Chiral Partners in a Chirally Broken World

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 ρ-meson — shows up in the vector spectrum (measured in ee-collisions and τ -decays). On the other hand, in the axialvector spectrum a broad bump appears — the a1-meson (also accessible in τ -decays). It is tempting to call ρ and a1 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 ρ-meson appears dominantly as a quark-antiquark state with small modifications from an attractive pion-pion interaction. The a1-meson, on the other hand, can be understood as a meson-molecule state mainly formed by the attractive interaction between pion and ρ-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 ρ as a pion-pion molecule or a1 as a quark-antiquark state lead to less satisfying results. Finally speculations on possible in-medium changes of hadron properties are presented.