Real and Complex Singlet-Scalar Benchmarks with a Vector-Like Down Quark for $B\to X_s{\hat{I}}^3$ 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 $\mathcal{S}=S_R,\hat{I}¦$. The scalar is considered in two forms, a real field $S_R=S_R^{†}$ and a complex field $\hat{I}¦\ne \hat{I}{¦}^{†}$. The interaction $-\hat{I}{»}_i\mathcal{S}{\bar{D}}_L{d}_{Ri}+h.c.$ generates the radiative transitions $b\to s{\hat{I}}^3$ 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 $C_{7{\hat{I}}^3}^{\mathrm{NP}}/C_{8G}^{\mathrm{NP}}=Q_D=-1/3$ at the matching scale for $\hat{I}”B=1$ dipole transitions. For $M_D=m_{\mathcal{S}}=1\mathrm{TeV}$ and $|\hat{I}{»}_s^{\ast }\hat{I}{»}_b|=1$, the low scale contribution is $|C_{7{\hat{I}}^3}^{\mathrm{NP},\mathrm{eff}}(\hat{I}{¼}_b)|\simeq 1.1\times 10^{-3}$, This is about $0.4\%$ of the Standard Model value $|C_{7{\hat{I}}^3}^{\mathrm{SM},\mathrm{eff}}(\hat{I}{¼}_b)|\simeq 0.30$. 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 $|\hat{I}{»}_s^{\ast }\hat{I}{»}_b|$ at the level of a few tenths for TeV-scale masses. Thus, in these minimal benchmarks, $B\to X_s{\hat{I}}^3$ is radiatively safe, while $B_s-{\bar{B}}_s$ mixing gives the stronger constraint in the complex-scalar $\hat{I}¦$ benchmark.

30 pages, 15 figures