Note on Tests of the Factorization Hypothesis and the Determination of Meson Decay Constants

We discuss various tests of the factorization hypothesis making use of the close relationship between semi-leptonic and factorized nonleptonic decay amplitudes. It is pointed out that factorization leads to truely model-independent predictions for the ratio of nonleptonic to semi-leptonic decay rates, if in the nonleptonic decay a spin one meson of arbitrary mass or a pion take the place of the lepton pair. Where the decay constants of those mesons are known, these predictions represent ideal tests of the factorization hypothesis. In other cases they may be used to extract the decay constants. Currently available data on the decays $\bar B^0 \to D^+\pi^-,\, D^{*+}\pi^-,\, D^+\varrho^-,\, D^{*+}\varrho^-$ are shown to be in excellent agreement with the factorization results. A weighted average of the four independent values for the QCD coefficient $a_1$ extracted from the data gives $a_1=1.15\pm 0.06$ suggesting that it may be equal to the Wilson coefficient $c_1(\mu)$ evaluated at the scale $\mu = m_b$.Comment: (9 pages, ReVTeX, no figures), HD-THEP-92-3

\Lambda_b \to \Lambda_c P(V) Nonleptonic Weak Decays

The two-body nonleptonic weak decays of \Lambda_b \to \Lambda_c P(V) (P and V represent pseudoscalar and vector mesons respectively) are analyzed in two models, one is the Bethe-Salpeter (B-S) model and the other is the hadronic wave function model. The calculations are carried out in the factorization approach. The obtained results are compared with other model calculations.Comment: 18 pages, Late

Lattice QCD calculation of Bˉ→Dlνˉ\bar{B}\to Dl\bar{\nu} decay form factors at zero recoil

A lattice QCD calculation of the $\bar{B}\to Dl\bar{\nu}$ decay form factors is presented. We obtain the value of the form factor $h_+(w)$ at the zero-recoil limit $w=1$ with high precision by considering a ratio of correlation functions in which the bulk of the uncertainties cancels. The other form factor $h_-(w)$ is calculated, for small recoil momenta, from a similar ratio. In both cases, the heavy quark mass dependence is observed through direct calculations with several combinations of initial and final heavy quark masses. Our results are $h_+(1) = 1.007(6)(2)(3)$ and $h_-(1)=-0.107(28)(04)(^{10}_{30})$. For both the first error is statistical, the second stems from the uncertainty in adjusting the heavy quark masses, and the last from omitted radiative corrections. Combining these results, we obtain a precise determination of the physical combination $F_{B\to D}(1)=1.058(^{20}_{17})$, where the mentioned systematic errors are added in quadrature. The dependence on lattice spacing and the effect of quenching are not yet included, but with our method they should be a fraction of $F_{B\to D}-1$.Comment: 32 pp, 10 figs; final, published versio

Bˉ0→π+X\bar B^0 \to \pi^+ X in the Standard Model

In this paper we investigate the possibility of studying $B\to \pi$ form factor using the semi-inclusive decays $\bar B^0 \to \pi^+ + X_q$. In general $B\to PX$ semi-inclusive decays involve several hadronic parameters. But for $\bar B^0 \to \pi^+ X_q$ decays we find that in the factorization approximation, the only unknown hadronic parameters are the form factors $F^{B\to \pi}_{0,1}$. Therefore these form factors can be studied in $\bar B^0 \to \pi^+ X_q$ decays. Using theoretical model calculations for the form factors the branching ratios for $\bar B^0 \to \pi^+ X_d(\Delta S = 0)$ and $\bar B^0 \to \pi^+ X_s (\Delta S = -1)$, with the cut $E_{\pi} > 2.1$ GeV, are estimated to be in the ranges of $(3.1\sim 4.9) \times 10^{-5}(F^{B\to \pi}_1(0)/0.33)^2$ and $(2.5\sim 4.2)\times 10^{-5}(F_1^{B\to \pi}(0)/0.33)^2$, respectively, depending on the value of $\gamma$. The combined branching ratio for $\bar B^0 \to \pi^+ (X_d+ X_s)$ is about $7.4\times 10^{-5} (F^{B\to \pi}_1(0)/0.33)^2$ and is insensitive to $\gamma$. We also discuss CP asymmetries in these decay modes.Comment: RevTex 8 pages and two figure

Non-perturbatively Improved Heavy-Light Mesons: Masses and Decay Constants

We present a study of the heavy-light spectrum and of the D- and B-meson decay constants. The results wer e obtained in the quenched approximation, by using the non-perturbatively improved Clover lattice action at beta=6.2, with a sample of 100 configurations, on a 24^3 x 64 lattice. After a careful analysis of th e systematic errors present in the extraction of the physical results, by assuming quite conservative discretization errors, we find f_Ds=231 +/- 12^{+6}_{-1} MeV, f_D = 211 +/- 14^{+0}_{-12} MeV, f_Ds/f_D=1.10(2), f_Bs = 204 +/- 16^{+28}_{-0} MeV, f_B = 179 +/- 18^{+26}_{-9} MeV, f_Bs/f_B=1.14(3)^{+0}_{-1}. Our results, which have smaller discretization errors than many previous estimates at fixed value of the lattice spacing $a$, support a large value of f_B in the quenched approximation.Comment: 26 pages, 9 Postscript figure

