Infrared divergences and non-lightlike eikonal lines in Sudakov processes

We propose a method to analyze infrared contributions to non-inclusive processes in QCD. We use the one-loop Sudakov form factor as a working example. Borrowing techniques from renormalization theory, we construct counterterms for the contributions from the soft and collinear regions, and we relate them to eikonal Wilson lines taken along non-lightlike directions.Comment: Latex, 1 postscript figure. Version 2: presentation improved and typos corrected, results unchange

NLO corrections in MC event generator for angular distribution of Drell-Yan lepton pair production

Using a subtraction method, we derive the formulae suitable for use in Monte-Carlo event generators to give the angular distribution for the gluon-quark induced NLO corrections in Drell-Yan lepton pair production. We also give the corresponding helicity density matrix for W and Z boson production.Comment: 14 pages, 2 figure

Fragmentation Function in Non-Equilibrium QCD Using Closed-Time Path Integral Formalism

In this paper we implement Schwinger-Keldysh closed-time path integral formalism in non-equilibrium QCD to the definition of Collins-Soper fragmentation function. We consider a high p_T parton in QCD medium at initial time t_0 with arbitrary non-equilibrium (non-isotropic) distribution function f(\vec{p}) fragmenting to hadron. We formulate 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 modification of the Wilson lines in this definition of the non-equilibrium fragmentation function. This may be relevant to study hadron production from quark-gluon plasma at RHIC and LHC.Comment: 15 pages latex, Accepted for Publication in European Physical Journal

Generalized parton correlation functions for a spin-1/2 hadron

The fully unintegrated, off-diagonal quark-quark correlator for a spin-1/2 hadron is parameterized in terms of so-called generalized parton correlation functions. Such objects, in particular, can be considered as mother distributions of generalized parton distributions on the one hand and transverse momentum dependent parton distributions on the other. Therefore, our study provides new, model-independent insights into the recently proposed nontrivial relations between generalized and transverse momentum dependent parton distributions. We find that none of these relations can be promoted to a model-independent status. As a by-product we obtain the first complete classification of generalized parton distributions beyond leading twist. The present paper is a natural extension of our previous corresponding analysis for spin-0 hadrons.Comment: 41 pages, 3 figures; v2: added referenc

Restoration of kTk_T factorization for low pTp_T 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.Comment: 12 pages, 2 figures, version to appear in EPJ

Double transverse spin asymmetries in vector boson production

We investigate a helicity non-flip double transverse spin asymmetry in vector boson production in hadron-hadron scattering, which was first considered by Ralston and Soper at the tree level. It does not involve transversity functions and in principle also arises in W-boson production for which we present the expressions. The asymmetry requires observing the transverse momentum of the vector boson, but it is not suppressed by explicit inverse powers of a large energy scale. However, as we will show, inclusion of Sudakov factors causes suppression of the asymmetry, which increases with energy. Moreover, the asymmetry is shown to be approximately proportional to x_1 g_1(x_1) x_2 \bar g_1(x_2), which gives rise to additional suppression at small values of the light cone momentum fractions. This implies that it is negligible for Z or W production and is mainly of interest for \gamma^* at low energies. We also compare the asymmetry with other types of double transverse spin asymmetries and discuss how to disentangle them.Comment: 12 pages, Revtex, 2 Postscript figures, uses aps.sty, epsf.sty; figures replaced, a few minor other correction

Drell-Yan production at small q_T, transverse parton distributions and the collinear anomaly

Using methods from effective field theory, an exact all-order expression for the Drell-Yan cross section at small transverse momentum is derived directly in q_T space, in which all large logarithms are resummed. The anomalous dimensions and matching coefficients necessary for resummation at NNLL order are given explicitly. The precise relation between our result and the Collins-Soper-Sterman formula is discussed, and as a by-product the previously unknown three-loop coefficient A^(3) is obtained. The naive factorization of the cross section at small transverse momentum is broken by a collinear anomaly, which prevents a process-independent definition of x_T-dependent parton distribution functions. A factorization theorem is derived for the product of two such functions, in which the dependence on the hard momentum transfer is separated out. The remainder factors into a product of two functions of longitudinal momentum variables and x_T^2, whose renormalization-group evolution is derived and solved in closed form. The matching of these functions at small x_T onto standard parton distributions is calculated at O(alpha_s), while their anomalous dimensions are known to three loops.Comment: 32 pages, 2 figures; version to appear in Eur. Phys. J.

Next-to-leading order QCD calculations with parton showers II: soft singularities

Programs that calculate observables in quantum chromodynamics at next-to-leading order typically generate events that consist of partons rather than hadrons -- and just a few partons at that. These programs would be much more useful if the few partons were turned into parton showers, which could be given to one of the Monte Carlo event generators to produce hadron showers. In a previous paper, we have seen how to generate parton showers related to the final state collinear singularities of the perturbative calculation for the example of e+ + e- --> 3 jets. This paper discusses the treatment of the soft singularities.Comment: 26 pages with 5 figures. This version is close to the version to be publishe

Renormalization of a class of non-renormalizable theories

Certain power-counting non-renormalizable theories, including the most general self-interacting scalar fields in four and three dimensions and fermions in two dimensions, have a simplified renormalization structure. For example, in four-dimensional scalar theories, 2n derivatives of the fields, n>1, do not appear before the nth loop. A new kind of expansion can be defined to treat functions of the fields (but not of their derivatives) non-perturbatively. I study the conditions under which these theories can be consistently renormalized with a reduced, eventually finite, set of independent couplings. I find that in common models the number of couplings sporadically grows together with the order of the expansion, but the growth is slow and a reasonably small number of couplings is sufficient to make predictions up to very high orders. Various examples are solved explicitly at one and two loops.Comment: 38 pages, 1 figure; v2: more explanatory comments and references; appeared in JHE

Identified hadron production at high transverse momenta in p+p collisions at sqrt(NN) = 200 GeV in STAR

We report the transverse momentum (pT) distributions for identified charged pions, protons and anti-protons using events triggered by high deposit energy in the Barrel Electro-Magnetic Calorimeter (BEMC) from p + p collisions at psNN = 200 GeV. The spectra are measured around mid-rapidity (|y|<0.5) over the range of 3<pT<15 GeV/c with particle identification (PID) by the relativistic ionization energy loss (rdE/dx) in the Time Projection Chamber (TPC) in the Solenoidal Tracker at RHIC (STAR). The charged pion, proton and anti-proton spectra at high pT are compared with published results from minimum bias triggered events and the Next-Leading-Order perturbative quantum chromodynamic (NLO pQCD) calculations (DSS, KKP and AKK 2008). In addition, we present the particle ratios of pi-/pi+, pbar/p, p/pi+ and pbar/pi- in p + p collisions.Comment: 4 pages, 4 figures, Hot Quark 2008 proceedin