arXiv subjects

A. Le Yaouanc

Publications and source records attributed to A. Le Yaouanc.

At least 19 recordsLinked to original sources

arXiv2025

Isgur-Wise functions for $\boldsymbol{Λ_b \to Λ_c\left({1 \over 2}^\pm \right)}$ transitions in the Bakamjian-Thomas Relativistic Quark Model

We study the transitions ${Λ_b \to Λ_c\left({1 \over 2}^\pm \right)}$ in the Bakamjian-Thomas (BT) relativistic quark model formalism, which describes hadrons with a fixed number of constituents. In the heavy quark limit, the BT model yields covariant form factors and Isgur-Wise (IW) scaling, regardless of the spectroscopic model used to describe the bound states. It has been extensively applied to heavy mesons where subtle properties of the IW limit of QCD, including the Bjorken-Uraltsev sum rules, have been shown to be satisfied. The present paper, where the BT construction is applied to baryons, is unavoidably technical because one is dealing with a three-body problem. The complications originate from the natural choice of the Jacobi coordinates ${\vec ρ}$ (relative space coordinate between the two light spectator quarks) and ${\vec λ}$ (relative space coordinate between the center-of-mass of the two light quarks and the heavy quark). The corresponding orbital angular momenta are denoted by ${\vec \ell}_ρ$ and ${\vec \ell}_λ$, with ${\vec \ell}_ρ+ {\vec \ell}_λ= {\vec L}$. For the transitions $Λ_b \to Λ_c\left({1 \over 2}^\pm\right)$, i.e. $L = 0 \to L = 0$ or $L = 0 \to L = 1$, one can see that the moduli $\ell_ρ$ and $\ell_λ$ can take an infinite number of values. For $L = 0 \to L = 0$ one has the constraint $\ell_λ= \ell_ρ$ and for $L = 0 \to L = 1$ the constraint is $\ell_λ= \ell_ρ\pm 1$. We compute explicitly the IW function $ξ_Λ(w)$ in the elastic case $Λ_b \left({1 \over 2}^+ \right) \to Λ_c \left({1 \over 2}^+ \right)$ and the much more involved IW function $σ_Λ(w)$ in the inelastic case $Λ_b \left({1 \over 2}^+ \right) \to Λ_c \left({1 \over 2}^- \right)$. These functions exhibit the expected properties of covariance and IW scaling.

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arXiv2024

The $a_1$ factorisation coefficient in ${\overline{B}^0} \to D^{()+}M^{-}$ and ${\overline{B}^0} \to D^{()+}D_s^{(*)-}$ decays: measurements versus theory

Using recent measurements of exclusive B-meson decays we extract the $a_1$ factorization parameter in ${\overline{B}^{0}_{d}} \to D^{(*)^+} K^-/π^-$ decay channels. { The values obtained in the four channels are very similar, in agreement with the theoretical expectations obtained in the $m_Q \to \infty$ limit, but the measured values differ definitely from the expected central values. } Such differences have already been observed. Using recent data, we improve the accuracy by {a factor close to two} in this comparison. We study possible interpretations for such a difference and conclude that the claimed accuracy of corrections due to soft gluon contributions and finite mass effects has to be revisited before arguing for possible "New-Physics" effects. We observe that the corrections to the $m_Q \to \infty$ limit are larger in the spectator topology than effects from exchange amplitude contributions. We discuss also the way expected ratios of $a_1$ values, involving hypotheses from theory, are used to obtain the fraction of $B^0_s$ meson production in jets at LHC and conclude that the uncertainties attached to this approach are not well established. Finally, the $a_1$ values extracted from $\overline{B}^{0}_{d} \to D^{(*)+} D_s^-$ decays are found to be similar, within uncertainties, to the ones obtained with $K^-$ emission, once expected penguin contributions are corrected. Using the same approach, we note that $a_1$ values measured in channels with a $D_s^{*-}$ emission are about two standard deviations lower than $a_1(D^{(*)+}K^-$).

