Chiral Partners in a Chirally Broken World

TL;DR

This paper explores the nature of chiral partners in a world with broken chiral symmetry, proposing that rho and a_1 mesons differ fundamentally in their structure, with implications for understanding hadron spectra and in-medium modifications.

Contribution

It introduces a novel interpretation that rho and a_1 mesons are fundamentally different in structure, with rho as a quark-antiquark state and a_1 as a meson-molecule, explaining their spectral features.

Findings

Rho-meson is predominantly a quark-antiquark state.

A_1-meson is mainly a meson-molecule formed by pion and rho interactions.

The interpretation reproduces the vector and axial-vector spectra well.

Abstract

The isovector--vector and the isovector--axial-vector current are related by a chiral transformation. These currents can be called chiral partners at the fundamental level. In a world where chiral symmetry was not broken, the corresponding current-current correlators would show the same spectral information. In the real world chiral symmetry is spontaneously broken. A prominent peak -- the rho-meson -- shows up in the vector spectrum (measured in (e^+ e^-)-collisions and tau-decays). On the other hand, in the axial-vector spectrum a broad bump appears -- the a_1-meson (also accessible in tau-decays). It is tempting to call rho and a_1 chiral partners at the hadronic level. Strong indications are brought forward that these ``chiral partners'' do not only differ in mass but even in their nature: The rho-meson appears dominantly as a quark-antiquark state with small modifications from an attractive pion-pion interaction. The a_1-meson, on the other hand, can be understood as a meson-molecule state mainly formed by the attractive interaction between pion and rho-meson. A key issue here is that the meson-meson interactions are fixed by chiral symmetry breaking. It is demonstrated that one can understand the vector and the axial-vector spectrum very well within this interpretation. It is also shown that the opposite cases, namely rho as a pion-pion molecule or a_1 as a quark-antiquark state lead to less satisfying results. Finally speculations on possible in-medium changes of hadron properties are presented.