Jet quenching and gluon to hadron fragmentation function in non-equilibrium QCD at RHIC and LHC

Theoretical understanding of the observed jet quenching measurements at RHIC and LHC is challenging in QCD because it requires understanding of parton to hadron fragmentation function in non-equilibrium QCD. In this paper, by using closed-time path integral formalism, we derive the gauge invariant definition of the gluon to hadron fragmentation function in non-equilibrium QCD which is consistent with factorization theorem in non-equilibrium QCD from first principles.     

Pair production of charged MSSM Higgs bosons by gluon fusion

The production of pairs of charged Higgs bosons as predicted by the minimal supersymmetric standard model (MSSM) via the gluon fusion mechanism is investigated. The amplitudes at the leading one-loop order for the parton process are calculated with the complete set of MSSM particles. Numerical results are presented for the cross section of the inclusive hadron process at the LHC. Received: 20 September 1999 / Published online: 27 January 2000     

小横动量半深度非弹性散射的量子色动力学因子化

论证了在小横动量区域内半深度非弹性散射量子色动力学因子化公式. 为完成因子化, 引进了依赖于横动量的部分子分布函数和碎裂函数, 并扣除了软胶子辐射. 在单圈图的情形下, 证明了因子化的成立, 同时论证了在微扰论的任意阶该因子化的正确性.     

Associated production of one particle and a Drell-Yan pair in hadronic collisions

We propose a collinear factorization formula for the associated production of one particle and a Drell-Yan pair in hadronic collisions. It is shown that additional collinear singularities appearing in the next-to-leading order calculations that cannot be factorized into parton and fragmentation functions are systematically renormalized by introducing fracture functions. Next-to-leading order coefficient functions for cross-sections double differential in the fractional energy of the identified hadron and lepton pair invariant mass are presented.     

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.     

Improved calculation of distributions sensitive to the three gluon vertex ine + e −→4-jets using a coherent parton shower simulator

The calculation of hadron distributions ine ⁺ e ^?→4-jets using the 4-parton matrix element diverges unless cuts are imposed on the parton phase space. Experimentally cuts can be applied only on the hadron spectrum and not at the 4-parton level. Test observables for the three gluon vertex relying on jet-jet angular correlations are found to be particularly sensitive to these parton cuts. The contribution from the parton phase space below the cut region is calculated to modified logarithmic approximation accuracy using a Monte Carlo simulator HERWIG and is found to be of order 45%. This modifies the predictions of the tests so that differences between QCD and ‘QED’ are diminished significantly. A tagging method based on the average energy of particles in a jet is found to be best at identifying both gluon jets with a possible 9:1 success to failure ratio and it allows the presence of the three gluon vertex to be verified.     

Multiple parton scattering in nuclei: twist-four nuclear matrix elements and off-forward parton distributions

Multiple parton scatterings inside a large nucleus generally involve higher-twist nuclear parton matrix elements. The gluon bremsstrahlung induced by multiple scattering depends not only on direct parton matrix elements but also on momentum-crossed ones, due to the Landau–Pomeranchuk–Migdal interference effect. We show that both types of twist-four nuclear parton matrix elements can be factorized approximately into the product of twist-two nucleon matrix elements in the limit of extremely large nuclei, A→∞, as assumed in previous studies. Due to the correlative nature of the twist-four matrix elements under consideration, it is actually the off-forward parton distributions that appear naturally in this decomposition, rather than the ordinary diagonal distributions probed in deeply-inelastic scattering. However, we argue that the difference between these two distribution classes is small in certain kinematic regimes. In these regions, the twist-four nuclear parton matrix elements are evaluated numerically and compared to the factorized form for different nuclear sizes within a schematic model of the two-nucleon correlation function. The nuclear size dependence is found to be A^4/3 in the limit of large A, as expected. We find that the factorization is reasonably good when the momentum fraction carried by the gluon field is moderate. The deviation can be more than a factor of 2, however, for small gluon momentum fractions, where the gluon distribution is very large.     

