Next-to-Leading Order Jet Physics with BLACKHAT

Transcription

1 IPPP/09/96 MIT-CTP-4095 SLAC PUB 3868 SB/F/37-09 UCLA/TEP/09/0 Nxt-to-Lading Ordr Jt Physics with BLACKHAT C. F. Brgr a, Z. Brn b, L. J. Dixon c, F. Fbrs Cordro d, D. Ford, f, T. Glisbrg c, H. Ita b, D. A. Kosowr g and D. Maîtr h a Cntr for Thortical Physics, MIT, Cambridg, MA 039, USA b Dpartmnt of Physics and Astronomy, UCLA, Los Angls, CA , USA c SLAC National Acclrator Laboratory, Stanford Univrsity, Stanford, CA 94309, USA d Univrsidad Simón Bolívar, Dpartamnto d Física, Apartado 89000, Caracas 080A, Vnzula Thory Division, Physics Dpartmnt, CERN, CH Gnva 3, Switzrland f NIKHEF Thory Group, Scinc Park 05, NL 098 XG Amstrdam, Th Nthrlands g Institut d Physiqu Théoriqu, CEA Saclay, F 99 Gif-sur-Yvtt cdx, Franc h Dpartmnt of Physics, Univrsity of Durham, DH 3LE, UK W prsnt svral rsults obtaind using th BLACKHAT nxt-to-lading ordr QCD program library, in conjunction with SHERPA. In particular, w prsnt distributions for vctor boson plus,,3- production at th Tvatron and at th asymptotic running nrgy of th Larg Hadron Collidr, including nw Z + 3- distributions. Th Z + - prdictions for th scond- P T distribution ar compard to CDF data. W prsnt th -mission probability at N in W + - vnts at th LHC, whr th tagging s ar takn to b th ons furthst apart in psudorapidity. W analyz furthr th larg lft-handd W ± polarization, idntifid in our prvious study, for W bosons producd at high P T at th LHC. RADCOR 009-9th Intrnational Symposium on Radiativ Corrctions (Applications of Quantum Fild Thory to Phnomnology), Octobr , Ascona, Switzrland Spakr. Work supportd in part by US Dpartmnt of Enrgy contract DE-AC0-76SF0055. c Copyright ownd by th author(s) undr th trms of th Crativ Commons Attribution-NonCommrcial-SharAlik Licnc.

2 . Introduction Th dawn of th Larg Hadron Collidr (LHC) ra brings rnwd incntiv to continu improving thortical prdictions of Standard-Modl backgrounds to nw physics sarchs. For many sarchs, including som channls for th Higgs boson and for dark mattr particls, th signals will b xcsss in + lpton or + missing distributions. Such signals can b mimickd by Standard-Modl procsss; accordingly, a thorough and quantitativly rliabl thortical prdiction is ndd. This rquirs a calculation through nxt-to-lading ordr (N) in QCD. Lading-ordr () computations, whil an important first stp, suffr from a strong dpndnc on th unphysical rnormalization and factorization scals. At this ordr, thy ntr only through th strong coupling α s and parton distribution functions, uncompnsatd by any bhavior of th short-distanc partonic matrix lmnts. Bcaus th QCD coupling is larg and runs quickly, th absolut normalization of cross sctions has a substantial dpndnc on scals. For rasonabl scal variations, th dpndnc is of th ordr of ±40% for th V + 3- procsss w shall study, with V a havy lctrowak vctor boson. Th dpndnc also grows substantially with incrasing numbr of s. At N, th virtual corrctions introduc a compnsating dpndnc on th scals. Th scal dpndnc shrinks to ±0%, and w obtain a quantitativly rliabl answr. Shaps of distributions can also show a dramatic scal dpndnc with poor scal choics. Som shaps do display noticabl gnuin N corrctions, indpndnt of scal issus. N prdictions for V + n- production at hadron collidrs rquir svral ingrdints: tr-lvl V + (n + )-parton matrix lmnts, which provid th contribution; intrfrnc of on-loop and tr amplituds for V + (n + ) partons (virtual contribution); tr-lvl V + (n + 3)-parton matrix lmnts (ral-mission contribution); a subtraction approximation capturing th singular bhavior of th ral-mission trm; th intgral of th approximation ovr th singular phas spac (ral-subtraction trm). Ths contributions must b convolutd with parton distribution functions, obtaind from N fits, and intgratd ovr th final phas spac, incorporating appropriat xprimntal cuts. Schmatically, w combin th contributions as follows, dσ N V+n dobs = dx, f f [ dφ n δ Obs σ tr V+n + + ( dφ n δ Obs σ -loop V+n + σ app ) V+n dφ n+ δ Obs ( σ tr V+n+ σ app V+n+) ], (.) whr dφ n dnots th V +n-parton phas spac; dx, f f th intgral ovr th appropriat parton distributions, a sum ovr typs bing implicit; δ Obs, th binning function for th dsird distribution; σ tr, th tr-lvl squard matrix lmnts; σ -loop, th virtual corrctions; σ app, th approximation to th ral-mission contribution; and σ app, th approximation s intgral ovr singular phas spac. Th st of subtraction trms nsurs that ach of th trms in this quation is sparatly finit, and thus may b computd numrically.

