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arXiv · 2012.03256

Unpolarized Quark and Gluon TMD PDFs and FFs at N$^3$LO

Ming-xing Luo·Tong-Zhi Yang·Hua Xing Zhu·Yu Jiao Zhu
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Abstract

In this paper we calculate analytically the perturbative matching coefficients for unpolarized quark and gluon Transverse-Momentum-Dependent (TMD) Parton Distribution Functions (PDFs) and Fragmentation Functions (FFs) through Next-to-Next-to-Next-to-Leading Order (N$^3$LO) in QCD. The N$^3$LO TMD PDFs are calculated by solving a system of differential equation of Feynman and phase space integrals. The TMD FFs are obtained by analytic continuation from space-like quantities to time-like quantities, taking into account the probability interpretation of TMD PDFs and FFs properly. The coefficient functions for TMD FFs exhibit double logarithmic enhancement at small momentum fraction $z$. We resum such logarithmic terms to the third order in the expansion of $\alpha_s$. Our results constitute important ingredients for precision determination of TMD PDFs and FFs in current and future experiments.

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Ming-xing Luo, Tong-Zhi Yang, Hua Xing Zhu, Yu Jiao Zhu. 2020-12-06. Unpolarized Quark and Gluon TMD PDFs and FFs at N$^3$LO. https://doi.org/10.1007/jhep06(2021)115

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