Forward gluon production in hadron–hadron scattering with pomeron loops

We discuss new physical phenomena expected in particle production in hadron–hadron collisions at high energy, as a consequence of pomeron loop effects in the evolution equations for the color glass condensate. We focus on gluon production in asymmetric, ‘dilute–dense’, collisions: a dilute projectile scatters off a dense hadronic target, whose gluon distribution is highly evolved. This situation is representative for particle production in proton–proton collisions at forward rapidities (say, at LHC) and admits a dipole factorization similar to that of deep inelastic scattering (DIS). We show that at sufficiently large forward rapidities, where the pomeron loop effects become important in the evolution of the target wavefunction, gluon production is dominated by ‘black spots’ (saturated gluon configurations) up to very large values of the transverse momentum, well above the average saturation momentum in the target. In this regime, the produced gluon spectrum exhibits diffusive scaling, so like DIS at sufficiently high energy.     

Quarkonium plus prompt-photon associated hadroproduction and nuclear shadowing

Quarkonium hadroproduction in association with a photon at high energies provides a probe of the dynamics of the strong interactions as it is dependent on the nuclear gluon distribution. Therefore, it could be used to constrain the behavior of the nuclear gluon distribution in proton–nucleus and nucleus–nucleus collisions. Such processes are useful to single out the magnitude of the shadowing/antishadowing effects in the nuclear parton densities. In this work we investigate the influence of nuclear effects in the production of J/ψ+γ and ?+γ and estimate the transverse momentum dependence of the nuclear modification factors. The theoretical framework considered in the J/ψ (?) production associated with a direct photon at the hadron collider is the non-relativistic QCD (NRQCD) factorization formalism.     

Fragmentation function in non-equilibrium QCD using closed-time path integral formalism

In this paper we implement the Schwinger–Keldysh closed-time path integral formalism in non-equilibrium QCD in accordance to the definition of the Collins–Soper fragmentation function. We consider a high-p _T parton in QCD medium at initial time τ ₀ with an arbitrary non-equilibrium (non-isotropic) distribution function fragmenting to a hadron. We formulate the parton-to-hadron fragmentation function in non-equilibrium QCD in the light-cone quantization formalism. It may be possible to include final-state interactions with the medium via a modification of the Wilson lines in this definition of the non-equilibrium fragmentation function. This may be relevant to the study of hadron production from a quark–gluon plasma at RHIC and LHC.     

Collective Perspective on Advances in Dyson-Schwinger Equation QCD

We survey contemporary studies of hadrons and strongly interacting quarks using QCD's Dyson-Schwinger equations, addressing the following aspects: confinement and dynamical chiral symmetry breaking; the hadron spectrum; hadron elastic and transition form factors, from small- to large-Q²; parton distribution functions; the physics of hadrons containing one or more heavy quarks; and properties of the quark gluon plasma.     

Factorization scheme and parton distributions in the polarized virtual photon target

We investigate spin-dependent parton distributions in the polarized virtual photon target in perturbative QCD up to the next-to-leading order (NLO). In the case , where is the mass squared of the probe (target) photon, the parton distributions can be predicted completely up to NLO, but they are factorization-scheme dependent. We analyze the parton distributions in six different factorization schemes and discuss their scheme dependence. We study, in particular, the QCD and QED axial anomaly effects on the first moments of the parton distributions to see the interplay between the axial anomalies and factorization schemes. We also show that the factorization-scheme dependence is characterized by the large-x behaviors of the quark distributions in the virtual photon. The gluon distribution is predicted to be the same up to NLO among the six factorization schemes examined. In particular, the first moment of the gluon distribution is found to be factorization-scheme independent up to NLO. Received: 24 January 2001 / Published online: 18 May 2001     

Collective Perspective on Advances in Dyson–Schwinger Equation QCD

We survey contemporary studies of hadrons and strongly interacting quarks using QCD's Dyson-Schwinger equations, addressing the following aspects: confinement and dynamical chiral symmetry breaking; the hadron spectrum; hadron elastic and transition form factors, from small-to large-Q2; parton distribution functions; the physics of hadrons containing one or more heavy quarks; and properties of the quark gluon plasma.     

Single Transverse Spin Asymmetries at Parton Level

Two factorization approaches have been proposed for single transverse spin asymmetries. One is the cofiinear factorization, the other is the transverse-momentum-dependent factorization. They have been previously derived in a formal way by using diagram expansion at hadron level. If the two factorizations hold or can be proven, they should also hold when we replace hadrons with patton states. We examine these two factorizations at patton level with massless partons. It is nontrivial to generate these asymmetries at parton level with massless patrons because the asymmetries require helicity-flip and nonzero absorptive parts in scattering amplitudes. By constructing suitable patton states with massless partons we derive the two factorizations for the asymmetry in Drell-Yan processes. It is found from our results that the collinear factorization derived at parton level is not the same as that derived at hadron level. Our results with massless partons confirm those derived with single massive parton state in our previous works.     

