arXiv subjects

J. -C. Raynal

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

At least 19 recordsLinked to original sources

arXiv2016

Finite mass corrections for B -> D(*), D** \ell νdecays in the Bakamjian-Thomas relativistic quark model

The Bakamjian-Thomas relativistic quark model for hadron current matrix elements, while non-covariant at finite mass, is successful in the heavy quark limit : form factors are covariant and satisfy Isgur-Wise scaling and Bjorken-Uraltsev sum rules. Motivated by the so-called "1/2 vs. 3/2 puzzle" in B decays to positive parity D**, we examine the implications of the model at finite mass. In the elastic case 1/2^- -> 1/2^-, the HQET constraints for the O(1/m_Q) corrections are analytically fulfilled. A number of satisfying regularities is also found for inelastic transitions. We compute the form factors using the wave functions given by the Godfrey-Isgur potential. For 1/2^- \to 3/2^+ the departures from the heavy quark limit are small, but we find a strong enhancement in 1/2^- -> 1/2^+ (for 0^- -> 0^+). This enhancement is linked to a serious difficulty of the model at finite mass for the inelastic transitions, namely a violation of the HQET constraints at zero recoil formulated by Leibovich et al. These are nevertheless satisfied in the non-relativistic limit for the light quark. We conclude that these HQET rigorous constraints are crucial in the construction of a sensible relativistic quark model of inelastic form factors.

hep-ph↗

arXiv2016

Sum rules of Bjorken-Uraltsev type in the Bakamjian-Thomas relativistic quark model

The Bakamjian-Thomas relativistic quark model, describing hadrons with a fixed number of constituents, yields in the heavy quark limit of QCD covariant Isgur-Wise functions and satisfies the whole tower of lowest moment sum rules (Bjorken-Uraltsev type sum rules). We first recall, as well as earlier results, the new formalism presented in our recent papers on Lorentz representations, which provide an elegant framework for the analysis of this model in the heavy quark limit and stress the results which have been already obtained in this direction. Then, we give some very explicit demonstrations of the fact that the Bakamjian-Thomas framework satifies the sum rules by considering simple cases of Isgur-Wise functions. In addition to the specific Bjorken and Uraltsev sum rules, an important sum rule that involves only heavy mesons with light cloud $j^P = {1 \over 2}^-$ and their radial excitations is demonstrated. This latter sum rule is phenomenologically interesting because it constrains the derivatives of the radially excited Isgur-Wise functions at zero recoil. On the other hand, we recall the limitations of the Bakamjian-Thomas scheme. At finite mass, current matrix elements with the current coupled to the heavy quark are no longer covariant, and higher moment sum rules that hold in the heavy quark limit of QCD are not satisfied.

hep-ph↗

arXiv2014

Isgur-Wise functions and unitary representations of the Lorentz group : the meson case j = 1/2

We pursue the group theoretical method to study Isgur-Wise functions. We apply the general formalism, formerly applied to the baryon case j^P = 0^+ (for Λ_b -> Λ_c \ell ν), to mesons with j^P = 1/2^-, i.e. $\overline{B} -> D(D^{(*)})\ellν. In this case, more involved from the angular momentum point of view, only the principal series of unitary representations of the Lorentz group contribute. We obtain an integral representation for the IW function xi(w) with a positive measure, recover the bounds for the slope and the curvature of xi(w) obtained from the Bjorken-Uraltsev sum rule method, and get new bounds for higher derivatives. We demonstrate also that if the lower bound for the slope is saturated, the measure is a delta-function, and xi(w) is given by an explicit elementary function. Inverting the integral formula, we obtain the measure in terms of the IW function, allowing to formulate criteria to decide if a given ansatz for the Isgur-Wise function is compatible or not with the sum rule constraints. Moreover, we have obtained an upper bound on the IW function valid for any value of w. We compare these theoretical constraints to a number of forms for ξ(w) proposed in the literature. The "dipole" function ξ(w) = (2/(w+1))^(2c) satisfies all constraints for c \geq 3/4, while the QCD Sum Rule result including condensates does not satisfy them. Special care is devoted to the Bakamjian-Thomas relativistic quark model in the heavy quark limit and to the description of the Lorentz group representation that underlies this model. Consistently, the IW function satisfies all Lorentz group criteria for any explicit form of the meson Hamiltonian at rest.

