Mixing angle of $K_1$ axial vector mesons

TL;DR

This paper investigates the mixing angle of $K_1$ axial vector mesons, analyzing experimental data and theoretical models to determine whether it is closer to 33° or 57°, and concludes that around 33° is more consistent with current evidence.

Contribution

The study clarifies the favored range of the $K_1$ mixing angle by comparing experimental results with lattice and phenomenological analyses, ruling out the 57° scenario.

Findings

$ heta_{K_1} ext{ is around }33^\u00b0$ based on data consistency.

$ heta_{K_1} ext{ near }57^\u00b0$ is inconsistent with lattice and decay observations.

The preferred mixing angle aligns with lattice calculations and decay phenomenology.

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 $\theta_{K_1}=(33.6\pm4.3)^\circ$. 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 $57^\circ$.