Unquenched quark-model calculation of excited $\rho$ resonances and P-wave $\pi \pi$ phase shifts

The $\rho (770)$ vector resonance, its radial recurrences, and the corresponding P-wave $\pi \pi$ phase shifts are investigated in an unquenched quark model with all classes of relevant decay channels included, viz. pseudoscalar-pseudoscalar, vector-pseudoscalar, vector-vector, vector-scalar, axialvector-pseudoscalar, and axialvector-vector, totalling 26 channels. Two of the few model parameters are fixed at previously used values, whereas the other three are adjusted to the $\rho (770)$ resonance and the lower P-wave $\pi \pi$ phases. Preliminary results indicate the model’s capacity to reproduce these phases as well as the $\rho$ mass and width. However, at higher energies the phase shifts tend to rise too sharply. A possible remedy is an extension of the model so as to handle resonances in the final states for most of the included decay channels. Work in progress.