hep-ph↗

arXiv2010

Note on new interesting baryon channels to measure the photon polarization in b -> s gamma

At LHC a large number of b-flavored baryons will be produced. In this note we propose new baryon modes to determine the photon helicity of the penguin transition $b \to s γ$. The decay $Λ_b \to Λγ$ has the drawback that the $Λ$, being neutral and long-lived, will escape detection most of the time. To overcome this difficulty, transitions of the type $Λ_b \to Λ^{*} γ$ have been proposed, where $Λ^{*}$ denotes an excited state decaying strongly within the detector into the clean mode $p K^-$. The doublet $Ξ_b$, that decays weakly, has a number of good features. The charged baryon $Ξ_b^-$ will decay into the mode $Ξ^- γ$, where the ground state hyperon $Ξ^-$, although it will decay most of the time outside the detector, can be detected because it is charged. We consider also the decay of $Ξ_b$ into $Ξ^{*} γ$, where a higher mass state $Ξ^{*}$ can decay strongly within the detector. We point out that the initial transverse polarization of $Ξ_b$ has to be known in all cases. To determine this parameter through the transition $Ξ_b \to J/Ψ Ξ$, we distinguish between different cases, and underline that in some situations one needs {\it theoretical input} on the asymmetry parameter $α_{Ξ_b}$ of the primary decay. {\it A fortiori} the same considerations apply to the case of the $Λ_b$.

hep-ph↗

arXiv2009

Isgur-Wise functions and unitary representations of the Lorentz group : the baryon case j = 0

We propose a group theoretical method to study Isgur-Wise functions. A current matrix element splits into a heavy quark matrix element and an overlap of the initial and final clouds, related to the IW functions, that contain the long distance physics. The light cloud belongs to the Hilbert space of a unitary representation of the Lorentz group. Decomposing into irreducible representations one obtains the IW function as an integral formula, superposition of irreducible IW functions with positive measures, providing positivity bounds on its derivatives. Our method is equivalent to the sum rule approach, but sheds another light on the physics and summarizes and gives all its possible constraints. We expose the general formalism, thoroughly applying it to the case j = 0 for the light cloud, relevant to the semileptonic decay Lambda_b -> Lambda_c + l + nu. In this case, the principal series of the representations contribute, and also the supplementary series. We recover the bound for the curvature of the j = 0 IW function xi_Lambda (w) that we did obtain from the sum rule method, and we get new bounds for higher derivatives. We demonstrate also that if the lower bound for the curvature is saturated, then xi_Lambda (w) is completely determined, given by an explicit elementary function. We give criteria to decide if any ansatz for the Isgur-Wise function is compatible or not with the sum rules. We apply the method to some simple model forms proposed in the literature. Dealing with a Hilbert space, the sum rules are convergent, but this feature does not survive hard gluon radiative corrections.

hep-ph↗

arXiv2008

Bound on the curvature of the Isgur-Wise function of the baryon semileptonic decay Lambda_b -> Lambda_c + l + nu

