Real and Complex Singlet-Scalar Benchmarks with a Vector-Like Down Quark for $B\to X_s\gamma$ and $B_s-{\bar{B}}_s$ Mixing

Abstract

We study a simple extension of the Standard Model with a vector-like down-type quark $D$ and a neutral singlet scalar $\mathcal{S}=S_R,\Phi$. The scalar is considered in two forms, a real field $S_R=S_R^{†}$ and a complex field $\Phi \ne {\Phi }^{†}$. The interaction $-{\lambda }_i\mathcal{S}{\bar{D}}_L{d}_{Ri}+h.c.$ generates the radiative transitions $b\to s\gamma$ and $b\to sg$ at one loop. Since $\mathcal{S}$ has no electric charge or color, the gauge boson is emitted from the internal $D$ line, giving $C_{7\gamma }^{\mathrm{NP}}/C_{8G}^{\mathrm{NP}}=Q_D=-1/3$ at the matching scale for $\Delta B=1$ dipole transitions. For $M_D=m_{\mathcal{S}}=1\mathrm{TeV}$ and $|{\lambda }_s^{\ast }{\lambda }_b|=1$, the low scale contribution is $|C_{7\gamma }^{\mathrm{NP},\mathrm{eff}}({\mu }_b)|\simeq 1.1\times 10^{-3}$, This is about $0.4\%$ of the Standard Model value $|C_{7\gamma }^{\mathrm{SM},\mathrm{eff}}({\mu }_b)|\simeq 0.30$. We also discuss \(B_s-\bar B_s\) mixing. In the real-scalar case, the direct and crossed box diagrams cancel in the exact minimal limit. In the complex-scalar case, the direct box contribution remains and gives a bound on the flavor $|{\lambda }_s^{\ast }{\lambda }_b|$ at the level of a few tenths for TeV-scale masses. Thus, in these minimal benchmarks, $B\to X_s\gamma$ is radiatively safe, while $B_s-{\bar{B}}_s$ mixing gives the stronger constraint in the complex-scalar $\Phi$ benchmark.

30 pages, 15 figures

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