Peak locations and relative phase of different decay modes of the $a_1$ axial vector resonance in diffractive production

TL;DR

This paper demonstrates that a single $a_1$ resonance can appear as two separate peaks in different decay channels, with phase differences influenced by the production process, clarifying previous ambiguities about its properties.

Contribution

It reveals that the $a_1$ resonance's two observed peaks are due to decay mode differences and production dynamics, not two separate resonances.

Findings

Two distinct mass peaks for the $a_1$ resonance observed in different decay modes.

Phase difference between decay amplitudes increases rapidly due to diffractive production.

Clarification of the $a_1$ resonance's mass, width, and decay characteristics.

Abstract

We show that a single $I=1$ spin-parity $J^{PC}= 1^{++}$ $a_1$ resonance can manifest itself as two separated mass peaks, one decaying into an S-wave $\rho\pi$ system and the second decaying into a P-wave $f_0(980)\pi$ system, with a rapid increase of the phase difference between their amplitudes arising mainly from the structure of the diffractive production process. This study clarifies questions related to the mass, width, and decay rates of the $a_1$ resonance raised by the recent high statistics data of the COMPASS collaboration on $a_1$ production in $\pi N \rightarrow \pi \pi \pi N$ at high energies.