Hadronic events at the Z pole have been investigated in search for Colour
Reconnection effects and QCD coherence. Colour Reconnection effects are
searched for in three-jet events and the data results are compared to the
predictions of different Monte Carlo models. QCD colour coherence effects are
tested through the multiplicity distributions of hadrons with restricted
momenta, and the LEP1 e+e- data is compared to HERA e+p data under the
equivalence assumption of the e+e- hemisphere with the current region of the
Breit frame of reference.Comment: 4 pages, 4 figures, contribution to ICHEP06 proceeding

Azzurri, P.

English

arXiv

Hadronic events at the Z pole have been investigated in search for Colour Reconnection effects and QCD coherence. Colour Reconnection effects are searched for in three-jet events and the data results are compared to the predictions of different Monte Carlo models. QCD colour coherence effects are tested through the multiplicity distributions of hadrons with restricted momenta, and the LEP1 e+e- data is compared to HERA e+p data under the equivalence assumption of the e+e- hemisphere with the current region of the Breit frame of reference

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arXiv:hep-ex/0610075 v1   25 Oct 2006October 26, 2006 0:50 WSPC/Trim Size: 10in x 7in for Proceedings qcd˙azzurriSTUDIES OF FRAGMENTATION ANDCOLOUR RECONNECTION AT LEPP. AZZURRIScuola Normale Superiore, Piazza dei Cavalieri 7, 56126 Pisa, ItalyE-mail: paolo.azzurri@sns.itHadronic events at the Z pole have been investigated in search for Colour Reconnection effectsand QCD coherence. Colour Reconnection effects are searched for in three-jet events and the dataresults are compared to the predictions of different Monte Carlo models. QCD colour coherenceeffects are tested through the multiplicity distributions of hadrons with restricted momenta, andthe LEP1 e+e− data is compared to HERA e+p data under the equivalence assumption of thee+e− hemisphere with the current region of the Breit frame of reference.1. Colour Reconnection effects atthe Z poleColour Reconnection (CR) effects are higher-order and/or non perturbative QCD effectsarising in the hadronisation of multi-partonsystems. There is a specific interest in theseeffects due to related uncertainties when per-forming precision measurements of invariantmasses in multi-jet events, and in particularfor the measurement of the W mass, wherepossible CR effects in the W+W− → qqqqchannel are the main limitation on the over-all mW precision.To assess CR effects it has beenproposed1 to search for CR effects in qqggsystems in hadronic Z decays, benefitinggreatly from larger statistics with respect tothe W pair data. In hadronic Z decays CReffects would enhance the probability to finda colour singlet gluon system isolated fromthe qq state. Such events would show up asthree-jet events with a zero charge gluon jet,associated with a gap of particles around thegluon jet.1.1. OPAL resultsThe OPAL collaboration has selected gluonjets from Z decays in events with two oppo-site tagged quark jets. A total of 439 gluonjets are selected with an expected purity of82% and an average energy of 40 GeV. Study-ing the distribution of charged particles atsmall rapidities (y ≤ 2) around the gluon-jet axis, the expected multiplicity depletiondue to CR effects is not observed, and theAriadne2 CR model was excluded at the levelof five standard deviations3.In a subsequent publication by OPAL6lower energy gluon jets are selected in three-jet Z decays, where two jets are lifetime-tagged as heavy quark jets, and the thirdgluon jet has an average energy of 21 GeV.A gap in rapidity of both charged and neu-tral particles is ensured by requiring an upperbound on the minimum particle rapidity inthe gluon jet (ymin < 1.4) and a lower bondon the maximum difference between the ra-pidity of adjacent particles (∆ymax > 1.3).The selection leads to a sample of 655 gluonjets with an expected purity of 86%. CReffects are expected to enhance the rates ofthose events for which the leading part of thegluon jet is neutral. The enhancements pre-dicted by the Ariadne2 and GAL4 CR mod-els are not observed in the data, and retuningthe parameters of the two models to describeboth the gluon jet data and the inclusive Zdata, leads to a huge degradation of the χ2values of the global fit, therefore excludingthese two CR models. For this analysis, theexcess predicted by the Herwig CR model51October 26, 2006 0:50 WSPC/Trim Size: 10in x 7in