3 W us th BLACKHAT program library [,, 3, 4] to comput th virtual corrctions σ -loop, and th SHERPA packag [5] to comput σ tr and th rquird approximation (σ app and σ app ). Th approximation uss th Catani Symour dipol approach [6]. Th phas-spac intgration is prformd with SHERPA, implmnting a multi-channl approach [7]. Th BLACKHAT library implmnts on-shll mthods for on-loop amplituds numrically. Such amplituds can b writtn as a sum of cut trms C n, containing branch cuts in kinmatic invariants, and rational trms R n, fr of branch cuts, A n = C n + R n. (.) All th branch cuts appar in th form of logarithms and dilogarithms, and can b writtn as a sum ovr a basis of scalar intgrals bubbls I i, triangls Ii 3, and boxs Ii 4, C n = i d i I i 4 + i c i I3 i + b i I. i (.3) i (Massiv particls in th loop also rquir tadpol intgrals.) W tak all xtrnal momnta to b four dimnsional, xprssibl in trms of spinors. Th cofficints of ths intgrals, b i,c i, and d i, as wll as th rational rmaindr R n, ar rational functions of spinor variabls (in th form of spinor products). Th BLACKHAT library computs ths cofficints numrically, lvraging off rcnt analytic progrss. In particular, it xploits gnralizd unitarity [8, 9]. W us Ford s approach [0] to comput b i and c i, making us also of th subtraction approach to intgral rduction first introducd by Ossola, Papadopoulos and Pittau []. To obtain th rational trms w hav implmntd both loop-lvl on-shll rcursion [], and a massiv continuation approach du to Badgr [3], which is rlatd to th D-dimnsional gnralizd unitarity [4] approach of Gil, Kunszt and Mlnikov [5]. On-loop matrix lmnt computations can suffr from numrical instabilitis. In BLACK- HAT, this problm is solvd by dtcting pics of th amplitud which do not hav a sufficint accuracy and rcomputing thm with highr prcision using th multiprcision packag QD [6]. This approach has th advantag of solving th problm using th sam approach for wll-bhavd points and for numrically unstabl ons. As discussd in rfs. [, 4], with a sris of tsts th simplst of which chcks whthr th infrard divrgncs hav th propr valus thr is no nd for a priori knowldg of what st of circumstancs can lad to instabilitis. In ach contribution whr prcision loss is dtctd, BLACKHAT automatically switchs to highr prcision, rgardlss of th undrlying caus. With on-shll mthods this happns infrquntly and thrfor has only a mild ffct on th ovrall computation tim. W hav prviously usd ths softwar tools to provid th first phnomnologically usful N study of th production of a W boson in association with up to thr s [3, 4]. In this Contribution, w xtnd our prvious studis with a mor dtaild look at th qustion of scal choics; at aspcts of th polarization of Ws producd at high P T ; and at a nw distribution displaying th probability of mitting a into a rapidity gap. W also prsnt th first N rsults on Z + 3- production at hadron collidrs, in a lading-color approximation dsignd to b accurat within a fw prcnt. In all cass, w dcay th vctor boson to lptons, W + l + ν l, W l ν l, and Z l + l, using th appropriat vctor boson linwidth. W includ th virtual photon contribution to l + l production. Othr rcnt stat-of-th-art N rsults may b found in rf. [7]. Th 3

