  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
$m_{a1}^{res}=1.435(53)(^{+0}_{-109})$ 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 $m_{b_1}^{res}=1.414(36)(^{+0}_{-83})$.