for Proceedings qcd˙azzurri2is much less prominent, so that no definiteconclusion could be obtained on this model.1.2. L3 resultsThe L3 collaboration has also publishedstudies of CR effects in three-jet hadronicZ decays7. Events are selected with twolifetime-tagged quark jets and an anti-taggedgluon jet. Observables based on angular sep-arations of particles in the inter-jet regionsare found to be very sensitive to colour sin-glet gluon productions and CR effects. Thedata χ2 confidence level (CL) based on theseobservables are then ∼ 10−8 for the AriadneCR model and ∼ 10−6 for the GAL CR mod-els, so that both these CR models are ex-cluded with their default settings. The sameobservables exclude also the Herwig5 modelwith a ∼ 10−9 CL including CR effects, butalso exclude, with a ∼ 10−8 CL, the samemodel with no CR effects, suggesting thatHerwig can’t simulate with sufficient preci-sion the soft hadronisation effects importantfor CR studies.1.3. DELPHI resultsIn recent preliminary studiesfrom DELPHI8, three-jet events are selectedfrom Z decays, and the quark or gluon jetsare singled out by energy ordering. The lead-ing system of both kind of jets are selectedby demanding a rapidity gap of charged par-ticles for ∆y ≤ 1.5. In this way about 50,000gluon jets and 50,000 quark jets are selected.Studying the total charge of the leading sys-tem, a higher rate of neutral systems is foundin the gluon jets data with respect to thepredictions of string models, while no suchenhancement is found in the quark jets sam-ple. The excess of leading neutral gluon jetsis measured to be roughly 10% with a sig-nificance of three standard deviations, andcould be due to CR effects or colour-octetneutralisation of the gluon field (glueballs).1.4. ALEPH resultsIn a new paper by the ALEPH collaboration9Z decays to three jets are also used to test CRmodels. The main fragmentation parametersof the CR models considered2,4,5 have beenre-tuned with fits to the hadronic Z globalevent shape and charged particle momentumdistributions, and without degrading the fitsχ2 values with respect to the models with noCR.To select three-jet events the Durhamclustering scheme is applied to hadronic Z de-cays with a resolution parameter ycut = 0.02,and only events which cluster into exactlythree-jets are selected. The events are alsorequired to be planar, with no isolated andenergetic photon. The three jets are requiredto be well-contained in the detector accep-tance and separated by inter-jet angles largerthan 40◦. Jets are energy-ordered and thesoftest jet (jet 3) is assigned to the gluon jet,with an expected purity of 70%.ALEPHjet 3   dataJETSETJETSET+GALquark jetbackgroundnc+n(D y)1/N 3jets dN/dn00.020.040.060.080.10.120.140.160 2 4 6 8 10 12 14 16 18ALEPHjet 3  dataJETSETJETSET+GALQ31/N 3jets dN/dQ00.0050.010.0150.020.0250.030.0350.04-4 -2 0 2 4 6Fig. 1. Number of charged and neutral particles inthe 0 < y < 1.5 interval of jet 3, compared to theprediction of a fragmentation model with and with-out GAL CR effects 4 (left). Charge distribution ofjet 3 with a rapidity gap in the 0 < y < 1.5 interval(right).The particle multiplicity within the cen-tral rapidity interval 0 < y < 1.5 of jet 3 isshown in figure 1(left). Focusing on the firstbin with no particles in the rapidity interval(rapidity gap) it can be seen that there isan excess of data events with respect to thepredictions of the fragmentation model withOctober 26, 2006 0:50 WSPC/Trim Size: 10in x 7in for Proceedings qcd˙azzurri3no CR effects, but the data excess is smallerthan the predictions of the same model withCR effects4. The differences of the datayields and the models are enhanced by re-quiring zero total charge for jet 3, as visiblein figure 1(right).ALEPHjet 3JETSETARIADNE JETSET+BE32JETSET+GALJETSET+GAL(0.04)ARIADNE AR1yud-0.3-0.2-0.100.10.20.30.40.50 0.5 1 1.5 2 2.5Fig. 2. Relative model-data differences in the rateof neutral gluon jets as a function of the requiredrapidity gap.The differences δ=(model-data)/data ofthe rate of neutral gluon jets, as a function ofthe required rapidity gap is shown in figure 2for different models. It can be seen that atlarge rapidity gaps the data is in disagree-ment both with models with or without CReffects included. To fit the data rates withthe Ariadne and GAL CR models, it wouldbe necessary to decrease their CR strengthparameters roughly by a factor five, from 0.1to 0.02, in disagreement with the 1/N2c ≃ 1/9prescription for the reconnection probability.Figure 3 shows the δ values