Energy evolution for the Sivers asymmetries in hard processes

We study the transverse momentum dependent (TMD) parton distributions in the newly proposed quasi-parton distribution function framework in Euclidean space. In this framework, the parton distributions can be extracted from lattice observables in a systematic expansion of 1/P z where P z is the hadron momentum. A soft factor subtraction is found to be essential to make the TMDs calculable on lattice. We show that the quasi-TMDs with the associated soft factor subtraction can be applied in hard QCD scattering processes such as Drell-Yan lepton pair production in hadronic collisions. This allows future lattice calculations to provide information on the non-perturbative inputs and energy evolutions for the TMDs. Extension to the generalized parton distributions and quantum phase space Wigner distributions will lead to a complete nucleon tomography on lattice. 1 1. Introduction. Transverse momentum dependent (TMD) parton distributions have attracted great attentions in hadron physics research [1]. They provide a unique aspect of the partonic structure of nucleon, by extending the conventional description of Feynman parton distribution to the transverse dimension. Experimental investigations of the TMDs in the last few years have stimulated great theoretical developments, such as the QCD factorization, the energy (scale) evolution, and the universality of the TMDs [2-6]. These developments have laid solid foundation in phenomenological applications in hard QCD processes and hence allow us to extract the TMDs from the experiments.In addition to the experimental accesses, the lattice QCD shall also be able to compute the TMDs. Early attempts to formulate the TMDs on lattice have been performed in Refs. [7] following the definitions of . These results have generated great interests in the hadron physics community. In order to obtain the TMDs applicable in phenomenology, we have to include the soft factor subtraction (see discussions below), which could not be included in the set-up of Refs. [7]. In this paper, we investigate the TMD formalism based on the recent proposal [8] to calculate the parton distributions (PDFs) in Euclidean space directly, in the large momentum effective theory approach (LaMET) [9]. This effective theory allows parton physics to be calculated in lattice QCD at large hadron momentum P z in a systematic approximation. In particular, the PDF observables are evaluated as the matrix elements of the space-like correlators between the nucleon states which has a finite momentum P z . Final results are obtained by a systematic expansion of 1/P z . The PDFs extracted in this way are also referred as qusi-PDFs [8].To compute the parton distributions on lattice is conceptually important in the applications of QCD in hadron physics [7][8][9][10][11][12]. Progresses have been made concerning the technique issues associated with the applications of the quasi-PDFs, mainly on the integrated parton distributions [10][11][12]. In the current paper, we will apply the idea of Ref.[8] to the TMD case and, in p...

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“…(20) of Ref. [14]. With soft factor subtraction at the TMD level, the expression for the quark distribution is much simpler in current scheme.…”

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confidence: 99%

Soft factor subtraction and transverse momentum dependent parton distributions on the lattice

et al. 2015

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“…That the extrapolation is actually wrong is indicated phenomenologically by the results of Sun and Yuan [4]. At large-b T , the fitted Gaussian for the TMD pdfs combined with evolution governed by a quadratic g K gives a Q-dependent Gaussian behavior for the integrandW :…”

Section: Pos(dis2015)189mentioning

confidence: 97%

“…The overall motivation is to understand the evolution of transverse-momentum-dependent (TMD) parton densities (etc) especially at the relatively low values of Q that have considerable current interest, as can be seen from many talks in this session on spin physics. We are particularly concerned with the non-perturbative part of the evolution, since there appear to be inconsistencies between the evolution found in fits [2,3] to higher Q Drell-Yan data, and the slower evolution preferred (e.g., [4,5]) by more recent data at lower Q. When TMD functions are Fourier transformed into a space of transverse coordinates b T , non-perturbative contributions are at large b T .…”

Section: Introductionmentioning

confidence: 99%

TMD factorization and evolution at large $b_T$

Collins¹,

Rogers²

2016

Proceedings of XXIII International Workshop on Deep-Inelastic Scattering — PoS(DIS2015)

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In using transverse-momentum-dependent (TMD) parton densities and fragmentation functions, important non-perturbative information is at large transverse position b T . This concerns both the TMD functions and their evolution. Fits to high energy data tend to predict too rapid evolution when extrapolated to low energies where larger values of b T dominate. I summarize a new analysis of the issues. It results in a proposal for much weaker b T dependence at large b T for the evolution kernel, while preserving the accuracy of the existing fits. The results are particularly important for using transverse-spin-dependent functions like the Sivers function.

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“…In this work, we apply CSS formalism [8,9] to calculate the energy Q 2 evolution effect. The detail about this calculation has been stated in [10,11,12,13,14,15,16].…”

Section: Energy Evolutionmentioning

confidence: 99%