TeV-scale vector leptoquark from Pati-Salam unification with vectorlike families

In this paper, we show an explicit way to realize a TeV-scale vector leptoquark from the Pati-Salam unification with extra vectorlike families. The leptoquark mass is constrained to be heavier than PeV scale by the measurement of a flavor violating kaon decay, $K_L\to \mu e$, in conventional models. This strong constraint can be avoided by introducing vectorlike families consistently with the quark and lepton masses and Cabbibo-Kobayashi-Maskawa and Pontecorvo-Maki-Nakagawa-Sakata matrices. In this model, the vector leptoquark can be sufficiently light to explain the recent $b\to s\mu \mu$ anomaly, while the $b\to c\tau \nu$ anomaly is difficult to be explained due to the strong constraints from the $Z^{\prime }$ boson and vectorlike quark searches at the LHC. When the $b\to s\mu \mu$ anomaly is explained, we show that $\mathcal{O}(0.2)\%$ tuning is required in the fermion matrix, the future experiments in $\mu \to e\gamma$ and $\mu \text{−}e$ conversions will cover most available parameter space, and sizable neutral meson mixings, induced by the extra Higgs doublets, are unavoidable.

Figure 1

The degree of tuning, the current constraints and future sensitivity in the $(s_Q+s_{\ell },s_Q-s_{\ell })$ plane, where $s_Q≔s_{Q_L}=s_{Q_R}$ and $s_{\ell }≔s_{{\ell }_L}=s_{{\ell }_R}$. The density plot shows the degree of tuning ${\mathrm{\Delta }}_{\mathrm{FT}}^{-1}$. The gray and blue shaded regions are excluded by the measurement of $\mathrm{BR}(K_L\to \mu e)$ and $\mathrm{BR}(\mu \to e\gamma )$, respectively. The blue and green lines show values of $\mathrm{BR}(\mu \to e\gamma )$ and $\mu \text{−}e$ conversion observables. See the text for further details.

Figure 2

The same plot as Fig. 1 on the $(s_L,s_R)$ plane where $s_L≔s_{Q_L}=-s_{{\ell }_L}/1.1$ and $s_R≔s_{Q_R}=-s_{{\ell }_R}/1.1$.

Figure 3

The limits on the heavy Higgs boson mass $m_H$ from the observables concerned with the neutral meson mixings: $|C_{B_d}|$ (green), $|C_{B_s}|$ (yellow), $C_{B_d/B_s}$ (red) and $\mathrm{Im}{C}_K$ (blue). The excluded region for each observable is filled with the same color as the corresponding line. $\tan \beta$ is fixed at $\tan \beta =2.0$ (50) in the left (right) panel.