Particle multiplicity of unbiased gluon jets from \mathrme^+\mathrme^- three-jet events

The charged particle multiplicities of two- and three-jet events from the reaction ee Z are measured for Z decays to light quark (uds) flavors. Using recent theoretical expressions to account for biases from event selection, results corresponding to unbiased gluon jets are extracted over a range of jet energies from about 11 to 30 GeV. We find consistency between these results and direct measurements of unbiased gluon jet multiplicity from and Z decays. The unbiased gluon jet data including the direct measurements are compared to corresponding results for quark jets. We perform fits based on analytic expressions for particle multiplicity in jets to determine the ratio of multiplicities between gluon and quark jets as a function of energy. We also determine the ratio of slopes, , and of curvatures, , where y specifies the energy scale. At 30 GeV, we find and , where the uncertainties are the statistical and systematic terms added in quadrature. These results are in general agreement with theoretical predictions. In addition, we use the measurements of the energy dependence of and to determine an effective value of the ratio of QCD color factors, . Our result, (total), is consistent with the QCD value of 2.25. Received: 25 October 2001 / Revised version: 20 January 2002 / Published online: 5 April 2002     

胶子喷注和夸克喷注性质的蒙特卡洛研究

用蒙特卡洛方法研究了91.2GeV e⁺e^－碰撞产生的3喷注事件.用3个喷注之间的夹角来标识各个喷注,分别计算了3个喷注的能量及能量分布,并在相同能量下计算了3个喷注的多重数,横动量及其分布.通过与能量相同的2喷注事件中单夸克喷注的上述性质的比较,得到了从3喷注事件中挑选胶子喷注和夸克喷注的一种简便方法.这样挑选出来的胶子和夸克喷注在性质上与QCD的理论预言一致,并且胶子和夸克喷注的平均多重数比值的计算结果与实验观测值符合     

Gluon and quark jets in a recursive model motivated by quantum chromodynamics

We compute observable quantities like the multiplicity and momentum distributions of hadrons in gluon and quark jets in the framework of a recursive cascade model, which is strongly motivated by the fundamental interactions of QCD. Fragmentation occurs via 3 types of breakups: quark → meson+ quark, gluon→meson+gluon, gluon→quark+ antiquark. In our model gluon jets are softer than quark jets. The ratio of gluon jet to quark jet multiplicity is found to be 2 asymptotically, but much less at lower energies. Some phenomenological consequences for λ decay are discussed.     

Energy dependence of the differences between the quark and gluon jet fragmentation

Three jet events arising from decays of the Z boson, collected by the DELPHI detector, were used to measure differences in quark and gluon fragmentation. Gluon jets were anti-tagged by identifying b quark jets. Unbiased quark jets came from events with two jets plus one photon. Quark and gluon jet properties in different energy ranges were compared for the first time within the same detector. Quark and gluon jets of nearly the same energy in symmetric three jet event topologies were also compared. Using three independent methods, the average value of the ratio of the mean charged multiplicities of gluon and quark jets is $$< r >=1.241 pm 0.015 (stat.)pm 0.025 (syst.).$$ Gluon jets are broader and produce fragments with a softer energy spectrum than quark jets of equivalent energy. The string effect has been observed in fully symmetric three jet events. The measured ratio R_γ of the charged particle flow in the qq? inter-jet region of the qq?g and qq?γ samples agrees with the perturbative QCD expectation. The dependence of the mean charged multiplicity on the hadronic center-of-mass energy was analysed in photon plus n-jet events. The value for α_s(M _Z) determined from these data using a QCD prediction with corrections at leading and next-to-leading order is $$←pha_s(M_Z)=0.116pm 0.003 (stat.)pm 03009 (syst.).$$     