4 production of W + 3 s has also bn computd at N using a lading-color approximation and xtrapolation [8, 9].. Scal Choics Th rnormalization and factorization scals ar not physical scals. Physical quantitis should b indpndnt of thm. A dpndnc on thm is nonthlss prsnt in thortical prdictions that ar truncatd at a fixd ordr in prturbation thory. At lading ordr, th dpndnc ariss solly through α s and th parton distributions, rspctivly. W adopt th usual practic and choos th two to b qual, µ R = µ F = µ. N rsults gratly rduc th dpndnc compard to, but of cours thy do not liminat it compltly. W still nd to choos this scal. W should xpct a good choic for µ to b nar a typical nrgy scal for th obsrvabl w ar computing, in ordr to minimiz th uncomputd logarithms in highr-ordr trms. Howvr, multi- procsss such as V +,3- production hav many intrinsic scals, and it is not clar a priori how to distill thm into a singl numbr. For any givn point in th fully-diffrntial cross sction, thr is a rang of scals on could plausibly choos. For xampl, on might choos th sam fixd scal µ for all vnts. Howvr, bcaus thr can b a larg dynamic rang in momntum scals (particularly at th LHC, whr transvrs nrgis wll abov M W ar common), it is natural to pick th scal µ dynamically, vnt by vnt, as a function of th vnt s kinmatics dσ / d [ pb / GV ] > 30 GV, η < 3 µ R = µ F = W > 0 GV, η <.5 W E/ T > 30 GV, M T R = 0.4 [siscon] > 0 GV W s + X s = 4 TV N dσ / d [ pb / GV ] > 30 GV, η < 3 ^ µ R = µ F = H T > 0 GV, η <.5 W E/ T > 30 GV, M T R = 0.4 [siscon] > 0 GV W s + X s = 4 TV N 7 / N N scal dpndnc 6 5 scal dpndnc Scond Jt.5 / N N scal dpndnc scal dpndnc Scond Jt Figur : and N prdictions for th scond distribution in W + 3 production at th LHC. Th only diffrnc btwn th lft and right panls is th scal choic: µ = ET W on th lft and µ = Ĥ T on th right. Th formr choic is clarly problmatic and should not b usd in phnomnological studis. Th bottom panls show th and N prdictions, varid by a factor of two around th cntral scal, and dividd by th N valu at th cntral scal. Prvious studis (s.g. rfs. [0, ]) hav usd th transvrs nrgy of th vctor boson, ET V, as th scal choic. For many distributions at th Tvatron, this is satisfactory. With th largr dynamic rang at th LHC, th choic bcoms problmatic. Indd, for som obsrvabls, such as th transvrs-nrgy distribution of th scond-hardst in W + 3- production, shown in th 4

5 dσ / dp T [ fb / GV ] P T > 30 GV, η <. µ R = µ F = Z > 5 GV, η < η < or. < η <.8 66 GV < M < 6 GV R = 0.7 [anti-k T ], R - > 0.7 Z / γ * + 3 s + X s =.96 TV N dσ / dp T [ fb / GV ] P T > 30 GV, η <. ^ µ R = µ F = H T / > 5 GV, η < η < or. < η <.8 66 GV < M < 6 GV R = 0.7 [anti-k T ], R - > 0.7 Z / γ * + 3 s + X s =.96 TV N 3 / N N scal dpndnc scal dpndnc.5 / N N scal dpndnc scal dpndnc Third Jt P T Third Jt P T Figur : Th N P T distribution of th third in Z + 3- production at th Tvatron. For th lft panl th scal choic µ = ET Z is usd, and for th right panl µ = Ĥ T /. Although th two N rsults ar compatibl, th rsults hav larg shap diffrncs, illustrating that µ = Ĥ T / is a bttr choic than µ = ET Z at th Tvatron as wll. Th lpton and cuts match th CDF ons [0]. lft panl of fig., it gos disastrously wrong, lading to ngativ valus of th distribution for byond 475 GV. Evn at th Tvatron, th scal choic µ = ET V is not ncssarily a good on; for xampl, with this choic, th lft panl of fig. displays a larg chang in shap btwn and N in th P T distribution of th third hardst in Z + 3- production. This difficulty rflcts th mrgnc of a larg logarithm ln(µ/e), whr E is a typical nrgy scal, spoiling th validity of th prturbativ xpansion. W j p _ ( ) p p W _ ( ) p j j j 3 (a) j j 3 (b) Figur 3: Two distinct W + 3 configurations with rathr diffrnt valus for th W transvrs nrgy. In configuration (a) an nrgtic W balancs th nrgy of th s, whil in (b) th W is rlativly soft. Configuration (b) gnrally dominats ovr (a) whn th transvrs nrgis gt larg. To undrstand th problm with th scal choic µ = ET V, considr th two configurations dpictd in fig. 3. In configuration (a), th W has a transvrs nrgy largr than that of th s, and accordingly sts th scal for th procss. In configuration (b), th two lading s roughly balanc in, whil th W has much lowr transvrs nrgy. Hr, th W scal is too low, and not charactristic of th procss. In th tail of th distribution, w xpct configuration (b) to dominat, bcaus it rsults in a largr scond- for fixd cntr-of-mass partonic nrgy; contributions from highr cntr-of-mass nrgis will b supprssd by th fall-off of th parton distributions. Can w choos a scal that trats th diffrnt final-stat objcts mor dmocratically? Th 5

