Event shapes and subjet distributions at HERA

Transcription

1 Evnt shaps and subjt distributions at HERA arxiv:hp-x/5v Dc 5 C. Glasman (on bhalf of th Collaboration) Univrsidad Autónoma d Madrid, Spain Abstract Rcnt rsults on subjt distributions from ar prsntd. h masurd normalisd cross sctions wr usd to study th pattrn of parton radiation. h comparison of th masurmnts with lading-logarithm parton-showr Mont Carlo modls and prturbativ QCD calculations shows a good agrmnt btwn data and prdictions. Rsults on vnt-shap man valus and distributions ar also prsntd. hs masurmnts wr usd to tst th prdictions of th powr-corrction modl for hadronisation. A univrsal valu, within %, of th ffctiv paramtr ᾱ of th modl was obtaind. Introduction At lowst-ordr QCD, th diagrams that contribut to nutral currnt (NC) dp inlastic p scattring (DIS) at HERA ar th boson-gluon fusion (BGF) (Vg, whr V = γ or Z, Fig. a) and QCD-Compton (QCDC) (V g, Fig. b) procsss. Figur c shows an xampl of a highr-ordr diagram. Any obsrvabl can b xprssd as th convolution of th parton dnsitis in th proton, f a, tims th matrix lmnts, f a (x,µ F ) Matrix Elmnts, a whr µ F is th factorisation scal. h matrix lmnts, in addition to x and µ F, dpnd also on th strong coupling constant, α s, and th rnormalisation scal µ R. h sum runs ovr all typ of partons a. hus, in th rgions of phas spac whr th parton dnsitis ar wll constraind, masurmnts of.g. jt cross sctions can b usd to prform tsts of prturbativ QCD (pqcd) and dtrminations of α s. h hadronic final stat in NC DIS can also b usd to study th pattrn of parton radiation by mans.g. of subjts insid jts. Subjts obsrvabls ar calculabl in pqcd and so thy provid stringnt tsts of th thory. On th othr hand, th hadronisation procss, a non-prturbativ ffct, can b studid by mans of th vnt shaps. Rcnt dvlopmnts on th modl of powr-law corrctions [] hav promptd rvivd intrst in undrstanding hadronisation within th framwork of pqcd. alk givn at HEP5 Intrnational Europhysics Confrnc on High Enrgy Physics, Lisbon, Portugal, July st 7 th, 5. Ramón y Cajal Fllow.

2 γ /Z g γ /Z g γ /Z g g p proton rmnant p proton rmnant p proton rmnant (a) (b) (c) Figur : Exampls of Fynman diagrams for dp inlastic p scattring procsss at lowstordr QCD: (a) boson-gluon fusion and (c) QCD Compton. (c) Exampl of a highr-ordr diagram. Subjt distributions h invstigation of th intrnal structur of jts givs insight into th transition btwn a parton producd in a hard procss and th xprimntally obsrvabl jt of hadrons. At sufficintly high jt transvrs nrgy,, whr th ffcts of fragmntation can b nglctd, th jt structur can b calculatd prturbativly. h lowst non-trivial-ordr contribution to th jt substructur is givn by O(α s ) calculations for NC DIS in th laboratory (LAB) fram. Nxt-to-lading-ordr (NLO) calculations of jt substructur can b obtaind in th LAB fram sinc, in such a cas, it is possibl to hav thr partons insid on jt. h k clustr algorithm[] was usd in th longitudinally invariant inclusiv mod [] to dfin jts in th hadronic final stat. h intrnal structur of th jts can b studid by mans of th subjt topology. Subjts wr rsolvd within a jt by considring all particls associatd with th jt and rpating th application of th k algorithm until, for vry pair of particls i and j th uantity d ij = min(e,i,e,j ) [(η i η j ) +(φ i φ j ) ], whr E,i, η i and φ i ar th transvrs nrgy, psudorapidity and azimuth of particl i, rspctivly, was gratr than d cut = y cut ( ). All rmaining clustrs wr calld subjts. h subjt multiplicity dpnds upon th valu chosn for th rsolution paramtr y cut. h pattrn of QCD radiation from a primary parton has bn studid [4] by masuring normalisd cross sctions as a function of subjt obsrvabls: th ratio btwn th subjt transvrs nrgy and that of th jt, E sbj, th diffrnc btwn th subjt psudorapidity (azimuth) and that of th jt, η sbj η jt ( φ sbj φ jt ), and α sbj, th angl, as viwd from th jt cntr, btwn th highst transvrs nrgy subjt and th bam lin in th psudorapidityazimuth plan. h masurmnts wr don for Q > 5 GV, whr Q is th momntum transfr. Jts of > 4 GV and < ηjt <.5 wr slctd. h final sampl consistd of thos jts which had two subjts for y cut =.5. h O(α s ) and O(αs ) QCD calculations usd to compar with th data ar basd on th program Disnt [5]. For ths calculations, th numbr of flavours was st to fiv; th rnormalisation and factorisation scals wr both st to µ R = µ F = Q; α s was calculatd at two

