Nondecoupling of a terascale isosinglet quark and rare $K$ and $B$ decays

We examine recent extensions of the standard model with an up-type vectorlike isosinglet $T$ quark that mixes dominantly with the top quark. We take under scrutiny the nondecoupling effects which may reveal such a new heavy fermion through loop diagrams relevant for rare decays such as $K\to \pi \nu \overline{\nu }$, $B\to \pi (K)\nu \overline{\nu }$, and $B_{s,d}\to {\mu }^{+}{\mu }^{-}$. After demonstrating in detail the cancellation between the leading nondecoupling terms, we show that two residual forms $\sim s^2\ln m_T^2$ and $\sim s^4{m}_T^2$ act in a complementary way, so that the maximal allowed values of the decay rates are practically independent of $m_T$. While they correspond to $\sim 20\%$ or $\sim 30\%$ corrections to the SM rates for $K\to \pi \nu \overline{\nu }$ and $B\to \pi (K)\nu \overline{\nu }$, an increase by $\sim 50\%$ for $B_{s,d}\to {\mu }^{+}{\mu }^{-}$ decays offers a possibility to reveal an additional isosinglet state by measurements of these decays at the Large Hadron Collider.

Figure 1

Allowed parameter space from EWPO, lying below the upper curve determined from $R_b$, or the lower curve determined from the $T$ parameter.

Figure 2

Loop diagrams: (a) to (c), in which the potentially leading nondecoupling $\sim s^2{x}_T$ reduces to merely $\sim s^2\ln x_T$ as demonstrated in Eq. (10), and the diagram (d) giving the second remaining form $\sim s^4{x}_T$.

Figure 3

Maximal possible enhancements with respect to the SM for the BSM branching ratios $R_{s,d}$, $R_L$, and $R_{+}$, going from top down. For comparison we show the corresponding enhancement for the $B-\overline{B}$ mixing, as the lowest curve.

Figure 4

The complementary behavior with respect to $m_T$ of the two relics of nondecouplings, entering $Y^{\mathrm{BSM}}=Y^{\mathrm{SM}}+\Delta Y$ in Eq. (21) relevant for $R_{s,d}$: the decreasing $\sim s^2$ and the increasing $\sim s^4$ term in Eq. (21), and their almost $m_T$-independent sum on the upper curve.

Figure 5

Full plot for possible enhancement of the Br ($B\to {\mu }^{-}{\mu }^{+}$), given by the functional dependence of the $R_{s,d}$ on the parameters of the model. Let us note that by projecting the top of the displayed surface on the $(R_{s,d},m_T)$ plane, one obtains the uppermost curve in Fig. 3.

Figure 6

LHM parameter region, as restricted by Buras et al., touches the EWPO curve from Fig. 1 in the point $(s=0.16,m_T=2\mathrm{TeV})$.