Analytic forms for the e+e− annihilation cross sections around a resonance including initial state radiation

Abstract

For the first time, the exact analytic integration of the product between the Kuraev-Fadin radiative function and the Born-level cross section has been achieved for e+e− annihilation near a narrow resonance. The analytic result is in a perfect agreement with the one obtained through direct numerical integration. The extraction of resonance parameters is demonstrated through the unfolding of the initial state radiation effect. The analytic integration significantly accelerates the regression process by more than 160 times compared to numerical integration. Moreover, it facilitates the determination of experimental measurements for physical parameters, such as the two-dimensional confidence region of the branching fraction and the relative phase between the strong and electromagnetic amplitudes, within just one hour instead of one week typically required for numerical integration. Published by the American Physical Society 2024