NNLO QCD corrections to γ + η c (η b ) exclusive production in electron-positron collision

Abstract

Based on the NRQCD factorization formalism, we calculate the next-to-nextto-leading order QCD corrections to the heavy quarkonium η c (η b ) production associated with a photon at electron-positron colliders. By matching the amplitudes calculated in full QCD theory to a series of operators in NRQCD, the short-distance coefficients up to NNLO QCD radiative corrections are determined. It turns out that the full set of master integrals that we obtained could be analytically expressed in terms of Goncharov Polylogarithms, integrals over polylogarithms and complete elliptic integrals, which mostly do not exist in the literature and could be employed in the analyses of other physical processes. In phenomenology, numerical calculations of NNLO K-factors and cross sections of e + e − → γ + η c (η b ) processes in BESIII and B-factory experiments are performed, which may stand as a test of the NRQCD higher order calculation while confronting to the data.

Observation of e+e−→γχc1 and search for Jia1, Wang2, Shen3 et al. 2018Phys. Rev. D164150View full textAdd to dashboardCite

“…Quarkonium formation is governed by nonperturbative long-distance effects [1]. Nonrelativistic quantum chromodynamics (NRQCD) factorization was used to compute the cross section for several processes, including the double-charmonium production cross section [2,3], e þ e − → γχ cJ (J ¼ 0, 1, 2) [4][5][6][7][8] and e þ e − → γη c [5,6,9,10] at B factories with relativistic and higher-order corrections included.…”

Two-loop integrals for CP-even heavy quarkonium production and decays: elliptic sectors

“…Together with those 86 integrals calculated in our previous work [46], all master integrals appearing in the calculation of NNLO QCD correction to CP-even heavy quarkonium exclusive production and decays, such as γ * γ → QQ and e + e − → γ + QQ [68], are ready. The master integrals take the form of mutilple polylogarithms, iterative integrals over complete elliptic integrals and multiple polylogarithms.…”

Elliptic polylogarithms and iterated integrals on elliptic curves. Part I: general formalism

“…(2.4) to a linear combination of integrals of the same kernels. For example, any product can be linearised using partial fractioning, 26) and all higher powers can be recast in the form of a total derivative in x,…”

“…While multiple polylogarithms have a large range of applicability, they are not the end of the story. Recently, a growing number of integrals appearing in higher-order calculations in the SM, but also in N = 4 super-Yang-Mills theory or open string theory, have been identified, whose analytical calculation requires functions beyond multiple polylogarithms [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29]. Indeed, the appearance of non-polylogarithmic structures in quantum field theory had been noticed already more than fifty years ago in the computation of the two-loop corrections to the electron self-energy in QED [30].…”