6 total partonic transvrs nrgy, Ĥ T = ET i + E T + /, (.) partons i or a fixd fraction of it, is such a choic. As w can s in th right panls of figs. and, this choic rsults in stabl and snsibl N prdictions and also in a rlativly flat ratio of th N and prdictions. For prdictions, it is bttr to us such a scal whn N rsults ar unavailabl. A similar typ of scal choic, basd on th combind invariant mass of th s, has bn motivatd by soft-collinar ffctiv thory []. Local scals associatd with branching historis as usd in parton showrs hav rcntly bn studid for W + 3- production at [9]. 3. Z + Jts at th Tvatron At hadron collidrs, Z boson production manifsts itslf primarily in ithr chargd-lpton pair production, or th production of missing transvrs nrgy (whn th Z dcays to nutrinos). Th lattr procss is an important background to a wid varity of suprsymmtry sarchs (whn no chargd lpton is rquird), and to dark mattr sarchs mor gnrally. Th l + l mod has a significantly lowr rat, but it is an xcllnt calibration procss, as th Z can b rconstructd prcisly. It is also an xcllnt procss for confronting N prdictions with xprimntal data. W hav computd th N Z +,,3- production cross sctions for th Tvatron (p p collisions at s =.96 TV), with th Z dcaying into a chargd lpton pair. W applid th sam cuts usd by th CDF collaboration [0] in thir masurmnt of ths procsss for Z +, P T > 30 GV, E T > 5 GV, R > 0.7, 66 < M + < 6 GV, η <., η <, η < or. < η <.8, (3.) whr th lctron cuts apply to both lctrons and positrons, and th cuts apply to all s. W cut on th psudo-rapidity η rathr than CDF s cut on rapidity y; th two cuts coincid at but diffr slightly at N. W mployd thr diffrnt infrard-saf algorithms [3], SISCon (with mrging paramtr f = 0.75), k T and anti-k T, all with R = 0.7. Production of an l + l pair can also b mdiatd by a virtual photon; w includ ths contributions as wll, although thy ar supprssd by th cut on th lpton-pair invariant mass M +. Fig. 4 shows how th Z +,,3- cross sction dpnds on a fixd scal µ, indpndnt of th vnt kinmatics, for th anti-k T algorithm and with th cuts (3.). Hr choosing µ M Z is appropriat, bcaus th cross sction is dominatd by low-p T s. Th uppr thr panls show th scal dpndnc of th cross sction at N, compard to that at, in Z+ -, Z+ -, and Z+ 3- production, rspctivly. Thy illustrat th lssnd dpndnc at N. Th bottom panl shows th ratio of N to rsults for all thr cass, dmonstrating th incrasing snsitivity to scal variations at with incrasing numbr of s. This is xpctd, bcaus thr is an additional powr of α s (µ) multiplying th cross sction for ach additional. Accordingly, th impact of an N calculation also grows with th numbr of s. Th rsults for th k T and SISCon algorithms (not shown) ar similar. Fig. 5 compars th thortical prdictions for th scond- P T distribution in Z + - production with data from CDF [0]. CDF usd th midpoint algorithm [4]. This algorithm is 6

