One-loop QCD corrections to SSA in unweighted Drell-Yan processes

Abstract

We study one-loop QCD corrections to the single transverse spin asymmetry in Drell-Yan process. The invariant mass of virtual photon and angular distributions of final lepton in Collins-Soper frame are measured. Especially, the transverse momentum of virtual photon is integrated out. Collinear twist-3 factorization formalism is adopted for the asymmetry. We use Feynman gauge in this work. To eliminate dependent twist-3 distribution functions, equation of motion for quark is used. The results satisfy both QED and QCD gauge invariance. It is confirmed that all divergences from virtual and real corrections can be removed consistently by collinear subtraction. Finite hard coefficients for the convolution of $\bar{q}(x)$ and $T_F(x_1,x_2)$ are presented.

Figures (7)

• Figure 1: Tree diagrams contributing to $W^{\mu\nu}$. The conjugated diagram of (b) is not shown, but included in the calculation.
• Figure 2: Diagrams for the hard part of one-loop virtual correction to $W^{\mu\nu}$. The right part of (a-h) is not drawn, which is a tree level photon-quark vertex. The last diagram (i) contains both left part and right part. All conjugated diagrams are not shown, but included in the calculation.
• Figure 3: The diagrams for the hard part of real corrections related to twist-3 two-point correlation functions. The conjugated diagram of (c) is not shown. The black dot represents quark-photon interaction.
• Figure 4: Diagrams for the hard part of SGP contributions in $\bar{q}+qg$ channel.(a-d) are of the left parts and the last two diagrams are of the right part. The black dot represents photon-quark interaction. The propagator with short bar is on-shell. Conjugated diagrams are not shown.
• Figure 5: Diagrams for the hard part of hard pole contributions from $\bar{q}+qg$ channel. (a,b,c) are of the left part and the last two diagrams are of the right part. Conjugated diagrams are not shown.