In the heavy quark limit of QCD, using the Operator Product Expansion, the formalism of Falk for hadrons or arbitrary spin, and the non-forward amplitude, as proposed by Uraltsev, we formulate sum rules involving the Isgur-Wise function $ξ_Λ (w)$ of the baryon transition $Λ_b \to Λ_c \ell \overlineν_{\ell}$, where the light cloud has $j^P=0^+$ for both initial and final baryons. We recover the lower bound for the slope $ρ_Λ^2 = - ξ'_Λ(1) \geq 0$ obtained by Isgur et al., and we generalize it by demonstrating that the IW function $ξ_Λ (w)$ is an alternate series in powers of $(w-1)$, i.e. $(-1)^n ξ_Λ^{(n)} (1) \geq 0$. Moreover, exploiting systematically the sum rules, we get an improved lower bound for the curvature in terms of the slope, $σ_Λ^2 = ξ"_Λ(1) \geq {3 \over 5} [ρ_Λ^2 + (ρ_Λ^2)^2]$. This bound constrains the shape of the Isgur-Wise function and it will be compelling in the analysis of future precise data on the differential rate of the baryon semileptonic decay $Λ_b \to Λ_c \ell \overlineν_{\ell}$, that has a large measured branching ratio, of about 5%.

hep-ph↗

arXiv2008

Relation between Light Cone Distribution Amplitudes and Shape Function in B mesons

The Bakamjian-Thomas relativistic quark model provides a Poincaré representation of bound states with a fixed number of constituents and, in the heavy quark limit, form factors of currents satisfy covariance and Isgur-Wise scaling. We compute the Light Cone Distribution Amplitudes of $B$ mesons $ϕ_{\pm}^B(ω)$ as well as the Shape Function $S(ω)$, that enters in the decay $B \to X_s γ$, that are also covariant in this class of models. The LCDA and the SF are related through the quark model wave function. The former satisfy, in the limit of vanishing constituent light quark mass, the integral relation given by QCD in the valence sector of Fock space. Using a gaussian wave function, the obtained $S(ω)$ is identical to the so-called Roman Shape Function. From the parameters for the latter that fit the $B \to X_sγ$ spectrum we predict the behaviour of $ϕ_{\pm}^B(ω)$. We discuss the important role played by the constituent light quark mass. In particular, although $ϕ_-^B(0) \not= 0$ for vanishing light quark mass, a non-vanishing mass implies the unfamiliar result $ϕ_-^B (0) = 0$. Moreover, we incorporate the short distance behaviour of QCD to $ϕ_+^B (ω)$, which has sizeable effects at large $ω$. We obtain the values for the parameters $\barΛ \cong 0.35$ GeV and $λ_B^{-1} \cong 1.43$ GeV$^{-1}$. We compare with other theoretical approaches and illustrate the great variety of models found in the literature for the functions $ϕ_{\pm}^B (ω)$; hence the necessity of imposing further constraints as in the present paper. We briefly review also the different phenomena that are sensitive to the LCDA.

hep-ph↗

arXiv2007

Memorino on the `1/2 vs. 3/2 Puzzle' in $\bar B \to l \bar νX_c$ -- a Year Later and a Bit Wiser

The OPE treatment that has been so successful in describing inclusive $\bar B \to l \bar νX_c$ decays yields sum rules (in particular the Uraltsev sum rule and its higher moments) implying the dominance of the $P$ wave $j_q = 3/2$ charm states in $X_c$ over their $j_q=1/2$ counterparts. This prediction is supported by other general arguments as well as quark model calculations, which illustrate the OPE results, and by preliminary lattice findings. Its failure would indicate a significant limitation in our theoretical understanding of $\bar B \to l \bar νX_c$. Some experimental issues have been clarified since a preliminary version of this note had appeared, yet the verdict on the composition of the final states {\em beyond} $D$, $D^*$ and the two narrow $j_q = 3/2$ resonances remains unsettled. Establishing which hadronic configurations -- $D/D^* + π, D/D^* + 2 π, ...$ -- contribute, what their quantum numbers are and their mass distributions will require considerable experimental effort. We explain the theoretical issues involved and why a better understanding of them will be of significant value. Having significant contributions from a mass continuum distribution below 2.5 GeV raises serious theoretical questions for which we have no good answer. Two lists are given, one with measurements that need to be done and one with items of theoretical homework. Some of the latter can be done by employing existing theoretical tools, whereas others need new ideas.