3 loops using Λ (5) = MV, which corrsponds to α MS s(m Z ) =.75. h MRS99 [6] paramtrisations of th proton parton dnsity functions (PDFs) wr usd. hcross-sction(/σ)(dσ/d(e sbj ))isprsntdinfig.a. hdistributionofthfraction oftransvrsnrgycontainstwontrisprjtandissymmtricwithrspcttoe sbj =.5 by construction. h data distribution has a pak at E sbj =.5, which shows that th two subjts tnd to hav similar transvrs nrgis. h distribution for th diffrnc in psudorapidity is shown in Fig. b and also has two ntris pr jt. h masurd cross sction has a two-pak asymmtric structur, with a dip at η sbj η jt, which shows that th subjts cannot b rconstructd too clos togthr. Figur a prsnts th normalisd cross sction as a function of φ sbj φ jt. hr ar two ntris pr jt in this distribution. h data distribution has a pak at φ sbj φ jt =..; th supprssion at φ sbj φ jt coms also from th fact that th subjts cannot b rsolvd whn thy ar too clos togthr. h distribution as a function of α sbj (on ntry pr jt) incrass as α sbj incrass (s Fig. b). his shows that th highst transvrs nrgy subjt tnds to b in th rar dirction. his is consistnt with th asymmtric paks obsrvd in th η sbj η jt distribution. (/σ) dσ/d(e sbj ) (prl.) 98- NLO LO > 4 GV - < η jt <.5 Q > 5 GV y cut =.5 (/σ) dσ/d(η sbj -η jt ).5 (prl.) 98- NLO LO > 4 GV - < η jt <.5 Q > 5 GV y cut =.5.5 (data-nlo)/nlo thortical uncrtainty (data-nlo)/nlo thortical uncrtainty (a) E sbj η sbj -η jt (b) Figur : Normalisd diffrntial subjt cross sctions as functions of (a) E sbj and (b) η sbj η jt. For comparison, th prdictions of Disnt at LO (dashd histograms) and NLO (solid histograms) ar includd. h fixd-ordr QCD calculations ar compard to th data in Figs. and. h QCD prdictions giv a good dscription of th data in shap, within %. his shows that th mchanism driving thsubjt topologyarth g andg subprocsss asimplmntd in th pqcd calculations. o study in mor dtail th pattrn of parton radiation, th prdictions of uark- and gluoninducd procsss ar compard sparatly with th data in Fig. 4. h NLO calculations prdict that th two-subjt rat is dominatd by uark-inducd procsss: th rlativ contri-

4 (/σ) dσ/d φ sbj -φ jt (prl.) 98- NLO LO (/σ) dσ/dα sbj.6 (prl.) 98- NLO LO > 4 GV - < η jt <.5 Q > 5 GV y cut =.5.4. > 4 GV - < η jt <.5 Q > 5 GV y cut =.5 (data-nlo)/nlo thortical uncrtainty (data-nlo)/nlo thortical uncrtainty φ sbj -φ jt (dg) α sbj (rad) (a) (b) Figur : Normalisd diffrntial subjt cross sctions as functions of (a) φ sbj φ jt and (b) α sbj. For comparison, th prdictions of Disnt at LO (dashd histograms) and NLO (solid histograms) ar includd. bution of uark- (gluon-) inducd procsss is 8% (8%). h prdictions for ths two typs of procsss ar diffrnt: in uark-inducd procsss, th two subjts hav mor similar transvrs nrgis (Fig. 4a) and ar closr to ach othr (Figs. 4b and 4c) than in gluon-inducd procsss. h comparison with th masurmnts shows that th data ar bttr dscribd by th calculations for jts arising from a g pair than thos coming from a pair. Evnt shaps Evnt-shap obsrvabls ar particularly snsitiv to th dtails of th non-prturbativ ffcts of hadronisation and can b usd to tst th modls for ths ffcts. In this typ of analysis, th data ar compard to modl prdictions which combin NLO calculations and th thortical xpctations of th powr-corrctions (PC) modl, which is charactrisd by an ffctiv coupling ᾱ. h total prdiction for any vnt-shap obsrvabl isthn givn by th sum of th prturbativ and PC prdictions. Prvious rsults supportd th concpt of powr corrctions in th approach of Dokshitzr t al., but a larg sprad of th rsults suggstd that highrordr corrctions wr ndd. Now, rsummd nxt-to-lading-logarithm (NLL) calculations matchd to NLO ar availabl and so it is possibl to study vnt-shap man valus as wll as distributions. h vnt-shap obsrvabls studid ar thrust,, broadning, B, th C paramtr and th jt mass, M, i = p i ˆn i i p B = p i ˆn i i p i 4

