Subtracted dispersion relations for in-medium meson correlators in QCD sum rules

We analyze subtracted dispersion relations for meson correlators at finite baryon density and temperature. Such relations are needed for QCD sum rules. We point out the importance of scattering terms, as well as finite, well-defined subtraction constants. Both are necessary for consistency, in particular for the equality of the longitudinal and transverse correlators in the limit of vanishing three-momentum of mesons relative to the medium. We present detailed calculations in various mesonic channels for the case of the Fermi gas of nucleons.     

Heavy-baryon properties with NLO accuracy in perturbative QCD

We present an analysis of the static properties of heavy baryons at next-to-leading order in the perturbative expansion of QCD. We obtain analytical next-to-leading order three-loop results for the two-point correlators of baryonic currents with one finite-mass quark field for a variety of quantum numbers of the baryonic currents. We consider both the massless limit and the HQET limit of the correlator as special cases of the general finite-mass formula and find agreement with previous results. We present closed-form expressions for the moments of the spectral density. We determine the residues of physical baryon states using sum-rule techniques.     

Gluon condensate from superconvergent QCD sum rule

Sum rules for the nonperturbative piece of correlators (specifically, the vector current correlator) are discussed. The sum rule subtracting the perturbative part is of the superconvergent type. Thus it is dominated by the bound states and the low-energy production cross section. It leads to a determination of the gluon condensate _sG². We find _sG²0.048±0.030 GeV⁴.     

Instantons and meson correlation functions in QCD

Various QCD correlators are calculated in the instanton liquid model in zeromode approximation and 1/N _c expansion. Previous works are extended by including dynamical quark loops. In contrast to the original “perturbative” 1/N _c approximation, not all quark loops are suppressed. Renormalization of the instanton density allows the identification of the density with the gluon condensate even in presence of dynamical quark loops. In the flavor singlet meson correlators a chain of quark bubbles survives the N _c → ∞ limit causing a massive η′ in the pseudoscalar correlator while keeping massless pions in the triplet correlator. The correlators are plotted and meson masses and couplings are obtained from a spectral fit. They are compared to the values obtained from numerical studies of the instanton liquid and to experimental results.     

Heavy-to-light correlators beyond the light cone

We present the first systematic analysis of the off-light-cone effects in correlators relevant for the extraction of the heavy-to-light form factors within the method of light-cone sum rules. In a model with scalar constituents, the correlator is calculated in two different ways: (i) by performing the expansion of the Bethe-Salpeter amplitude of the light meson near the light cone x ² = 0 and (ii) by adopting the known solution for the Bethe-Salpeter amplitude which allows one to calculate the correlator without invoking any expansion. We demonstrate that the contributions to the correlator from the off-light-cone terms x ² ≠ 0 are not suppressed by any large parameter compared to the contribution of the light-cone term x ² = 0. For decays of heavy particles of mass in the range 1.5–5 GeV, the light-cone correlator is shown to systematically overestimate the full correlator, numerically the difference being 10–20%. The text was submitted by the authors in English.     

Hadron correlators and the structure of the quark propagator

The structure of the quark propagator of QCD in a confining background is not known. We make an ansatz for it, as hinted by a particular mechanism for confinement, and analyze its implications in the meson and baryon correlators. We connect the various terms in the Källen-Lehmann representation of the quark propagator with appropriate combinations of hadron correlators, which may ultimately be calculated in lattice QCD. Furthermore, using the positivity of the path integral measure for vector like theories, we reanalyze some mass inequalities in our formalism. A curiosity of the analysis is that, the exotic components of the propagator (axial and tensor), produce terms in the hadron correlators which, if not vanishing in the gauge field integration, lead to violations of fundamental symmetries. The non observation of these violations implies restrictions in the space-time structure of the contributing gauge field configurations. In this way, lattice QCD can help us analyze the microscopic structure of the mechanisms for confinement.Supported in part by CICYT (AEN91-0234) and DGICYT grant (PB91-0119-C02-01)     

Decoherence in quantum mechanics

We study decoherence in a simple quantum mechanical model using two approaches. Firstly, we follow the conventional approach to decoherence where one is interested in solving the reduced density matrix from the perturbative master equation. Secondly, we consider our novel correlator approach to decoherence where entropy is generated by neglecting observationally inaccessible correlators. We show that both methods can accurately predict decoherence time scales. However, the perturbative master equation generically suffers from instabilities which prevents us to reliably calculate the system’s total entropy increase. We also discuss the relevance of the results in our quantum mechanical model for interacting field theories.     