Investigation of the splitting of quark and gluon jets

The splitting processes in identified quark and gluon jets are investigated using longitudinal and transverse observables. The jets are selected from symmetric three-jet events measured in Z decays with the Delphi detector in 1991-1994. Gluon jets are identified using heavy quark anti-tagging. Scaling violations in identified gluon jets are observed for the first time. The scale energy dependence of the gluon fragmentation function is found to be about two times larger than for the corresponding quark jets, consistent with the QCD expectation . The primary splitting of gluons and quarks into subjets agrees with fragmentation models and, for specific regions of the jet resolution , with NLLA calculations. The maximum of the ratio of the primary subjet splittings in quark and gluon jets is . Due to non-perturbative effects, the data are below the expectation at small . The transition from the perturbative to the non-perturbative domain appears at smaller for quark jets than for gluon jets. Combined with the observed behaviour of the higher rank splittings, this explains the relatively small multiplicity ratio between gluon and quark jets. Received: 18 February 1998 / Published online: 24 April 1998     

夸克喷注与胶子喷注角分布特性的研究

用蒙特卡洛模拟Jetset 7.4产生质心能量为91.2GeV的正负电子对撞事件. 在引入喷注的圆锥角后, 对不同味的夸克喷注和由不同味夸克发射的胶子产生的喷注的角分布特性进行了仔细研究. 结果发现, 在相同的能量下, 胶子喷注的角分布范围比夸克喷注的角分布范围要明显宽一些. 在带电粒子数、横动量相同的条件下, 胶子喷注的平均圆锥角比夸克喷注的平均圆锥角大很多. 喷注的平均圆锥角随带电多重数以及喷注的横动量的分布都呈线性正关联. 由不同味的夸克发射的胶子产生的喷注的圆锥角分布特性相同；而不同味的夸克喷注的圆锥角分布存在明显的差异.     

A study of top quark production at HERA using parton shower simulation of DIS events

A study of the hadronic properties of top quark events at HERA is made in the hope that some characteristics of such events may emerge that distinguish them from light flavour QCD events. Electronproton collisions are simulated using a parton shower Monte Carlo event generator which includes both initial and final gluon radiation and also incorporates certain gluon interference effects. It is found that applying a multiplicity cut of 35 together with considering only charged current events gives a top to back-ground ratio of about 1 and a total of 40 top events at an integrated luminosity of 500 pb^?1 for a top quark mass of 60 GeV. Unfortunately no clear peak in the mass distribution can be obtained as the background and top quark peaks coincide after application of the multiplicity cut. If the top quark mass is 100 GeV there will be only about 6 top quark events under these conditions.     

Multiplicities of \pi^0, \eta,\rm K^0 and of charged particles in quark and gluon jets

We compared the multiplicities of and of charged particles in quark and gluon jets in 3-jet events, as measured by the OPAL experiment at LEP. The comparisons were performed for distributions unfolded to 100% pure quark and gluon jets, at an effective scale which took into account topological dependences of the 3-jet environment. The ratio of particle multiplicity in gluon jets to that in quark jets as a function of for or was found to be independent of the particle species. This is consistent with the QCD prediction that the observed enhancement in the mean particle rate in gluon jets with respect to quark jets should be independent of particle species. In contrast to some theoretical predictions and previous observations, we observed no evidence for an enhancement of meson production in gluon jets with respect to quark jets, beyond that observed for charged particles. We measured the ratio of the slope of the average charged particle multiplicity in gluon jets to that in quark jets, C, and we compared it to a next-to-next-to-next-to leading order calculation. Our result, is about one standard deviation higher than the perturbative prediction. Received: 31 March 2000 / Published online: 25 September 2000     

A comparison of b and uds quark jets to gluon jets

Symmetric three-jet events are selected from hadronic Z⁰ decays such that the two lower energy jets are each produced at an angle of about 150° with respect to the highest energy jet. In some cases, a displaced secondary vertex is reconstructed in one of the two lower energy jets, which permits the other lower energy jet to be identified as a gluon jet through anti-tagging. In other cases, the highest energy jet is tagged as a b jet or as a light quark (uds) jet using secondary vertex or track impact parameter and momentum information. Comparing the two lower energy jets of the events with a tag in the highest energy jet to the anti-tagged gluon jets yields a direct comparison of b, uds and gluon jets, which are produced with the same energy of about 24 GeV and under the same conditions. We observe b jets and gluon jets to have similar properties as measured by the angular distribution of particle energy around the jet directions and by the fragmentation functions. In contrast, gluon jets are found to be significantly broader and to have a markedly softer fragmentation function than uds jets. For the k _⊥ jet finder with y _cut=0.02, we find $${«ngle n^{? ch.}»ngle {? gluon}?er «ngle n^{? ch.}»ngle {? b} {? quark}}=1.089pm 0.024 ({? stat.})pm0.024 ({? syst.})$$ $${«ngle n^{? ch.}»ngle {? gluon}?er «ngle n^{? ch.}»ngle {? uds} {? quark}}=1.390pm 0.038 ({? stat.})pm0.032 ({? syst.})$$ as the ratios of the mean charged particle multiplicity in the gluon jets compared to the b and uds jets. Results are also reported using the cone jet finder.     

