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

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

2010-08-19

arxiv.org/abs/1008.3245v1

Chin.Phys.C35:411-418,2011

Physics

High Energy Physics

High Energy Physics - Phenomenology

8 pages, 5 figures

Scientific paper

10.1088/1674-1137/35/5/001

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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