The twofold emergence of the $a_1$ axial vector meson in high energy hadronic production

Abstract

The high statistics COMPASS results on diffractive dissociation $\pi N \rightarrow \pi \pi \pi N$ suggest that the isospin $I=1$ spin-parity $J^{PC}= 1^{++}$ $a_1(1260)$ resonance could be split into two states: $a_1(1260)$ decaying into an S-wave $\rho\pi$ system, and $a_1^\prime(1420)$ decaying into a P-wave $f_0(980)\pi$ system. We analyse the reaction by incorporating our previous treatment of resonant re-scattering corrections in the Drell-Deck forward production process. Our results show that the COMPASS results are fully consistent with the existence of a single axial-vector $a_1$ resonance. The characteristic structure of the production process, which differs in the two orbital angular momentum states, plays a crucial role in this determination. Provided the theoretical analysis of the reaction is done in a consistent manner, this single resonance produces two peaks at different locations in the two channels, with a rapid increase of the phase difference between their amplitudes arising mainly from the structure of the production process itself, and not from a dynamical resonance effect. In addition, this analysis clarifies questions related to the mass, width, and decay rates of the $a_1$ resonance.