hep-ph↗

arXiv2007

Isospin breaking in the yield of heavy meson pairs in e+e- annihilation near threshold

We revisit the problem of interplay between the strong and the Coulomb interaction in the charged-to-neutral yield ratio for $B {\bar B}$ and $D {\bar D}$ pairs near their respective thresholds in $e^+e^-$ annihilation. We consider here a realistic situation with a resonant interaction in the isospin I=0 channel and a nonresonant strong scattering amplitude in the I=1 state. We find that the yield ratio has a smooth behavior depending on the scattering phase in the I=1 channel. The same approach is also applicable to the $K {\bar K}$ production at the $ϕ(1020)$ resonance, where the Coulomb effect in the charged-to-neutral yield ratio is generally sensitive to the scattering phases in both the isoscalar and the isovector channels. Furthermore, we apply the same approach to the treatment of the effect of the isotopic mass difference between the charged and neutral mesons and argue that the strong-scattering effects generally result in a modification to the pure kinematical effect of this mass difference.

hep-ph↗

arXiv2006

The Isgur-Wise function in the BPS limit

From sum rules in the heavy quark limit of QCD, using the non-forward amplitude, we demonstrate that if the slope rho^2 = -xsi'(1) of the Isgur-Wise function xsi(w) attains its lower bound 3/4 (as happens in the BPS limit proposed by Uraltsev), the IW function is completely determined, given by the function xsi(w) = [2/(w+1)]^(3/2).

hep-ph↗

arXiv2006

Explicit form of the Isgur-Wise function in the BPS limit

Using previously formulated sum rules in the heavy quark limit of QCD, we demonstrate that if the slope rho^2 = -xi'(1) of the Isgur-Wise function xi(w) attains its lower bound 3/4, then all the derivatives (-1)^L xi^(L)(1) attain their lower bounds (2L+1)!!/2^(2L), obtained by Le Yaouanc et al. This implies that the IW function is completely determined, given by the function xi(w) = [2/(w+1)]^(3/2). Since the so-called BPS condition proposed by Uraltsev implies rho^2 = 3/4, it implies also that the IW function is given by the preceding expression.

hep-ph↗

arXiv2006

The tensor force in Heavy Quark Effective Theory

We extend the formalism of Leibovich, Ligeti, Stewart and Wise in the 1/m_Q expansion of Heavy Quark Effective Theory for the B semileptonic decays into excited D[(3/2)^+] mesons to the opposite parity states D[(3/2)^-]. For D[(3/2)^+] the 1/m_Q current perturbation dominates over the leading term at zero recoil, while for D[(3/2)^-] the 1/m_Q perturbation due to L_mag dominates also at zero recoil. We show that the corresponding 1/m_Q magnetic coupling is proportional to the mixing between the states D[(3/2)^-] and D[(1/2)^-] induced by the tensor force. We point out some subtleties that appear in this respect in HQET.

hep-ph↗

arXiv2005

Memorino on the `1/2 vs. 3/2 Puzzle' in $\bar B \to l \bar νX_c$

After the successes the OPE description has scored in describing $\bar B \to l \bar νX_c$ decays, we need to study what can be said about the composition of the hadronic final state $X_c$. The same OPE treatment yields sum rules implying the dominance of $j_q = 3/2$ charm states in $X_c$ over their $j_q=1/2$ counterparts. This prediction is supported by other general arguments as well as quark model calculations. At present it is unclear to which degree data conform to these predictions. More experimental information is essential. We want to ask our experimental colleagues for a redoubled effort to establish, which hadronic configurations -- $D/D^* + π, D/D^* + 2 π, ...$ -- make up $Γ(\bar B \to l \bar νX_c)$ beyond $\bar B \to l \bar νD/D^*$, what their quantum numbers are and their mass distributions. The latter is most relevant for the determination of hadronic mass moments in $\bar B \to l \bar νX_c$. Since all this will require considerable effort on their part, we want to explain the theoretical issues involved, why they carry `gravitas' -- i.e. are weighty -- and why a better understanding of them will be of significant value. In this brief memo we sketch the underlying arguments based on heavy quark theory, the OPE, a special class of quark models and lattice QCD in a nutshell. After summarizing the experimental situation we conclude with two lists, namely one with measurements that need to be done and one with items of theoretical homework. Some of the latter can be done by employing existing theoretical tools, whereas others need new ideas.

