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

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.

💡 Research Summary

The paper investigates the impact of a vector‑like fourth family of quarks on the radiative flavor‑changing transition $b\to s\gamma$. The authors extend the Standard Model by adding an SU(2)$L$ doublet $Q=(Q_u,Q_d)^T$ and two singlets $U$ and $D$, all carrying the same gauge quantum numbers as the SM quark doublet and singlets. In addition to the usual SM Yukawa couplings $y{u,d}$, the Lagrangian contains mixing terms $\epsilon_{u,d}^{L,R}$ that couple the new vector‑like fields to the SM quarks through the Higgs doublet, and pure vector‑like Yukawa couplings $\lambda_{u,d}$ that couple $Q$ directly to $U$ and $D$ via the Higgs. After electroweak symmetry breaking the 5 × 5 mass matrices for up‑ and down‑type quarks are diagonalized by unitary matrices $U_{u,d}^{L,R}$, leading to a generalized CKM matrix that is no longer unitary.

A central observation is that the coexistence of doublet and singlet vector‑like states permits a chirality flip to occur inside the loop rather than on the external $b$‑quark line. Consequently the dominant contribution to the dipole operator $Q_7$ (and its chirality‑flipped counterpart $Q_7’$) scales as
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