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A. Le Yaouanc

Publications and source records attributed to A. Le Yaouanc.

At least 55 records · Page 3Linked to original sources
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

B_s-\bar{B_s} mixing with a chiral light quark action

We study the $B^0_s-\bar{B^0_s}$ mixing amplitude in Standard Model by computing the relevant hadronic matrix element in the static limit of lattice HQET with the Neuberger light quark action. In the quenched approximation, and after matching to the $\bar{\rm MS}$ scheme in QCD, we obtain $B^{\bar{\rm MS}}_{B_s}(m_b)=0.940(16)(22)$.

hep-lat↗
arXiv2005

Asymptotic behavior of the ghost propagator in SU3 lattice gauge theory

We study the asymptotic behavior of the ghost propagator in the quenched SU(3) lattice gauge theory with Wilson action. The study is performed on lattices with a physical volume fixed around 1.6 fm and different lattice spacings: 0.100 fm, 0.070 fm and 0.055 fm. We implement an efficient algorithm for computing the Faddeev-Popov operator on the lattice. We are able to extrapolate the lattice data for the ghost propagator towards the continuum and to show that the extrapolated data on each lattice can be described up to four-loop perturbation theory from 2.0 GeV to 6.0 GeV. The three-loop values are consistent with those extracted from previous perturbative studies of the gluon propagator. However the effective $Λ_{\ms}$ scale which reproduces the data does depend strongly upon the order of perturbation theory and on the renormalization scheme used in the parametrization. We show how the truncation of the perturbative series can account for the magnitude of the dependency in this energy range. The contribution of non-perturbative corrections will be discussed elsewhere.

hep-lat↗
arXiv2005

Instanton traces in lattice gluon correlation functions

Strong coupling constant computed in Landau gauge and MOM renormalization scheme from lattice two and three gluon Green Functions exhibits an unexpected behavior in the deep IR, showing a maximum value around $1 {\rm GeV}$. We analise this coupling below this maximum within a semiclassical approach, were gluon degrees of freedom at very low energies are described in terms of the classical solutions of the lagrangian, namely instantons. We provide some new results concerning the relationship between instantons and the low energy dynamics of QCD, by analising gluon two- and three-point Green functions separately and with the help of a cooling procedure to eliminate short range correlations.

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↗
arXiv2004

Modified instanton profile effects from lattice Green functions

We trace here instantons through the analysis of pure Yang-Mills gluon Green functions in the Landau gauge for a window of IR momenta (0.4 GeV $< k < 0.9$ GeV). We present lattice results that can be fitted only after substituting the BPST profile in the Instanton liquid model (ILM) by one based on the Diakonov and Petrov variational methods. This also leads us to gain information on the parameters of ILM.

hep-ph↗
arXiv2004

Bounds on the derivatives of the Isgur-Wise function with a non-relativistic light quark

In a preceeding study in the heavy quark limit of QCD, it has been demonstrated that the best lower bound on the curvature of the Isgur-Wise function Xsi(w) is Xsi"(1) > (4rho2+3(rho2)2) > 15/16. The quadratic term (rho2)2 is dominant in a non-relativistic expansion in the light quark, both Xsi"(1) and (rho2)2 scaling like (R2m2)2, where m is the light quark mass and R the bound state radius. The non-relativistic limit is thus a good guide-line in the study of the shape of Xsi(w). In the present paper we obtain similar bounds on all the derivatives of XsiNR(w), the IW function with the light quark non-relativistic, and we demons- trate that these bounds are optimal. We formulate a general method, based on the positivity of matrices of moments of the ground state wave function, that allows to bound the n-th derivative XsiNR(n)(w) in terms of the m-th ones (m < n). We argue that this method can be generalized to the true Isgur-Wise function of QCD Xsi(w).

hep-ph↗
arXiv2004

Lattice measurement of the Isgur-Wise functions tau_1/2 and tau_3/2

We propose a method to compute the Isgur-Wise form factors tau_1/2(1) and tau_3/2(1) for the decay of B mesons into orbitally excited (P wave) D** charmed mesons on the lattice in the static limit. We also present the result of an exploratory numerical simulation which shows that the signal/noise ratio allows for a more dedicated computation. We find tau_1/2(1)=0.38(5) and tau_3/2(1)= 0.53(8), with yet unknown systematic errors. These preliminary numbers agree fairly well with theoretical expectation.

hep-lat↗
arXiv2004

Lattice measurement of the couplings g_infinity and g_Bstar_B_pi

We present the results of a quenched lattice QCD study of the coupling g_hat, in the static heavy quark limit. After combining this with our previous results obtained by using propagating heavy quarks with a mass around the physical charm quark, we are able to interpolate to the b-quark sector. Our results are g_hat_infinity = 0.48 +/- 0.03 +/- 0.11, g_hat_b = 0.58 +/- 0.06 +/- 0.10, and g_Bstar_ B_p = 47 +/- 5 +/- 8.