hep-ph↗

arXiv2005

Sum rules for leading and subleading form factors in Heavy Quark Effective Theory using the non-forward amplitude

Within the OPE, we the new sum rules in Heavy Quark Effective Theory in the heavy quark limit and at order 1/m_Q, using the non-forward amplitude. In particular, we obtain new sum rules involving the elastic subleading form factors chi_i(w) (i = 1,2, 3) at order 1/m_Q that originate from the L_kin and L_mag perturbations of the Lagrangian. To the sum rules contribute only the same intermediate states (j^P, J^P) = ((1/2)^-, 1^-), ((3/2)^-, 1^-) that enter in the 1/m_Q^2 corrections of the axial form factor h_(A_1)(w) at zero recoil. This allows to obtain a lower bound on -delta_(1/m^2)^(A_1) in terms of the chi_i(w) and the shape of the elastic IW function xi(w). An important theoretical implication is that chi'_1(1), chi_2(1) and chi'_3(1) (chi_1(1) = chi_3(1) = 0 from Luke theorem) must vanish when the slope and the curvature attain their lowest values rho^2->3/4, sigma^2->15/16. These constraints should be taken into account in the exclusive determination of |V_(cb)|.

hep-ph↗

arXiv2005

Lagrangian perturbations at order 1/m$_{\bf Q}$ and the non-forward amplitude in Heavy Quark Effective Theory

We pursue the program of the study of the non-forward amplitude in HQET. We obtain new sum rules involving the elastic subleading form factors $χ_i(w)$ $(i = 1,2, 3)$ at order $1/m_Q$ that originate from the ${\cal L}_{kin}$ and ${\cal L}_{mag}$ perturbations of the Lagrangian. To obtain these sum rules we use two methods. On the one hand we start simply from the definition of these subleading form factors and, on the other hand, we use the Operator Product Expansion. To the sum rules contribute only the same intermediate states $ (j^P, J^P) = ({1 \over 2}^-, 1^-), ({3\over 2}^-, 1^-)$ that enter in the $1/m_Q^2$ corrections of the axial form factor $h_{A_1}(w)$ at zero recoil. This allows to obtain a lower bound on $- δ_{1/m^2}^{(A_1)}$ in terms of the $χ_i(w)$ and the shape of the elastic IW function $ξ(w)$. We find also lower bounds on the $1/m_Q^2$ correction to the form factors $h_+(w)$ and $h_1(w)$ at zero recoil. An important theoretical implication is that $χ'_1(1)$, $χ_2(1)$ and $χ'_3(1)$ ($χ_1(1) = χ_3(1) = 0$ from Luke theorem) must vanish when the slope and the curvature attain their lowest values $ρ^2 \to {3 \over 4}$, $σ^2 \to {15 \over 16}$. We discuss possible implications on the precise determination of $|V_{cb}|$.

hep-ph↗

arXiv2005

The decays $\bar{B} \to D^{**}π$ and the Isgur-Wise functions $τ_{1/2}(w)$, $τ_{3/2}(w)$

