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

Abstract

We can obtain a second conventional formula (${\rm CF_{II}}$) with two components by extending the conventional formula ${\rm CF_{I}}$ with one component for Bose-Einstein Correlation (BEC). We used ${\rm CF_{II}}$ to analyze the BEC at $Z^0$-pole as part of the OPAL collaboration. $R_1({\rm G})=0.91\pm 0.03$ fm ($\lambda_1=0.61\pm 0.03$) and $R_2({\rm G})=2.57\pm 0.44$ 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.