

Ward, B.F.L.

Placzek, W.

CERN Document Server

arXiv:hep-ph/0009352v1  29 Sep 2000For Publisher’s useCOHERENT EXCLUSIVE EXPONENTIATION FOR PRECISION MONTECARLO CALCULATIONS OF FERMION PAIR PRODUCTION /PRECISION PREDICTIONS FOR (UN)STABLE W+W− PAIRSB.F.L. WARDA,B,C , S. JADACHA,B,D,E , W. P LACZEKB,F , M. SKRZYPEKB,E,AND Z. WASB,EADepartment of Physics and Astronomy, University of Tennessee, Knoxville, TN37996-1200, USABTH Div., CERN, CH-1211 Geneva 23, SwitzerlandCSLAC, Stanford UNiversity, Stanford, CA 94309, USADTheory Div., DESY, D-22603 Hamburg, GermanyEInstitute of Nuclear Physics, ul. Kawiory 26a, PL-30-055 Krakow, PolandF Institute of Computer Science, Jagellonian University, ul. Nawojki 11, 30-072 Krakow,PolandUTHEP-00-0901, SEPT., 2000Presented by B.F.L. Ward at ICHEP2000, Osaka, Japan, July 27, 2000We present the new Coherent Exclusive Exponentiation (CEEX), in comparison to the older Exclu-sive Exponentiation (EEX) and the semi-analytical Inclusive Exponentiation (IEX), for the processe+e− → ff¯+nγ, f = µ, τ, d, u, s, c, b, with validity for centre of mass energies from τ lepton thresholdto 1 TeV. We analyse 2f numerical results at the Z-peak, 189 GeV and 500 GeV. We also presentprecision calculations of the signal processes e+e− → 4f in which the double resonant W+W− in-termediate state occurs using our YFSWW3-1.14 MC. Sample 4f Monte Carlo data are explicitlyillustrated in comparison to the literature at LEP2 energies. These comparisons show that a TU forthe signal process cross section of 0.4% is valid for the LEP2 200 GeV energy. LC energy results arealso shown.1 IntroductionAt the end of the LEP2 operation, the totalcross section for the process e−e+ → f f¯+nγwill have to be calculated with the precision0.2% - 1%, depending on the event selection.In addition, the awarding of the 1999 NobelPrize to G. ’t Hooft and M. Veltman empha-sises the importance of the on-going preci-sion studies of the Standard Model processese+e− → W+W− + n(γ) → 4f + n(γ) atLEP2 energies, as well as the importance ofthe planned future higher energy studies ofsuch processes in LC physics programs.In what follows, we present precision pre-dictions for both sets of processes, using ournew coherent exponentiation (CEEX) 1 the-ory (KKMC) for the former set and our olderand ﬁrmly established exclusive exponentia-tion (EEX) 2 theory (YFSWW3-1.14 MC 4)for the latter set. Both CEEX and and EEXare based on the YFS exclusive exponentia-tion theory of Yennie, Frautschi and Suura 3.A detailed description 1,4,2 of our two ap-proaches to the precision exponentiation the-ory may be found in Refs. 1,4,2. As we indi-cate below, we have compared our KK MCcalculations with with EEX, its semianalyt-ical partner IEX, and ZFITTER 6.21 5 andwe have compared our YFSWW3-1.14 MCcalculations with RacoonWW 6 and with theBeenakker et al.7 semi-analytical approach.The paper proceeds as follows. In Sec.2 we discuss the implementation of CEEX inour KK MC in relation to EEX. In Sec. 3 wepresent some of its new results for 2f + n(γ)processes at high energies. In Sec. 4 wepresent the EEX theory realization in ourFor Publisher’s useYFSWW3-1.14 MC. In Sec. 5 we presentsome of its new results on WW + n(γ) →4f +m(γ) processes at high energies. Sec. 6contains our summary remarks.2 KK MCThe main diﬀerences between CEEX andEEX are best illustrated by focusing on theprocess of interest, which ise−(p1, λ1) + e+(p2, λ2)→ f(q1, λ′1) + f¯(q2, λ′2)+ γ(k1, σ1) + ...