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Staple-shaped Wilson line operators are necessary for the study of transversemomentum-dependent parton distribution functions (TMDPDFs) in lattice QCD andbeyond. In this work, we study the renormalization of such operators in thegeneral case of an asymmetric staple. We analyze the mixing pattern of theseoperators using their symmetry properties, where we find that the possiblemixing is restricted within groups of four operators. We then present numericalresults using the regularization independent scheme, RI/MOM, to study theimportance of mixing using one operator in particular, the $\gamma_0$ operator.Based on these results, we consider the short distance ratio (SDR) scheme,which is desirable in the absence of mixing. Finally, we investigate a variantof the RI/MOM scheme, where the renormalization factors are computed at shortdistances.

Non-perturbative renormalization of asymmetric staple-shaped operators in twisted mass lattice QCD