We perform a phenomenological analysis of the decays $B \to D^{**}π$, where $D^{**}$ is a $P$-wave excited meson with total angular momentum $j = {1 \over 2}$ or ${3 \over 2}$ for the light cloud, recently measured by the Belle Collaboration in the modes $\bar{B}^0\to D^{**+}π^-$ (Class I) and $B^- \to D^{**0}π^-$ (Class III). Making the reasonable assumption of naive factorization, that we test in $B \to D(D^*)π$ decays, Class I decays allow to extract the Isgur-Wise form factors $τ_{1/2}(w)$, $τ_{3/2}(w)$ at $w \cong w_{max}$ ($q^2 \cong 0$). We obtain $τ_{1/2}(w_{max}) < 0.20$, $τ_{3/2}(w_{max}) = 0.31 \pm 0.12$. We discuss the question of the $w$ dependence of these IW functions. We find agreement with the Bakamjian-Thomas quark model of form factors and, extrapolating at $w=1$, with Bjorken and Uraltsev sum rules. We discuss also Class III decays, where the $D^{**0}$ $(j = {1 \over 2})$ emission diagram contributes. We extract the corresponding $f_{D_{1/2}}$ decay constant, that is in agreement with theoretical estimates at finite mass. Finally, we must warn that $1/m_Q$ corrections could be large and upset the results of the present stage of this analysis. On the other hand, we confront present data on the semileptonic rate of $B$ mesons to excited states with theoretical expectations.

hep-ph↗

arXiv2005

Subleading form factors at order 1/m_Q in terms of leading quantities using the non-forward amplitude in HQET

We consider the non-forward amplitude within the Heavy Quark Effective theory. We show that one can obtain new information on the subleading corrections in 1/m_Q. We illustrate the method by deriving new simple relations between the functions Xsi_3(w) and Lambdabar Xsi(w) and the sums Sum_n DeltaE^(n)_j tau^(n)_j(1) tau^(n)_j(w) (j=1/2,3/2), that involve leading quantities, namely the Isgur-Wise functions tau^(n)_j(w) and the level spacings DeltaE^(n)_j. The simplicity of our results follows from the fact that, for the non-forward amplitude B(v_i)->D^(n)(v')->B(v_f), there are three variables (w_i,w_f,w_if)=(v_i.v',v_f.v',v_i.v_f) independent in a certain domain, and we consider the zero recoil frontier (w,1,w) where only a finite number of j^P states contribute (1/2^+,3/2^+). These sum rules reduce to known results at w=1, for Lambdabar obtainted by Voloshin, and for Xsi_3(1) obtained by Le Yaouanc et al. and by Uraltsev, and generalizes them to all values of w. We discuss phenomenological applications of these results, in particular the check of Bakamjian-Thomas quark models and the comparison with the QCD Sum Rules approach.

hep-ph↗

arXiv2004

Sum rules in the heavy quark limit of QCD and Isgur-Wise functions

Using the OPE, we formulate new sum rules in the heavy quark limit of QCD. These sum rules imply that the elastic Isgur-Wise function $ξ(w)$ is an alternate series in powers of $(w-1)$. Moreover, one gets that the $n$-th derivative of $ξ(w)$ at $ w=1$ can be bounded by the $(n-1)$-th one, and an absolute lower bound for the $n$-th derivative $(-1)^n ξ^{(n)}(1) \geq {(2n+1)!! \over 2^{2n}}$. Moreover, for the curvature we find $ξ''(1) \geq {1 \over 5} [4 ρ^2 + 3(ρ^2)^2]$ where $ρ^2 = - ξ'(1)$. We show that the quadratic term ${3 \over 5} (ρ^2)^2$ has a transparent physical interpretation, as it is leading in a non-relativistic expansion in the mass of the light quark. These bounds should be taken into account in the parametrizations of $ξ(w)$ used to extract $|V_{cb}|$. These results are consistent with the dispersive bounds, and they strongly reduce the allowed region of the latter for $ξ(w)$. The method is extended to the subleading quantities in $1/m_Q$, namely $ξ_3(w)$ and $\barΛξ(w)$.}]

hep-ph↗