The dependence of the emission size on the hadron mass

TL;DR

This paper investigates how the emission size of different hadrons depends on their mass, demonstrating that the hierarchy of sizes aligns with quantum principles like the uncertainty principle and virial theorem.

Contribution

It provides a unified explanation for the mass dependence of emission sizes in hadronic decays using quantum mechanical principles.

Findings

The hierarchy r_{ππ} > r_{KK} > r_{ΛΛ} is consistent with the Heisenberg uncertainty principle.

The virial theorem applied to QCD potentials also describes the size dependence.

Other theoretical approaches are discussed in relation to the observed size hierarchy.

Abstract

The size of the emission volume of pions and kaons, r_{\pi\pi} and r_{KK}, were measured in the hadronic Z^0 decays through the two-pion and two-kaon Bose-Einstein correlations near threshold. Recently the emitter size of the two identical baryons, \Lambda \Lambda (\bar \Lambda \bar \Lambda), was evaluated from the dependence of the fraction of the spin S=1 state on the energy near threshold where it is affected by the Pauli exclusion principle. Here we show that the r dependence on the particle masses, namely the hierarchy r_{\pi\pi} > r_{KK} > r_{\Lambda \Lambda} observed in the Z^0 hadronic decays, is well described in terms of the Heisenberg uncertainty principle. A good description can also be obtained via the virial theorem when applied to a general QCD potential. Other available approaches are also discussed.