The effects of absolute energy calibration on BESⅢ physics are discussed in detail, which mainly involve the effects on τ mass measurement, cross section scan measurement, and generic error determination in other measurements.
Using the sequential decay process e ＋ e- → J/ψ→ΛΛ, Λ→ pπ- , Λ→ pπ＋ as an example, the procedure for deducing the full angular distribution is illustrated by adopting both the Jacob-Wick and Jackson conventions in the helicity formalism. To make sure that the final physical result is free of phase conventions, we point out that the coefficients that relate the angular momentum states in different coordinate systems of reference frames have to be taken into account properly in the procedure. The fact that those coefficients are constants suggests that the Jackson convention is favorable in dealing with the processes with sequential decays.
The proposed beam energy measurement system at BEPC II is composed of three parts： the laser source and optics system, the laser-electron interaction system and the HPGe detector system. The working principles of each system are expounded together with the calculation for preliminary design. The normaliza- tions of laser and electron beams are put forth and used for the evaluation of intensity of the backscattering photon. The simulation of HPGe detector is also performed for understanding the working properties.
Based on 58 million J/ψ events collected by the BESⅡ detector at the BEPC, J/ψ→ΛΛ π＋π- is observed for the first time. The branching fraction is measured to be Br（J/ψ→ΛΛ π＋π-）=（4.30±0.13±0.99）×10-3, excluding the decays to intermediate states, namely J/ψ→Ξ-Ξ＋, J/ψ→Σ（1385）-Σ（1385）＋, and J/ψ→Σ（1385）＋Σ（1385）-. The branching fractions for these intermediate resonance channels are measured to be：Br（J/ψ→Ξ-Ξ＋）=（0.90±0.03±0.18）×10-3, Br（J/ψ→Σ（1385）-Σ（1385）＋）=（1.23±0.07±0.30）×10-3,and Br（J/ψ→Σ（1385）＋Σ（1385）-）=（1.50±0.08±0.38）×10-3, respectively. The angular distribution is of the form dN/d（cosθ）α（1＋αcos2θ） with α=（0.35±0.29±0.06） for J/ψ→Ξ-Ξ＋, α=（-0.54±0.22±0.10） for J/ψ→Σ（1385）-Σ（1385）＋, and α=（-0.35±0.29±0.06） for J/ψ→Σ（1385）＋Σ（1385）-.
A test statistic is proposed to perform the goodness-of-fit test in the unbinned maximum likelihood fit. Without using a detailed expression of the efficiency function, the test statistic is found to be strongly correlated with the maximum likelihood function if the efficiency function varies smoothly. We point out that the correlation coefficient can be estimated by the Monte Carlo technique. With the established method, two examples are given to illustrate the performance of the test statistic.