7 s =.96 TV 4000 Z / γ * + + X 3000 σ [ fb ] Z / γ * + s + X µ 0 = M Z = GV N R = 0.7 [anti-k T ], R - > Z / γ * + 3 s + X P T > 30 GV, η <. > 5 GV, η < η < or. < η <.8 66 GV < M < 6 GV K-factor Z / γ * + + X Z / γ * + s + X Z / γ * + 3 s + X µ / µ 0 Figur 4: Th scal dpndnc of th cross sction for Z +,,3- production at th Tvatron, for th anti-k T algorithm using a lading-color approximation with n f trms, as a function of th common rnormalization and factorization scal µ, with µ 0 = M Z. Th bottom panl shows th K factors, or ratios btwn N and rsults, for th thr cass dσ / dp T [ fb / GV ] P T > 30 GV, η <. ^ µ R = µ F = H T / > 5 GV, η < η < or. < η <.8 66 GV < M < 6 GV R = 0.7 [anti-k T ], R - > 0.7 Z / γ * + s + X s =.96 TV N CDF data.5 / N CDF / N N scal dpndnc scal dpndnc Jt P T Figur 5: Th scond- P T distribution for Z + s at and N compard against CDF data [0]. infrard unsaf for Z + 3-s at N, so w us infrard-saf ons instad. Fig. 5 shows rsults for th anti-k T algorithm; th othr two algorithms yild similar rsults. It is worth noting that CDF did not attmpt to dconvolv th hadronization corrctions (stimatd using Pythia) from thir masurd data; rathr, thy providd a tabl of hadronization corrctions. This is hlpful bcaus it will allow for futur improvmnts to hadronization modls to b takn into account in thortical prdictions. Accordingly, w hav usd ths hadronization corrctions to gnrat a complt prdiction from th and N prturbativ prdictions. Th hadronization corrctions 7

8 ar significant for low P T, on th ordr of 0 % at 30 GV, and bcom rathr small at largr transvrs momnta. As xpctd, th scal-dpndnc band is much largr than th N on. Excpting prhaps th last bin, th agrmnt btwn th N prdiction and th data is quit good, spcially givn th diffrnt algorithms. Fig. 6 givs our prdictions for th thr P T distributions in Z + 3- production, using th anti-k T algorithm. With th choic of scal µ = Ĥ T /, only minor shap changs ar visibl btwn and N, for all thr distributions. Th N plots ar basd on a lading-color approximation along th lins of rfs. [3, 4], xcpt that pics proportional to th numbr of light quark flavors (n f ) ar includd. W xpct this approximation to b valid to a fw prcnt dσ / dp T [ fb / GV ] P T > 30 GV, η <. > 5 GV, η < η < or. < η <.8 Z / γ * + 3 s + X s =.96 TV N ^ µ R = µ F = H T / GV < M < 6 GV R = 0.7 [anti-k 0-3 T ], R - > 0.7 / N scal dpndnc.5 N scal dpndnc First Jt P T Scond Jt P T Third Jt P T 0.5 Figur 6: Th and N P T distributions for Z + 3- production for th lading, scond and third, for th anti-k T algorithm and scal choic µ = Ĥ T /. Th thin vrtical bars in th top panls indicat th intgration rrors. 4. W Polarization at th LHC dσ ( W s ) / dσ ( W s ) W + 3 s + X s = 4 TV W + / W - ratio dσ ( W s ) / dσ ( W s ) W + / W - ratio W + 3 s + X s = 4 TV Chargd Lpton Nutrino Figur 7: Th lft panl shows th ratio of th chargd-lpton distributions at th LHC for W + and W production in association with at last thr s, computd at N. Th right panl shows th corrsponding ratio for th nutrino, or quivalntly /. As notd in rf. [4], at th LHC th distributions of th daughtr lptons show a surprisingly strong shap dpndnc on whthr thy com from a W + or a W, indpndnt of th numbr 8

