arXiv subjects
Publications and source records attributed to M. P. Khanna.
We explore the possibility of extracting the weak phase $γ$ from pure tree decays $Λ_b \to Λ(D^0, \bar{D^0}, D^0_{CP})$ in a model independent way. The CP violating weak phase $γ$ can be determined cleanly, without any hadronic uncertainties, as these decay modes are free from the penguin pollutions. Furthermore, neither tagging nor time dependent studies are required to extract the angle $γ$ with these modes.
We note that it is possible to determine the weak phase γfrom the time dependent measurements of the decays $B_s^0(t) (\bar B_s^0 (t)) \to \bar D^0 ϕwithout any hadronic uncertainties. These decays are described by the color suppressed tree diagrams and hence are free from the penguin pollutions. We further demonstrate that γcan also be extracted with no hadronic uncertainties from an angular analysis of corresponding vector vector modes, $B_s^0(t) (\bar B_s^0 (t)) \to \bar D^{* 0} ϕ$. Although the branching ratios for these decay modes are quite small $ {\cal O} (10^{-5}-10^{-6})$, the strategies presented here appear to be particularly interesting for the "second generation" experiments at hadronic B factories.
We note that the two body nonleptonic pure tree decays $B_c^\pm \to D_s^\pm D^0(\bar D^0)$ and the corresponding vector-vector modes $B_c^\pm \to D_s^{* \pm} D^{*0}(\bar D^{* 0}) $ are well suited to extract the weak phase $γ$ of the unitarity triangle. The CP violating phase $γ$ can be determined cleanly as these decay modes are free from the penguin pollutions.
We investigate the possibility of observing the direct CP violation in the decay modes $B^- \to D^0 D_s^-$ and $D^0 D^-$ within the Standard Model. Including the contributions arising from the tree, annihilation, QCD as well as electroweak penguins with both time- and space-like components, we find that the direct CP asymmetry in $B^- \to D^0 D_s^-$ is very small $\sim 0.2$ % but in $B^- \to D^0 D^- $ decay it can be as large as 4%. Approximately $10^7$ charged $B$ mesons are required to experimentally observe the CP asymmetry parameter for the later case. Since this is easily accessible with the currently running B factories, the decay mode $B^- \to D^0 D^-$ may be pursued to look for CP violation.
Using a theoretical framework based on the next-to-leading order QCD improved effective Hamiltonian, we have estimated the branching ratios and asymmetry parameters for the two body charmless nonleptonic decay modes of $Λ_b$ baryon i.e. $Λ_b \to p (π/ρ),~p(K/K^*)$ and $Λ(π/ρ)$, within the framework of generalized factorization. The nonfactorizable contributions are parametrized in terms of the effective number of colors, $N_c^{eff}$. So in addition to the naive factorization approach ($N_c^{eff}=3 $), here we have taken two more values for $N_c^{eff}$ i.e., $N_c^{eff}=2 $ and $\infty $. The baryonic form factors at maximum momentum transfer ($ q_m^2 $) are evaluated using the nonrelativistic quark model and the extrapolation of the form factors from $q_m^2$ to the required $q^2$ value is done by assuming the pole dominance. The obtained branching ratios for $Λ_b \to pπ, ~pK$ processes lie within the present experimental upper limit .
An estimate has been made of the masses of heavy hadrons in nonrelativistic quark model, which includes spin and flavor-dependent hyperfine splitting for two quarks. The effect of variation of the wavefunction value at origin and the strong coupling constant, with flavor, has also been included in calculating the mass values.
The two body Cabibbo favored hadronic decays of charmed baryons $Λ^{+}_{c}$, $Ξ^{+}_{c}$ and $Ξ_{c}^{0}$ into an octet or decuplet baryon and a pseudoscalar meson are examined in the SU(3) symmetry scheme. The numerical estimates for decay widths and branching ratios of some of the modes are obtained and are in good agreement with experiment.
According to the Coleman-Glashow null theorem if all the symmetry breaking effects belong to the same regular representation (octet in the case of SU(3) and {\bf 15} in the case of SU(4)) and are generated in a tadpole type mechanism, the strangeness changing (charm changing) weak transitions generated through the S$_{6}$ (S$_{9}$) tadpole must vanish. Exploiting this null result, we find relations between the BBP coupling constants which allow us to write the coupling constants in terms of two parameters and baryon masses. Fixing these two parameters ( $g_{NNπ}$ and $g_{ΛΣπ}$) from experiments, we estimate the remaining coupling constants.