for the lead-ing quark jet. In this case the agreement ofdata with models with or without CR effectsis good, except for the Herwig model thatin both cases fails to reproduce the particlerapidity distributions, over a wide rapidityrange, and is therefore not suited for theseALEPHjet 1JETSETARIADNEJETSET+BE32JETSET+GALARIADNE AR1HERWIGHERWIG CRyud-0.3-0.2-0.100.10.20.30.40.50.60 0.5 1 1.5 2 2.5Fig. 3. Relative model-data differences in the rateof neutral quark jets as a function of the requiredrapidity gap.studies.2. QCD Coherence andCorrelations at the Z poleRecent analytical perturbative QCD calcu-lations, in conjunction with Local Parton-Hadron Duality (LPHD), suggest that, whilethe general multiplicity distribution of par-tons in a jet is broader than a Poisson dis-tribution, due to positive correlations in thegluon emissions, for gluons produced withlimited momenta transverse to the primaryparton, the emissions are independent due tocolour coherence, and their multiplicity dis-tribution becomes Poissonian10.To verify this perturbative predictionand to what extent it is affected by the hadro-nisation, it has been proposed to measurefactorial moments Fq and cumulants Kq, de-fined asFq = 〈n(n− 1) . . . (n− q − 1)〉/〈n〉qK2 = F2 − 1 K3 = F3 − 3F2 + 2K4 = F4 − 4F3 − 3F22 + 12F2 − 6where n is the number of particles in somephase-space region, and the angle bracketsOctober 26, 2006 0:50 WSPC/Trim Size: 10in x 7in for Proceedings qcd˙azzurri4denote the average over the observed events.The Kq moments are by construction themeasure of the q-particle correlations.Restricting the phase-space of the multi-plicity measurements cylindrically in trans-verse momentum (pT < pcutT ) the Poissonlimit is expected to be reached as pcutT de-creases, with Fq ≃ 1 and Kq ≃ 0. The samePoisson limit is not expected to be reachedwhen limiting the phase-space spherically inabsolute momentum (p < pcut)10.11.11.2F q q = 2OPALy > 0y > 1.52 jets, y > 0ZEUS11.251.51.752 q = 311.522.5310 -1 1 10q = 41234510 -1 1 10q = 5pT   cut   [GeV]Fig. 4. Factorial moments Fq of charged particleswith limited transverse momenta, as a function ofpcutT, compared to those measured in high thrust twojet events, in a restricted rapidity window, and inHERA e+p data from ZEUS 12.The OPAL collaboration has recentlypublished results on the measurements ofthese proposed correlation variables11. Re-sults for cylindrically cut Fq moments areshown in figure 4. Decreasing pcut the mo-ments decrease to a minimum at the com-mon value pcut ≃ 1 GeV, suggesting thatthe strong hadronisation effects mask the va-lidity of the perturbative calculations at thescale of 1 GeV.Results on cumulants reveal similarstructures and show evidence for the pres-ence of two- and three-particle correlations,while four-particle correlations K4 are com-patible with zero, within errors.Results on Fq moments measured byZEUS12 in e+p data are also shown in fig-ure 4 but do not reveal the same minimumthat could signal the border between pertur-bative and non-perturbative dynamics.To understand the differences, furthercuts have been applied to the LEP e+e− datato mimic the HERA e+p experimental con-ditions, including (i) a cut y > 1.5 to excludethe central rapidity region and (ii) a cut onthe event thrust T > 0.96 to select a puresample of two-jet events.With the additional cuts, also shown infigure 4, the qualitative behaviour of thee+e− and e+p measurements looks more sim-ilar, but the compatibility of the two mea-surements is still problematic. These resultssuggest that for soft particle production, theassumed equivalence of a single event hemi-sphere in e+e− events with the current regionin the e+p Breit frame may be misleading.References1. C. Friberg, G. Gustafson and J. Ha¨kkinenNucl.Phys. B490, 289 (1997).2. L. Lo¨nnblad, Z.Phys. C70, 107 (1996).3. The OPAL Collaboration, Eur.Phys.J. C11,217 (1999).4. J. Rathsman, Phys.Lett. B452, 364 (1999).5. G. Corcella et al., JHEP 0101, 010 (2001).6. The OPAL Collaboration, Eur.Phys.J. C35,293 (2004).7. The L3 Collaboration, Phys.Lett. B581, 19(2004).8. The DELPHI Collaboration, DELPHI 2005-015-CONF 735; M. Siebel, hep-ex/0505080.9. The ALEPH Collaboration, CERN-PH-EP/2006-020, submitted to Eur.Phys.J.C.10. S. Lupia, W. Ochs and J. Wosiek,Nucl.Phys. B540, 405 (1999).11. The OPAL Collaboration, Phys.Lett. B638,30 (2006).12. The ZEUS Collaboration, Phys.Lett. B510,36 (2001).

Studies of Fragmentation and Colour Reconnection at LEP

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