%0 Journal Article %1 Cheng2011Revisiting %A Cheng, Hai-Yang %D 2011 %K mixing %T Revisiting Axial-Vector Meson Mixing %U http://arxiv.org/abs/1110.2249 %X Various phenomenological studies indicate that the mixing angle \$þeta\_K\_1\$ of \$K\_1A\$ and \$K\_1B\$, the strange partners of the axial-vector mesons \$a\_1(1260)\$ and \$b\_1(1235)\$, respectively, lies in the vicinity of \$35^\circ\$ or \$55^\circ\$, but whether this angle is larger or smaller than \$45^\circ\$ still remains controversial. When the \$f\_1(1285)\$-\$f\_1(1420)\$ mixing angle \$þeta\_^3P\_1\$ and the \$h\_1(1170)\$-\$h\_1(1380)\$ mixing angle \$þeta\_^1P\_1\$ are determined from the mass relations, they depend on the masses of \$K\_1A\$ and \$K\_1B\$, which in turn depend on the mixing angle \$þeta\_K\_1\$. We show that the approximate decoupling of the light \$qq\$ state from the heavier \$s s\$ state, which is empirically valid for vector, tensor and \$3^--\$ mesons, when applied to isoscalar axial-vector mesons, will enable us to discriminate different solutions of \$þeta\_^3P\_1\$ and \$þeta\_^1P\_1\$ and pick up \$þeta\_K\_135^\circ\$. Indeed, for \$þeta\_K\_155^\circ\$, the predicted \$þeta\_^1P\_1\$ disagrees sharply with the recent lattice calculation and the implied large \$ss\$ content of \$h\_1(1170)\$ and \$q\bar q\$ component of \$h\_1(1380)\$ cannot explain the observation of their strong decays. We conclude that \$þeta\_K\_1\$ is smaller than \$45^\circ\$.

@article{Cheng2011Revisiting, abstract = {Various phenomenological studies indicate that the mixing angle \$\theta\_{K\_1}\$ of \$K\_{1A}\$ and \$K\_{1B}\$, the strange partners of the axial-vector mesons \$a\_1(1260)\$ and \$b\_1(1235)\$, respectively, lies in the vicinity of \$35^\circ\$ or \$55^\circ\$, but whether this angle is larger or smaller than \$45^\circ\$ still remains controversial. When the \$f\_1(1285)\$-\$f\_1(1420)\$ mixing angle \$\theta\_{^3P\_1}\$ and the \$h\_1(1170)\$-\$h\_1(1380)\$ mixing angle \$\theta\_{^1P\_1}\$ are determined from the mass relations, they depend on the masses of \$K\_{1A}\$ and \$K\_{1B}\$, which in turn depend on the mixing angle \$\theta\_{K\_1}\$. We show that the approximate decoupling of the light \$q\bar q\$ state from the heavier \$s \bar s\$ state, which is empirically valid for vector, tensor and \$3^{--}\$ mesons, when applied to isoscalar axial-vector mesons, will enable us to discriminate different solutions of \$\theta\_{^3P\_1}\$ and \$\theta\_{^1P\_1}\$ and pick up \$\theta\_{K\_1}\sim 35^\circ\$. Indeed, for \$\theta\_{K\_1}\sim 55^\circ\$, the predicted \$\theta\_{^1P\_1}\$ disagrees sharply with the recent lattice calculation and the implied large \$s\bar s\$ content of \$h\_1(1170)\$ and \$q\bar q\$ component of \$h\_1(1380)\$ cannot explain the observation of their strong decays. We conclude that \$\theta\_{K\_1}\$ is smaller than \$45^\circ\$.}, added-at = {2019-02-23T22:09:48.000+0100}, archiveprefix = {arXiv}, author = {Cheng, Hai-Yang}, biburl = {https://www.bibsonomy.org/bibtex/2da06bc83e85e45a81388635beff9a9c0/cmcneile}, citeulike-article-id = {9893024}, citeulike-linkout-0 = {http://arxiv.org/abs/1110.2249}, citeulike-linkout-1 = {http://arxiv.org/pdf/1110.2249}, day = 11, eprint = {1110.2249}, interhash = {483451dfb29bf136f729184cc0945b86}, intrahash = {da06bc83e85e45a81388635beff9a9c0}, keywords = {mixing}, month = oct, posted-at = {2011-10-12 08:45:54}, priority = {2}, timestamp = {2019-02-23T22:15:27.000+0100}, title = {{Revisiting Axial-Vector Meson Mixing}}, url = {http://arxiv.org/abs/1110.2249}, year = 2011 }