Measurements of the structure of quark and gluon jets in hadronic Z decays

An experimental investigation of the structure of identified quark and gluon jets is presented. Observables related to both the global and internal structure of jets are measured; this allows for tests of QCD over a wide range of transverse momentum scales. The observables include distributions of jet-shape variables, the mean and standard deviation of the subjet multiplicity distribution and the fragmentation function for charged particles. The data are compared with predictions of perturbative QCD as well as QCD-based Monte Carlo models. In certain kinematic regions the measurements are sensitive mainly to perturbatively calculable effects, allowing for a test of QCD. The comparisons are also extended into regions where nonperturbative effects become large, and in this way the transition from hard to soft QCD is investigated. It is found that by including leading and next-to-leading logarithmic contributions in the QCD predictions, the agreement with the data can be extended to lower transverse momentum scales, especially for gluon jets. Received: 2 February 1998 / Published online: August 9, 2000     

Test of colour reconnection models using three-jet events in hadronic Z decays

Hadronic Z decays into three jets are used to test QCD models of colour reconnection (CR). A sensitive quantity is the rate of gluon jets with a gap in the particle rapidity distribution and zero jet charge. Gluon jets are identified by either energy-ordering or by tagging two b-jets. The rates predicted by two string-based tunable CR models, one implemented in JETSET (the GAL model), the other in ARIADNE, are too high and disfavoured by the data, whereas the rates from the corresponding non-CR standard versions of these generators are too low. The data can be described by the GAL model assuming a small value for the R₀ parameter in the range 0.01-0.02.     

A comparison of b and uds quark jets to gluon jets

Symmetric three-jet events are selected from hadronic Z⁰ decays such that the two lower energy jets are each produced at an angle of about 150° with respect to the highest energy jet. In some cases, a displaced secondary vertex is reconstructed in one of the two lower energy jets, which permits the other lower energy jet to be identified as a gluon jet through anti-tagging. In other cases, the highest energy jet is tagged as a b jet or as a light quark (uds) jet using secondary vertex or track impact parameter and momentum information. Comparing the two lower energy jets of the events with a tag in the highest energy jet to the anti-tagged gluon jets yields a direct comparison of b, uds and gluon jets, which are produced with the same energy of about 24 GeV and under the same conditions. We observe b jets and gluon jets to have similar properties as measured by the angular distribution of particle energy around the jet directions and by the fragmentation functions. In contrast, gluon jets are found to be significantly broader and to have a markedly softer fragmentation function than uds jets. For thek _⊥ jet finder withy _cut=0.02, we find as the ratios of the mean charged particle multiplicity in the gluon jets compared to the b and uds jets. Results are also reported using the cone jet finder.     

The influence of fragmentation models in the production of hadron jets in electron–positron annihilation

The analysis of electron–positron annihilations to hadrons at high energies shows that apart from two-jet events, there are also signs of three-jet events which are interpreted according to the QCD, as a gluon radiated by a quark. In this paper, we investigate the fragmentation of quarks and gluons to hadron jets. We show that gluon jets have a higher multiplicity compared to quark jets of the same energy. Furthermore, inclusion of different flavours in the distributions shows that quark jets are flavour-dependent, but gluon jets are not. The differences between quark and gluon jets also manifest themselves in the fragmentation functions. We observe that the fragmentation for gluon jet is softer than that for quark jet, because the radiation of soft gluons is larger for gluon jets and that gluon cannot be present as a valence parton inside a produced hadron. We provide possible explanations for these features in this paper.     

