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

TL;DR

This paper investigates a minimal extension of the Standard Model involving a vector-like down quark and a singlet scalar, analyzing their effects on $B o X_s\gamma$ and $B_s-ar B_s$ mixing, and providing constraints on model parameters.

Contribution

It introduces a simple vector-like quark and scalar model, calculating new physics contributions to flavor-changing processes and deriving bounds on model parameters.

Findings

The new physics contribution to $C_{7 ext{gamma}}$ is about 0.4% of the Standard Model value.

In the real scalar case, contributions cancel in the minimal limit, making $B o X_s\gamma$ radiatively safe.

In the complex scalar case, $B_s-ar B_s$ mixing constrains the flavor couplings more strongly.

Abstract

We study a simple extension of the Standard Model with a vector-like down-type quark $D$ and a neutral singlet scalar ${\cal S}=S_R,\Phi$. The scalar is considered in two forms, a real field $S_R=S_R^\dagger$ and a complex field $\Phi\neq\Phi^\dagger$. The interaction $-\lambda_i{\cal S}\bar D_L d_{Ri}+{\rm h.c.}$ generates the radiative transitions $b\to s\gamma$ and $b\to sg$ at one loop. Since ${\cal S}$ has no electric charge or color, the gauge boson is emitted from the internal $D$ line, giving $C_{7\gamma}^{\rm NP}/C_{8G}^{\rm NP}=Q_D=-1/3$ at the matching scale for $\Delta B=1$ dipole transitions. For $M_D=m_{\cal S}=1~{\rm TeV}$ and $|\lambda_s^\ast\lambda_b|=1$, the low scale contribution is $|C_{7\gamma}^{\rm NP,eff}(\mu_b)|\simeq 1.1\times10^{-3}$, This is about $0.4\%$ of the Standard Model value $|C_{7\gamma}^{\rm SM,eff}(\mu_b)|\simeq 0.30$. 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.