Rho meson properties in the chiral theory framework

Abstract

We study the mass, width and couplings of the lightest resonance multiplet with I (J PC ) = 1 (1-) quantum numbers. Effective field theories based on chiral symmetry are employed in order to describe the form factor associated with the two pseudoscalar matrix element of the QCD vector current. The bare poles of the intermediate resonances are regularized through a Dyson-Schwinger-like summation. We explore the role of the resonance width in physical observables and make a coupled-channel analysis of the final-state interactions. This provides many interesting properties, like the pole mass $M_\rho^{\mathrm{pole}}= 764.1\pm 2.7^{+4.0}_{-2.5}$ MeV. At energies $E\gtrsim 1$ GeV, a second 1 (1-) resonance multiplet is considered in order to describe the data in a more consistent way. From the phenomenologically extracted resonance couplings, we obtain the chiral coupling $L_9^{\mathrm{r}}(\mu_0)= (7.04\pm 0.05^{+0.19}_{-0.27})\cdot 10^{-3}$ , at $\mu_0 = 770$ MeV, and show how the running with the scale μ affects the resonance parameters. A 1/N C counting is adopted in this work and the consistency of the large-NC expansion is tested. Finally, we make an estimation of the contribution from diagrams with resonances in crossed channels.