[Paper Review] Non-minimal UED confronts $B_{s} ightarrow\mu^{+}\mu^{-}$

Anindya Datta, Avirup Shaw|arXiv (Cornell University)|Jun 26, 2015

Particle physics theoretical and experimental studies52 references8 citations

TL;DR

This paper investigates the branching ratio of $B_s \to \mu^+\mu^-$ in a non-minimal Universal Extra Dimensional (nmUED) model with boundary-localized kinetic and Yukawa terms (BLKT/BLYT). It computes one-loop contributions from Kaluza-Klein (KK) excitations, showing that experimental data constrains the compactification scale $R^{-1}$ to be above 800 GeV for certain parameter choices—among the most stringent limits in nmUED. The analysis reveals that $B_s \to \mu^+\mu^-$ provides stronger constraints than electroweak precision observables for positive BLT parameters.

ABSTRACT

Addition of boundary localised kinetic and Yukawa terms to the action of a 5-dimensional Standard Model would non-trivially modify the Kaluza-Klein spectra and some of the interactions among the Kaluza-Klein excitations compared to the minimal version of this model, in which, these boundary terms are not present. In the minimal version of this framework known as Universal Extra Dimensional model, special assumptions are made about these unknown, beyond the cut-off contributions to restrict the number of unknown parameters of the theory to a minimal. We estimate the contribution of Kaluza-Klein modes to the branching ratios of $B_{s(d)} ightarrow\mu^{+}\mu^{-}$ in the framework of non-minimal Universal Extra Dimensional, at one loop level. The results have been compared to the experimental data to constrain the parameters of this model. From the measured decay branching ratio of $B_s ightarrow \mu^+ \mu^-$ (depending on the values of boundary localised parameters) lower limit on $R^{-1}$ can be as high as 800 GeV. We have briefly reviewed the bounds on nmUED parameter space coming from electroweak precision observables. The present analysis ($B_s ightarrow \mu^+ \mu^-$) has ruled out new regions of parameter space in comparison to the analysis of electroweak data. We have revisited the bound on $R^{-1}$ in Universal Extra Dimensional model, which came out to be 454 GeV. This limit on $R^{-1}$ in Universal Extra Dimensional framework is not as competitive as the limits derived from the consideration of relic density or Standard Model Higgs boson production and decay to $W^+ W^-$. Unfortunately, $B_{d} ightarrow\mu^{+}\mu^{-}$ decay branching ratio would not set any significant limit on $R^{-1}$ in a minimal or non-minimal Universal Extra Dimensional model.

Motivation & Objective

• To assess the impact of boundary-localized terms (BLKT/BLYT) on $B_s \to \mu^+\mu^-$ branching ratios in non-minimal UED.
• To constrain the compactification scale $R^{-1}$ using the precisely measured $B_s \to \mu^+\mu^-$ decay rate.
• To compare the sensitivity of $B_s \to \mu^+\mu^-$ data with electroweak precision observables (S, T, U) in constraining nmUED parameter space.
• To determine whether $B_d \to \mu^+\mu^-$ provides competitive constraints in this framework.

Proposed method

• One-loop calculation of $B_s \to \mu^+\mu^-$ decay amplitude in 5D nmUED with boundary-localized kinetic and Yukawa terms.
• Incorporation of Kaluza-Klein (KK) mode contributions up to the fifth level, with masses $m_n \sim \sqrt{m^2 + n^2/R^2}$.
• Use of Feynman gauge for loop calculations, including unphysical degrees of freedom from Goldstone and physical scalar sectors.
• Implementation of the GIM mechanism to cancel divergences in penguin diagrams.
• Parametrization of BLKT/BLYT coefficients as free parameters: $R_f$ for fermions and $R_V$ for gauge/Higgs sectors.
• Comparison of theoretical predictions with experimental branching ratio: $\text{Br}(B_s \to \mu^+\mu^-) = (3.2 \pm 0.7) \times 10^{-9}$.

Experimental results

Research questions

• RQ1 How do boundary-localized kinetic and Yukawa terms modify the KK spectrum and couplings in nmUED?
• RQ2 What is the one-loop contribution of KK excitations to $B_s \to \mu^+\mu^-$ in the nmUED framework?
• RQ3 How do experimental constraints on $\text{Br}(B_s \to \mu^+\mu^-)$ limit the compactification scale $R^{-1}$ in nmUED?
• RQ4 How do these bounds compare with those from electroweak precision observables (S, T, U)?
• RQ5 Does $B_d \to \mu^+\mu^-$ decay provide competitive constraints on nmUED parameters?

Key findings

• The branching ratio $\text{Br}(B_s \to \mu^+\mu^-)$ in nmUED is sensitive to boundary-localized term parameters $R_f$ and $R_V$, with significant modifications to the KK spectrum and couplings.
• For positive $R_f$ and $R_V$, the $B_s \to \mu^+\mu^-$ decay sets a lower bound on $R^{-1}$ of up to 800 GeV at 95% C.L., representing the most stringent constraint in the nmUED framework.
• The bound from $B_s \to \mu^+\mu^-$ is stronger than those from electroweak precision observables (S, T, U) for positive $R_f$ values.
• For negative $R_f$, the bounds from $B_s \to \mu^+\mu^-$ are weak due to heavier KK masses, and such regions are already excluded by electroweak data.
• The $B_d \to \mu^+\mu^-$ decay does not provide competitive constraints on $R^{-1}$ in either minimal or non-minimal UED.
• The analysis confirms consistency with the Z-boson mass across the entire allowed parameter space, including regions excluded by $B_s \to \mu^+\mu^-$.