Mixing angle of $K_1$ axial vector mesons

Abstract

Analyses of various experimental measurements all indicate that the mixing angle ${\theta }_{K_1}$ of $K_1(1270)$ and $K_1(1400)$ is in the vicinity of $33^{\circ }$ or $57^{\circ }$. However, whether ${\theta }_{K_1}$ is greater or less than $45^{\circ }$ is still quite controversial. For example, there were two very recent studies of the strong decays of $K_1$ mesons. One group claimed that ${\theta }_{K_1}\approx 60^{\circ }$, while the other group obtained ${\theta }_{K_1}=(33.6\pm 4.3{)}^{\circ }$. Since the determination of the mixing angles ${\alpha }_{{}^3{P}_1}$ and ${\alpha }_{{}^1{P}_1}$ with the former (latter) being the mixing angle of $f_1(1285)$ ($h_1(1170)$) and $f_1(1420)$ ($h_1(1380)$) in the flavor basis through mass relations depend on ${\theta }_{K_1}$, we show that ${\theta }_{K_1}\approx 57^{\circ }$ is ruled out as it leads to a too large deviation from ideal mixing in the ${}^1{P}_1$ sector, inconsistent with the lattice calculation of ${\alpha }_{{}^1{P}_1}$ and the observation of strong decays of $h_1(1170)$ and $h_1(1380)$. We find that for ${\theta }_{K_1}\approx (28-30{)}^{\circ }$, the corresponding ${\alpha }_{{}^3{P}_1}$ and ${\alpha }_{{}^1{P}_1}$ agree well with all lattice and phenomenological analyses. This again reinforces the statement that ${\theta }_{K_1}\sim 33^{\circ }$ is much more favored than $57^{\circ }$.

Comments: 5 pages, talk presented in The XV International Conference on Hadron Spectroscopy, 4-8 November 2013, Nara,Japan