Branching ratios of Bc→APB_c \to A P decays in the perturbative QCD approach

In this paper we calculate the branching ratios (BRs) of the 32 charmless hadronic $B_c \to A P$ decays ($A=a_1(1260),b_1(1235),K_1(1270),K_1(1400), f_1(1285),f_1(1420),h_1(1170),h_1(1380)$) by employing the perturbative QCD(pQCD) factorization approach. These considered decay channels can only occur via annihilation type diagrams in the standard model. From the numerical calculations and phenomenological analysis, we found the following results: (a) the pQCD predictions for the BRs of the considered $B_c$ decays are in the range of $10^{-6}$ to $10^{-8}$, while the CP-violating asymmetries are absent because only one type tree operator is involved here; (b) the BRs of $\Delta S= 0$ processes are generally much larger than those of $\Delta S =1$ ones due to the large CKM factor of $|V_{ud}/V_{us}|^2\sim 19$; (c) since the behavior for $^1P_1$ meson is much different from that of $^3P_1$ meson, the BRs of $B_c \to A(^1P_1) P$ decays are generally larger than that of $B_c \to A(^3P_1) P$ decays; (d) the pQCD predictions for the BRs of B_c \to (K_1(1270), K_1(1400)) \etap and $(K_1(1270), K_1(1400)) K$ decays are rather sensitive to the value of the mixing angle $\theta_K$.Comment: 1+17 pges, 1 figure, refs. added and some clarifications made, accepted for publication in Phys.Rev.

Localized direct CP violation in B±→ρ0(ω)π±→π+π−π±B^\pm\rightarrow \rho^0 (\omega)\pi^\pm\rightarrow \pi^+ \pi^-\pi^\pm

We study the localized direct CP violation in the hadronic decays $B^\pm\rightarrow \rho^0 (\omega)\pi^\pm\rightarrow\pi^+ \pi^-\pi^\pm$, including the effect caused by an interesting mechanism involving the charge symmetry violating mixing between $\rho^0$ and $\omega$. We calculate the localized integrated direct CP violation when the low invariant mass of $\pi^+\pi^-$ [$m(\pi^+\pi^-)_{low}$] is near $\rho^0(770)$. For five models of form factors investigated, we find that the localized integrated direct CP violation varies from -0.0170 to -0.0860 in the ranges of parameters in our model when $0.750<m(\pi^+\pi^-)_{low}<0.800$\,GeV. This result, especially the sign, agrees with the experimental data and is independent of form factor models. The new experimental data shows that the signs of the localized integrated CP asymmetries in the regions $0.470<m(\pi^+\pi^-)_{low}<0.770$\,GeV and $0.770<m(\pi^+\pi^-)_{low}<0.920$\,GeV are positive and negative, respectively. We find that $\rho$-$\omega$ mixing makes the localized integrated CP asymmetry move towards the negative direction, and therefore contributes to the sign change in those two regions. This behavior is also model independent. We also calculate the localized integrated direct CP violating asymmetries in the regions $0.470<m(\pi^+\pi^-)_{low}<0.770$\,GeV and $0.770<m(\pi^+\pi^-)_{low}<0.920$\,GeV and find that they agree with the experimental data in some models of form factors.Comment: 22 pages, 2 figures. arXiv admin note: text overlap with arXiv:hep-ph/0602043, arXiv:hep-ph/0302156 by other author