5 (/σ) dσ/d(e sbj ) (prl.) 98- -inducd g-inducd (NLO) > 4 GV - < η jt <.5 Q > 5 GV y cut =.5 (/σ) dσ/d(η sbj -η jt ).5.5 (prl.) 98- -inducd g-inducd (NLO) > 4 GV - < η jt <.5 Q > 5 GV y cut =.5 (/σ) dσ/d φ sbj -φ jt (prl.) 98- -inducd g-inducd (NLO) > 4 GV - < η jt <.5 Q > 5 GV y cut = E sbj η sbj -η jt φ sbj -φ jt (dg) (a) (b) (c) Figur4: Normalisddiffrntial subjt crosssctions asfunctionsof(a)e sbj, (b)ηsbj η jt and (c) φ sbj φ jt. For comparison, th NLO prdictions for uark- (solid histograms) and gluon-splitting (dashd histograms) ar includd. C = ij p i p j sin (θ ij ) ( i p M = ( i E i) i p i i ) ( i E, i) whr ˆn spcifis th thrust or γ axis, θ ij is th angl btwn two final-stat particls i and j, and p i (E i ) is th momntum (nrgy) of particl i. A suitabl fram in which to study vnt shaps at HERA is th Brit fram sinc in this fram, th sparation btwn th currnt jt and th proton rmnant is maximal. h vnt-shap variabls ar rconstructd for all th particls in th currnt hmisphr of th Brit fram. Masurmnts of vnt-shap mans hav bn mad [7] as a function of Q for ach obsrvabl in th kinmatic rgion givn by 8 < Q < 4 GV and.4 < x <.6 (s Fig. 5). Prdictions consisting of NLO + PC calculations hav bn fittd to th data, laving α s and ᾱ as fr paramtrs. Each obsrvabl was fittd sparatly. h NLO prdictions wr calculatd using th program Disastr++ [8]. h proton PDFs hav bn paramtrisd using th CEQ4M [9] sts. A rasonabl fit is obtaind for all th vnt-shap obsrvabls within th Q rang studid. Figur 6 shows th vnt-shap diffrntial distributions [7] for som of th obsrvabls in diffrnt rgions of Q. In this cas, th fit was don using NLO + NLL + PC. h NLO prdictions hav bn calculatd using th Disastr++ and Dispatch [] programs with th MRS99 proton PDF sts. h PC and matchd NLL prdictions wr calculatd using th Disrsum [] packag. In Disrsum, th powr corrction is applid as a shift of th distribution, which has th sam functional form as th powr corrction for th man. For B γ, thr is in addition a chang in shap. h rang of th fit for ach obsrvabl was rstrictd to th rgions whr th prdictions wr valid. A rasonabl fit is obtaind for all th vnt-shap obsrvabls within th rstrictd rangs studid. h xtractd valus of α s and ᾱ from th mans and diffrntial distributions ar shown in Figs. 7a and 7b, rspctivly. It is possibl to obtain a univrsal valu for ᾱ of.45 at th % lvl, xcpt for γ (mans) and C paramtr (distributions). h xtractd valus of ᾱ and α s (M Z ) from th mans show a disprsion that could b du to highr-ordr trms. h xtractd valus of α s (M Z ) from th distributions ar consistnt with th world avrag. 5

