Abstract
This work presents a lattice quantum chromodynamics (QCD) calculation of the nonperturbative Collins-Soper kernel, which describes the rapidity evolution of quark transverse-momentum-dependent parton distribution functions. The kernel is extracted at transverse momentum scales in the range 400 MeV $< q_T < 1.7$ GeV in a calculation with dynamical fermions and quark masses corresponding to a larger-than-physical pion mass, $m_\pi=538(1)$ MeV. It is found that different approaches to extract the Collins-Soper kernel from the same underlying lattice QCD matrix elements yield significantly different results and uncertainty estimates, revealing that power corrections, such as those associated with higher-twist effects, and perturbative matching between quasi and light-cone beam functions, cannot be neglected.
Highlights
Transverse-momentum-dependent parton distribution functions (TMDPDFs) describe the intrinsic transverse momentum qT of the partonic constituents of hadrons [1,2,3]
Significant efforts are underway to improve constraints on TMDPDFs both from current and planned experiments [8,9,10,11,12] and through theory calculations in the framework of lattice quantum chromodynamics (QCD) [13,14,15,16,17,18,19,20,21,22] using approaches such as large-momentum effective theory (LaMET) [23,24,25] or the Lorentz-invariant method based on ratios of TMDPDFs [13]
The quark Collins-Soper kernel γqζ ðμ; bTÞ can be computed in lattice QCD from a ratio of nonsinglet quasiTMDPDFs f TnsMD at different hadron momenta Pzi ≫ ΛQCD [26,27,32]: γqζ ðμ; bT
Summary
Transverse-momentum-dependent parton distribution functions (TMDPDFs) describe the intrinsic transverse momentum qT of the partonic constituents of hadrons [1,2,3]. TMDPDFs at different hadron momenta, quantities which are both calculable in lattice QCD and which can be related to TMDPDFs [27,29,30,31,32] This provides a pathway to firstprinciples QCD calculations of the kernel in the nonperturbative region, which will provide valuable complementary information to constraints from global analyses of experimental data. This prospect has motivated a series of proofof-principle lattice QCD investigations of the Collins-Soper kernel both directly [18,19,20,21,22] through the approach of Refs.
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