Pseudoscalar meson and vector meson interactions and dynamically generated axial-vector mesons

The axial-vector mesons $a_1(1260)$, $b_1(1235)$, $f_1(1285)$, $h_1(1170)$, $h_1(1380)$, and $K_1(1270)$ are dynamically generated in the unitized chiral perturbation theory. Such a picture has been tested extensively in the past few years. In this work, we calculate the interaction kernel up to $\mathcal{O}(p^2)$ and study the impact on the dynamically generated axial-vector states. In anticipation of future lattice QCD simulations, we calculate the scattering lengths and the pole positions as functions of the pion mass, with the light-quark mass dependence of the kaon, the eta, and the vector mesons determined by the $n_f=2+1$ lattice QCD simulations of the PACS-CS Collaboration.

Figure 1

The experimental axial-vector masses [33] in comparison with the corresponding UChPT results. The LO, NLO-6th, and NLO numbers denote the masses obtained from the LO kernel, the NLO kernel containing only the ${\kappa }_V$ term, and the complete NLO kernel. The error bars denote the uncertainties of the experimental masses while the shaded bands indicate the experimental widths. For the $K_1(1270)$, only the high-energy pole, coupling mainly to $\rho K$, is shown.

Figure 2

Scattering lengths in the dominant channels of each isospin, strangeness, and $G$-parity $(S,I^{(G)})$ sector.

Figure 3

Real part of the pole positions, $\mathrm{Re}\sqrt{s_0}$, as a function of $m_{\pi }$. The dashed lines indicate the thresholds of the corresponding coupled channels, respectively.

Figure 4

Imaginary part of the pole positions, $\mathrm{Im}\sqrt{s_0}$, as a function of $m_{\pi }$.