Fast computation of observed cross section for $\psi^{\prime} \to PP$ decays

TL;DR

This paper introduces an efficient analytical method to compute the observed cross section for $\psi^{\prime} o PP$ decays, significantly reducing computational time and aiding experimental data analysis.

Contribution

It develops a linear approximation approach to simplify the integral calculation of the cross section, achieving a 100-fold speed-up with high accuracy.

Findings

Analytical expression for cross section with 1% accuracy

Reduction of computation time by two orders of magnitude

Facilitates data analysis and systematic uncertainty assessment

Abstract

It has been conjectured that the relative phase between strong and electromagnetic amplitudes is universally $-90^{\circ}$ in charmonium decays. $\psi^{\prime}$ decaying into pseudoscalar pair provides a possibility to test this conjecture. However, the experimentally observed cross section for such a process is depicted by the two-fold integral which takes into account the initial state radiative (ISR) correction and energy spread effect. Using the generalized linear regression approach, a complex energy-dependent factor is approximated by a linear function of energy. Taking advantage of this simplification, the integration of ISR correction can be performed and an analytical expression with accuracy at the level of 1% is obtained. Then, the original two-fold integral is simplified into a one-fold integral, which reduces the total computing time by two orders of magnitude. Such a simplified expression for the observed cross section usually plays an indispensable role in the optimization of scan data taking, the determination of systematic uncertainty, and the analysis of data correlation.