+ γ(kn, σn).(1)The respective EEX total cross sectionσ =∞∑n=0∫mγdΦn+2 eY (mγ)Dn(q1, q2, k1, ..., kn)(2)corresponds to the attendant O(α1) distri-butions Dn as given in Ref.2 by formu-las such as, for n = 0, 1, D0 = β¯0 andD1(k1) = β¯0S˜(k1) + β¯1(k1), where the realsoft factors S˜(k) are deﬁned as usual 2. Theimportant point is that the IR-ﬁnite buildingblocks β¯n, for example, β¯0 =∑λ |MBornλ |2,in the multi-photon distributions are all interms of∑spin|...|2! Here, λ = fermion helici-ties and σ = photon helicity. In contrast, inthe analogous O(α1) case of CEEXσ =∞∑n=0∫mγdΦn+2∑λ,σ1,...,σn|eB(mγ)Mλn,σ1,...,σn(k1, ..., kn)|2(3)the diﬀeren-tial distributions for n = 0, 1 photons are, forexample, Mλ0 = βˆλ0 , λ = fermion helicitiesand Mλ1,σ1(k1) = βˆλ0sσ1(k1) + βˆλ1,σ1(k1), with the IR-ﬁnite building blocks βˆλ0 =(e−BMBorn+Virt.λ)∣∣O(α1)and βˆλ1,σ(k) = Mλ1,σ(k) − βˆλ0sσ(k). Ex-plicitly,this time everything is in terms of M-spin-amplitudes! This is the basic diﬀerence.25 .50 .75 1.00−.005−.002.000.002.005KK MC 1999, S.Jadach, Z. Wa¸s, B.F.L. Ward← Strong Cut No Cut →σMC−σSemσSem1− s′min/sEEX0 − Sem.An.BestFigure 1. Results for 189 GeV in the µµ¯ channel, forv < 0.999. We plot the difference between the KKMC result and semi-analytical (IEX) result dividedby the latter.between EEX/YFS AND CEEX. Completeexpressions for spin amplitudes with CEEXexponentiation, nγ arbitrary, are given inPhys. Lett. B449, 97 (1999) for the O(α1)case and in CERN-TH/2000-087,UTHEP-99-09-01, for the O(α2) case, all are based onGPS spinor conventions as given in CERN-TH-98-235, hep-ph/9905452.3 Results: CEEXIn Figs. 1, 2 and 3 we show the baselinetechnical precision test with the β¯0 level ma-trix element and physical precision tests ofσtot, AFB , and the IFI at LEP2 energies aseﬀected in the LEP2 MC Workshop 8. Withthese and related tests we achieve the techni-cal precision tag of 0.02% at LEP2 energies ,the physical tags of 0.2%(0.2− 0.4%) for theσtot(the AFB), and ﬁrm control on the IFI1:we see that the IFI ∼= 1.5% for energy cut0.3, that a |cosθ| < 0.9 cut reduces the IFIby 25%, and that the IFI is very small at theZ return, for example.4 YFSWW3-1.14 MCStarting from the underlying process of in-terest, Eq.(1), its cross section, Eq.(2),and the attendant W+W− produc-For Publisher’s usePhysical Precision Tests(a)(b)0.25 0.50 0.75 1.00−0.0250.0000.0250.0500.0750.100× × × × × × × × × ×⋆⋆⋆⋆ ⋆ ⋆ ⋆ ⋆ ⋆ ⋆KK MC 1999, S.Jadach, B.F.L. Ward, Z. Wa¸sσ−σrefσref1− s′min/s← Strong Cut No Cut →CEEX2, Int.ONCEEX2, Int.OFFEEX3, NO Int.× EEX2 of KORALZ 4.03⋆ CEEX2 + IFI at O(α1)0.25 0.50 0.75 1.00−0.0200.0000.0200.0400.060× × × × × × × × ××⋆⋆⋆⋆ ⋆ ⋆ ⋆⋆ ⋆ ⋆KK MC 1999, S.Jadach, B.F.L. Ward, Z. Wa¸sAFB−ArefFB1− s′min/s← Strong Cut No Cut →CEEX2, Int.ONCEEX2, Int.OFFEEX3, NO Int.× EEX2, KORALZ 4.03⋆ CEEX2 + IFI at O(α1)Figure 2. Absolute predictions for σtot, AFB:µµ¯, 189 GeV.Physical Precision Tests(a)(b)0.25 0.50 0.75 1.000.0000.0250.0500.0750.100 ⋆⋆⋆⋆⋆⋆ ⋆KK MC 1999, S.Jadach, B.F.L. Ward, Z. Wa¸sσintσtot.1− s′min/s← Strong Cut No Cut →O(α2)CEEXKORALZ 1-st ord.⋆ ⋆ ⋆ ZFITTER 6.x0.25 0.50 0.75 1.00−0.010−0.0050.0000.0050.010⋆⋆ ⋆ ⋆ ⋆ ⋆ ⋆ ⋆ ⋆ ⋆ ⋆KK MC 1999, S.Jadach, B.F.L. Ward, Z. Wa¸sσintσtot.1− s′min/s← Strong Cut No Cut →O(α2)CEEXKORALZ 1-st ord.