Measurement of charged-particle multiplicities in gluon and quark jets in pp collisions at square root of s = 1.8 TeV

We report the first largely model independent measurement of charged particle multiplicities in quark and gluon jets, Nq and Ng, produced at the Fermilab Tevatron in pp collisions with a center-of-mass energy of 1.8 TeV and recorded by the Collider Detector at Fermilab. The measurements are made for jets with average energies of 41 and 53 GeV by counting charged particle tracks in cones with opening angles of theta(c) = 0.28, 0.36, and 0.47 rad around the jet axis. The corresponding jet hardness Q = Ejet theta c varies in the range from 12 to 25 GeV. At Q = 19.2 GeV, the ratio of multiplicities r = Ng/Nq is found to be 1.64+/-0.17, where statistical and systematic uncertainties are added in quadrature. The results are in agreement with resummed perturbative QCD calculations.     

Charged particle multiplicity distributions for fixed number of jets inZ0 hadronic decays

The multiplicity distributions of charged particles in full phase space and in restricted rapidity intervals for events with a fixed number of jets measured by the DELPHI detector are presented. The data are well reproduced by the Lund Parton Shower model and can also be well described by fitted negative binomial distributions. The properties of these distributions in terms of the clan model are discussed. In symmetric 3-jet events the candidate gluon jet is found not to be significantly different in average multiplicity than the mean of the other two jets, thus supporting previous results of the HRS and OPAL experiments. Similar results hold for events generated according to the LUND PS and to the HERWIG models, when the jets are defined by the JADE jet finding algorithm. The method seems to be insensitive for measuring the color charge ratio between gluons and quarks.     

Collimation of average multiplicity in QCD jets

The collimation of average multiplicity inside quark and gluon jets is investigated in perturbative QCD in the modified leading logarithmic approximation (MLLA). The role of higher order corrections accounting for energy conservation and the running of the coupling constant leads to smaller multiplicity collimation as compared to leading logarithmic approximation (LLA) results. The collimation of jets produced in heavy-ion collisions has also been explored by using medium-modified splitting functions enhanced in the infrared sector. As compared to elementary collisions, the angular distribution of the jet multiplicity is found to broaden in QCD media at all energy scales.     

Jet calculus: A simple algorithm for resolving QCD jets

It is argued that, in the leading logarithm approximation (LLA) of asymptotically free quantum chromodynamics (QCD), a simple algorithm (jet calculus) can be justified for computing a large number of quantities related to the longitudinal and transverse structure of quark and gluon jets.We formulate the rules of jet calculus in two variables, x and y which are related to longitudinal (energy) and transverse momentum respectively. Throughout the paper, quark and gluon jets are contrasted. After reviewing what has been done on longitudinal spectra, we turn to the transverse structure of jets down to relative transverse momenta of the order of a few GeV (independently of the total energy). The relation of our work to that of Dokshitzer, D'Yakonov and Troyan is elucidated. We also study jets generated by (almost) real photons and compare both with standard “final” parton jets.We also discuss calorimeter measured quantities, compare our results with those of other authors and propose a new and easy way for measuring QCD-predictable anomalous dimensions.We finally give a Lagrangian formulation of jet calculus, as a non-local theory in 1 + 1 dimensions to be solved in the tree approximation.     

Opposite-side angular correlation of high-pT particles as a probe of gluons

Opposite-side angular distributions of high-p_T particles in the jet trigger experiments are studied in the lowest-order QCD. Gluon jets play a crucial role in understanding correlations between two high-p_T jets. The angular distribution of the positive-to-negative particle ratio and that of charmed particles can be good probes of the gluon density inside a nucleon.     

γ Radiative Decays to Light Quark Jets and Color Octet Mechanism

We study radiative decays of T to light quark jets in nonrelativistic QCD by taking both the color singlet and color octet b^-b operators into consideration. The cut for quark jet energy and cut for the angle between two quark jets are introduced. The sensitivity to the soft and collinear singularities in the loop integrals are greatly reduced by these cuts. With the jet energy cut of about 1 GeV, and the jet angle cut of about 36°, the branching ratio for γ→ rq^- is found to be 8.2 × 10^-4 from color singlet contributions. The color octet contributions could be much larger than that of color singlet, depending on the estimate of the color octet matrix elements. This process may provide a new test for the color octet mechanism in nonrelativistic QCD.