Charm hadroproduction within k T -factorization approach

In the problem of describing heavy-quark production in high-energy hadron collisions, a comparison is made between the theoretical status and numerical predictions of two approaches, the traditional parton model in the leading order (LO) and the k _T-factorization approach. Basic assumptions underlying relevant calculations are discussed. A very simple gluon structure function and a fixed coupling constant are chosen for the calculations in order to highlight distinctions associated with the use of nonidentical matrix elements in these two approaches. It is shown that, in the k _T-factorization approach, formal LO calculations performed with allowance for the Sudakov form factor include many terms usually treated as next-to-leading-order (NLO) contributions of the traditional parton model (or even contributions next to NLO ones, NNLO).     

The singular behavior of one-loop massive QCD amplitudes with one external soft gluon

We calculate the one-loop correction to the soft-gluon current with massive fermions. This current is process independent and controls the singular behavior of one-loop massive QCD amplitudes in the limit when one external gluon becomes soft. The result derived in this work is the last missing process-independent ingredient needed for numerical evaluation of observables with massive fermions at hadron colliders at the next-to-next-to-leading order.     

Restoration of kT factorization for low pT hadron hadroproduction

We discuss the applicability of the k _T factorization theorem to low-p _T hadron production in hadron–hadron collision in a simple toy model, which involves only scalar particles and gluons. It has been shown that the k _T factorization for high-p _T hadron hadroproduction is broken by soft gluons in the Glauber region, which are exchanged among a transverse-momentum-dependent (TMD) parton density and other subprocesses of the collision. We explain that the contour of a loop momentum can be deformed away from the Glauber region at low p _T , so the above residual infrared divergence is factorized by means of the standard eikonal approximation. The k _T factorization is then restored in the sense that a TMD parton density maintains its universality. Because the resultant Glauber factor is independent of hadron flavors, experimental constraints on its behavior are possible. The k _T factorization can also be restored for the transverse single-spin asymmetry in hadron–hadron collision at low p _T in a similar way, with the residual infrared divergence being factorized into the same Glauber factor.     

Gluonic three-jet cross section in hadron collisions at O(α s 4 ) with cone jet definition

The next-to-leading order three-jet cross section in hadron collisions is calculated in the simplified case, when the matrix elements of all QCD subprocesses are approximated by the pure gluon matrix element. The cone jet definition is used. Distribution of the three-jet invariant mass distribution is compared with experimental data obtained at the TEVATRON. The important property of reduced renormalization and factorization scale dependence of the next-to-leading order physical cross sections as compared to the Born cross section is demonstrated.     

Proton Spin Sum Rule from Large Momentum Effective Field Theory

In high energy scattering experiments, the proton spin is understood as the sum of the spin and orbital angular momentum of the quarks and gluons in Feynman’s parton picture. The Jaffe–Manohar form of the proton spin sum rule is justified as physical, and it is shown that the individual terms can be related to the proton matrix elements of certain quasi-obervables through a large momentum effective field theory. The relation is expressed as a factorization formula where the leading contribution to the quasi-observable is factorized into the parton observables and perturbative matching coefficients, and we present the results for the latter at one-loop order in perturbation theory. This will provide us with the basis to extract the proton spin content from the lattice QCD calculations of the quasi-observables.     

Suppression of back-to-back hadron pairs at forward rapidity in d+Au collisions at √s(NN)=200 GeV

Back-to-back hadron pair yields in d+Au and p+p collisions at √s(NN)=200 GeV were measured with the PHENIX detector at the Relativistic Heavy Ion Collider. Rapidity separated hadron pairs were detected with the trigger hadron at pseudorapidity |η|<0.35 and the associated hadron at forward rapidity (deuteron direction, 3.0<η<3.8). Pairs were also detected with both hadrons measured at forward rapidity; in this case, the yield of back-to-back hadron pairs in d+Au collisions with small impact parameters is observed to be suppressed by a factor of 10 relative to p+p collisions. The kinematics of these pairs is expected to probe partons in the Au nucleus with a low fraction x of the nucleon momenta, where the gluon densities rise sharply. The observed suppression as a function of nuclear thickness, p(T), and η points to cold nuclear matter effects arising at high parton densities.