Transverse momentum dependent PDFs at N 3 LO
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Springer
Received: June 24, 2020 Accepted: August 19, 2020 Published: September 22, 2020
Markus A. Ebert,a Bernhard Mistlbergerb and Gherardo Vitaa a
Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, U.S.A. b SLAC National Accelerator Laboratory, Stanford University, Stanford, CA 94039, U.S.A.
E-mail: [email protected], [email protected], [email protected] Abstract: We compute the quark and gluon transverse momentum dependent parton distribution functions at next-to-next-to-next-to-leading order (N 3 LO) in perturbative QCD. Our calculation is based on an expansion of the differential Drell-Yan and gluon fusion Higgs production cross sections about their collinear limit. This method allows us to employ cutting edge multiloop techniques for the computation of cross sections to extract these universal building blocks of the collinear limit of QCD. The corresponding perturbative matching kernels for all channels are expressed in terms of simple harmonic polylogarithms up to weight five. As a byproduct, we confirm a previous computation of the soft function for transverse momentum factorization at N3 LO. Our results are the last missing ingredient to extend the qT subtraction methods to N3 LO and to obtain resummed qT spectra at N3 LL0 accuracy both for gluon as well as for quark initiated processes. Keywords: Effective Field Theories, Perturbative QCD ArXiv ePrint: 2006.05329
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP09(2020)146
JHEP09(2020)146
Transverse momentum dependent PDFs at N3LO
Contents 1
2 Review of qT factorization
3
3 Beam functions from the collinear limit of cross sections
4
4 Results
7
5 Conclusions
11
A Ingredients for the calculation of the beam function A.1 Rapidity regularization A.2 Fourier transform A.3 Renormalization group equations A.4 Structure of the beam function counterterm A.5 αs renormalization and IR counterterms
13 13 13 14 15 15
B High-energy limit of the beam function kernels
16
1
Introduction
Transverse momentum dependent parton distribution functions (TMDPDFs) extend the concept of collinear PDFs, which describe the longitudinal momentum distribution of quarks and gluons inside protons, to also reflect their intrinsic transverse motion. They are important ingredients for describing high-energy scatterings at small transverse momentum, in particular the Drell-Yan process, an important benchmark observable of the Standard Model both at the Tevatron [1–4] and the LHC [5–12]. Similarly, they are required for predictions of the Higgs transverse momentum spectrum, a key observable that is of great interest for the LHC physics program [13–23]. TMDPDFs also arise in measurements of semi-inclusive deep-inelastic scattering (SIDIS) [24–30], where they are of particular interested because they provide a window into the proton structure [31, 32]. TMDPDFs measure both the longitudinal momentum fraction z and the transverse momentum ~qT carried by the struck parton. They are intrinsical
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