The Source Size Dependence on the M_hadron Applying Fermi and Bose Statistics and I-Spin Invariance

Abstract

The emission volume sizes of pions and Kaons, r_{\pi^\pm \pi^\pm} and r_{K^\pm K^\pm}, measured in the hadronic Z^0 decays via the Bose-Einstein Correlations (BEC), and the recent measurements of r_{\Lambda\Lambda} obtained by through the Pauli exclusion principle are used to study the r dependence on the hadron mass. A clear r_{\pi^\pm \pi^\pm} > r_{K^\pm K^\pm} > r_{\Lambda \Lambda} hierarchy is observed which seems to disagree with the basic string (LUND) model expectation. An adequate description of r(m) is obtained via the Heisenberg uncertainty relations and also by Local Parton Hadron Duality approach using a general QCD potential. These lead to a relation of the type r(m) ~ Constant/sqrt{m}. The present lack of knowledge on the f_o(980) decay rate to the K^0\bar{K}^0 channel prohibits the use of the r_{K^0_SK^0_S} in the r(m) analysis. The use of a generalised BEC and I-spin invariance, which predicts an BEC enhancement also in the K^{\pm}K^0 and \pi^{\pm}\pi^0 systems, should in the future help to include the r_{K^0_SK^0_S} in the r(m) analysis.