⋆ ⋆ ⋆ ZFITTER 6.xFigure 3. s′-cut dependence of δσ, No θ-cut: (a),189 GeV; (b), MZ .tion and decay, e−(p1) + e+(p2) →W−(q1) +W+(q2), W−(q1) →f1(r1) + f¯2(r2), W+(q2) → f′1(r′1) + f¯′2(r′2),we may isolate the Leading Pole Ap-proximation (LPAa,b) as follows:M(n)4f (p1, p2, r1, r2, r′1, r′2, k1, ..., kn)LPA=>M(n)LPA(p1, p2, r1, r2, r′1, r′2, k1, ..., kn)=∑γ Part′nsM(n),λ1λ2Prod(p1, p2, q1, q2, k1, ..., ka)×1D(q1)M(n)Dec1,λ1(q1, r1, r2, ka+1, ..., kb)×1D(q2)M(n)Dec2,λ2(q2, r′1, r′2, kb+1, ..., kn),(4)in an obvious notation 4 for the W±propagator denominators D(qi), etc.Here, we can identify two diﬀerent re-alizations, LPAa,b, of the leading poleresidues in Eq. (4) by following theprescriptions of Eden et al. 9 and Stu-art 10: in M =∑j ℓjAj ({qkql}), thecomplete set of spinor covariants {ℓj}may (b) or may not (a) be evaluatedat the pole positions for the respectiveLorentz scalar functions {Aj ({qkql})}, asthese latter already realize the ana-lyticity properties of the S-matrix bythemselves. We do both.The standard YFS methods 2(EEX-Type) give us the correspondinganalog of Eq.(2). In realizing the ex-act O(α) corrections in the latter equa-tion in the LPA, we have chosen, forour renormalization scheme, the Gµ-Scheme of Fleischer et al. 11 in version1.13 and the schemes A and B in ver-sion 1.14, where in A only the hard EWcorrection has αGµ whereas in B the en-tire O(α) correction has α(0). The anal-ysis in Ref. 12 tells us that the schemesA and B are improvements over theGµ scheme in version 1.13, as we haveveriﬁed in the context of the LEP2MC Workshop comparisons with Den-ner et al. As a consequence, we have aFor Publisher’s useECM = 200GeVECM = 500GeV−1.0 −0.5 0.0 0.5 1.0100101102103104sssssssss s s s s s s s s s s s s s s s s s s s s s s s s s s ss s ss ss ssssssss❝❝❝❝❝❝❝❝ ❝❝❝ ❝ ❝ ❝ ❝ ❝ ❝ ❝ ❝ ❝ ❝ ❝ ❝ ❝ ❝ ❝ ❝ ❝ ❝ ❝ ❝ ❝ ❝❝ ❝❝ ❝ ❝❝❝ ❝❝❝❝❝❝❝❝❝❝⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋄⋄⋄⋄⋄⋄⋄⋄⋄⋄⋄⋄⋄⋄⋄⋄⋄⋄⋄⋄⋄⋄⋄⋄⋄⋄⋄⋄⋄⋄⋄⋄⋄⋄⋄⋄⋄⋄⋄⋄⋄⋄⋄⋄⋄⋄⋄⋄⋄⋄s ISR: BARE⋆ Best: BARE❝ ISR: CALO⋄ Best: CALOdσd cos θγ[fb]cos θγ−1.0 −0.5 0.0 0.5 1.0100101102103sssssssssssss ss s s s s s s s s s s s s s s s ss s ss ss sssssssssssss❝❝❝❝❝❝❝❝❝❝❝ ❝❝ ❝❝ ❝ ❝ ❝ ❝ ❝ ❝ ❝ ❝ ❝ ❝ ❝ ❝ ❝ ❝ ❝ ❝ ❝ ❝❝ ❝❝ ❝❝❝ ❝❝ ❝❝❝❝❝❝❝❝❝⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋆⋄⋄⋄⋄⋄⋄⋄⋄⋄⋄⋄⋄⋄⋄⋄⋄⋄⋄⋄⋄⋄⋄⋄⋄⋄⋄⋄⋄⋄⋄⋄⋄⋄⋄⋄⋄⋄⋄⋄⋄⋄⋄⋄⋄⋄⋄⋄⋄⋄⋄dσd cos θγ[fb]cos θγFigure 4. Distribution of cosθγ with respect to thee+ beam−0.3÷−0.4% shift of the NORMALISA-TION of version 1.14 relative to version1.13. See G. Passarino 13 for more de-tails and references.5 Results: YFSWW3-1.14In Fig. 4, we show the hardest photonangular distribution, both at 200 GeVand at 500 GeV. We see that the NLEW correction is relevant both for theBARE and CALO event selections asdeﬁned Ref. 14 away from the beam di-rection. Similar eﬀects are discussed inRefs. 4, where we ﬁnd that the EW NLcorrection at LEP2 energies is large,∼ −2%, and is in general a non-trivialfunction of the kinematical variables.The authors in Ref. 6 have reached theanalogous conclusion.Indeed, in Table 1 we showa comparison between the resultsfrom RacoonWW and YFSWW3-1.14,where we have chosen the case of with-no cuts σtot[fb]final state program Born bestYFSWW3 219.770(23) 199.995(62)νµµ+τ−ν¯τ RacoonWW 219.836(40) 199.551(46)(Y–R)/Y −0.03(2)% 0.22(4)%YFSWW3 659.64(07) 622.71(19)ud¯µ−ν¯µ RacoonWW 659.51(12) 621.06(14)(Y–R)/Y 0.02(2)% 0.27(4)%YFSWW3 1978.18(21) 1937.40(61)ud¯sc¯ RacoonWW 1978.53(36) 1932.20(44)(Y–R)/Y −0.02(2)% 0.27(4)%Table 1. Total cross sections, CC03 from RacoonWW,YFSWW3,√s = 200GeV without cuts. Statistical er-rors – last digits in ( ), etc.