Implications of recent LHCb data on CPV in b-baryon four body decays

TL;DR

This paper studies CP violation in charmless four-body decays of b-baryons using U-spin symmetry, motivated by recent LHCb observations. It demonstrates that pure U-spin relations alone are insufficient for robust predictions, especially for Λ_b decays, and introduces a SCET-inspired, power-counting approach to isolate leading-power topologies. By combining CKM-driven interference with a dynamical amplitude analysis, the authors derive CPV relations and provide concrete predictions, notably $A_{CP}^{dir}(\\Lambda_b^0 \\rightarrow R(p \\pi^- \\pi^+ ) \\pi^- )$ around $-13\\%$, while highlighting symmetry-breaking uncertainties of order 10–20%. These results offer a practical framework to guide experimental CPV searches in b-baryon decays and underscore the Λ_b channels as accessible probes at LHCb for testing flavor and CP-violation dynamics.

Abstract

Motivated by the recent CPV observation, we investigate the CPV of b-baryon charmless four body decays under the U-spin symmetry. However, we find that only U-spin symmetry cannot provide effective predictions, particularly for $Λ_b$ decays. For giving more useful predictions, we also give a simple dynamic analysis. By counting the power($λ=\sqrt{\frac{Λ_{QCD}}{m_b}}$) of each topological diagram, we find that for the specific decay $B_b^2\to R(B_1^2 M^2 M^{\bar 2})M^2$, only one U-spin amplitude can contribute in the leading power, while for $B_b^2\to R(B_1^2 M^2)R( M^{\bar 2}M^2)$, only two U-spin amplitudes can contribute in this leading power. Then the most effective prediction can be given as \begin{align} &A_{CP}^{dir}(Λ_b^0 \to R( p π^- π^+ )π^-) = (-12.99 \pm 2.83\pm2.59\pm0.65)\%,\notag \end{align} Considering the $Λ_b$ can effectively produced in LHCb, we strongly encourage a more precise experimental investigation of it.

Figures (2)

• Figure 1: The leading power topological diagram of $B_b^2\to B_1^2 M^2 M^2 M^{\bar{2}}$. The blue line indicates the d and s quark/anti-quark, the black line indicates the b quark. The red line indicates the u quark and u anti-quark.
• Figure 2: The leading power topological diagram of $B_b^2\to B_1^2 M^2 M^2 M^{\bar{2}}$. The blue line indicates the d and s quark/anti-quark, the black line indicates the b quark. The red line indicates the u quark and u anti-quark. For expressing the dynamic information, we use the double lines to represent the collinear quark and the single to represent the soft quark.