hep-lat↗
arXiv2003

Quark propagator and vertex: systematic corrections of hypercubic artifacts from lattice simulations

This is the first part of a study of the quark propagator and the vertex function of the vector current on the lattice in the Landau gauge and using both Wilson-clover and overlap actions. In order to be able to identify lattice artifacts and to reach large momenta we use a range of lattice spacings. The lattice artifacts turn out to be exceedingly large in this study. We present a new and very efficient method to eliminate the hypercubic (anisotropy) artifacts based on a systematic expansion on hypercubic invariants which are not SO(4) invariant. A simpler version of this method has been used in previous works. This method is shown to be significantly more efficient than the popular ``democratic'' methods. It can of course be applied to the lattice simulations of many other physical quantities. The analysis indicates a hierarchy in the size of hypercubic artifacts: overlap larger than clover and propagator larger than vertex function. This pleads for the combined study of propagators and vertex functions via Ward identities.

hep-lat↗
arXiv2003

Lower bounds on the curvature of the Isgur-Wise function

Using the OPE, we obtain new sum rules in the heavy quark limit of QCD, in addition to those previously formulated. Key elements in their derivation are the consideration of the non-forward amplitude, plus the systematic use of boundary conditions that ensure that only a finite number of $j^P$ intermediate states (with their tower of radial excitations) contribute. A study of these sum rules shows that it is possible to bound the curvature $σ^2 = ξ''(1)$ of the elastic Isgur-Wise function $ξ(w)$ in terms of its slope $ρ^2 = - ξ'(1)$. Besides the bound $σ^2 \geq {5 \over 4} ρ^2$, previously demonstrated, we find the better bound $σ^2 \geq {1 \over 5} [4 ρ^2 + 3(ρ^2)^2]$. 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. At the lowest possible value for the slope $ρ^2 = {3 \over 4}$, both bounds imply the same bound for the curvature, $σ^2 \geq {15 \over 16}$. We point out that these results are consistent with the dispersive bounds, and, furthermore, that they strongly reduce the allowed region by the latter for $ξ(w)$.

hep-ph↗
arXiv2003

Sum rules in the heavy quark limit of QCD

In the leading order of the heavy quark expansion, we propose a method within the OPE and the trace formalism, that allows to obtain, in a systematic way, Bjorken-like sum rules for the derivatives of the elastic Isgur-Wise function $ξ(w)$ in terms of corresponding Isgur-Wise functions of transitions to excited states. A key element is the consideration of the non-forward amplitude, as introduced by Uraltsev. A simplifying feature of our method is to consider currents aligned along the initial and final four-velocities. As an illustration, we give a very simple derivation of Bjorken and Uraltsev sum rules. On the other hand, we obtain a new class of sum rules that involve the products of IW functions at zero recoil and IW functions at any $w$. Special care is given to the needed derivation of the projector on the polarization tensors of particles of arbitrary integer spin. The new sum rules give further information on the slope $ρ^2 = - ξ'(1)$ and also on the curvature $σ^2 = ξ'' (1)$, and imply, modulo a very natural assumption, the inequality $σ^2 \geq {5\over 4} ρ^2$, and therefore the absolute bound $σ^2 \geq {15 \over 16}$.

hep-ph↗
arXiv2002

The strong coupling constant at small momentum as an instanton detector

We present a study of $α_{MOM}(p)$ at small p computed from the lattice. It shows a dramatic $\propto p^4$ law which can be understood within an instanton liquid model. In this framework the prefactor gives a direct measure of the instanton density in thermalised configurations. A preliminary result for this density is 5.27(4) fm^{-4}.

hep-ph↗
arXiv2002

Bounds on the derivatives of the Isgur-Wise function from sum rules in the heavy quark limit of QCD

Using the OPE and the trace formalism, we have obtained a number of sum rules in the heavy quark limit of QCD that include the sum over all excited states for any value $j^P$ of the light cloud. We show that these sum rules imply that the elastic Isgur-Wise function $ξ(w)$ is an alternate series in powers of $(w-1)$. Moreover, we obtain sum rules involving the derivatives of the elastic Isgur-Wise function $ξ(w)$ at zero recoil, that imply that the $n$-th derivative can be bounded by the $(n-1)$-th one. For the curvature $σ^2 = ξ''(1)$, this proves the already proposed bound $σ^2 \geq {5 \over 4} ρ^2$. Moreover, we obtain the absolute bound for the $n$-th derivative $(-1)^n ξ^{(n)}(1) \geq {(2n+1)!! \over 2^{2n}}$, that generalizes the results $ρ^2 \geq {3 \over 4}$ and $σ^2 \geq {15 \over 16}$.

hep-ph↗