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The Impact of Universal Extra Dimensions on B -> X_s gamma, B -> X_s gluon, B -> X_s mu^+ mu^-, K_L -> pi^0 e^ +e^-, and epsilon'/epsilon

Andrzej J. Buras, Anton Poschenrieder, Michael Spranger, Andreas Weiler

TL;DR

This work analyzes the impact of a single universal extra dimension in the ACD model on flavor-changing neutral current processes. By computing KK contributions to gamma and gluon penguins, as well as magnetic and chromomagnetic penguins, and combining with existing Z-penguin results, the authors assess effects on B decays (B→Xsγ, B→Xsμ+μ−), K_L→π^0e+e−, and the CP-violating ratio ε′/ε. Key findings include a ~20% suppression of Br(B→Xsγ), a ~40% suppression of Br(B→Xs gluon), a ~12% enhancement of Br(B→Xsμ+μ−) with a shifted A_FB zero to hat s ≈ 0.142 for 1/R=300 GeV, and a modest (<10%) impact on Br(K_L→π^0e+e−) with ε′/ε generally suppressed. The results exhibit a MFV-consistent correlation between hat s0 in A_FB and Br(B→Xsγ), and they illustrate how a single new parameter, 1/R, governs a coherent pattern of enhancements and suppressions across FCNC observables, with potential constraints depending on future experimental and theoretical precision.

Abstract

We calculate the contributions of the Kaluza-Klein (KK) modes to the gamma-penguins, gluon-penguins, gamma-magnetic penguins and chromomagnetic penguins in the Appelquist, Cheng and Dobrescu (ACD) model with one universal extra dimension. Together with our previous calculation of Z^0 penguin diagrams (See http://arxiv.org/abs/hep-ph/0212143) this allows to study the impact of the KK modes on the decays B -> X_s gamma, B -> X_s gluon, B -> X_s mu^+ mu^- and K_L -> pi^0 e^+ e^- and on the CP-violating ratio epsilon'/epsilon. For the compactification scale 1/R= 300 GeV the perturbative part of the branching ratio for B -> X_s mu^+ mu^- is enhanced by 12 % while the zero in the A_FB asymmetry is shifted from \hat s_0=0.162 to \hat s_0=0.142. The sizable suppressions of Br(B -> X_s gamma) ~ 20 % and Br(B -> X_s gluon) ~ 40 % could have interesting phenomenological implications on the lower bound on 1/R provided the experimental and theoretical uncertainties will be decreased. Similar comments apply to epsilon'/epsilon that is suppressed relative to the Standard Model expectations with the size of the suppression depending sensitively on the hadronic matrix elements. The impact on K_L -> pi^0 e^+ e^- is below 10 %. We point out a correlation between the zero \hat s_0 in the A_FB asymmetry and Br(B -> X_s gamma) that should be valid in most models with minimal flavour violation.

The Impact of Universal Extra Dimensions on B -> X_s gamma, B -> X_s gluon, B -> X_s mu^+ mu^-, K_L -> pi^0 e^ +e^-, and epsilon'/epsilon

TL;DR

This work analyzes the impact of a single universal extra dimension in the ACD model on flavor-changing neutral current processes. By computing KK contributions to gamma and gluon penguins, as well as magnetic and chromomagnetic penguins, and combining with existing Z-penguin results, the authors assess effects on B decays (B→Xsγ, B→Xsμ+μ−), K_L→π^0e+e−, and the CP-violating ratio ε′/ε. Key findings include a ~20% suppression of Br(B→Xsγ), a ~40% suppression of Br(B→Xs gluon), a ~12% enhancement of Br(B→Xsμ+μ−) with a shifted A_FB zero to hat s ≈ 0.142 for 1/R=300 GeV, and a modest (<10%) impact on Br(K_L→π^0e+e−) with ε′/ε generally suppressed. The results exhibit a MFV-consistent correlation between hat s0 in A_FB and Br(B→Xsγ), and they illustrate how a single new parameter, 1/R, governs a coherent pattern of enhancements and suppressions across FCNC observables, with potential constraints depending on future experimental and theoretical precision.

Abstract

We calculate the contributions of the Kaluza-Klein (KK) modes to the gamma-penguins, gluon-penguins, gamma-magnetic penguins and chromomagnetic penguins in the Appelquist, Cheng and Dobrescu (ACD) model with one universal extra dimension. Together with our previous calculation of Z^0 penguin diagrams (See http://arxiv.org/abs/hep-ph/0212143) this allows to study the impact of the KK modes on the decays B -> X_s gamma, B -> X_s gluon, B -> X_s mu^+ mu^- and K_L -> pi^0 e^+ e^- and on the CP-violating ratio epsilon'/epsilon. For the compactification scale 1/R= 300 GeV the perturbative part of the branching ratio for B -> X_s mu^+ mu^- is enhanced by 12 % while the zero in the A_FB asymmetry is shifted from \hat s_0=0.162 to \hat s_0=0.142. The sizable suppressions of Br(B -> X_s gamma) ~ 20 % and Br(B -> X_s gluon) ~ 40 % could have interesting phenomenological implications on the lower bound on 1/R provided the experimental and theoretical uncertainties will be decreased. Similar comments apply to epsilon'/epsilon that is suppressed relative to the Standard Model expectations with the size of the suppression depending sensitively on the hadronic matrix elements. The impact on K_L -> pi^0 e^+ e^- is below 10 %. We point out a correlation between the zero \hat s_0 in the A_FB asymmetry and Br(B -> X_s gamma) that should be valid in most models with minimal flavour violation.

Paper Structure

This paper contains 29 sections, 92 equations, 8 figures, 8 tables.

Table of Contents

  1. Introduction
  2. The Five Dimensional ACD Model
  3. Penguin Diagrams in the ACD Model
  4. Preliminaries
  5. General Structure of the Calculation
  6. The functions $D$, $E$ $D'$ $E'$ and $Z$
  7. $B\to X_s\gamma$
  8. Preliminaries
  9. Effective Hamiltonian
  10. The Branching Ratio
  11. $B\to X_s~{\rm gluon}$
  12. Preliminaries
  13. $B\to X_{s} \mu^+\mu^-$
  14. Preliminaries
  15. Effective Hamiltonian
  16. ...and 14 more sections

Figures (8)

  • Figure 1: Penguin diagrams contributing to $F_n(x_t,x_n)$.
  • Figure 2: The functions $F(x_t,1/R)$ and $F_0(x_t)$ with $F=D,E,D',E'$ plotted versus $1/R$. The constant dashed lines are the SM values.
  • Figure 3: The branching ratio for $B\to X_s\gamma$ and $E_\gamma > 1.6$ GeV as a function of $1/R$. See text for the meaning of various curves.
  • Figure 4: The branching ratio for $B\to X_s g$ for $m_c/m_b = 0.22$ and $\mu_b$ = $2.5$, $5$, $7.5$ GeV. $Br(B\rightarrow X_s g )$ decreases with increasing $\mu_b$. The dashed lines represent the SM prediction.
  • Figure 5: $\frac{d}{d \hat{s}} Br(B\rightarrow X_s l^+ l^- )$ in the SM (dashed line) and the ACD model for $R^{-1} =250$ GeV. (a) Low $\hat{s}$ region and (b) full dilepton mass spectrum.
  • ...and 3 more figures