Analysis of OPAL Bose-Einstein Correlation at $Z^0$-pole by the second conventional formula

Abstract

We can obtain a second conventional formula ($\mathrm{C}{\mathrm{F}}_{\mathrm{II}}$) with two components by extending the conventional formula $\mathrm{C}{\mathrm{F}}_{\mathrm{I}}$ with one component for Bose-Einstein Correlation (BEC). We used $\mathrm{C}{\mathrm{F}}_{\mathrm{II}}$ to analyze the BEC at $Z^0$-pole as part of the OPAL collaboration. $R_1(\mathrm{G})=0.91\pm 0.03$ fm (${\lambda }_1=0.61\pm 0.03$) and $R_2(\mathrm{G})=2.57\pm 0.44$ fm (${\lambda }_1=0.35\pm 0.09$) are the estimated interaction region, where ${\lambda }_1$ and ${\lambda }_2$ are the degrees of coherence, and G is the Gaussian distribution, respectively. Long range correlation (LRC) is also studied.