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A. Le Yaouanc

Publications and source records attributed to A. Le Yaouanc.

At least 73 records · Page 4Linked to original sources
arXiv2002

A transparent expression of the A^2-Condensate's renormalisation

We give a more transparent understanding of the vacuum expectation value of the renormalised local operator A^2 by relating it to the gluon propagator integrated over the momentum. The quadratically divergent perturbative contribution is subtracted and the remainder, dominantly due to the O(1/p^2) correction to the perturbative propagator at large p^2 is logarithmically divergent. This provides a transparent derivation of the fact that this O(1/p^2) term is related to the vacuum expectation value of the local A^2 operator and confirms a previous claim based on the operator product expansion (OPE) of the gluon propagator. At leading logarithms the agreement is quantitative, with a standard running factor, between the local A^2 condensate renormalised as described above and the one renormalised in the OPE context.

hep-ph↗
arXiv2002

O.P.E. and Power Corrections to the QCD coupling constant

Lattice data seems to show that power corrections should be convoked to describe appropriately the transition of the QCD coupling constant running from U.V. to I.R. domains. Those power corrections for the Landau-gauge MOM coupling constant in a pure Yang-Mills theory (N_f=0) are analysed in terms of Operator Product Expansion (O.P.E.) of two- and three-point Green functions, the gluon condensate emerging from this study. The semi-classical picture given by instantons can be also used to look for into the nature of the power corrections and gluon condensate.

hep-ph↗
arXiv2002

A lattice estimate of the g_{D^* D pi} coupling

We present the results of the first direct determination of the g_{D^* D pi} coupling using lattice QCD. From our simulations in the quenched approximation, we obtain g_{D^* D pi} = 18.8 +/- 2.3^{+1.1}_{-2.0} and hat(g) = 0.67 +/- 0.08^{+0.04}_{-0.06}. It is in agreement with a recent experimental result from CLEO.

hep-lat↗
arXiv2002

An Instanton Picture O.P.E. Condensate?

Gluon two- and three-point Green Functions computed in Landau gauge from the lattice show the existence of power corrections to the purely perturbative expressions, that can be explained through an Operator Product Expansion as the influence of a non gauge invariant mass dimension two condensate. The relationship of this condensate with topological properties of QCD, namely instantons, will be studied, giving a first estimate of the contribution of instantons to this condensate based in the direct lattice measure, after a cooling process, of the instanton liquid properties.

hep-ph↗
arXiv2002

First lattice QCD estimate of the g_{D^* D pi} coupling

We present the results of the first lattice QCD study of the strong coupling g_{D^* D pi}. From our simulations in the quenched approximation, we obtain g_{D^* D pi} = 18.8 +/- 2.3^{+1.1}_{-2.0} and hat(g)_c = 0.67 +/- 0.08^{+0.04}_{-0.06}. Whereas previous theoretical studies gave different predictions, our result favours a large value for hat(g)_c. It agrees very well with the recent experimental value by CLEO. hat(g) varies very little with the heavy mass and we find in the infinite mass limit hat(g)_infinity = 0.69(18).

hep-ph↗
arXiv2002

Instantons and $ $ Condensate

We argue that the $ $ condensate found in the Landau gauge on lattices, when an Operator Product Expansion of Green functions is performed, might be explained by instantons. We use cooling to estimate the instanton contribution and extrapolate back the result to the thermalised configuration. The resulting $ $ is similar to $ $.

hep-ph↗
arXiv2002

OPE and Powers corrections on the QCD coupling constant

The running coupling constant can be estimated by computing gluon two- and three-point Green functions from the lattice. Computing in lattice implies working in a fixed gauge sector (Landau). An source of systematic uncertainty is then the contribution of non gauge-invariant condensates, as $ $, generating power corrections that might still be important at very high energies. We study the impact of this gluon condensate on the analysis of gluon propagator and vertex lattice data and on the estimate of $Λ_{\bar{\rm MS}}$. We finally try a qualitative description of this gluon condensate through the instanton picture

hep-ph↗
arXiv2001

Remarks on sum rules in the heavy quark limit of QCD

We underline a problem existing in the heavy quark limit of QCD concerning the rates of semileptonic B decays into P-wave $D_J(j)$ mesons, where $j = {1 \over 2}$ (wide states) or $j = {3 \over 2}$ (narrow states). The leading order sum rules of Bjorken and Uraltsev suggest $Γ[ \bar{B} \to D_{0,1} ({1 \over 2}) \ell ν] \ll Γ[ \bar{B} \to D_{1,2} ({3 \over 2}) \ell ν]$, in contradiction with experiment. The same trend follows also from a sum rule for the subleading $1/m_Q$ curent matrix element correction $ξ_3(1)$. The problem is made explicit in relativistic quarks models à la Bakamjian and Thomas, that give a transparent physical interpretation of the latter as due, not to a $L \cdot S$ force, but to the Wigner rotation of the light quark spin. We point out moreover that the selection rule for decay constants of $j = {3 \over 2}$ states, $f_{3/2} = 0$, predicts, assuming the model of factorization, the opposite hierarchy $Γ[ \bar{B} \to \bar{D}_{s_{1,2}} ({3 \over 2}) D^{(*)} ] \ll Γ[ \bar{B} \to \bar{D}_{s_{0,1}} ({1 \over 2}) D^{(*)} ]$.

