In this paper, we study the single spin asymmetry $A_{UT}^{\sin ({\varphi }_h-{\varphi }_S)}$ of a single hadron production in semi-inclusive deep inelastic scattering within the framework of transverse momentum dependent factorization up to the next-to-leading logarithmic order of QCD. The asymmetry is a contribution of the convolution of the Sivers function and the unpolarized fragmentation function. Specifically, the Sivers function in the coordinate space and perturbative region can represent the convolution of the $C$ coefficients and the corresponding collinear correlation functions, among which the Qiu-Sterman function is the most relevant one. We perform a detailed phenomenological analysis of the Sivers asymmetry at the kinematics of the HERMES and the COMPASS measurements. It is found that the obtained $x_B$-, $z_h$-, and $P_{h\perp }$-dependent asymmetries are basically consistent with the HERMES and the COMPASS measurements.

• Received 8 November 2019
• Accepted 24 March 2020

DOI:https://doi.org/10.1103/PhysRevD.101.074016

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Published by the American Physical Society