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Register a new userGlauber gluons in spectator amplitudes for $B to pi M$ decays
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We extract the Glauber divergences from the spectator amplitudes for two-body hadronic decays $B to M_1 M_2$ in the $k_T$ factorization theorem, where $M_2$ denotes the meson emitted at the weak vertex. Employing the eikonal approximation, the divergences are factorized into the corresponding Glauber phase factors associated with the $M_1$ and $M_2$ mesons. It is observed that the latter factor enhances the spectator contribution to the color-suppressed tree amplitude by modifying the interference pattern between the two involved leading-order diagrams. The first factor rotates the enhanced spectator contribution by a phase, and changes its interference with other tree diagrams. The above Glauber effects are compared with the mechanism in elastic rescattering among various $M_1 M_2$ final states, which has been widely investigated in the literature. We postulate that only the Glauber effect associated with a pion is significant, due to its special role as a $q bar q$ bound state and as a pseudo Nambu-Goldstone boson simultaneously. Treating the Glauber phases as additional inputs in the perturbative QCD (PQCD) approach, we find a good fit to all the $B to pipi$, $pirho$, $piomega$, and $pi K$ data, and resolve the long-standing $pipi$ and $pi K$ puzzles. The nontrivial success of this modified PQCD formalism is elaborated.
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The scattering amplitude of D Pi at the energy of the B mass can be calculated using Regge theory. Recent papers have used this to calculate the final state strong phases in the decays B to D Pi. It is argued that while the Regge amplitude can yield an absorption correction to the decay rate, it is not useful for determining the strong phase.
We analyze the asymmetry in the partial widths for the decays $B^{pm} to M {bar M} pi^{pm}$ ($ M = pi^+, K ^+, pi^0, eta$), which results from the interference of the nonresonant decay amplitude with the resonant amplitude for $B^{pm} to chi_{c0} pi^{pm} $ followed by the decay $chi_{c0} to M {bar M} $. The CP violating phase $gamma$ can be extracted from the measured asymmetry. We find that the partial width asymmetry for $B^pm to pi^+ pi^- pi^pm$ is about $0.33~sin gamma$, and about $0.45~ sin gamma$ for $B^pm to K^+ K^-pi^pm$, while it is somewhat smaller for $B^pm to pi^0 pi^0 pi^pm$ and $B^pm to eta eta pi^pm$. Potential sources of uncertainties in these results, primarily coming from poorly known input parameters, are discussed.
Two sources of strong phases in the decays $B$ to $pipi$ are identified: (1) quasi-elastic scattering corresponding to intermediate states like $pipi$ and $rhorho$, (2) ``$cbar{c}$ corresponding to intermediate states like $Dbar{D}$ and $D^{*}bar{D}^{*}$. Possibilities of using data to identify these two sources are discussed and illustrated. Present data suggests both sources may be significant.
While the factorization assumption works well for many two-body nonleptonic $B$ meson decay modes, the recent measurement of $bar Bto D^{(*)0}M^0$ with $M=pi$, $rho$ and $omega$ shows large deviation from this assumption. We analyze the $Bto D^{(*)}M$ decays in the perturbative QCD approach based on $k_T$ factorization theorem, in which both factorizable and nonfactorizable contributions can be calculated in the same framework. Our predictions for the Bauer-Stech-Wirbel parameters, $|a_2/a_1|= 0.43pm 0.04$ and $Arg(a_2/a_1)sim -42^circ$ and $|a_2/a_1|= 0.47pm 0.05$ and $Arg(a_2/a_1)sim -41^circ$, are consistent with the observed $Bto Dpi$ and $Bto D^*pi$ branching ratios, respectively. It is found that the large magnitude $|a_2|$ and the large relative phase between $a_2$ and $a_1$ come from color-suppressed nonfactorizable amplitudes. Our predictions for the ${bar B}^0to D^{(*)0}rho^0$, $D^{(*)0}omega$ branching ratios can be confronted with future experimental data.
The observed strong phase difference of 30^{o} between I=(3/2) and I=(1/2) final states for the decay B to D Pi is analyzed in terms of rescattering like D^{∗}Pi to D Pi, etc. It is concluded that for the decay B^{o}to D^{+} Pi^{-} the strong phase is only about 10^{o}. Implications for the determination of sin(2 Beta + gamma) are discussed.
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