On the role of the time scale Delta t in Bose-Einstein correlations

TL;DR

This paper reexamines the time scale parameter in Bose-Einstein correlations, proposing it as a measure of emission time rather than particle correlation strength, with implications for high-energy physics and heavy ion collisions.

Contribution

It clarifies the physical interpretation of the time scale parameter in BEC, linking it to emission time and deriving a formula for heavy ion collisions that matches experimental data.

Findings

In $Z^0$ decays, $t$ reflects emission time (~10^{-24} s).

In heavy ion collisions, $t$ scales with nucleus surface area, proportional to $A^{2/3}$.

Derived formula for $t$ agrees with experimental measurements.

Abstract

The time scale $\Delta t$ parameter, which appears in the Bose-Einstein Correlations (BEC) treated in term of the Heisenberg uncertainty relations, is reexamined. Arguments are given for the role of $\Delta t$ as a measure of the particles' emission time rather than representing the strength property of the correlated particles. Thus in the analyzes of the $Z^0$ hadronic the $\Delta t$ given value of ~$10^{-24}$ seconds is the particles' emission time prescribed by the $Z^0$ lifetime. In heavy ion collisions $\Delta t$ measures the emission time duration of the particles produced from a nucleus of atomic number $A$ which is here shown to be equal to $\Delta t =(m_{\pi}a^2)/(\hbar c^2})*A^{2/3}$ where a is about 1 fm, that is, proportional to the nucleus surface area. This dependence agrees rather well with the experimental $\Delta t$ values deduced from the BEC analyzes of heavy ion collisions.