$CP$ violation in two-body hadronic $Λ_b$ decays in the PQCD approach

TL;DR

This paper presents a comprehensive PQCD analysis of CP violation in two-body hadronic Λ_b decays to p h (h = π, ρ, a₁, K, K^{*}, K₁) at order $α_s^2$, incorporating subleading-twist distribution amplitudes for the baryon, proton, and mesons. By classifying all relevant topologies (tree and penguin) and computing their strong phases, the authors show that individual partial-wave CPVs can exceed $10\%$, but destructive interference among waves yields small net direct CPV in several channels, notably $Λ_b\to pπ^-$ and $Λ_b\to pK^-$. The study highlights large CPV in certain angular observables, especially up-down asymmetries in $Λ_b\to pK_1(1270,1400)$ and $p a_1(1260)$ decays, with $A_{CP}^{UD}$ potentially above $20\%$, offering robust experimental probes at LHCb. The work also documents SU(3) flavor-breaking effects of about $30\%$ and discusses the sensitivity of predictions to mixing angles, higher-twist DAs, and threshold resummation, underscoring the potential to firmly establish baryon CPV in upcoming data.

Abstract

We systematically investigate the $CP$-averaged branching ratios and $CP$ violations (CPVs) for the two-body hadronic decays $Λ_b\to ph$, where $h$ runs through the mesons $π^-$, $ρ^-$, $a_1^-(1260)$, $K^-$, $K^{\ast -}$, $K_1^-(1270)$ and $K_1^-(1400)$, in the perturbative QCD approach to order $α_s^2$ in the strong coupling. Various topological amplitudes are obtained by incorporating subleading-twist hadron distribution amplitudes, which exhibit reasonable hierarchical patterns, sizable strong phases, and non-negligible higher-power corrections. The predicted direct CPVs in $Λ_b\to pπ^-,pK^-$, different from those in similar $B$ meson decays, are as small as the current data. The low CPV in $Λ_b\to pπ^-$ results from the cancellation between the $S$- and $P$-wave CPVs, while the one in $Λ_b\to pK^-$ is determined by the tiny $S$-wave CPV. However, individual partial-wave CPVs can exceed $10\%$, consistent with direct CPVs in $B$ meson decays. The CPVs in the $Λ_b\to pK_1^-(1270),pK_1^-(1400)$ channels are relatively larger. In particular, CPVs above $20\%$ appear in the up-down asymmetries associated with the final-state angular distributions of $Λ_b\to pK_1^-(1270),pK_1^-(1400)$, followed by the secondary $K_1\to Kππ$ decays. These observables offer promising prospects for firmly establishing baryon CPVs. The decay asymmetry parameters of $Λ_b\to ph$ are also predicted for future experimental confrontations.

Figures (19)

• Figure 1: Topological diagrams contributing to the $\Lambda_b\to ph$ decays.
• Figure 2: Dependencies of $Br(\Lambda_b\to p\mu\bar{\nu}_\mu)$ (left) and $Br(\Lambda_b\to pD_s^-)$ (right) on $\omega_0$.
• Figure 3: (left) Numerical results of the $T(d5)$ contribution to the $S$-wave from the VEGAS+ after $15$ iterations with increasing numbers of samples; (right) same as the left panel but for the $P$-wave.
• Figure 4: The Bessel functions $B^{(1)}$ (left) and $B^{(2)}$ (right).
• Figure 5: The function $B^{(2)}(x)-\text{Sign}(x)/\sqrt{|x|}$ (left) ; the function $\text{Sign}(x)/\sqrt{|x|}$ (right).