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Universal extra dimensions and Z->b bar-b

J. F. Oliver, J. Papavassiliou, A. Santamaria

TL;DR

This work analyzes the one-loop impact of a single universal extra dimension on the Z to bb̄ vertex. Using a gaugeless-limit approach and Ward identities, the authors show the leading corrections scale as $\delta g_L^{\mathrm{UED}} \sim \frac{\sqrt{2}G_F m_t^2}{(4\pi)^2} F_{\mathrm{UED}}(a)$ with $a=\pi R m_t$, and that $F_{\mathrm{UED}}(a) \approx \frac{a^2}{12}$ for small $a$, corresponding to an $m_t^4 R^2$ dependence. The KK tower introduces no $\log(R)$ terms due to KK-number conservation, and the resulting phenomenology yields a 95% CL bound $R^{-1} > 300$ GeV, comparable to bounds from the $\rho$ parameter; subleading $M_W^2/m_t^2$ corrections can further affect the constraint. The work systematically derives the 5D Lagrangian, KK spectrum, and couplings, highlighting the top-quark–driven enhancements and its implications for precision electroweak tests of universal extra dimensions.

Abstract

We study, at the one loop level, the dominant contributions from a single universal extra dimension to the process (Z\to b\bar{b}). By resorting to the gaugeless limit of the theory we explain why the result is expected to display a strong dependence on the mass of the top-quark, not identified in the early literature. A detailed calculation corroborates this expectation, giving rise to a lower bound for the compactification scale which is comparable to that obtained from the $ρ$ parameter. An estimate of the subleading corrections is furnished, together with a qualitative discussion on the difference between the present results and those derived previously for the non-universal case.

Universal extra dimensions and Z->b bar-b

TL;DR

This work analyzes the one-loop impact of a single universal extra dimension on the Z to bb̄ vertex. Using a gaugeless-limit approach and Ward identities, the authors show the leading corrections scale as with , and that for small , corresponding to an dependence. The KK tower introduces no terms due to KK-number conservation, and the resulting phenomenology yields a 95% CL bound GeV, comparable to bounds from the parameter; subleading corrections can further affect the constraint. The work systematically derives the 5D Lagrangian, KK spectrum, and couplings, highlighting the top-quark–driven enhancements and its implications for precision electroweak tests of universal extra dimensions.

Abstract

We study, at the one loop level, the dominant contributions from a single universal extra dimension to the process (Z\to b\bar{b}). By resorting to the gaugeless limit of the theory we explain why the result is expected to display a strong dependence on the mass of the top-quark, not identified in the early literature. A detailed calculation corroborates this expectation, giving rise to a lower bound for the compactification scale which is comparable to that obtained from the parameter. An estimate of the subleading corrections is furnished, together with a qualitative discussion on the difference between the present results and those derived previously for the non-universal case.

Paper Structure

This paper contains 4 sections, 27 equations, 4 figures.

Table of Contents

  1. Introduction
  2. The Lagrangian
  3. Calculating $Z \rightarrow b \bar{b}$
  4. Conclusions

Figures (4)

  • Figure 1: The only diagram contributing to the SM $G^0 b \bar{b}$ vertex in the gaugeless limit for massless $b$-quarks.
  • Figure 2: The dominant diagram contributing to the UED $G^0 b \bar{b}$ vertex in the gaugeless limit for massless $b$-quarks.
  • Figure 3: Dominant UED contributions to the $Zb\bar{b}$ vertex.
  • Figure 4: Diagrams giving subleading contributions to the $G^{0}b\bar{b}$ vertex.