Flavor Violation in Warped Extra Dimensions and CP Asymmetries in B Decays

TL;DR

The paper investigates whether TeV-scale color-octet states arising in warped extra dimensions or Topcolor can modify CP asymmetries in $b\to s$ hadronic decays. It derives tree-level flavor-changing couplings of color-octet gauge bosons to the third generation, yielding an effective Hamiltonian term $\delta{\cal H}_{\rm eff}$ that can shift gluonic penguin Wilson coefficients $\delta C_i(m_b)$ by an amount proportional to $-\pi \alpha_s(M_G) (v/M_G)^2$ and a complex phase $e^{-i\omega}$. Using factorization for hadronic matrix elements, the work shows potentially large deviations in CP asymmetries of penguin-dominated modes such as $B_d\to\phi K_s$, $B_d\to\eta' K_s$, and $B_d\to\pi^0 K_s$ whenever $M_G$ is in the TeV range and $|D_L^{bs}|\sim |V_{ts}|$, with the heavy gluon also driving $\Delta m_{B_s}$ well above SM expectations. The results suggest that flavor-violating color-octet exchanges could provide first evidence of the new dynamics, and that the same mechanism appears in realistic Topcolor setups, linking fermion mass generation to flavor observables. Overall, the paper provides a concrete, testable bridge between extra-dimensional/topcolor dynamics and flavor observables, with implications for BaBar/Belle and forthcoming LHC data.

Abstract

We show that CP asymmetries in $b\to s$ hadronic decays are potentially affected by the presence of massive color-octet particles strongly coupled to the third generation quarks. Theories with warped extra dimensions provide natural candidates in the Kaluza-Klein excitations of gluons in scenarios where flavor-breaking by bulk fermion masses results in the localization of fermion wave-functions. Topcolor models, in which a new gauge interaction leads to top-condensation and a large top mass, also result in the presence of these color-octet states with TeV masses . We find that large effects are possible in modes such as $B\toφK_s$, $B\to η' K_s$ and $B\toπ^0 K_s$ among others.

Figures (5)

• Figure 1: Yukawa coupling of a left-handed zero mode fermion for a TeV-brane localized right-haded fermion.
• Figure 2: Coupling of the first KK excitation of a gauge boson to a zero mode fermion vs. the bulk mass parameter c, normalized to the four-dimensional gauge coupling $g$.
• Figure 3: The quantity to be extracted from the CP violation asymmetry in $B_d^0\to\phi K_s$ vs. the heavy gluon mass and for various values of the decay amplitude phase $\omega$. The curves correspond to $\pi/3$ (solid), $\pi/4$ (dashed) and $\pi/6$ (dot-dash), and $\pi/10$ (dotted). The horizontal band corresponds to the world average value s2bwa as extracted from $B_d\to J/\psi K_s$, $sin(2\beta)_{\psi K_s}=0.731\pm 0.056$.
• Figure 4: The quantity to be extracted from the CP violation asymmetry in $B_d^0\to\eta'K_s$ vs. the heavy gluon mass and for various values of the decay amplitude phase $\omega$. The curves correspond to $\pi/3$ (solid), $\pi/4$ (dashed) and $\pi/6$ (dot-dash), and $\pi/10$ (dotted). The horizontal band corresponds to the world average value s2bwa as extracted from $B_d\to J/\psi K_s$, $sin(2\beta)_{\psi K_s}=0.731\pm 0.056$.
• Figure 5: The quantity to be extracted from the CP violation asymmetry in $B_d^0\to\pi^0K_s$ vs. the heavy gluon mass and for various values of the decay amplitude phase $\omega$. The curves correspond to $\pi/3$ (solid), $\pi/4$ (dashed) and $\pi/6$ (dot-dash), and $\pi/10$ (dotted). The horizontal band corresponds to the world average value s2bwa as extracted from $B_d\to J/\psi K_s$, $sin(2\beta)_{\psi K_s}=0.731\pm 0.056$.