arXiv subjects

A. Le Yaouanc

Publications and source records attributed to A. Le Yaouanc.

97 records · Page 6Linked to original sources

arXiv1995

Factorization versus Duality in Nonleptonic decays, a Quark Model Approach

We study in a quark model the contradiction between factorization and duality found in nonleptonic decays at next to leading order in $1/N_c$, concentrating on quark exchange mechanism. The contradiction originates in the fact that the standard factorization assumption approximates the asymptotic final states by a non-orthogonal set of states, thus leading to an overcounting of the decay probability. We consider a system with two heavy quarks treated as classical color sources with constant velocity, and two mass-degenerate antiquarks. Exploiting permutation symmetry in an adiabatic approximation, we find that final state interaction restores duality. Three $O(1/N_c)$ effects are exhibited: i) a proper treatment of orthogonality yields a global correction $1/N_c\to 1/2N_c$ within a generalized factorization à la BSW, (such a factor was present in an Ansatz by Shifman), ii) the distorsion of the meson wave functions at the time of the weak decay, iii) relative phases generated by the later evolution. The latter effect becomes dominant for light antiquarks or for a small velocity of the final mesons, and may thoroughly modify the factorization picture. For exclusive decay it may interchange the role of class I and class II final channels, and for semi-inclusive decay it may lead to an equal sharing of the probability between the two sets of final states. In the heavy antiquark and large velocity limit, the replacement $1/N_c\to 1/2N_c$ is the dominant correction.

hep-ph↗

arXiv1994

The $B \to K^\ast ψ$ Polarization Puzzle

We point out that current estimates of form factors fail to explain the non-leptonic decays $B \to ψK(K^{\ast})$ and that the combination of data on the semi-leptonic decays $D \to K(K^{\ast})\ell ν$ and on the non-leptonic decays $B \to ψK(K^{\ast})$ (in particular recent po\-la\-ri\-za\-tion data) severely constrain the form (normalization and $q^2$ dependence) of the heavy-to-light meson form factors, if we assume the factorization hypothesis for the latter. From a simultaneous fit to \bpsi and \dk data we find that strict heavy quark limit scaling laws applied to the form factors do not hold when going from $D$ to $B$ and must have large corrections that make softer the dependence on the masses. This is in contrast with the matrix elements themselves which are found to need smaller $1/m_Q$ corrections to the asymptotic heavy quark scaling laws. We also find that $A_1(q^2)$ should increase slower with \qq than $A_2, V, f_+$. We propose a simple parametrization of these corrections based on a quark model or on an extension of the \hhs laws to the \hl case, complemented with an approximately constant $A_1(q^2)$. This model may be viewed as assuming a precocious validity of strict heavy quark scaling laws for the current matrix elements. Although this model reproduces qualitatively the wanted features for mass and $q^2$ dependence, and thus reduces the discrepancy with data, it is insufficient to reach a full agreement with the experiment. In our opinion the puzzle is still there.

hep-ph↗

arXiv1994

Critical Analysis of Theoretical Estimates for $B$ to Light Meson Form Factors and the $B \to ψK(K^{\ast})$ Data

We point out that current estimates of form factors fail to explain the non-leptonic decays $B \to ψK(K^{\ast})$ and that the combination of data on the semi-leptonic decays $D \to K(K^{\ast})\ell ν$ and on the non-leptonic decays $B \to ψK(K^{\ast})$ (in particular recent po\-la\-ri\-za\-tion data) severely constrain the form (normalization and $q^2$ dependence) of the heavy-to-light meson form factors, if we assume the factorization hypothesis for the latter. From a simultaneous fit to \bpsi and \dk data we find that strict heavy quark limit scaling laws do not hold when going from $D$ to $B$ and must have large corrections that make softer the dependence on the masses. We find that $A_1(q^2)$ should increase slower with \qq than $A_2, V, f_+$. We propose a simple parametrization of these corrections based on a quark model or on an extension of the \hhs laws to the \hl case, complemented with an approximately constant $A_1(q^2)$. We analyze in the light of these data and theoretical input various theoretical approaches (lattice calculations, QCD sum rules, quark models) and point out the origin of the difficulties encountered by most of these schemes. In particular we check the compatibility of several quark models with the heavy quark scaling relations.

