Parity doubling of nucléons, Delta and Omega baryons across the deconfinement phase transition

In this work we analyse positive- and negative-parity channels for the nucleon (spin $1/2$ octet), $\Delta$ and $\Omega$ baryons (spin $3/2$ decuplet) using lattice QCD. In Nature, at zero temperature, chiral symmetry is spontaneously broken, causing positive- and negative-parity ground states to have different masses. However, chiral symmetry is expected to be restored (for massless quarks) around the crossover temperature, implying that the two opposite parity channels should become degenerate. Here we study what happens in a temperature range which includes both the hadronic and the quark gluon plasma (QGP) phase. By analysing the correlation and spectral functions via exponential fits and the Maximum Entropy Method respectively, we have found parity doubling for the nucleon and $\Delta$ baryon channels in the QGP phase. For the $\Omega$ baryon we see a clear signal of parity doubling at the crossover temperature, which is however not complete, due to the nonzero strange quark mass. Moreover, in-medium effects in the hadronic phase are evident for all three baryons, in particular for the negative-parity ground states. This might have implications for the hadron resonance gas model. In this work we used the FASTSUM anisotropic $N_f = 2 + 1$ ensembles.