# Axial resonances *a* _{1}(1260), *b* _{1}(1235) and their decays from the lattice

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## Abstract

The light axial-vector resonances *a* _{1}(1260) and *b* _{1}(1235) are explored in *N* _{ f } = 2 lattice QCD by simulating the corresponding scattering channels *ρπ* and *ωπ*. Interpolating fields \( \overline{q}q \) 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 } ⋍ 266 MeV and *L* ⋍ 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 \( m_{{{a_1}}}^{\mathrm{res}}=1.435\left( {53} \right)\left( {_{-109}^{+0 }} \right) \) compared to \( m_{{{a_1}}}^{\exp }=1.230\left( {40} \right) \) GeV. The *a* _{1} width \( {\varGamma_{{{a_1}}}}(s)\equiv {{{{g^2}p}} \left/ {s} \right.} \) is parametrized in terms of the coupling and we obtain \( {g_a}{{_{{_1}}}_{\rho}}_{\pi }=1.71\left( {39} \right) \) GeV compared to \( g_{{{a_1}\rho \pi}}^{\exp }=1.35\left( {30} \right) \) GeV derived from \( \Gamma_{{{a_1}}}^{\exp }=425\left( {175} \right) \) 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} ≳ *m* _{ ω } + *m* _{ π } 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 \( m_{{{b_1}}}^{res }=1.414\left( {36} \right)\left( {_{-83}^{+0 }} \right) \)

## Keywords

Lattice QCD QCD## Notes

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