Abstract
Transverse-momentum-dependent parton distribution functions and wave functions (TMDPDFs/TMDWFs) can be extracted from lattice calculations of appropriate Euclidean matrix elements of staple-shaped Wilson line operators. We investigate the mixing pattern of such operators under lattice renormalization using symmetry considerations. We perform an analysis for operators with all Dirac structures, which reveals mixings that are not present in one-loop lattice perturbation theory calculations. We also present the relevant one-loop matching in a renormalization scheme that does not introduce extra non-perturbative effects at large distances, both for the TMDPDFs and for the TMDWFs. Our results have the potential to greatly facilitate numerical calculations of TMDPDFs and TMDWFs on the lattice.
Highlights
Understanding the transverse structure of hadrons is an important step towards the three-dimensional imaging of hadrons
One of the key quantities that characterizes such transverse structure is the transverse-momentum-dependent parton distribution functions (TMDPDFs), which are a natural generalization of collinear PDFs to incorporate the transverse momentum of partons in the hadron, and provide crucial inputs for describing multiscale, noninclusive observables at high-energy colliders such as the LHC [1]
II, we give a brief overview of the quasi-TMDPDFs and TMDWFs in large momentum effective theory (LMET), both are defined in terms of stapleshaped Wilson line operators along spatial directions
Summary
Understanding the transverse structure of hadrons is an important step towards the three-dimensional imaging of hadrons. Functions (TMDWFs) or LF wave functions, from which one can obtain all parton densities They are defined by the same staple-shaped Wilson line operators, and the lattice computation follows a similar strategy as that for the TMDPDFs [15]. We discuss the renormalization and matching of quasiTMDPDFs and -TMDWFs in a scheme where no extra nonperturbative effects are introduced at large distances in the renormalization stage, in the same spirit as the hybrid renormalization [34] proposed recently for the quasi-PDFs. The rest of the paper is organized as follows: in Sec. II, we give a brief overview of the quasi-TMDPDFs and TMDWFs in LMET, both are defined in terms of stapleshaped Wilson line operators along spatial directions.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
