Direct $CP$ violation in ${\mathrm{\Lambda }}_b$ decays

We study direct $CP$-violating asymmetries (CPAs) in the two-body ${\mathrm{\Lambda }}_b$ decays of ${\mathrm{\Lambda }}_b\to pM(V)$ with $M(V)=K^{-}(K^{*-})$ and ${\pi }^{-}({\rho }^{-})$ based on the generalized factorization method in the standard model (SM). After simultaneously explaining the observed decay branching ratios of ${\mathrm{\Lambda }}_b\to (p{K}^{-},p{\pi }^{-})$ with ${\mathcal{R}}_{\pi K}\equiv \mathcal{B}({\mathrm{\Lambda }}_b\to p{\pi }^{-})/\mathcal{B}({\mathrm{\Lambda }}_b\to p{K}^{-})$ being $0.84\pm 0.09$, we find that their corresponding direct CPAs are $(5.8\pm 0.2,-3.9\pm 0.2)\%$, in comparison with $(-5_{-5}^{+26},-31_{-1}^{+43})\%$ based on the perturbative QCD calculation and $(-10\pm 8\pm 4,6\pm 7\pm 3)\%$ from the CDF experiment, respectively. For ${\mathrm{\Lambda }}_b\to (p{K}^{*-},p{\rho }^{-})$, the decay branching ratios and CPVs are predicted to be $(2.5\pm 0.5,11.4\pm 2.1)\times {10}^{-6}$ with ${\mathcal{R}}_{\rho K^{*}}=4.6\pm 0.5$ and $(19.6\pm 1.6,-3.7\pm 0.3)\%$, respectively. The uncertainties for the CPAs in these decay modes as well as ${\mathcal{R}}_{\pi K,\rho K^{*-}}$ mainly arise from the quark mixing elements and nonfactorizable effects, whereas those from the hadronic matrix elements are either totally eliminated or small. We point out that the large CPA for ${\mathrm{\Lambda }}_b\to p{K}^{*-}$ is promising to be measured by the CDF and LHCb experiments, which is a clean test of the SM.

Figure 1

Contributions to ${\mathrm{\Lambda }}_b\to pM(V)$ from (a) color-allowed tree-level and (b) penguin diagrams.