Flavor Violation Tests of Warped/Composite SM in the Two-Site Approach

TL;DR

This paper analyzes flavor violation in a 4D two-site EFT that encapsulates the SM plus the first KK excitations from a warped extra dimension. It identifies $oldsymbol{\epsilon_K}$ and $\text{BR}(b\rightarrow s\gamma)$ as the key flavor observables constraining the model, uncovering a tension due to opposite dependence on composite-site Yukawas. By matching the 5D QCD coupling to the 4D coupling and enforcing perturbativity, the authors show that heavy-state masses around $oldsymbol{M_*\sim \mathcal{O}(5)\ ext{TeV}}$ can satisfy both observables, with potential relaxation to $oldsymbol{\sim O(3)\text{ TeV}}$ under mild Yukawa tuning at the cost of stronger $Z\bar{b}b$ constraints. The analysis connects the two-site EFT to 5D AdS scenarios, particularly those with a bulk Higgs, and discusses implications for LHC phenomenology and future flavor-precision tests. Overall, the work demonstrates that warped extra-dimensional flavor structures can be consistent with current flavor data at multi-TeV scales, while making concrete predictions for CP-violating and rare-decay observables.

Abstract

We study flavor violation in the quark sector in a purely 4D, two-site effective field theory description of the Standard Model and just their first Kaluza-Klein excitations from a warped extra dimension. The warped 5D framework can provide solutions to both the Planck-weak and flavor hierarchies of the SM. It is also related (via the AdS/CFT correspondence) to partial compositeness of the SM. We focus on the dominant contributions in the two-site model to two observables which we argue provide the strongest flavor constraints, namely, epsilon_K and BR(b -> s gamma), where contributions in the two-site model occur at tree and loop-level, respectively. In particular, we demonstrate that a "tension" exists between these two observables in the sense that they have opposite dependence on composite site Yukawa couplings, making it difficult to decouple flavor-violating effects using this parameter. We choose the size of the composite site QCD coupling based on the relation of the two-site model to the 5D model (addressing the Planck-weak hierarchy), where we match the 5D QCD coupling to the 4D coupling at the loop-level and assuming negligible tree-level brane-localized kinetic terms. We estimate that a larger size of the 5D gauge coupling is constrained by the requirement of 5D perturbativity. We find that \sim O(5) TeV mass scale for the new particles in the two-site model can then be consistent with both observables. We also compare our analysis of epsilon_K in the two-site model to that in 5D models, including both the cases of a brane-localized and bulk Higgs.

Figures (10)

• Figure 1: Feynman diagram for $\Delta S = 2$ process via heavy gluon exchange
• Figure 2: Feynman diagrams for b $\rightarrow$ s $\gamma$ via heavy gluon and heavy fermions
• Figure 3: Feynman diagrams for b $\rightarrow$ s $\gamma$ via charged Higgs
• Figure 4: Feynman diagrams for b $\rightarrow$ s $\gamma$ via Higgs using mass insertion
• Figure 5: Scatter plot for shift in $\hbox{BR}(b \rightarrow s \gamma)$ and $\hbox{Im}\,(C_{4K})$ for $M_* = 5\ \hbox{TeV}$, the composite site gauge coupling $g_{s*} = 3$ and different values of $Y_*^{u,d}$ (defined here as the geometric mean of the composite site Yukawa couplings $|Y_{*\,ij}^{u,d}|$). The allowed region is below and to the left of the (red) solid lines. For $g_{s*} = 6$, the allowed region is below the dashed line and to the left of the solid (red) line. (see discussion in section \ref{['numerical']}).