Analytical formula for the cross section of hadron production from $e^{+}e^{-}$ collisions around the narrow charmouinum resonances

Abstract

The paper reports an analytical formula for the production cross section of $e^{+}e^{-}$ annihilation to hadrons in the vicinity of a narrow resonance, particularly in the $\tau$-charm region, while considering initial state radiation. Despite some approximations in its derivation, the comparison between the analytical formula and direct integration of ISR shows good accuracy, indicating that the analytical formula meets current experimental requirements. Furthermore, the paper presents a comparison of the cross section between the analytical formula and calculations using the {\sc ConExc} Monte Carlo generator. The efficiency of the analytical formula in significantly reducing computing time makes it a favorable choice for the regression procedure to extract the parameters of narrow charmonium resonances in experiments.