9 of s. Fig. 7 shows th ratio of th N transvrs nrgy distributions for th W ± boson dcay products in inclusiv W + 3- production at th LHC, chargd lptons in th lft panl and nutrinos in th right panl. Th diffrncs btwn W + and W distributions ar quit dramatic. Th lft panl shows a larg ratio for W + to W at small ET which dclins at largr E T. In contrast, th corrsponding ratio for th ET ν, or quivalntly th missing transvrs nrgy / in th vnt, starts somwhat smallr but incrass rapidly with. Th significant diffrnc in bhavior btwn W + and W suggsts a mans for sparating W bosons producd in top quark dcays from thos producd from light quarks; th Ws from top dcays do not xhibit a similar phnomnon. 0.8 W + + s f L f R f s = 4 TV p T, > 30 GV N W - + s s = 4 TV p T, > 30 GV f L f R f 0 N p T,W [GV] p T,W [GV] Figur 8: Th and N prdictions for polarization fractions of th lft-handd, f L (top curv), righthandd f R (middl curv) and longitudinal f 0 (bottom curv) fractions for W + s at th LHC. Th lft panl givs th polarization for W + and th right panl for W. For high transvrs momntum, P T,W, th W bosons bcom prdominantly lft-handd. This disparat bhavior is xplaind by a nt lft-handd polarization for both W + and W at high transvrs momntum. This ffct is asily visibl at, and it dos not gt washd out at N. In fig. 8, w giv th fraction of W bosons in ach of th thr polarization stats, lft-handd, right-handd and longitudinal ( f L, f R, f 0, rspctivly) for W + - production at th LHC, at both and N. As sn in th figur, at high transvrs momntum th W ± bosons ar prfrntially lft handd. Although th cross-sctions for W + and W ar rathr diffrnt, thir polarizations ar narly idntical. Intrstingly, w also find that whn th W s hav a transvrs momntum of mor than 50 GV, th polarization is quit indpndnt of th transvrs nrgy cuts. With W ± bosons lft-hand polarizd at larg E W T, th W + tnds to mit th lft-handd nutrino forward rlativ to its dirction of motion (rsulting in a largr transvrs nrgy) and th right-handd positron backward (smallr transvrs nrgy). In contrast, th W prfrs to mit th lft-handd lctron forward. At high, such dcays produc an nhancmnt in th nutrino distribution and a dpltion in th chargd-lpton distribution, for W + rlativ to W, consistnt with th rsults displayd in fig. 7. W not that this phnomnon is distinct from th wll-known dilution of th W rapidity asymmtry at th Tvatron, whn passing to th dcay lpton, which can b xplaind using angular momntum consrvation solly along th bam axis [5]. 5. Emission into Rapidity Gaps In prvious work [], w providd th first N study of th probability of mitting a third in W + - vnts, as a function of th rapidity intrval btwn two lading- s at th LHC. 9

10 This distribution was studid arlir at at th Tvatron and compard to CDF data [6]. Jt mission probabilitis ar rlvant to Higgs sarchs in vctor-boson fusion [7], in which colorsinglt xchang lads to a paucity of radiation in th cntral rgion btwn two forward tag s. On th othr hand, QCD backgrounds with color xchang, as in W + - production, will gnrally lad to significant radiation..5 dσ ( W s ) / dσ ( W - + s ) 0.5 : ( W s + X ) / ( W - + s + X ) N: ( W s + X ) / ( W - + s + X ) s = 4 TV η Figur 9: Th ratio of th inclusiv W + 3- cross sction to th W + - cross sction as a function of th psudorapidity sparation η btwn th two most widly sparatd s that pass th cuts. Th solid (black) lin givs th N rsult, whil th dashd (blu) lin givs th rsults. To mimic vctor-boson fusion sarchs, howvr, th appropriat tag s ar not th two hardst ons (by ), but rathr th two most sparatd in psudorapidity. Thrfor, in fig. 9 w prsnt th ratio of th W + 3- cross sction to th W + - cross sction as a function of th psudorapidity sparation η btwn th two most sparatd s. Th mission probability riss roughly linarly with η. Th N rsult is somwhat lss than th on at larg η. (Th ratio for W + is quit similar.) This plot is similar to on for Higgs production in association with s [8], obtaind from high-nrgy factorization considrations. It would b intrsting to compar rsults obtaind in this way to N rsults for th sam quantitis. 6. Conclusions In this Contribution w prsntd som nw rsults for W + 3- production obtaind from BLACKHAT combind with SHERPA, xpanding on arlir scal-dpndnc studis [3, 4]. W also dmonstratd that W bosons producd at larg P T ar indd polarizd lft-handd, xplaining an asymmtry btwn W + and W in th transvrs nrgy distributions of th daughtr lptons. Bcaus Ws from top dcays do not xhibit this polarization ffct, it may prov ffctiv for distinguishing such W s from ons producd by light quarks. W prsntd th first N study of th probability of mitting a third btwn th two most widly sparatd s in W + - production. W also prsntd th first N rsults for Z + 3- production. W obsrvd that vn at th Tvatron, choosing th rnormalization and factorization scal to qual th vctor boson transvrs nrgy is not a particularly good choic, as it inducs larg shap changs btwn and N. A publicly availabl vrsion of BLACKHAT is in prparation and is currntly bing tstd in divrs projcts (s.g. rf. [9]). This vrsion uss th proposd Ls Houchs intrfac for on- 0

