arXiv subjects

J. -C. Raynal

Publications and source records attributed to J. -C. Raynal.

51 records · Page 3Linked to original sources

arXiv1997

Quantitative Predictions for $B$ semileptonic decays into $D,D^*$ and the orbitally excited $D^{**}$ in quark models à la Bakamjian-Thomas

Once chosen the dynamics in one frame, the rest frame in this paper, the Bakamjian and Thomas method allows to define relativistic quark models in any frame. These models have been shown to provide, in the infinite quark mass limit, fully covariant current form factors as matrix elements of the quark current operator. In this paper we use the rest frame dynamics fitted from the meson spectrum by various authors, already shown to provide a reasonable value for $ρ^2$. From the general formulae for the scaling invariant form factors $ξ^{(n)}(w)$, $τ_{1/2}^{(n)}(w)$ and $τ_{3/2}^{(n)}(w)$, we predict quantitavely the $B$ semileptonic branching ratios to the ground state and orbitally excited charmed mesons $D, D^\ast$ and $D^{\ast\ast}$. We check Bjorken's sum rule and discuss the respective contributions to it. We find $ξ(w)\simeq (2/(1+w)) ^2$, resulting from the fact that the ground state wave function is Coulomb-like. We also find $τ_{3/2}\simeq 0.5 (2/(1+w))^3$ and $τ_{1/2}(w)\ll τ_{3/2}(w)$. Very small branching ratios into $j=1/2$ orbitally excited $D$'s results. The overall agreement with experiment is rather good within the present accuracy which is poor for the orbitally excited charmed mesons. We predict a ratio $Br(B\to D^\ast_2 l ν)/Br(B\to D_1 l ν)=1.55\pm 0.15$ as a mere consequence of the heavy quark symmetry. If some faint experimental indications that $Br(B\to D_1 l ν)\simeq Br(B\to D^\ast_2 l ν)$ were confirmed, it would indicate a sizeable $O(1/m_c)$ correction.

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arXiv1997

Slope of the Isgur-Wise function in the heavy mass limit of quark models à la Bakamjian-Thomas

The slope of the Isgur-Wise function for ground state mesons is evaluated for the heavy mass limit of quark models à la Bakamjian-Thomas, which has been previously discussed by us in general terms. A full calculation in various spectroscopic models with relativistic kinetic energy gives a rather stable result $ρ^2 \approx 1$, much lower than previous estimates. Attention is paid to a careful comparison of this result with the ones of QCD fundamental methods (lattice QCD, QCD sum rules) and with experimental data.

hep-ph↗

arXiv1996

New Heavy Quark Limit Sum Rules involving Isgur-Wise Functions and Decay Constants

We consider the dominant $c\bar{c}$ contribution to $ΔΓ$ for the $B_s^0$-$\bar{B}_s^0$ system in the heavy quark limit for both $b$ and $c$ quarks. In analogy with the Bjorken-Isgur-Wise sum rule in semileptonic heavy hadron decay, we impose duality between the parton model calculation of $ΔΓ$ and its estimation by a sum over heavy mesons. Varying the mass ratio $m_c/m_b$ and assuming factorization and saturation by narrow resonances $(N_c \to \infty$), we obtain new sum rules that involve the Isgur-Wise functions $ξ^{(n)}(w)$ and $τ^{(n)}_{1/2}(w)$ and the decay constants $f^{(n)}$, $f^{(n)}_{1/2}$ ($n$ stands for any radial excitation). Alternatively, we deduce the sum rules with another method free of the factorization hypothesis, from the saturation of the expectation value of a product of two currents by heavy hadrons and by the corresponding free quarks. The sum rules read $\sum\limits_{n}{f^{(n)} \over f^{(0)}} ξ^{(n)}(w) = 2 \sum\limits_{n}{f^{(n)}_{1/2} \over f^{(0)}} τ^{(n)}_{1/2}(w) = 1$, valid for all $w$. Moreover, we obtain, in the heavy quark limit, $f^{(n)}_{3/2} = 0$. As a consequence, unlike the BIW sum rule, the slope of the elastic function $ξ(w)$ is related to radial excitations alone. These are generalizations, rigorous for QCD in the heavy quark limit, of results that have an easy understanding in the non-relativistic quark model.

hep-ph↗

arXiv1996

$B\to D^{\ast\ast}$ semileptonic decay in covariant quark models à la Bakamjian Thomas