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arXiv2020

Heavy baryon wave functions, Bakamjian-Thomas approach to form factors, and observables in ${Λ_b \to Λ_c\left({1 \over 2}^\pm \right) \ell \overlineν}$ transitions

Motivated by the calculation of observables in the decays $Λ_b \to Λ_c\left({1 \over 2}^\pm \right) \ell \overlineν$, as tests of Lepton Flavor Universality, we present a calculation of form factors in the quark model. Our scheme combines a spectroscopic model, providing the internal wave functions, and the Bakamjian-Thomas relativistic formalism to deduce the wave functions in motion and current matrix elements, that amount in the heavy quark limit to the Isgur-Wise (IW) function. For baryons we meet difficulties using standard spectroscopic models, leading us to propose a simple phenomenological model : a Q-pointlike-diquark model, non-relativistic with harmonic oscillator forces, with a reasonable low-lying spectrum and good slope of the IW function. We extract this slope from Lattice data and find $ρ_Λ^2 \sim 2$. We are not able to reproduce the right $ρ_Λ^2$ when using standard linear + Coulomb potential models, both with three quarks $Qqq$ or in a Q-pointlike-diquark picture. These difficulties seem to derive from the high sensitivity of $ρ_Λ^2$ to the structure of the light quark subsystem. After fixing the parameters of our interim model to yield correct spectrum and $ρ_Λ^2$, we compute observables. Bjorken sum rule shows that the inelastic IW function is large, and therefore $Λ_b \to Λ_c \left({1 \over 2}^-, {3 \over 2}^- \right) \ell \overlineν$ could be studied at LHCb. Some observables in the $τ$ case present zeroes for specific values of $q^2$ that could be tests of the Standard Model.

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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.

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arXiv2016

Angular analysis of B -> J/psi K1 : towards a model independent determination of the photon polarization with B-> K1 gamma

We propose a model independent extraction of the hadronic information needed to determine the photon polarization of the b-> s gamma process by the method utilizing the B -> K1 gamma -> K pi pi gamma angular distribution. We show that exactly the same hadronic information can be obtained by using the B -> J/psi K1 -> J/psi K pi pi channel, which leads to a much higher precision.

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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.

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arXiv2015

mu-Squared Dependent Deviation of the Non Perturbative ZA,MOM from the True Axial Renormalisation Constant, Implied by Ward Identity

It is recalled why, as already stated in a previous paper, there seems to be an inconsistency in identifying the non perturbative ZA,MOM as the renormalisation of the axial current, or equivalently, in setting as normalisation condition that the renormalised vertex=1 at p^2 = mu^2 at some renormalisation scale mu, where p is the momentum in the legs. Indeed, unlike the vector case, the Ward-Takahashi (WT) identity for the axial current is shown to imply both the renormalisation scale independence of ZA and a mu2 dependence of ZA,MOM. This mu^2 dependence is simply related to certain invariants in the pseudoscalar vertex and can persist in the chiral limit due to the spontaneous breaking of chiral symmetry (pion pole). It is seen clearly in the mu^2 dependence of some lattice calculations of ZA,MOM/ZV,MOM near the chiral limit.

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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.

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arXiv2013

B decays to radially excited D

We discuss the possibility to measure in present experiments, especially LHCb, the non leptonic decay branching ratio $B \to D' π$, and emphasize phenomenological implications on $B \to D' l ν$ semileptonic decay. We have estimated by lattice QCD the $D'$ decay constant $f_{D'}$ that parameterizes the $D'$ emission contribution to the Class-III non leptonic decay $B^- \to D^0 π^-$. In addition, we provide a new estimate of the decay constants $f_{D_{s,q}}$ which read $f_{D_{s}}=252(3)$ MeV and $f_{D_{s}}/f_{D}=1.23(1)(1)$.

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arXiv2012

The Infrared Behaviour of the Pure Yang-Mills Green Functions

We review the infrared properties of the pure Yang-Mills correlators and discuss recent results concerning the two classes of low-momentum solutions for them reported in literature; i.e. decoupling and scaling solutions. We will mainly focuss on the Landau gauge and pay special attention to the results inferred from the analysis of the Dyson-Schwinger equations of the theory and from "{\it quenched}" lattice QCD. The results obtained from properly interplaying both approaches are strongly emphasized.

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arXiv2011

Vacuum expectation value of A^2 from LQCD

We argue from LQCD that there is a non vanishing v.e.v of $A_a^μA^a_μ$ in QCD in the Landau gauge. We use operator product expansion to provide a clear definition of $A_a^μA^a_μ$ and extract a number both in the quenched and unquenched case.

