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

Self Cite

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.

Section: Jhep01(2018)091mentioning

confidence: 88%

Section: Jhep01(2018)091mentioning

confidence: 97%

Section: Jhep01(2018)091mentioning

confidence: 99%

See 1 more Smart Citation

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

Chen

Liang

Qiao

2018

Self Cite

“…where we have the following coefficients: 43) and where the other coefficients are given by cyclic permutations:…”

Section: Solution In Terms Of Multiple Elliptic Polylogarithmsmentioning

confidence: 99%

All orders structure and efficient computation of linearly reducible elliptic Feynman integrals

Hidding¹,

Moriello²

2019

We define linearly reducible elliptic Feynman integrals, and we show that they can be algorithmically solved up to arbitrary order of the dimensional regulator in terms of a 1-dimensional integral over a polylogarithmic integrand, which we call the inner polylogarithmic part (IPP). The solution is obtained by direct integration of the Feynman parametric representation. When the IPP depends on one elliptic curve (and no other algebraic functions), this class of Feynman integrals can be algorithmically solved in terms of elliptic multiple polylogarithms (eMPLs) by using integration by parts identities. We then elaborate on the differential equations method. Specifically, we show that the IPP can be mapped to a generalized integral topology satisfying a set of differential equations in ǫ-form. In the examples we consider the canonical differential equations can be directly solved in terms of eMPLs up to arbitrary order of the dimensional regulator. The remaining 1-dimensional integral may be performed to express such integrals completely in terms of eMPLs. We apply these methods to solve two-and three-points integrals in terms of eMPLs. We analytically continue these integrals to the physical region by using their 1-dimensional integral representation.

“…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].…”

Section: Introductionmentioning

confidence: 99%

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

Broedel

Duhr

Dulat

et al. 2018

167

232

We introduce a class of iterated integrals, defined through a set of linearly independent integration kernels on elliptic curves. As a direct generalisation of multiple polylogarithms, we construct our set of integration kernels ensuring that they have at most simple poles, implying that the iterated integrals have at most logarithmic singularities. We study the properties of our iterated integrals and their relationship to the multiple elliptic polylogarithms from the mathematics literature. On the one hand, we find that our iterated integrals span essentially the same space of functions as the multiple elliptic polylogarithms. On the other, our formulation allows for a more direct use to solve a large variety of problems in high-energy physics. We demonstrate the use of our functions in the evaluation of the Laurent expansion of some hypergeometric functions for values of the indices close to half integers.