Chiral enhancement in the vector-like fourth family: Case of $b \to s γ$

Abstract

We demonstrate that a vector-like fourth family of quarks induces a genuine chiral enhancement in $b\to sγ$, which is absent in the Standard Model (SM). The coexistence of doublet and singlet states allows the chirality flip to occur inside the loop, leading to contributions proportional to the heavy vector-like mass. The resulting amplitude is enhanced by a factor $\overlineλ_d v_H/m_b$, which can be as large as $\mathcal{O}(40)$ for moderate Yukawa couplings. This leads to sizable deviation from the SM prediction even for $\mathcal{O}(\mathrm{TeV})$ vector-like quark masses and small mixing angles. We find that $\mathrm{Br}(\overline{B}\to X_sγ)$ provides the most stringent constraint on this scenario among a wide range of precision observables.

Figures (3)

• Figure 1: Diagrams contribute to the Wilson coefficient $C_7$. Those for $C_8$ can be obtained by replacing the photon $\gamma$ to the gluon $g$ in the diagrams (A) and (B).
• Figure 2: $\text{Br}({\overline{B}}\to{X_s\gamma})$ of the cases (1), (2), (3) and (4) on the left-top, right-top, bottom-left and bottom-right panels, respectively. The thick black line is the experimental central value. The deviations are $1\sigma$, $2\sigma$ and $3\sigma$ on the dashed, dot-dashed and dotted lines, respectively. $R_{B_s}$, that is the ratio of $\Delta M_{s}$ to the SM prediction, reaches 3 $\%$ (0.1 $\%$) on the brown (green) lines. The quark mass and CKM fit is failed in the orange and brown colored region in the bottom panels.
• Figure 3: $A_{{\mathrm{CP}}}$ with respect to $\mathrm{Arg}\overline{\lambda}_d$. The solid red, dot-dashed green and dashed yellow lines are respectively the cases (1), (2) and (3) where $\epsilon^d_{A_{2,3}} = 0.1$ with $A=L,R,V$.