Jian-Ping Ma

Transverse-momentum-dependent gluon distributions and semi-inclusive processes at hadron colliders

We study transverse-momentum-dependent (TMD) gluon distributions and related factorization theorems for gluon-initiated semi-inclusive processes at hadron colliders. Gauge-invariant TMD gluon distributions are introduced, and their relations to the integrated (Feynman) parton distributions are established when the transverse momentum is large. Through explicit calculations, soft-collinear factorization is verified at one-loop order for scalar particle ( e. g. Higgs) production. Summation over large double logarithms is performed through solving Collins-Soper equation. We reproduce the known result in the limit that the transverse momentum of the scalar is large.

Collins-Soper equation for the energy evolution of transverse-momentum and spin dependent parton distributions

The hadron-energy evolution (Collins and Soper) equation for all the leading-twist transverse-momentum and spin dependent parton distributions is derived in the impact parameter space. Based on this equation, we present a resummation formulas for the spin dependent structure functions of the semi-inclusive deep-inelastic scattering.

Corrections for two photon decays of χc0 and χc2 and color octet contributions

Using the fact that the c-quark inside a charmonium moves with a small velocity v in the charmonium rest-frame, one can employ an expansion in v to study decays of charmonia and results at the leading order for chi(c0,2) --> gammagamma exist in the literature. We study corrections at the next-to-leading order in the framework of nonrelativistic QCD(NRQCD) factorization. The study presented here is different than previous approaches where chi(c0,2) is taken as a bound-state of a c (c) over bar pair and a nonrelativistic wave-function is used for the pair. We find that the corrections are consist not only of relativistic corrections, but also of corrections from Fock state components of chi(c0,2) in which the c (c) over bar pair is in a color-octet state. For chi(c,2) there is also a contribution from a Fock state component in which the pair is in a F-wave state. We determine the factorization formula for decay widths in the form of NRQCD matrix elements representing nonperturbative effects related to chic(0,2), and calculate the perturbative coefficients at tree-level. Because the NRQCD matrix elements are unknown, a detailed prediction for the decay chi(c0,2) --> gammagamma cannot be made, but the effect of these corrections can be determined at certain level. Estimations show that the effect is significant and cannot be neglected

Transverse momentum dependent factorization for quarkonium production at low transverse momentum

Quarkonium production in hadron collisions at low transverse momentum q(perpendicular to) << M with M as the quarkonium mass can be used for probing transverse momentum dependent (TMD) gluon distributions. For this purpose, one needs to establish the TMD factorization for the process. We examine the factorization at the one-loop level for the production of eta(c) or eta(b). The perturbative coefficient in the factorization is determined at one-loop accuracy. Comparing the factorization derived at tree level and that beyond the tree level, a soft factor is, in general, needed to completely cancel soft divergences. We have also discussed possible complications of TMD factorization of p-wave quarkonium production.

On unique predictions for single spin azimuthal asymmetry

Abstract.Theoretically there are two approaches to predict single spin azimuthal asymmetries. One is to take transverse momenta of the partons into account by using transverse momentum dependent parton distributions, while another is to take asymmetries as twist-3 effects. The non-perturbative effects in these approaches are parameterized with different matrix elements, and predictions can be different. Recently, gauge invariant definitions of transverse momentum dependent parton distributions were derived. With these definitions it can be shown that there are relations between non-perturbative matrix elements in these two approaches. These relations may enable us to unify two approaches and to have unique predictions for single spin azimuthal asymmetries. In this letter we derive these relations by using time-reversal symmetry and show that even with these relations the single spin azimuthal asymmetry in a Drell-Yan process is predicted differently in different approaches.

Partonic state and single transverse spin asymmetry in Drell-Yan process

Single transverse-spin asymmetries have been studied intensively both in experiment and theory. Theoretically, two factorization approaches have been proposed. One is by using transverse-momentum-dependent factorization and the asymmetry comes from the so called Sivers function. Another is by using collinear factorization where the non- perturbative effect is parameterized by a twist-3 hadronic matrix element. However, the factorized formulas for the asymmetries in the two approaches are derived at hadron level formally by diagram expansion, where one works with various part on density matrices of hadrons. If the two factorizations hold, they should also hold at parton level. We examine this for Drell-Yan processes by replacing hadrons with partons. By calculating the asymmetry, Sivers function and the twist-3 matrix element at nontrivial leading order of alpha(s), we find that we can reproduce the result of the transverse-momentum-dependent factorization. But we can only verify the result of the collinear factorization partly. Two formally derived relations between Sivers function and the twist-3 matrix element are also examined with negative results.

Factorization approach for inclusive production of doubly heavy baryon

We study inclusive production of doubly heavy baryon at a e(+)e(-) collider and at hadron colliders through fragmentation. We study the production by factorizing nonpertubative and perturbative effects. In our approach the production can be thought as a two-step process: a pair of heavy quarks can be produced perturbatively and then the pair is transformed into the baryon. The transformation is nonperturbative. Since a heavy quark moves with a small velocity in the baryon in its rest frame, we can use NRQCD to describe the transformation and perform a systematic expansion in the small velocity. At the leading order we find that the baryon can be formed from two states of the heavy-quark pair, one state is with the pair in S-3(1) state and in color 3, another is with the pair in S-1(0) state and in color 6. Two matrix elements are defined for the transformation from the two states, their perturbative coefficients in the contribution to the cross section at a e+e- collider and to the function of heavy quark fragmentation are calculated. Our approach is different than previous approaches where only the pair in S-3(1) state and in color is taken into account. Numerical results for e(+)e(-) colliders at the two B-factories and for hadronic colliders LHC and Tevatron are given

Scale dependence of twist-3 quark-gluon operators for single spin asymmetries

We derive the scale dependence of twist-3 quark-gluon operators, or ETQS matrix elements, at one-loop. These operators are used to factorize transverse single spin asymmetries, which are studied intensively both in experiment and theory. The scale dependence of two special cases are particularly interesting. One is of soft-gluon-pole matrix elements, another is of soft-quark-pole matrix elements. From our results the evolutions in the two cases can be obtained. A comparison with existing results of soft-gluon-pole matrix elements is made. (c) 2012 Elsevier B.V. All rights reserved.

Soft-gluon-pole contribution in single transverse-spin asymmetries of Drell-Yan processes

We use multi-parton states to examine the leading order collinear factorization of single transverse-spin asymmetries in Drell-Yan processes. Twist-3 operators are involved in the factorization. We find that the so-called soft-gluon-pole contribution in the factorization must exist in order to make the factorization correct. This contribution comes from the corresponding cross-section at one-loop, while the hard-pole contribution in the factorization comes from the cross-section at tree-level. Although the two contributions come from results at different orders, their perturbative coefficient functions in the factorization are at the same order. This is in contrast to factorizations only involving twist-2 operators. The soft-gluon-pole contribution found in this work is in agreement with that derived in a different way. For the hard-pole contributions we find an extra contribution from an extra part on process contributing to the asymmetries. We also solve apart of discrepancy in evolutions of the twist-3 operator. The method presented here for analyzing the factorization can be generalized to other processes and can be easily used for studying factorizations at higher orders, because the involved calculations are of standard scattering amplitudes.

Classification and asymptotic scaling of the light-cone wave-function amplitudes of hadrons

Abstract.We classify the hadron light-cone wave-function amplitudes in terms of parton helicity, orbital angular momentum, and quark-flavor and color symmetries. We show in detail how this is done for the pion,