⇒ 0.4% TU.out cuts, as carried out in the context ofthe LEP2 MC Workshop. From theseresults and others similar to them wearrive at the theoretical precision tagof 0.4% at 200 GeV for the WW sig-nal cross section at LEP2. See G. Pas-sarino 13 for more details and refer-ences.6 ConclusionsOur conclusion for the CEEX KK MCdiscussion is that the CEEX is a clearupgrade path for the EEX in a spin am-plitude level MC. We have shown that,for LEP2, the total TU is 0.2%(0.2-0.4%) for σtot(AFB), for typical cuts –for the LC at 0.5 TeV, these are a factorof 2 worse, and for γγ∗ the TU is 0.3%for LEP2 (there is no ﬁrm result forLC). The IFI (ISR⊗FSR) is includedand under ﬁrm control. Our conclu-sions for YFSWW3-1.14 are that theEW NL correction 11 in O(α), which isalso realized in RacoonWW, is impor-tant both for the normalisation and forthe diﬀerential distributions. The TUat 200 GeV, based on comparisons withRacoonWW, is 0.4%.AcknowledgementsThe authors all thank the CERN THDiv. and the CERN ALEPH, DEL-PHI, OPAL and L3 Collaborations forFor Publisher’s usetheir support and kind hospitality dur-ing the course of this work. S. J. thanksthe DESY TH. Div. for its supportand kind hospitality while a part ofthis work was done. This work wassupported in part by the Polish Gov-ernment grants KBN 2P03B08414 and2P03B14715, the Maria Sk lodowska-Curie Joint Fund II PAA/DOE-97-316,and by the US Department of En-ergy Contracts DE-FG05-91ER40627and DE-AC03-76ER00515.References1. S. Jadach, B. F. L. Ward andZ. Was, DESY-99-106, CERN-TH-2000-087, UTHEP-99-0901, andreferences therein.2. S. Jadach and B. F. L. Ward, Phys.Lett. B274, 470(1992); Comp.Phys. Commun. 56, 351 (1990); S.Jadach, B. F. L. Ward and Z. Was,ibid. 79, 531 (1994); S. Jadach etal., ibid. 102, 229 (1997), and refer-ences therein.3. D. R. Yennie, S. C. Frautschi andH. Suura, Ann. Phys. (NY) 13,379 (1961).4. S. Jadach et al., Phys. Lett. B417,326 (1998); Phys. Rev. D61,113010 (2000); UTHEP-00-0101.5. D. Bardin et al., hep-ph/9908433,and references therein.6. A. Denner et al., hep-ph/9912261,9912290, 9912447; Phys. Lett.B475, 127 (2000); BI-TP 2000/06;hep-ph/0006307.7. W. Beenakker et al., hep-ph/9902333, 9811481, and referencestherein.8. M. Kobel et al., hep-ph/0007180.9. R. J. Eden et al., The AnalyticS-Matrix, (Cambridge UniversityPress, Cambridge, 1966).10. R. G. Stuart, Nucl. Phys. B498,28 (1997); Eur. Phys. J. C4, 259(1998); hep-ph/9706431, 9706550.11. J. Fleischer et al., Zeit. Phys. C42,409 (1989), and references therein.12. B. F. L. Ward, Phys. Rev. D36,939 (1987).13. G. Passarino, in these Proceedings.14. M. W. Gruenwald et al., hep-ph/0005309.

Coherent Exclusive Exponentiation for Precision Monte Carlo Calculations of Fermion Pair Production: Precision Predictions for (Un)stable $W^{+}W^{-}$ Pairs

Coherent Exclusive Exponentiation for Precision Monte Carlo Calculations
  of Fermion Pair Production / Precision Predictions for (Un)stable W+W- Pairs

Coherent Exclusive Exponentiation for Precision Monte Carlo Calculations of Fermion Pair Production / Precision Predictions for (Un)stable W+W- Pairs

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