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arXiv2010

The low-momentum ghost dressing function and the gluon mass

We study the low-momentum ghost propagator Dyson-Schwinger equation (DSE) in Landau gauge, assuming for the truncation a constant ghost-gluon vertex, as it is extensively done, and a simple model for a massive gluon propagator. Then, regular DSE solutions (the zero-momentum ghost dressing function not diverging) appear to emerge and we show the ghost propagator to be described by an asymptotic expression reliable up to the order ${\cal O}(q^2)$. That expression, depending on the gluon mass and the zero-momentum Taylor-scheme effective charge, is proven to fit pretty well the low-momentum ghost propagator obtained through big-volume lattice simulations.

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arXiv2010

Quark pseudoscalar vertex and quark mass function with clover fermions : spontaneous symmetry breaking, OPE, symmetry restoration at small volume

We study the quark mass function on hypercubic lattices, in a large range of physical volumes and cutoffs. To avoid the very large Wilson term artefact, we exploit the relation between the quark mass function and the pseudoscalar vertex in the continuum. We extrapolate to the chiral limit. In function of the physical volume, we observe a striking discontinuity in the properties of chiral extrapolation around a physical volume $L_c 6 (GeV}^{-1}=1.2 fm$. It is present in the quark mass function, which collapses to zero, as well as in the pion mass and the quark condensate as directly calculated from the pseudoscalar correlator. It is strongly reminiscent of the phenomenon of chiral symmetry restoration observed by Neuberger and Narayanan at $N_C=\infty$ around the same physical length. In the case of spontaneous symmetry breaking, we confirm that the OPE of the quark mass function, involving the quark condensate, is not operative at the available momenta, even taking into account the unusually large high order corrections to the Wilson coefficient calculated by Chetyrkin and Maier ; the gap remains large, around a factor 2, even at the largest momenta available to us (p \simeg GeV)

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arXiv2009

A Ghost Story: Ghosts and Gluons in the IR regime of QCD

We discuss the different methods to obtain reliable informations about the deep infra-red behaviour of the gluon and ghost Green functions in QCD. We argue that a clever combination of analytical inputs and numerical ones is necessary. We illustrate this statement about the distinction between two classes of solutions of the ghost propagator Dyson-Schwinger equation (GPDSE). We conclude that the solution II ("decoupling") with a finite renormalised ghost dressing function at zero momentum is strongly favored by lattice QCD, We derive a method to solve numerically the GPDSE using lattice inputs concerning the gluon propagator. We derive an analytical small momentum expansion of the Ghost dressing function. We prove from the large cut-off behaviour of the ghost propagator renormalisation constant, $\widetilde Z_3$, that the bare ghost dressing function is infinite at the infinite cut-off limit.

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arXiv2009

Gribov's horizon and the ghost dressing function

We study a relation recently derived by K. Kondo at zero momentum between the Zwanziger's horizon function, the ghost dressing function and Kugo's functions $u$ and $w$. We agree with this result as far as bare quantities are considered. However, assuming the validity of the horizon gap equation, we argue that the solution $w(0)=0$ is not acceptable since it would lead to a vanishing renormalised ghost dressing function. On the contrary, when the cut-off goes to infinity, $u(0) \to \infty$, $w(0) \to -\infty$ such that $u(0)+w(0) \to -1$. Furthermore $w$ and $u$ are not multiplicatively renormalisable. Relaxing the gap equation allows $w(0)=0$ with $u(0) \to -1$. In both cases the bare ghost dressing function, $F(0,Λ)$, goes logarithmically to infinity at infinite cut-off. We show that, although the lattice results provide bare results not so different from the $F(0,Λ)=3$ solution, this is an accident due to the fact that the lattice cut-offs lie in the range 1-3 GeV$^{-1}$. We show that the renormalised ghost dressing function should be finite and non-zero at zero momentum and can be reliably estimated on the lattice up to powers of the lattice spacing ; from published data on a $80^4$ lattice at $β=5.7$ we obtain $F_R(0,μ=1.5$ GeV)$\simeq 2.2$.

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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.

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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%.

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arXiv2008

Ghost-gluon running coupling, power corrections and the determination of $Λ_{\bar {\rm MS}}$

We compute a formula including OPE power corrections to describe the running of a QCD coupling non-perturbatively defined through the ghost and gluon dressing functions. This turns out to be rather accurate. We propose the ``{\it plateau}''-procedure to compute $Λ_{\bar{\rm MS}}$ from the lattice computation of the running coupling constant. We show a good agreement between the different methods which have been used to estimate $Λ_{\bar{\rm MS}}^{N_f=0}$. We argue that $Λ_{\bar{\rm MS}}$ or the strong coupling constant computed with different lattice spacings may be used to estimate the lattice spacing ratio.

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