hep-ph↗
arXiv2001

Large pion pole in Z_{S}^{MOM}/Z_{P}^{MOM} from Wilson action data

We show that, contrarily to recent claims, data from the Wilson (unimproved) fermionic action at three different beta values demonstrate the presence of a large Goldstone boson contribution in the quark pseudoscalar vertex, quantitatively close to our previous estimate based on the SW action with c_{SW}=1.769. We show that discretisation errors on Z_{S}^{MOM}/Z_{P}^{MOM} seem to be much smaller than the Goldstone pole contribution over a very large range of momenta. The subtraction of this non perturbative contribution leads to numbers close to one-loop BPT.

hep-lat↗
arXiv2001

On P-wave meson decay constants in the heavy quark limit of QCD

In previous work it has been shown that, either from a sum rule for the subleading Isgur-Wise function $ξ_3(1)$ or from a combination of Uraltsev and Bjorken SR, one infers for $P$-wave states $|τ_{1/2}(1)| \ll |τ_{3/2}(1)|$. This implies, in the heavy quark limit of QCD, a hierarchy for the {\it production} rates of $P$-states $Γ(\bar{B}_d \to D ({1 \over 2}) \ell ν) \ll Γ(\bar{B}_d \to D ({3 \over 2}) \ell ν)$ that seems at present to be contradicted by experiment. It was also shown that the decay constants of $j = {3 \over 2}$ $P$-states vanish in the heavy quark limit of QCD, $f_{3/2}^{(n)} = 0$. Assuming the {\it model} of factorization in the decays $\bar{B}_d \to \bar{D}_s^{**}D$, one expects the opposite hierarchy for the {\it emission} rates $Γ(\bar{B}_d \to \bar{D}_s ({3 \over 2}) D) \ll Γ(\bar{B}_d \to \bar{D}_s ({1 \over 2}) D)$, since $j = {1 \over 2}$ $P$-states are coupled to vacuum. Moreover, using Bjorken SR and previously discovered SR involving heavy-light meson decay constants and IW functions, one can prove that the sums $\sum\limits_n ({f^{(n)} \over f^{(0)}})^2$, $\sum\limits_n ({f_{1/2}^{(n)} \over f^{(0)}})^2$ (where $f^{(n)}$ and $f_{1/2}^{(n)}$ are the decay constants of $S$-states and $j = {1\over 2}$ $P$-states) are divergent. This situation seems to be realized in the relativistic quark models à la Bakamjian and Thomas, that satisfy HQET and predict decays constants $f^{(n)}$ and $f_{1/2}^{(n)}$ that do not decrease with the radial quantum number $n$.

hep-ph↗
arXiv2001

Uraltsev Sum Rule in Bakamjian-Thomas Quark Models

We show that the sum rule recently proved by Uraltsev in the heavy quark limit of QCD holds in relativistic quark models à la Bakamjian and Thomas, that were already shown to satisfy Isgur-Wise scaling and Bjorken sum rule. This new sum rule provides a {\it rationale} for the lower bound of the slope of the elastic IW function $ρ^2 \geq {3 \over 4}$ obtained within the BT formalism some years ago. Uraltsev sum rule suggests an inequality $|τ_{3/2}(1)| > |τ_{1/2}(1)|$. This difference is interpreted in the BT formalism as due to the Wigner rotation of the light quark spin, independently of a possible LS force. In BT models, the sum rule convergence is very fast, the $n = 0$ state giving the essential contribution in most of the phenomenological potential models. We underline that there is a serious problem, in the heavy quark limit of QCD, between theory and experiment for the decays $B \to D^*_{0,1}(broad) \ell ν$, independently of any model calculation.

hep-ph↗
arXiv2001

Duality in semileptonic inclusive B-decays in potential models: regular versus singular potentials

Making use of the nonrelativistic potential model for the description of mesons, and working in the Shifman-Voloshin limit, we compare the integrated rate $Γ(B\to X_clν)$ calculated as a sum of the individual decay rates to the quantum-mechanical analog of the OPE. In the case of a potential regular at the origin, we find a well-defined duality violation, which is however exponentially small. It corresponds to the charm resonances kinematically forbidden in the decay process, but apparently picked up by the OPE. For singular potentials, we do not obtain a full OPE series, but only a limited Taylor expansion, since the cofficients become infinite beyond some order. In this case, we do not find an indication of duality violation: the difference is smaller than the last term of the limited expansion. This emphasizes that the case of singular potentials, which may be relevant for QCD, deserves further study.

