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Combining Direct & Indirect Kaon CP Violation to Constrain the Warped KK Scale

Oram Gedalia, Gino Isidori, Gilad Perez

TL;DR

The paper analyzes flavor constraints in warped RS models with a bulk Higgs, showing that while bulk localization can alleviate the ${\epsilon_K}$ bound by increasing the Yukawa scale, the direct CP-violating observable ${\rm Re}(\epsilon'/\epsilon_K)$ grows with the Yukawa size and yields a stronger lower bound on the KK scale. By computing full overlap corrections and loop-induced dipole contributions, the authors derive bounds ${M_{KK}} \gtrsim 5.5$–$7.5$ TeV depending on the Higgs profile (parameterized by ${\beta}$) and discuss UV-sensitive operator effects when the Higgs is IR-brane localized. The results imply a significant little hierarchy problem and challenge LHC discovery prospects for the relevant KK states, motivating possible RS flavour alignment mechanisms. Overall, the work provides a detailed, overlap-corrected assessment of direct and indirect kaon CP-violation constraints in bulk-Higgs RS scenarios and highlights the importance of ${\epsilon'/\epsilon_K}$ in shaping the viable parameter space.

Abstract

The Randall-Sundrum (RS) framework has a built in protection against flavour violation, but still generically suffers from little CP problems. The most stringent bound on flavour violation is due to epsilon_K, which is inversely proportional to the fundamental Yukawa scale. Hence the RS epsilon_K problem can be ameliorated by effectively increasing the Yukawa scale with a bulk Higgs, as was recently observed in arXiv:0810.1016. We point out that incorporating the constraint from epsilon'/ε_K, which is proportional to the Yukawa scale, raises the lower bound on the KK scale compared to previous analyses. The bound is conservatively estimated to be 5.5 TeV, choosing the most favorable Higgs profile, and 7.5 TeV in the two-site limit. Relaxing this bound might require some form of RS flavour alignment. As a by-product of our analysis, we also provide the leading order flavour structure of the theory with a bulk Higgs.

Combining Direct & Indirect Kaon CP Violation to Constrain the Warped KK Scale

TL;DR

The paper analyzes flavor constraints in warped RS models with a bulk Higgs, showing that while bulk localization can alleviate the bound by increasing the Yukawa scale, the direct CP-violating observable grows with the Yukawa size and yields a stronger lower bound on the KK scale. By computing full overlap corrections and loop-induced dipole contributions, the authors derive bounds – TeV depending on the Higgs profile (parameterized by ) and discuss UV-sensitive operator effects when the Higgs is IR-brane localized. The results imply a significant little hierarchy problem and challenge LHC discovery prospects for the relevant KK states, motivating possible RS flavour alignment mechanisms. Overall, the work provides a detailed, overlap-corrected assessment of direct and indirect kaon CP-violation constraints in bulk-Higgs RS scenarios and highlights the importance of in shaping the viable parameter space.

Abstract

The Randall-Sundrum (RS) framework has a built in protection against flavour violation, but still generically suffers from little CP problems. The most stringent bound on flavour violation is due to epsilon_K, which is inversely proportional to the fundamental Yukawa scale. Hence the RS epsilon_K problem can be ameliorated by effectively increasing the Yukawa scale with a bulk Higgs, as was recently observed in arXiv:0810.1016. We point out that incorporating the constraint from epsilon'/ε_K, which is proportional to the Yukawa scale, raises the lower bound on the KK scale compared to previous analyses. The bound is conservatively estimated to be 5.5 TeV, choosing the most favorable Higgs profile, and 7.5 TeV in the two-site limit. Relaxing this bound might require some form of RS flavour alignment. As a by-product of our analysis, we also provide the leading order flavour structure of the theory with a bulk Higgs.

Paper Structure

This paper contains 12 sections, 49 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Analysis
  3. Flavour Structure with a Bulk Higgs
  4. RS Contributions to ${\epsilon_K}$ and $b\to s\gamma$
  5. The Constraint of ${\epsilon^\prime/\epsilon_K}$
  6. The Case of an IR-Brane Higgs with UV Sensitive Operators
  7. Conclusion
  8. Overlap Corrections
  9. One-Loop Coefficients of the Dipole Operators
  10. The One-Loop Integral
  11. Diagonalization of the Quark Mass Matrix
  12. Coefficients of the Effective Operators

Figures (2)

  • Figure 1: Contribution to $b \rightarrow s\gamma$ and ${\epsilon^\prime/\epsilon_K}$ from Yukawa interactions.
  • Figure 2: The combination of the bounds on $M_{KK}$, as a function of $y^d$, for (a) $\beta=1$, which corresponds to the two site model; (b) $\beta=0$, which corresponds to the weakest bound.