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-next-to-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, Chen's iterated integrals, and elliptic functions, 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 $e^+e^-\rightarrow γ+ η_c(η_b)$ 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.

Figures (5)

• Figure 1: Typical LO, NLO, and NNLO Feynman diagrams of the $e^+e^-\rightarrow \gamma+\eta_c(\eta_b)$ processes.
• Figure 2: Typical master integrals in elliptic sectors.
• Figure 3: The cross sections of exclusive $\gamma+\eta_c$ production up to NNLO in electron-positron collision with center-of-mass energy from $4.0$ to $5.5$ GeV. The subscript denotes the magnitude of charm quark mass.
• Figure 4: The renormalzation scale dependence of NLO and NNLO K-factors for $\gamma+\eta_c$ exclusive production at the B-factory. Here, the factorization scale $\mu_\Lambda= 1$ GeV, subscripts $1.4$ and $1.5$ mean the charm quark mass in GeV.
• Figure 5: The renormalzation scale dependence of NLO and NNLO K-factors for $\gamma+\eta_b$ exclusive production at the B-factory. Here, the factorization scale $\mu_\Lambda= m_b$, subscripts $4.7$ and $4.8$ mean the bottom quark mass in GeV.