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.

The two-loop quantum chromodynamics (QCD) radiative corrections to the B c meson leptonic decay rate are calculated in the framework of the non-relativistic QCD (NRQCD) factorization formalism. Two types of master integrals appearing in the calculation are obtained analytically for the first time. We calculate the short-distance coefficient of the leading matrix element to order α 2 s by matching the full perturbative QCD calculation results to the corresponding NRQCD results. The result presented in this work helps the evaluation of both the B c leptonic decay constant and the Cabibbo-Kobayashi-Maskawa (CKM) matrix element |V cb | to the full next-to-next-to-leading-order (NNLO) degree of accuracy.The advent of the non-relativistic quantum chromodynamics (NRQCD) factorization formalism has improved the reliability of investigations on heavy quarkonium [1], thereby also improving the understanding of the strong interaction. It has been noted that for quarkonium production and decays, in many cases, the leading-order calculation in the framework of NRQCD is inadequate. However, the discrepancies between the leading-order calculations and the experimental results can be mostly rectified by including higher-order corrections, which has stimulated various investigations in this respect.The B c meson system, which contains two different flavors of heavy quarks, possesses some peculiar characteristics different from those of heavy quarkonium and has recently attracted considerable interest, especially with the progress of the LHCb experiment [2]. Although the B c meson is highly elusive in experiments, the information obtained from investigations thereof is extremely valuable, including insights into certain aspects of quantum chromodynamics (QCD), the weak interaction and even new physics. In the b c system, the higher excited states will predominantly cascade down into the ground state, the pseudoscalar B c meson, through hadronic or electromagnetic transitions, and this state will then decay into lighter hadrons or leptons via the weak interaction.Using the NRQCD formalism, the B c meson decay amplitude can be expressed in terms of perturbative QCD (pQCD)-calculable shortdistance coefficients multiplied by non-pertubative NRQCD matrix elements. The expression for the leading-order (LO) B c meson leptonic decay width is simple and has long been known, and the next-to-leading-order calculation was completed by Braaten and Fleming two decades ago [3]. In this work, we compute in pQCD the two-loop radiative corrections to the pseudoscalar B c meson leptonic decay rate, i.e., the short-distance coefficient for the leading matrix element at next-to-next-to-leading-order (NNLO), by matching the perturbative result in full QCD with the corresponding perturbative calculation in NRQCD.The calculation of massive two-loop Feynman integrals is rather difficult, especially with two mass scales. For this reason, only a few master integrals with different massive propagators have been successfully calculated [4][5][6]. The method o...

X(16.7) as the solution of the NuTeV anomaly * Yi Liang( ) 1;1) Long-Bin Chen( ) 1,2;2) Cong-Feng Qiao( ) 1,2;3)

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.

NLO QCD corrections to η c +h c (1P)/ψ 1,2 (1D) production at B-factories * CHEN Long-Bin( ) 1,2;1) JIANG Jun( ) 1;2) QIAO Cong-Feng( ) 1,2;3)