hep-ph↗

arXiv1994

Determination of the CP Violating Phase $γ$ by a Sum Over Common Decay Modes to $B_s$ and $\bar{B}_s$

To help the difficult determination of the angle $γ$ of the unitarity triangle, Aleksan, Dunietz and Kayser have proposed the modes of the type $K^-D^+_s$, common to $B_s$ and $\bar{B}_s$. We point out that it is possible to gain in statistics by a sum over all modes with ground state mesons in the final state, i.e. $K^-D^+_s$, $K^{*-}D_+^s$, $K^-D^{*+}_s$, $K^{*-}D^{*+}_s$. The delicate point is the relative phase of these different contributions to the dilution factor $D$ of the time-dependent asymmetry. Each contribution to $D$ is proportional to a product $F^{cb}$ $F^{ub}$ $f_{D_s}$ $f_K$ where $F$ denotes form factors and $f$ decay constants. Within a definite phase convention, lattice calculations do not show any change in sign when extrapolating to light quarks the form factors and decay constants. Then, we can show that all modes contribute constructively to the dilution factor, except the $P$-wave $K^{*-}D^{*+}_s$, which is small. Quark model arguments based on wave function overlaps also confirm this stability in sign. By summing over all these modes we find a gain of a factor 6 in statistics relatively to $K^-D^+_s$. The dilution factor for the sum $D_{tot}$ is remarkably stable for theoretical schemes that are not in very strong conflict with data on $B \to ψK(K^*)$ or extrapolated from semileptonic charm form factors, giving $D_{tot} \geq 0.6$, always close to $D(K^- D^+_s)$.

hep-ph↗

arXiv1994

B Decays, an Introductory Survey

To start the $b$-decay session we briefly introduce and comment some important theoretical tools which are currently used in $b$ physics. Heavy Quark Symmetry and its consequences for heavy to heavy and heavy to light semi-leptonic decays, as well as for leptonic decays, are briefly summarised. It is stressed that symmetry must be completed with dynamical calculations. A critical discussion of the nearest pole dominance (VMD) assumption is performed. Parton model and its higher twist corrections are discussed on the example of lifetimes. Finally non-leptonic decays are considered via the example of the exclusive calculation of $ΔΓ$ in the $B_s-\overline B_s$ system. The popular factorization assumption is discussed and seems to be rather good.

hep-ph↗

arXiv1994

B To Light Meson Form Factors

The heavy to light form factors in $B$ decays are discussed. Critical discussion of theoretical approaches is made with special emphasis on their failure to describe the $B \to K^{(\ast )}ψ$ data.

hep-ph↗

arXiv1993

Semileptonic Decays and CKM Matrix Elements in a TCF

We argue that a Tau-Charm factory (TCF) could improve our knowledge of CKM matrix elements since it is an incomparable tool to check the models and methods applied to extract $V_{bu}$ from $B$ decay partial widths. We report on some recent proposals to improve on parton model. Turning to exclusive decays, we compare the predictions from quark models, QCD sum rules, effective Lagrangians and lattice QCD. Quark models have anticipated on heavy quark symmetry. Their difficutly to account for the $q^2$ dependence might be partly cured by relativistic corrections. QCD sum rules and lattice seem to disagree on the $q^2$ dependence of axial form factors. We discuss the extrapolation from $D$ to $B$. Present uncertainties do not allow to predict reliably the $B\raπ,ρl ν$ matrix elements. We argue that QCD sum rules are in a good position to study $q^2$ dependence down to $q^2=0$. Lattice QCD is able to check the heavy quark scaling laws for the heavy to light semileptonic decays. It seems to confirm the increase of $A_2/A_1$ from $D$ to $B$ meson predicted by the scaling laws. Finally semileptonic decays in a TCF would give incomparable informations on $Kπ$ phase shifts, and on $K^{**}$ resonances.

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