hep-ph↗
arXiv2001

Testing Landau gauge OPE on the Lattice with a $ $ Condensate

Using the operator product expansion we show that the $O(1/p^2)$ correction to the perturbative expressions for the gluon propagator and the strong coupling constant resulting from lattice simulations in the Landau gauge are due to a non-vanishing vacuum expectation value of the operator $A^μA_μ$. This is done using the recently published Wilson coefficients of the identity operator computed to third order, and the subdominant Wilson coefficient computed in this paper to the leading logarithm. As a test of the applicability of OPE we compare the $ $ estimated from the gluon propagator and the one from the coupling constant in the flavourless case. Both agree within the statistical uncertainty: $\sqrt{< A^μA_μ>} \simeq 1.64(15)$ GeV. Simultaneously we fit $\Lams = $ 233(28) MeV in perfect agreement with previous lattice estimates. When the leading coefficients are only expanded to two loops, the two estimates of the condensate differ drastically. As a consequence we insist that OPE can be applied in predicting physical quantities only if the Wilson coefficients are computed to a high enough perturbative order.

hep-ph↗
arXiv2000

Consistent OPE Description of Gluon Two- and Three-point Green Function?

We perform an OPE analysis of the flavorless non-perturbative gluon propagator and the symmetric three-gluon vertex in the Landau gauge. The first subdominant operator is $A_μA^μ$ which can condensate in the Landau gauge ``vacuum'' although being a non-gauge invariant operator. We neglect all higher dimension operators. Then the gluon propagator and the symmetric three gluon vertex only depend on one common unknown condensate. We propose a consistency check from lattice data. At two loops for the leading coefficient and with $1/p^2$ corrections at tree-level order the two fitted values for the condensate do not agree. At three loops we argue that the today unknown $β_2^{\rm MOM}$ should be equal to $1.5(3)\times β_2^{\widetilde{\rm MOM}}=7400(1500)$ to fulfill the OPE relation. Inclusion of the power corrections' anomalous dimensions should improve further the agreement. We show that these techniques cannot be applied to the asymmetric three gluon vertex with one vanishing momentum.

hep-ph↗
arXiv2000

Semileptonic inclusive heavy meson decay: duality in a nonrelativistic potential model in the Shifman-Voloshin limit

Quark-hadron duality in the inclusive semileptonic decay $B\to X_c lν$ in the Shifman-Voloshin limit $Λ\ll δm=m_b - m_c \ll m_b, m_c$ is studied within a nonrelativistic potential model. The integrated semileptonic decay rate is calculated in two ways: first, by constructing the Operator Product Expansion, and second by a direct summation of the exclusive channels. Sum rules (Bjorken, Voloshin, etc.) for the potential model are derived, providing a possibility to compare the two representations for $Γ(B\to X_c lν)$. An explicit difference between them referred to as duality-violation effect is found. The origin of this effect is related to higher charm resonances which are kinematically forbidden in the decay process but are nevertheless picked up by the OPE. Within the considered $1/m_c^2$ order the OPE and the sum over exclusive channels match each other, up to the contributions of higher resonances, by virtue of the sum rules. In particular this is true for the terms of order $δm^2/m_c^2$ and $Λδm/m_c^2$ which are present in each of the decay channels and cancel in the sum of these channels due to the Bjorken and Voloshin sum rules, respectively. The size of the duality violation effects is estimated to be of the order $O(Λ^{2+b}/m_c^2δm^b)$ with $b>0$ depending on the details of the potential. Constraints for a better accuracy are discussed.

hep-ph↗
arXiv2000

Duality in the non-relativistic harmonic oscillator quark model in the Shifman-Voloshin limit : a pedagogical example

The detailed way in which duality between sum of exclusive states and the free quark model description operates in semileptonic total decay widths, is analysed. It is made very explicit by the use of the non relativistic harmonic oscillator quark model in the SV limit, and a simple interaction current with the lepton pair. In particular, the Voloshin sum rule is found to eliminate the mismatches of order $δm/m_b^2$.

hep-ph↗
arXiv2000

One Interesting New Sum Rule Extending Bjorken's to order {1/m_Q}

We explicitly check quark-hadron duality to order $(m_b-m_c)Λ/m_b^2$ for $b \to c lν$ decays in the limit $m_b-m_c \ll m_b$ including ground state and orbitally excited hadrons. Duality occurs thanks to a new sum rule which expresses the subleading HQET form factor $ξ_3$ or, in other notations, $a_+^{(1)}$ in terms of the infinite mass limit form factors and some level splittings. We also demonstrate the sum rule, which is not restricted to the condition $m_b-m_c \ll m_b$, applying OPE to the longitudinal axial component of the hadronic tensor without neglecting the $1/m_b$ subleading contributions to the form factors. We argue that this method should produce a new class of sum rules, depending on the current, beyond Bjorken, Voloshin and the known tower of higher moments. Applying OPE to the vector currents we find another derivation of the Voloshin sum rule. From independent results on $ξ_3$ we derive a sum rule which involves only the $τ_{1/2}^{(n)}$ and $τ_{3/2}^{(n)}$ form factors and the corresponding level splittings. The latter strongly supports a theoretical evidence that the $B$ semileptonic decay into narrow orbitally-excited resonances dominates over the decay into the broad ones, in apparent contradiction with some recent experiments. We discuss this issue.

hep-ph↗