Long-established results for the low-energy photon-photon scattering, γγ → γγ, have recently been questioned. We analyze that claim and demonstrate that it is inconsistent with experience. We demonstrate that the mistake originates from an erroneous manipulation of divergent integrals and discuss the connection with another recent claim about the Higgs decay into two photons. We show a simple way of correctly computing the low-energy γγ scattering.

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.

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.