6 >. <- >.5 >.5 <B.5. (prl.) 98- Unfittd data DISASER++ & PC DISASER++ > <M >. <C> <- γ >.4 > >.4 <B γ..4. <B γ > <Q> (GV) <Q> (GV) Figur 5: h mans of vnt-shap obsrvabls fittd with NLO + PC. Masurmnts of an vnt-shap obsrvabl snsitiv to highr-ordr ffcts hav bn mad [7]. h out-of-plan momntum, K OU = i pout i, which is dfind as th nrgy flow out of th plan dfind by th proton dirction and th axis which maximiss th thrust, is snsitiv both to prturbativ and non-prturbativ contributions. h lowst non-trivial contribution coms fromnon-prturbativ ffcts or fromo(αs) contributions. Figur7c shows thmasurmnts of K OU /Q in two rangs of Q. h data ar wll dscribd by th prdictions of th lading-logarithm parton-showr modl of Lpto []. his constituts th first comparison of calculations which includ lading-ordr + NLL + PC with th data, in th high-q rang only. h dscription of th data by th prdiction is rasonabl, but a mor prcis tst of th modl nds highr-ordr calculations. 4 Summary Subjt normalisd cross sctions hav bn masurd in NC DIS using 8.7 pb of data collctd with th dtctor at HERA with a cntr-of-mass nrgy of 8 GV. A rasonabl dscription of th data is obtaind by th QCD prdictions. his mans that th pattrn of parton radiation as implmntd in a NLO calculation rproducs th bhaviour of th data. In addition, th data ar wll dscribd by th calculations for jts arising from th splitting of a uark into a uark-gluon pair. Evnt-shap mans and distributions hav bn masurd in NC DIS using 8. pb of data collctd with th dtctor at HERA with a cntr-of-mass nrgy of 8 GV. Calculations including NLO + PC, and including rsummd NLL prdictions matchd to NLO for th diffrntial distributions, giv a rasonabl dscription of th data. h xtractd valus of th powr-corrction paramtr, ᾱ, ar consistnt within %. h xtractd valus of th strong coupling constant ar consistnt with th world avrag. Howvr, mor thortical input is ndd to fully xploit th potntial of ths masurmnts. 6

7 /N dn/db γ 7 5 <Q> = GV <Q> = 6 GV (prl.) <Q> = 9 GV <Q> = 8 GV 98-{ <Q> = 4 GV <Q> = GV NLO + NLL + PC (fittd) NLO + NLL + PC (unfittd) /N dn/dm 7 5 <Q> = GV <Q> = 6 GV (prl.) <Q> = 9 GV <Q> = 8 GV 98-{ <Q> = 4 GV <Q> = GV NLO + NLL + PC (fittd) NLO + NLL + PC (unfittd) /N dn/dc 7 5 <Q> = GV <Q> = 6 GV (prl.) <Q> = 9 GV <Q> = 8 GV 98-{ <Q> = 4 GV <Q> = GV NLO + NLL + PC (fittd) NLO + NLL + PC (unfittd) B γ M C (a) (b) (c) Figur 6: Evnt-shap distributions as functions of (a) B γ, (b) M and (c) C, fittd with NLL rsummd calculations matchd to NLO + PC. Acknowldgmnts I would lik to thank my collagus of th Collaboration for thir hlp in prparing this rport. Rfrncs [] Y. Dokshitzr and B. Wbbr, Phys. Ltt. B 5 (997) 45. [] S. Catani t al., Nucl. Phys. B 46 (99) 87. [] S.D. Ellis and D.E. Sopr, Phys. Rv. D 48 (99) 6. [4] Coll., Contributd papr N-84 to th HEP5 Intrnational Europhysics Confrnc on High Enrgy Physics, July st-7th, 5, Lisbon, Portugal. [5] S. Catani and M.H. Symour, Nucl. Phys. B 485 (997) 9. Erratum in Nucl. Phys. B 5 (998) 5. [6] A.D. Martin t al., Eur. Phys. Jour. C 4 (998) 46; A.D. Martin t al., Eur. Phys. Jour. C 4 (). [7] Coll., Contributd papr N-8 to th HEP5 Intrnational Europhysics Confrnc on High Enrgy Physics, July st-7th, 5, Lisbon, Portugal. [8] D. Graudnz, Proc. of th Ringbrg Workshop on Nw rnds in HERA physics, B.A. Knihl, G. Krämr and A. Wagnr (ds.). World Scintific, Singapor (998). Also in hp-ph/9786 (997); D. Graudnz, Prprint hp-ph/9744, 997. [9] H.L. Lai t al., Phys. Rv. D 55 (997) 8. [] M. Dasgupta and G.P. Salam, JHEP 8 (). 7

8 α.5.45 B M - s.d. rrors 95% confidnc rgion (stat. + xp. sys. rrors) (prl.) 98- α.55.5 γ s.d. rrors 95% confidnc rgion (stat. + xp. sys. rrors) (prl.) 98- C M B γ.4 B γ γ.5 C (a) α s (M Z ) α s (M Z ) (b) Evnts 4 (prl.) 98-5 < Q < 8 GV LEPO ))+NLL+PC LO(O(α s < Q < 5 GV /Q Figur 7: Extractd α s (M Z ) and ᾱ paramtrs from (a) man valus and (b) distributions. (c) Distribution of K OU /Q compard with Lpto and lading-ordr + NLL + PC calculation. (c) K OU [] G. Inglman, A. Edin and J. Rathsman, Comp. Phys. Comm. (997) 8. 8