Transverse-momentum-dependent wave functions and soft functions at one-loop in large momentum effective theory

• Published in: The journal of high energy physics 2022-09, Vol.2022 (9), p.46-44, Article 46
• Main Authors: Deng, Zhi-Fu, Wang, Wei, Zeng, Jun
• Format: Article
• Language: English
• Subjects: Classical and Quantum Gravitation; Collaboration; Cosmology; Differential equations; Effective Field Theories of QCD; Elementary Particles; First principles; Form factors; High energy physics; Laboratories; Lattice QCD; Light; Mathematical analysis; Momentum; Operators (mathematics); Parton Distributions; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Quarks; Regular Article - Theoretical Physics; Relativity Theory; String Theory; Time correlation functions; Wave functions
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP09(2022)046

A bstract In large-momentum effective theory (LaMET), the transverse-momentum-dependent (TMD) light-front wave functions and soft functions can be extracted from the simulation of a four-quark form factor and equal-time correlation functions. In this work, using expansion by regions we provide a one-loop proof of TMD factorization of the form factor. For the one-loop validation, we also present a detailed calculation of O ( α s ) perturbative corrections to these quantities, in which we adopt a modern technique for the calculation of TMD form factor based the integration by part and differential equation. The one-loop hard functions are then extracted. Using lattice data from Lattice Parton Collaboration on quasi-TMDWFs, we estimate the effects from the one-loop matching kernel and find that the perturbative corrections depend on the operator to define the form factor, but are less sensitive to the transverse separation. These results will be helpful to precisely extract the soft functions and TMD wave functions from the first-principle in future.