Muon $(g-2)$ and Flavor Puzzles in the $U(1{)}_X^{}$-gauged Leptoquark Model

Abstract

We present an economical model where an $S_1^{}$ leptoquark and an anomaly-free $U(1{)}_X^{}$ gauge symmetry with $X=B_3^{}-2L_{\mu }^{}/3-L_{\tau }^{}/3$ are introduced, to account for the muon anomalous magnetic moment $a_{\mu }^{}\equiv (g_{\mu }^{}-2)$ and flavor puzzles including $R_{K^{(\ast {)}_{}}}^{}$ and $R_{D^{(\ast {)}_{}}}^{}$ anomalies together with quark and lepton flavor mixing. The $Z_{}^{\prime }$ gauge boson associated with the $U(1{)}_X^{}$ symmetry is responsible for the $R_{K^{(\ast {)}_{}}}^{}$ anomaly. Meanwhile, the specific flavor mixing patterns of quarks and leptons can be generated after the spontaneous breakdown of the $U(1{)}_X^{}$ gauge symmetry via the Froggatt-Nielsen mechanism. The $S_1^{}$ leptoquark which is also charged under the $U(1{)}_X^{}$ gauge symmetry can simultaneously explain the latest muon $(g-2)$ result and the $R_{D^{(\ast {)}_{}}}^{}$ anomaly. In addition, we also discuss several other experimental constraints on our model.

Comments: 34 pages, 5 figures, more discussions added, published in JHEP