Single Transverse-Spin Asymmetry and Sivers Function in Large Momentum Effective Theory

TL;DR

This paper develops a non-perturbative approach using large momentum effective theory to calculate single transverse-spin asymmetries via the Sivers function, enabling direct lattice QCD computations.

Contribution

It formulates a method to compute the Sivers function and spin asymmetry non-perturbatively using LaMET, with verification at one-loop order and small transverse distance limit.

Findings

Derived a formula relating quasi distributions to the Sivers function.

Verified the approach at one-loop order in the small transverse distance limit.

Showed cancellation of soft functions and matching kernels in the ratio.

Abstract

We apply recent developments in large momentum effective theory (LaMET) to formulate a non-perturbative calculation of the single-transverse spin asymmetry in terms of the quasi transverse-momentum-dependent quark distribution functions from the so-called Sivers mechanism. When the spin asymmetry is defined as the ratio of the quark Sivers function over the spin averaged distribution, it can be directly calculated in terms of the relevant quasi distributions with the soft functions and perturbative matching kernels cancelling out. Apart from the general formula presented, we have verified the result in the small transverse distance limit at one-loop order, which reduces to a collinear expansion at twist-three level.