11 loop matrix lmnts. It has bn tstd with both C++ and Fortran clints. Th public vrsion will provid all procsss that hav bn carfully tstd with th full BLACKHAT cod. In th mor distant futur, th nxt bnchmark procss for BLACKHAT + SHERPA is th production of a W boson in association with four s at N. Using th tchniqus dscribd abov, th virtual part of th N cross sction sms within rach. Computing th ral mission matrix lmnts, and intgrating thm ovr th svn-particl phas spac (including th dcay of th vctor boson) appars to b rathr challnging with th currnt tools, du to th larg numbr of intgration channls. It is intrsting to not that in this cas th bottlnck no longr sms to b th virtual contributions to th cross sction. Th rsults summarizd hr ar indicativ of th typ of physics that can b carrid out using BLACKHAT in conjunction with SHERPA. W look forward to comparing prdictions from ths tools to th forthcoming LHC data. Acknowldgmnts W thank Jpp Andrsn, Rikkrt Frdrix, and Markus Stoy for hlpful convrsations. This rsarch was supportd by th US Dpartmnt of Enrgy undr contracts DE FG03 9ER4066, DE AC0 76SF0055 and DE FC0 94ER4088. DAK s rsarch is supportd by th Europan Rsarch Council undr Advancd Invstigator Grant ERC AdG 830. This rsarch usd rsourcs of Acadmic Tchnology Srvics at UCLA, PhnoGrid using th GridPP infrastructur, and th National Enrgy Rsarch Scintific Computing Cntr, which is supportd by th Offic of Scinc of th U.S. Dpartmnt of Enrgy undr Contract No. DE AC0 05CH3. Rfrncs [] C. F. Brgr, Z. Brn, L. J. Dixon, F. Fbrs Cordro, D. Ford, H. Ita, D. A. Kosowr and D. Maîtr, Phys. Rv. D 78, (008) [ [hp-ph]]. [] C. F. Brgr t al., [hp-ph]. [3] C. F. Brgr, Z. Brn, L. J. Dixon, F. Fbrs Cordro, D. Ford, T. Glisbrg, H. Ita, D. A. Kosowr and D. Maîtr, Phys. Rv. Ltt. 0, 00 (009) [ [hp-ph]]. [4] C. F. Brgr t al., Phys. Rv. D 80, (009) [ [hp-ph]]. [5] T. Glisbrg, S. Höch, F. Krauss, M. Schönhrr, S. Schumann, F. Sigrt and J. Wintr, JHEP 090 (009) 007 [08.46 [hp-ph]]; T. Glisbrg and F. Krauss, Eur. Phys. J. C 53, 50 (008) [ [hp-ph]]. [6] S. Catani and M. H. Symour, Nucl. Phys. B 485, 9 (997) [Erratum-ibid. B 50, 503 (998)] [hp-ph/960533]. [7] R. Kliss and R. Pittau, Comput. Phys. Commun. 83, 4 (994) [hp-ph/940557]. [8] Z. Brn, L. J. Dixon and D. A. Kosowr, Nucl. Phys. B 53, 3 (998) [hp-ph/970839]; JHEP 0408, 0 (004) [hp-ph/040493]. [9] R. Britto, F. Cachazo and B. Fng, Nucl. Phys. B 75, 75 (005) [hp-th/0403]. [0] D. Ford, Phys. Rv. D 75, 509 (007) [ [hp-ph]]. [] G. Ossola, C. G. Papadopoulos and R. Pittau, Nucl. Phys. B 763, 47 (007) [hp-ph/ ].

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