Possible large $CP$ violation in charmed ${\mathrm{\Lambda }}_b$ decays

We propose that the cascade decay ${\mathrm{\Lambda }}_b\to D(\to K^{+}{\pi }^{-})N(\to p{\pi }^{-})$ may serve as the discovery channel for baryonic $CP$ violation. This decay chain is contributed by, dominantly, the amplitudes with the intermediate $D$ state as $D^0$ or ${\overline{D}}^0$. The large weak phase between the two kinds of amplitudes suggests the possibility of significant $CP$ violation. While the presence of undetermined strong phases may complicate the dependence of $CP$ asymmetry, our phenomenological analysis demonstrates that $CP$ violation remains prominent across a broad range of strong phases. The mechanism also applies to similar decay modes such as ${\mathrm{\Lambda }}_b\to D(\to K^{+}{K}^{-})\mathrm{\Lambda }$. Considering the anticipated luminosity of LHCb, we conclude that these decay channels offer a promising opportunity to uncover $CP$ violation in the baryon sector.

Figure 1

Sketch of the full decay chain ${\mathrm{\Lambda }}_b\to D(\to K^{+}{\pi }^{-})N(\to p{\pi }^{-})$.

Figure 2

The dependence of the asymmetries $A_1$ and $A_2$ on the strong phase $\delta ={\delta }_{B1}={\delta }_{B3}$ in case 1. The left, middle, and right panels correspond to the three benchmarks (a) $r_{B1}=r_{B3}=r_0/2$, (b) $r_{B1}=r_{B3}=r_0$, and (c) $r_{B1}=r_{B3}=2r_0$.

Figure 3

Two-dimensional dependence of the asymmetry $A_1$ on the strong phases in case 2. The left, middle, and right panels correspond to the three benchmarks (a) $r_{B1}=r_{B3}=r_0/2,r_{B2}=r_{B4}=2r_0$, (b) $r_{B1}=r_{B2}=r_{B3}=r_{B4}=r_0$, and (c) $r_{B1}=r_{B3}=2r_0,r_{B2}=r_{B4}=r_0/2$. The dashed lines on the graph represent contours with associated red values of $A_1$.

Figure 4

Two-dimensional dependence of the asymmetry $A_2$ on the strong phases in case 2. The left, middle, and right panels correspond to the three benchmarks (a) $r_{B1}=r_{B3}=r_0/2,r_{B2}=r_{B4}=2r_0$, (b) $r_{B1}=r_{B2}=r_{B3}=r_{B4}=r_0$, and (c) $r_{B1}=r_{B3}=2r_0,r_{B2}=r_{B4}=r_0/2$. The dashed lines on the graph represent contours with associated red values of $A_2$.

Figure 5

Two-dimensional dependence of the asymmetry $A_1$ on the strong phases in case 3. The left, middle, and right panels correspond to the three benchmarks (a) $r_{B1}=r_{B3}=r_0/2,r_{B2}=r_{B4}=2r_0$, (b) $r_{B1}=r_{B2}=r_{B3}=r_{B4}=r_0$, and (c) $r_{B1}=r_{B3}=2r_0,r_{B2}=r_{B4}=r_0/2$. The dashed lines on the graph represent contours with associated red values of $A_1$.

Figure 6

Two-dimensional dependence of the asymmetry $A_2$ on the strong phases in case 3. The left, middle, and right panels correspond to the three benchmarks (a) $r_{B1}=r_{B3}=r_0/2,r_{B2}=r_{B4}=2r_0$, (b) $r_{B1}=r_{B2}=r_{B3}=r_{B4}=r_0$, and (c) $r_{B1}=r_{B3}=2r_0,r_{B2}=r_{B4}=r_0/2$. The dashed lines on the graph represent contours with associated red values of $A_2$.