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

Abstract

By employing the method of differential equations, we compute the various types of two-loop master integrals involved in CP-even heavy quarkonium exclusive production and decays. All the integrals presented in this paper can be casted into canonical forms and expressed in terms of Goncharov polylogarithms and Harmonic polylogarithms. These master integrals are frequently used in the calculation of NNLO corrections of the heavy quarkonium production processes, as γ * γ → QQ, e + e − → γ + QQ, and H/Z 0 → γ + QQ, and decay processes. They are also applicable in the calculation of NNLO corrections to CP-even quarkonium inclusive production and decay processes.

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

“…The calculation details of all the master integrals can be found in refs. [25,31]. To the best of our knowledge, this is the first time that a NNLO calculation for multiscale process about heavy quarkonium has been achieved analytically.…”

“…With the reduction of the obtained two-loop amplitudes, we find all related scalar integrals may be attributed to a set of 133 master integrals. Using the method of differential equation [22,23], and by virtue of the recent development in choosing basis properly [24], it was found that 86 of the 133 master integrals can be expressed as functions of Harmonic and Goncharov polylogarithms [25]. The calculation of massive multi-loop Feynman integrals is a challenging task due to the appearance of new mathematical structures, which cannot be reduced to the well-known multiple polylogarithms yet.…”

“…. 39); F is a 86-dimensional basis vector that had been calculated in our previous work [25]; W and Y are 37 × 37 and 37 × 86 matrices, respectively; Q i (i = 1, 2) are also 37-dimensional basis vectors; and A 1 is a linear function of the massive sunrise integrals (E 1 , E 2 ), write as…”

“…JHEP01 (2018)091 with F 1 being the first integral of vector F [25]. Note that (W, Y, Q 1 , Q 2 ) are rational functions of kinematics and hence are free of ǫ.…”

Three-loop planar master integrals for heavy-to-light form factors

“…[25]. This choice simplifies the solution of differential equations significantly, and has been successfully applied in [26][27][28][29][30][31][32][33][34][35][36][37] and many other works. In addition, we utilize several properties of the master integrals around the (pseudo-)singularities to reduce the determination of the boundary condition to simple or even trivial integrals.…”