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 $\rho \pi$ and $\omega \pi$. Interpolating fields $\bar{q}q$ and $\rho \pi$ or $\omega \pi$ are used to extract the s-wave phase shifts for the first time. The $\rho$ and $\omega$ are treated as stable and we argue that this is justified in the considered energy range and for our parameters $m_{\pi }\simeq 266$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 $m_{a1}^{res}=1.435(53){(}_{-109}^{+0})$ GeV compared to $m_{a1}^{exp}=1.230(40)$ GeV. The $a_1$ width ${\Gamma }_{a1}(s)=g^{2}p/s$ is parametrized in terms of the coupling and we obtain $g_{a_1\rho \pi }=1.71(39)$ GeV compared to $g_{a_1\rho \pi }^{exp}=1.35(30)$ GeV derived from ${\Gamma }_{a1}^{exp}=425(175)$ MeV. In the $b_1$ channel, we find energy levels related to $\pi (0)\omega (0)$ and $b_1(1235)$, and the lowest level is found at $E_1\gtrsim m_{\omega }+m_{\pi }$ but is within uncertainty also compatible with an attractive interaction. Assuming the coupling $g_{b_1\omega \pi }$ extracted from the experimental width we estimate $m_{b_1}^{res}=1.414(36){(}_{-83}^{+0})$.

15 pages, 4 figures, updated to match published version

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• Towards a theory of hadron resonances
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