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A. Le Yaouanc

Publications and source records attributed to A. Le Yaouanc.

At least 37 records · Page 2Linked to original sources
arXiv2008

IR finiteness of the ghost dressing function from numerical resolution of the ghost SD equation

We solve numerically the Schwinger-Dyson (SD hereafter) ghost equation in the Landau gauge for a given gluon propagator finite at k=0 (alpha_gluon=1) and with the usual assumption of constancy of the ghost-gluon vertex ; we show that there exist two possible types of ghost dressing function solutions, as we have previously inferred from analytical considerations : one singular at zero momentum, satisfying the familiar relation alpha_gluon+2 alpha_ghost=0 between the infrared exponents of the gluon and ghost dressing functions(in short, respectively alpha_G and alpha_F) and having therefore alpha_ghost=-1/2, and another which is finite at the origin (alpha_ghost=0), which violates the relation. It is most important that the type of solution which is realized depends on the value of the coupling constant. There are regular ones for any coupling below some value, while there is only one singular solution, obtained only at a critical value of the coupling. For all momenta k<1.5 GeV where they can be trusted, our lattice data exclude neatly the singular one, and agree very well with the regular solution we obtain at a coupling constant compatible with the bare lattice value.

hep-ph↗
arXiv2008

On the IR behaviour of the Landau-gauge ghost propagator

We examine analytically the ghost propagator Dyson-Schwinger Equation (DSE) in the deep IR regime and prove that a finite ghost dressing function at vanishing momentum is an alternative solution (solution II) to the usually assumed divergent one (solution I). We furthermore find that the Slavnov-Taylor identities discriminate between these two classes of solutions and strongly support the solution II. The latter turns out to be also preferred by lattice simulations within numerical uncertainties.

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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.

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arXiv2007

Divergent IR gluon propagator from Ward-Slavnov-Taylor identities?

We exploit the Ward-Slavnov-Taylor identity relating the 3-gluons to the ghost-gluon vertices to conclude either that the ghost dressing function is finite and non vanishing at zero momentum while the gluon propagator diverges (although it may do so weakly enough not to be in contradiction with current lattice data) or that the 3-gluons vertex is non-regular when one momentum goes to zero. We stress that those results should be kept in mind when one studies the Infrared properties of the ghost and gluon propagators, for example by means of Dyson-Schwinger equations.

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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.

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arXiv2006

The Infrared Behaviour of the Pure Yang-Mills Green Functions

We study the infrared behaviour of the pure Yang-Mills correlators using relations that are well defined in the non-perturbative domain. These are the Slavnov-Taylor identity for three-gluon vertex and the Schwinger-Dyson equation for ghost propagator in the Landau gauge. We also use several inputs from lattice simulations. We show that lattice data are in serious conflict with a widely spread analytical relation between the gluon and ghost infrared critical exponents. We conjecture that this is explained by a singular behaviour of the ghost-ghost-gluon vertex function in the infrared. We show that, anyhow, this discrepancy is not due to some lattice artefact since lattice Green functions satisfy the ghost propagator Schwinger-Dyson equation. We also report on a puzzle concerning the infrared gluon propagator: lattice data seem to favor a constant non vanishing zero momentum gluon propagator, while the Slavnov-Taylor identity (complemented with some regularity hypothesis of scalar functions) implies that it should diverge.

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arXiv2006

Is the QCD ghost dressing function finite at zero momentum ?

We show that a finite non-vanishing ghost dressing function at zero momentum satisfies the scaling properties of the ghost propagator Schwinger-Dyson equation. This kind of Schwinger-Dyson solutions may well agree with lattice data and provides an interesting alternative to the widely spread claim that the gluon dressing function behaves like the inverse squared ghost dressing function, a claim which is at odds with lattice data. We demonstrate that, if the ghost dressing function is less singular than any power of $p$, it must be finite non-vanishing at zero momentum: any logarithmic behaviour is for instance excluded. We add some remarks about coupled Schwinger-Dyson analyses.

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arXiv2006

Non-perturbative Power Corrections to Ghost and Gluon Propagators

We study the dominant non-perturbative power corrections to the ghost and gluon propagators in Landau gauge pure Yang-Mills theory using OPE and lattice simulations. The leading order Wilson coefficients are proven to be the same for both propagators. The ratio of the ghost and gluon propagators is thus free from this dominant power correction. Indeed, a purely perturbative fit of this ratio gives smaller value ($\simeq 270$MeV) of $Λ_{\ms}$ than the one obtained from the propagators separately($\simeq 320$MeV). This argues in favour of significant non-perturbative $\sim 1/q^2$ power corrections in the ghost and gluon propagators. We check the self-consistency of the method.

hep-lat↗
arXiv2006

Non-Perturbative Approach to the Landau Gauge Gluodynamics

We discuss a non-perturbative lattice calculation of the ghost and gluon propagators in the pure Yang-Mills theory in Landau gauge. The ultraviolet behaviour is checked up to NNNLO yielding the value $Λ^{n_f=0}_{\ms}=269(5)^{+12}_{-9}\text{MeV}$, and we show that lattice Green functions satisfy the complete Schwinger-Dyson equation for the ghost propagator for all considered momenta. The study of the above propagators at small momenta showed that the infrared divergence of the ghost propagator is enhanced, whereas the gluon propagator seem to remain finite and non-zero. The result for the ghost propagator is consistent with the analysis of the Slavnov-Taylor identity, whereas, according to this analysis, the gluon propagator should diverge in the infrared, a result at odds with other approaches.

hep-lat↗
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

Lattice renormalization of the static quark derivative operator

We give the analytical expressions and numerical values of radiative corrections to the covariant derivative operator on the static quark line, used for the lattice calculation of the Isgur-Wise form factors $τ_{1/2}(1)$ and $τ_{3/2}(1)$. Those corrections induce an enhancement of renormalized quantities if an hypercubic blocking is applied to the Wilson line, whereas there is a reduction without such a blocking.

hep-lat↗
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 $|V_{cb}|$.

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