Master integrals for two-loop QCD corrections to quark quasi PDFs
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Springer
Received: June 23, 2020 Accepted: September 7, 2020 Published: October 13, 2020
Long-Bin Chen,a Wei Wangb,1 and Ruilin Zhuc,d,2 a
School of Physics and Materials Science, Guangzhou University, Guangzhou 510006, China b INPAC, Shanghai Key Laboratory for Particle Physics and Cosmology, MOE Key Lab for Particle Astrophysics and Cosmology, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai, 200240, China c Department of Physics and Institute of Theoretical Physics, Nanjing Normal University, Nanjing, Jiangsu 210023, China d Nuclear Science Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, U.S.A.
E-mail: [email protected], [email protected], [email protected] Abstract: We compute the master integrals for the two-loop QCD corrections to quark quasi parton distribution functions (PDFs) in the large momentum effective theory (LaMET). With a proper canonical basis, we derive the analytical results for the three families of master integrals using the method of differential equations. The final expressions for the master integrals are given in terms of Goncharov polylogarithms. These results allow us to extract the two-loop short-distant matching coefficients between quark quasi and lightcone PDFs in LaMET, and are valuable to improve the determination of the nucleon PDFs from first principles in future. Keywords: Perturbative QCD, Lattice QCD ArXiv ePrint: 2006.10917
1 2
Corresponding author. Corresponding author.
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP10(2020)079
JHEP10(2020)079
Master integrals for two-loop QCD corrections to quark quasi PDFs
Contents 1 Introduction
1
2 Notations and conventions
2
3 The canonical basis
4 9 11 12 12
5 Analytic results and validations 5.1 Results for off-shell quarks 5.2 Results for on-shell quarks 5.3 Validations
12 12 14 15
6 Discussions and conclusions
16
1
Introduction
In high energy physics, theoretical predictions for physical observables like cross sections are usually made under QCD factorization scheme, in which the scattering amplitude is split into a perturbative hard-kernel and low-energy matrix elements. The perturbative coefficient arises from the short-distant degrees of freedom, while the long-distant inputs, parton distribution functions (PDFs) and others, describe the longitudinal momentum distribution of unpolarized/polarized partons inside a hadron. The involved partons in the hadron move nearly at the speed of light. Thereby it is extremely difficult to directly calculate the PDFs from first-principles of QCD, i.e. Lattice QCD. Previous attempts in Lattice QCD make use of the operator product expansion and calculate the moments of PDFs. This approach was successful only for the lowest few moments of the lightcone PDFs [1], but studies of higher moments suffer from significantly large noises in the simulation. Thus a complete description of PDFs from first-principles is not established yet. Recently a breakthrough to circumvent the above problem was p
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