Exploring CP Violation with BcB_c Decays

We point out that the pure ``tree'' decays $B_c^\pm\to D^\pm_s D$ are particularly well suited to extract the CKM angle $\gamma$ through amplitude relations. In contrast to conceptually similar strategies using $B^\pm\to K^\pm D$ or $B_d\to K^{\ast0} D$ decays, the advantage of the $B_c$ approach is that the corresponding triangles have three sides of comparable length and do not involve small amplitudes. Decays of the type $B_c^\pm\to D^\pm D$ -- the $U$-spin counterparts of $B_c^\pm\to D^\pm_s D$ -- can be added to the analysis, as well as channels, where the $D^\pm_s$- and $D^\pm$-mesons are replaced by higher resonances.Comment: 9 pages, LaTeX, 3 figures, reference adde

The CP violating phase γ\gamma from global fit of rare charmless hadronic B decays

We study constraints on the CP violating phase $\gamma$ in the Kobayashi-Maskawa model using available experimental data. We first follow the conventional method to up date the constraint on $\gamma$ by performing a $\chi^2$ analysis using data from $|\epsilon_K|$, $\Delta m_{B_{d,s}}$ and $|V_{ub}/V_{cb}|$. We also include the recent information on $\sin2\beta$ in the analysis. We obtain the best fit for $\gamma$ to be $66^\circ$ and the 95% C.L. allowed range to be $42^\circ \sim 87^\circ$. We then develop a method to carry out a $\chi^2$ analysis based on SU(3) symmetry using data from $B\to \pi \pi$ and $B\to K \pi$. We also discuss SU(3) breaking effects from model estimate. We find that present data on $B\to \pi\pi, K \pi$ can also give some constraint on $\gamma$ although weaker than the earlier method limited by the present experimental errors. Future improved data will provide more stringent constraint. Finally we perform a combined fit using data from $|\epsilon_K|$, $\Delta m_{B_{d,s}}$, $|V_{ub}/V_{cb}|$, $\sin2\beta$ and rare charmless hadronic B decays. The combined analysis gives $\gamma=67^\circ$ for the best fit value and $43^\circ \sim 87^\circ$ as the 95% C.L. allowed range. Several comments on other methods to determine $\gamma$ based on SU(3) symmetry are also provided.Comment: Revised verion with the new experimental data from Belle and Babar included in the analysis to obtain the global fit for the CP violating phase gamma. RevTex, 32 pages and 8 figure

1/m_Q Corrections to the Bethe-Salpeter Equation for \Lambda_{Q} in the Diquark Picture

Corrections of order 1/m_Q (Q=b or c) to the Bethe-Salpeter (B-S) equation for \Lambda_Q are analyzed on the assumption that the heavy baryon \Lambda_Q is composed of a heavy quark and a scalar, light diquark. It is found that in addition to the one B-S scalar function in the limit m_Q -> \infty, two more scalar functions are needed at the order 1/m_Q. These can be related to the B-S scalar function in the leading order. The six form factors for the weak transition \Lambda_b -> \Lambda_c are expressed in terms of these wave functions and the results are consistent with heavy quark effective theory to order 1/m_Q. Assuming the kernel for the B-S equation in the limit m_Q -> \infty to consist of a scalar confinement term and a one-gluon-exchange term we obtain numerical solutions for the B-S wave functions, and hence for the $\Lambda_b \to \Lambda_c$ form factors to order 1/m_Q. Predictions are given for the differential and total decay widths for \Lambda_b -> \Lambda_c l \bar{\nu}, and also for the nonleptonic decay widths for \Lambda_b -> \Lambda_c plus a pseudoscalar or vector meson, with QCD corrections being also included.Comment: Latex, 24 pages, two figure

Weak Decays in the light--front Quark Model

We study the form factors of heavy--to--heavy and heavy--to--light weak decays using the light--front relativistic quark model. For the heavy--to--heavy B \ra D^{(\ast)} semileptonic decays we calculate the corresponding Isgur--Wise function for the whole kinematic region. For the heavy--to--light B\ra P and B\ra V semileptonic decays we calculate the form factors at $q^2 = 0$; in particular, we have derived the dependence of the form factors on the $b$--quark mass in the m_b \ra \infty limit. This dependence can not be produced by extrapolating the scaling behavior of the form factors at $q^2_{max}$ using the single--pole assumption. This shows that the $q^2$ dependence of the form factors in regions far away from the zero--recoil could be much more complicated than that predicted by the single--pole assumption.Comment: 24 pages, Latex, Postscript figure included at the en

Combining CP Asymmetries in B→KπB \to K \pi Decays

We prove an approximate relation, to leading order in dominant terms, between CP-violating rate differences in $B^0/\bar{B}^0 \to K^{\pm}\pi^{\mp}$ and $B^{\pm} \to K^{\pm}\pi^0$. We show how data from these two processes may be combined in order to enhance the significance of a nonzero result.Comment: 9 pages, latex, no figures, submitted to Phys. Rev. Letters, revise