Once chosen the dynamics in one frame, for example the rest frame, the Bakamjian and Thomas method allows to define relativistic quark models in any frame. These models have been shown to provide, in the heavy quark limit, fully covariant current form factors as matrix elements of the quark current operator. They also verify the Isgur-Wise scaling and give a slope parameter $ρ^2>3/4$ for all the possible choices of the dynamics. In this paper we study the $L=1$ excited states and derive the general formula, valid for any dynamics, for the scaling invariant form factors $τ_{1/2}^{(n)}(w)$ and $τ_{3/2}^{(n)}(w)$. We also check the Bjorken-Isgur-Wise sum rule already demonstrated elsewhere in this class of models.

hep-ph↗

arXiv1996

Exact Duality and Bjorken Sum Rule in Heavy Quark Models à la Bakamjian-Thomas

The heavy mass limit of quark models based on the Bakamjian-Thomas cons\-truction reveals remarkable features. In addition to previously demonstrated properties of covariance and Isgur-Wise scaling, exact duality, leading to the Bjorken-Isgur-Wise sum rule, is proven, for the first time to our knowledge in relativistic quark models. Inelastic as well as elastic contributions to the sum rule are then discussed in terms of ground state averages of a few number of operators corresponding to the nonrelativistic dipole operator and various relativistic corrections.

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arXiv1995

Covariant quark model of form factors in the heavy mass limit

We show that quark models of current matrix-elements based on the Bakamjian-Thomas construction of relativistic states with a fixed number of particles, plus the additivity assumption, are covariant in the heavy-quark limit and satisfy the full set of heavy-quark symmetry relations discovered by Isgur and Wise. We find the lower bound of $ρ^2$ in such models to be $3/4$ for ground state mesons, independently of any parameter. Another welcome property of these models is that in the infinite momentum limit the wave functions vanish outside the domain $0\le x \le 1$.

hep-ph↗

arXiv1995

Uncertainties on the CP Phase $\bfalpha$ due to Penguin Diagrams

A major problem in the determination of the the CP angle $α$, that should be measured through modes of the type $B_d, \bar{B}_d \to ππ, \cdots ,$ is the uncertainty coming from Penguin diagrams. We consider the different ground state modes $ππ$, $πρ$, $ρρ$, and, assuming the FSI phases to be negligible, we investigate the amount of uncertainty coming from Penguins that can be parametrized by a dilution factor $D$ and an angle shift $Δα$. The parameter $D$ is either 1 or very close to 1 in all these modes, and it can be measured independently, up to a sign ambiguity, by the $t$ dependence. Assuming factorization, we show that $Δα$ is much smaller for the modes $ρπ$ and $ρρ$ than for $ππ$, and we plot their allowed region as a function of $α$ itself. Moreover, we show that most of the modes contribute to the asymmetry with the same sign, and define for their sum an effective $D_{eff}$ and an effective $Δα_{eff}$, an average of $Δα$ for the different modes. It turns out that $D_{eff}$ is of the order of 0.9, $Δα_{eff}$ is between 5 $\%$ and 10 $\%$ and, relative to $ππ$, the statistical gain for the sum is of about a factor 10. Finally, we compute the ratios $Kπ/ππ, \cdots$ that test the strength of the Penguins and depend on the CP angles, as emphasized by Silva and Wolfenstein and by Deandrea et al.

hep-ph↗

arXiv1995

WEAK TRANSITIONS OF HEAVY MESONS AND THE QUARK MODEL

We underline the general features of the constituent quark model and its success in the description of the spectrum and transitions of hadrons made up of light or heavy quarks, briefly compared to first principles of QCD. To show the present usefulness of the techniques and intuitive insight of the model we present a semirelativistic quark model of meson form factors that exhibits Isgur-Wise scaling and corrections to it. As examples of applications, we consider semileptonic form factors and non-leptonic decays of heavy flavor mesons. We address the issue of the violation of factorization, and show how the quark model can give hints on the problem.

hep-ph↗

arXiv1995

MIXING AND CP VIOLATION IN D MESONS

We review mixing and CP violation in $D$ mesons, emphasizing the differences with the other pseudoscalar mesons in the Standard Model, and show that $D$ mesons can be useful to look for physics beyond the Standard Model.

hep-ph↗

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.

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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.

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