Semi-analytical calculation of gluon fragmentation into 1 S 0 [1,8] quarkonia at next-to-leading order
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Springer
Received: October 29, Revised: March 7, Accepted: March 27, Published: April 17,
2018 2019 2019 2019
Peng Zhang,a,b Chen-Yu Wang,a Xiao Liu,a Yan-Qing Ma,a,b,c Ce Menga and Kuang-Ta Chaoa,b,c a
School of Physics and State Key Laboratory of Nuclear Physics and Technology, Peking University, Beijing 100871, China b Center for High Energy Physics, Peking University, Beijing 100871, China c Collaborative Innovation Center of Quantum Matter, Beijing 100871, China
E-mail: [email protected], [email protected], [email protected], [email protected], [email protected], [email protected] Abstract: We calculate the NLO corrections for the gluon fragmentation functions to [1] [8] a heavy quark-antiquark pair in 1S0 or 1S0 state within NRQCD factorization. We use integration-by-parts reduction to reduce the original expression to simpler master integrals (MIs), and then set up differential equations for these MIs. After calculating the boundary conditions, MIs can be obtained by solving the differential equations numerically. Our results are expressed in terms of asymptotic expansions at singular points of z (lightcone momentum fraction carried by the quark-antiquark pair), which can not only give FFs results with very high precision at any value of z, but also provide fully analytical structure at these singularities. We find that the NLO corrections are significant, with K-factors larger than 2 in most regions. The NLO corrections may have important impact on heavy quarkonia (e.g. ηc and J/ψ) production at the LHC. Keywords: NLO Computations, QCD Phenomenology ArXiv ePrint: 1810.07656
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP04(2019)116
JHEP04(2019)116
Semi-analytical calculation of gluon fragmentation [1,8] into 1S0 quarkonia at next-to-leading order
Contents 1
2 Calculation of LO FFs 2.1 Definitions 2.2 LO SDCs
3 3 5
3 Real NLO corrections 3.1 Reduction to MIs 3.2 Calculation of MIs
6 6 8
4 Virtual NLO corrections
10
5 Renormalization
11
6 Results and discussion 6.1 Final results 6.2 Numerical results
12 12 13
A IBP reduction with unregularized rapidity divergence
17
B Removable singularities and their effects
19
C Boundary conditions of MIs in real corrections
21
D Calculation of MIs in virtual corrections
23
E Coefficients
24
1
Introduction
Study of heavy quarkonium production is important to understand both perturbative and non-perturbative physics in QCD. Currently, the most widely used theory for quarkonium production is the non-relativistic QCD (NRQCD) factorization [1]. Although many important processes have been calculated to next-to-leading order in αs expansion [2–25], there are still some notable difficulties in quarkonium production within the NRQCD framework (see, e.g. [26]). To further explore the quarkonium production mechanism, it may be better to study quarkonium production at high transverse momentum pT region, where long-distance interactions between quarkonium and initial-state particles are suppressed and thus factorizat
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