Determination of Decay Width Error and Luminosity in ψ(2S) Scan

Abstract: The observed cross sections of processes e⁺e^－→e⁺e^－,μ⁺μ^－,π⁺π^－J/ψ and hadrons at 24 energy points in the vicinity of ψ(2S) resonance have been measured by BES(Beijing Spectrometer). The resonance cross sections for above four final states take the Breit-Wigner forms. By combining the cross sections of resonance part,continuum(QED or QCD) part and their interferences together with radiative corrections,and then convoluted with the energy spread of BEPC(Beijing Electron and Positron Collider),the χ² fit of these 4 observed cross sections with the assumption of e-μ-τ universality gives the decay widths and branching ratios of ψ(2S):Γ_t,Γ_μ,Γ_h,Γ_π+π－J/ψ,B_μ,B_h,B_π+π-J/ψ. This article mainly describes the methods for calculating the intregral luminosity and for determining the fitting errors of ψ(2S) decay widths and branching ratios in this scan experiment. The intregral luminosity for each energy point is calculated by using the data of e₊e_－ final state and the iteration method with assumption of lepton universality,that is B_e=B_μ . The errors of decay widths and branching ratios are determined by Monte Carlo sampling method.