[Paper Review] $Z ightarrow b {\bar b}$ in non-minimal Universal Extra Dimensional Model

Tapoja Jha, Anindya Datta|arXiv (Cornell University)|Oct 19, 2014

Particle physics theoretical and experimental studies2 references8 citations

TL;DR

This paper calculates the one-loop radiative correction to the $Zb\bar{b}$ coupling in a non-minimal Universal Extra Dimensional (nmUED) model, where boundary-localized kinetic and Yukawa terms (BLKT/BLYT) are introduced as free parameters. It finds that with suitable choices of these parameters, the 95% confidence level lower limit on the compactification scale $R^{-1}$ increases to approximately 800 GeV—significantly higher than the 350 GeV limit in the minimal UED model—due to enhanced suppression of the $Zb\bar{b}$ coupling deviation from the SM prediction.

ABSTRACT

We calculate the effective $Z b\bar b$ coupling at one loop level, in the framework of non-minimal Universal Extra Dimensional (nmUED) model. Non-minimality in Universal Extra Dimensional (UED) framework is realized by adding kinetic and Yukawa terms with arbitrary coefficients to the action at boundary points of the extra space like dimension. A recent estimation of the Standard Model (SM) contribution to $Zb\bar{b}$ coupling at two loop level, points to a $1.2σ$ discrepancy between the experimental data and the SM estimate. We compare our calculation with the difference between the SM prediction and the experimental estimation of the above coupling and constrain the parameter space of nmUED. We also review the limit on compactification radius of UED in view of the new theoretical estimation of SM contribution to $Z b\bar{b}$ coupling. For suitable choice of coefficients of boundary-localized terms, 95\% C.L. lower limit on $R^{-1}$ comes out to be in the ballpark of 800 GeV in the framework of nmUED; while in UED, the lower limit on $R^{-1}$ is 350 GeV which is a marginal improvement over an earlier estimate.

Motivation & Objective

• To calculate the one-loop radiative correction to the $Zb\bar{b}$ vertex in the non-minimal Universal Extra Dimensional (nmUED) model.
• To investigate how boundary-localized terms (BLKTs and BLYTs) modify the $Zb\bar{b}$ coupling and affect the constraints on the compactification scale $R^{-1}$.
• To compare the nmUED prediction with the observed 1.2$\sigma$ discrepancy between the SM estimate and experimental measurement of $R_b$.
• To re-evaluate the lower bound on $R^{-1}$ in the minimal UED model using the updated two-loop SM estimate of $Zb\bar{b}$ coupling.
• To constrain the parameter space of nmUED by comparing theoretical predictions with experimental data on $R_b$.

Proposed method

• The model extends the minimal UED framework by introducing arbitrary coefficients for boundary-localized kinetic and Yukawa terms (BLKT/BLYT) in the five-dimensional action.
• Feynman diagrams involving Kaluza-Klein (KK) excitations of top quarks, W bosons, and charged Higgs/Goldstone bosons are computed at one-loop level to evaluate the $Zb\bar{b}$ vertex correction.
• The calculation is performed in the 't Hooft-Feynman gauge with a regularization scheme that renders the total amplitude finite and independent of $\sin^2\theta_W$, ensuring gauge invariance.
• The effective $Zb\bar{b}$ coupling is decomposed into left- and right-chiral components, with the left-chiral correction dominated by top quark and charged Higgs loops.
• The function $F_{\text{nmUED}}$, representing the deviation of the $Zb\bar{b}$ coupling from the SM prediction, is computed numerically and compared with the experimental $R_b$ deviation.
• Constraints on $R^{-1}$, $R_f$ (fermion BLKT), and $R_\phi$ (Higgs/Boson BLKT) are derived using the 95% confidence level upper limit on $F_{\text{nmUED}}$.

Experimental results

Research questions

• RQ1 How do boundary-localized kinetic and Yukawa terms in the nmUED model modify the one-loop correction to the $Zb\bar{b}$ coupling?
• RQ2 What is the impact of non-minimal parameters ($R_f$, $R_\phi$) on the lower bound of the compactification scale $R^{-1}$?
• RQ3 Can the nmUED model resolve the 1.2$\sigma$ discrepancy between the SM prediction and experimental measurement of $R_b$?
• RQ4 How does the inclusion of BLKTs affect the sensitivity of the $Zb\bar{b}$ coupling to new physics compared to the minimal UED model?
• RQ5 What are the allowed regions in the $R_\phi$-$R_f$ parameter space for different values of $R^{-1}$ at 95% confidence level?

Key findings

• The 95% confidence level lower limit on the compactification scale $R^{-1}$ in the minimal UED model is found to be 350 GeV, a marginal improvement over previous estimates.
• In the non-minimal UED model, with non-zero boundary-localized terms, the lower limit on $R^{-1}$ increases significantly to approximately 800 GeV for suitable choices of $R_f$ and $R_\phi$.
• The function $F_{\text{nmUED}}$, representing the deviation of the $Zb\bar{b}$ coupling from the SM, is highly sensitive to the fermion BLKT parameter $R_f$, while the Higgs/Boson BLKT parameter $R_\phi$ has a much milder effect.
• The dominant contribution to the $Zb\bar{b}$ vertex correction arises from loops involving KK excitations of top quarks and charged Higgs/Goldstone bosons, with a finite and $\sin^2\theta_W$-independent amplitude.
• The second class of diagrams, involving KK-W bosons and top quarks, requires careful regularization due to ultraviolet divergences, but the final result is finite and independent of $\sin^2\theta_W$ after proper renormalization.
• Contour plots in the $R_\phi$-$R_f$ plane show that for a fixed $R^{-1}$, increasing $R_f$ expands the allowed parameter space, with the left side of each contour representing the region consistent with the 95% C.L. limit on $F_{\text{nmUED}}$.