Fast computation of observed cross section for ψ′→PP decays

Abstract

It has been conjectured that the relative phase between strong and electromagnetic amplitudes is universally −90 • in charmonium decays. ψ ′ 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.

Analysis of the Relationship between Land Use, Development, and Construction near a Rail Traffic Station and Passenger Flow Volume: The Case of Tianjin Metro Line 1

“…Definition of Concepts. In the initial stage of the study, we classify the 22 stations along Line 1 into several groups and calculate a "rail circle" for each station [3].…”

“…In accordance with the circle theory of rail stations, the present study takes the area within 200 m to constitute the "core circle" and 200-500 m to constitute the "edge circle." [3] Commercial stations are traveled to voluntarily by shoppers, while other stations are more or less mandatory for their commuters (depending on those people's home and work locations); thus, commercial stations are more sensitive to distance. Therefore, the study considers the area in a 200 m study radius around commercial stations and in a 300 m radius around other stations.…”