Universal Extra Dimensions and b -> s gamma

TL;DR

We address how flat universal extra dimensions modify the radiative decay $b \rightarrow s \gamma$. The analysis derives the one-loop KK contributions, dominated by KK states of the charged would-be-Goldstone boson and the top quark in the one-Higgs-doublet case, and uses the effective Hamiltonian with $C_7$, $C_8$, and loop functions $A(x)$ and $B(y)$ to run to $\mu \sim m_b$; the results are compared with SM expectations and $T$-parameter constraints. We find that with a single Higgs doublet the KK-WGB contribution sets $R^{-1} \gtrsim 300$ GeV, comparable to the $T$ parameter bound. In two-Higgs-doublet model II the zero-mode and KK charged-Higgs contributions cancel the WGB KK piece, removing the bound on $R^{-1}$ and weakening the $m_H$ limit relative to 4D. In two-Higgs-doublet model I the KK-WGB and KK charged-Higgs contributions add, yielding stronger bounds on $R^{-1}$ for small $\tan\beta$ (e.g., $R^{-1} \gtrsim 550$ GeV for $\tan\beta=2$, $m_H=100$ GeV) and shifting Higgs mass limits upward for certain parameter choices. These results show that extra-dimensional flavor constraints are highly sensitive to the Higgs sector, with implications for model-building and collider phenomenology.

Abstract

We analyze the effect of flat universal extra dimensions (i.e., extra dimensions accessible to all SM fields) on the process b -> s gamma. With one Higgs doublet, the dominant contribution at one-loop is from Kaluza-Klein (KK) states of the charged would-be-Goldstone boson (WGB) and of the top quark. The resulting constraint on the size of the extra dimension is comparable to the constraint from T parameter. In two-Higgs doublet model II, the contribution of zero-mode and KK states of physical charged Higgs can cancel the contribution from WGB KK states. Therefore, in this model, there is no constraint on the size of the extra dimensions from the process b -> s gamma and also the constraint on the mass of the charged Higgs from this process is weakened compared to 4D. In two Higgs doublet model I, the contribution of the zero-mode and KK states of physical charged Higgs and that of the KK states of WGB are of the same sign. Thus, in this model and for small tan beta, the constraint on the size of the extra dimensions is stronger than in one Higgs doublet model and also the constraint on the mass of the charged Higgs is stronger than in 4D.

Figures (2)

• Figure 1: The deviation of the rate of $b \rightarrow s \gamma$ from the SM prediction in model II as a function of size of one extra dimension ($R^{-1}$) and charged Higgs mass ($m_H$) for $\tan \beta = 10$ (figure (a)) and as a function of $\tan \beta$ and $m_H$ for $R^{-1} = 300$ GeV (figure (b)). In figure (b), the dashed lines are the result in $4D$. The $1 \sigma$ deviation corresponds to $18 \%$.
• Figure 2: The deviation of the rate of $b \rightarrow s \gamma$ from the SM prediction in model I as a function of size of one extra dimension ($R^{-1}$) and charged Higgs mass ($m_H$) for $\tan \beta = 2$ (figure (a)) and as a function of $\tan \beta$ and $m_H$ for $R^{-1} = 300$ GeV (figure (b)). In figure (b), the dashed lines are the result in $4D$. The $1 \sigma$ deviation corresponds to $18 \%$.