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arXiv · 1008.3245

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

Wang Bo-Qun·Mo Xiao-Hu·Wang Ping·Ban Yong
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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.

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Wang Bo-Qun, Mo Xiao-Hu, Wang Ping, Ban Yong. 2010-08-19. Fast computation of observed cross section for $\psi^{\prime} \to PP$ decays. https://doi.org/10.1088/1674-1137/35/5/001

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