Di-Pion Decays of Heavy Quarkonium in the Field Correlator Method

TL;DR

This paper models di-pion transitions in heavy quarkonium using a parameter-free approach based on the field correlator method, successfully matching experimental di-pion mass distributions.

Contribution

It introduces a parameter-free formula for di-pion mass distributions in heavy quarkonium transitions, incorporating chiral symmetry and PCAC constraints.

Findings

Derived a one-parameter formula for di-pion mass distribution.

Calculated process-dependent parameter η using SHO wave functions.

Achieved agreement with experimental di-pion mass spectra.

Abstract

Mechanism of di-pion transitions $nS\to n'S\pi\pi(n=3,2; n'=2,1)$ in bottomonium and charmonium is studied with the use of the chiral string-breaking Lagrangian allowing for the emission of any number of $\pi(K,\eta),$ and not containing fitting parameters. The transition amplitude contains two terms, $M=a-b$, where first term (a) refers to subsequent one-pion emission: $\Upsilon(nS)\to\pi B\bar B^*\to\pi\Upsilon(n'S)\pi$ and second term (b) refers to two-pion emission: $\Upsilon(nS)\to\pi\pi B\bar B\to\pi\pi\Upsilon(n'S)$. The one-parameter formula for the di-pion mass distribution is derived, $\frac{dw}{dq}\sim$(phase space) $|\eta-x|^2$, where $x=\frac{q^2-4m^2_\pi}{q^2_{max}-4m^2_\pi},$ $q^2\equiv M^2_{\pi\pi}$. The parameter $\eta$ dependent on the process is calculated, using SHO wave functions and imposing PCAC restrictions (Adler zero) on amplitudes a,b. The resulting di-pion mass distributions are in agreement with experimental data.