Axial resonances a1(1260), b1(1235) and their decays from the lattice

Abstract

The light axial-vector resonances $a_1(1260)$ and $b_1(1235)$ are explored in Nf=2 lattice QCD by simulating the corresponding scattering channels $ρπ$ and $ωπ$. Interpolating fields $\bar{q} q$ and $ρπ$ or $ωπ$ are used to extract the s-wave phase shifts for the first time. The $ρ$ and $ω$ are treated as stable and we argue that this is justified in the considered energy range and for our parameters $m_π\simeq 266~$MeV and $L\simeq 2~$fm. We neglect other channels that would be open when using physical masses in continuum. Assuming a resonance interpretation a Breit-Wigner fit to the phase shift gives the $a_1(1260)$ resonance mass $m_{a1}^{res}=1.435(53)(^{+0}_{-109})$ GeV compared to $m_{a1}^{exp}=1.230(40)$ GeV. The $a_1$ width $Γ_{a1}(s)=g^2 p/s$ is parametrized in terms of the coupling and we obtain $g_{a_1ρπ}=1.71(39)$ GeV compared to $g_{a_1ρπ}^{exp}=1.35(30)$ GeV derived from $Γ_{a1}^{exp}=425(175)$ MeV. In the $b_1$ channel, we find energy levels related to $π(0)ω(0)$ and $b_1(1235)$, and the lowest level is found at $E_1 \gtrsim m_ω+m_π$ but is within uncertainty also compatible with an attractive interaction. Assuming the coupling $g_{b_1ωπ}$ extracted from the experimental width we estimate $m_{b_1}^{res}=1.414(36)(^{+0}_{-83})$.