Quark-hadron duality,axial anomaly and mixing

Interplay between axial anomaly and quark-hadron duality in the presence of strong mixing is considered. The anomaly sum rule for meson transition form factors based on the dispersive representation of axial anomaly and quark-hadron duality in octet channel is analyzed. The comparison of this sum rule to the experimental data on the transition form factors of the η and η′ mesons shows that the interval of duality in this channel is rather small, contradicting the usual understanding of quark-hadron duality. The same values of interval of duality are supported by considering the two-point correlator in the local duality limit. This contradiction may be resolved by introducing of some nonperturbative non-one-pion exchange correction to the relevant spectral density. The form and value of this correction are discussed.     

Bound-state perturbation method via SVZ sum rules in quantum mechanics

The perturbation method for bound states within the framework of the Shifman-Vainshtein-Zakharov sum rule method is studied on simple systems (linear harmonic oscillator, hydrogen atom) in external electric fields. It is pointed out that for stronger fields reasonable results for the ground-state energy can only be achieved when sum rules are written for the correction to the Euclidean Green function caused by the external field. Moreover, if the system is bound by a singular (Coulomb) potential, one needs to sum higher perturbative corrections to the Green function and to find a realistic approximation of the continuum contribution to the sum rules. The results are of relevance e.g. for calculations of nucleon magnetic moments and toponium properties via SVZ sum rules in QCD.     

OPE, charm-quark mass, and decay constants of D and Ds mesons from QCD sum rules

We present a sum-rule extraction of the decay constants of the charmed mesons D and Ds from the two-point correlator of pseudoscalar currents. First, we compare the perturbative expansion for the correlator and the decay constant performed in terms of the pole and the running MSˉ masses of the charm quark. The perturbative expansion in terms of the pole mass shows no signs of convergence whereas reorganizing this very expansion in terms of the MSˉ mass leads to a distinct hierarchy of the perturbative expansion. Furthermore, the decay constants extracted from the pole-mass correlator turn out to be considerably smaller than those obtained by means of the MSˉ-mass correlator. Second, making use of the OPE in terms of the MSˉ mass, we determine the decay constants of both D and Ds mesons with an emphasis on the uncertainties in these quantities related both to the input QCD parameters and to the limited accuracy of the method of sum rules.     

Effects of perturbative exchanges in a QCD string model

The QCD string model for baryons derived by Yu. A. Simonov and used for the calculation of baryon magnetic moments in a previous paper is extended to include also perturbative gluon and meson exchanges. The mass spectrum of the baryon multiplet is studied. For the meson interaction, either pseudoscalar or pseudovector coupling is used. Predictions are compared with the experimental data. Besides these exchanges, the influence of excited quark orbitals on the baryon ground state are considered by performing a multichannel calculation. The nucleon-Δ splitting increases due to the mixing of higher quark states, while the baryon magnetic momenta decrease. The multichannel calculation with perturbative exchanges is shown to yield reasonable magnetic moments, while the mass spectrum is close to experiment.     

On the short distance behavior of the critical Ising model perturbed by a magnetic field

We apply here a recently developed approach to compute the short distance corrections to scaling for the correlators of all primary operators of the critical two-dimensional Ising model in a magnetic field. The essence of the method is the fact that if one deals with OPE Wilson coefficients instead of correlators, all-order IR safe formulas can be obtained for the perturbative expansion with respect to the magnetic field. This approach yields in a natural way the expected fractional powers of the magnetic field, which are clearly absent in the naive perturbative expression for correlators. The technique of the Mellin transform has been used to compute the IR behavior of the regularized integrals. As a corollary of our results, by comparing the existing numerical data for the lattice model we give an estimate of the vacuum expectation value of the energy operator of the continuous theory.     

Heavy-light current correlators at order \alpha_\mathrm{s}^2 in QCD and HQET

The non-diagonal correlators of vector and scalar currents are considered at three-loop order in QCD. The full mass dependence is computed in the case where one of the quarks is massless and the other one carries mass M. We exploit the decoupling relations between the full theory and the heavy quark effective theory (HQET) in order to obtain the logarithmic parts of the leading threshold terms. With the help of conformal mapping and Padé approximation numerical estimates for the non-logarithmic terms are extracted which in turn lead to a prediction of the correlator in HQET at order . As applications of the vector and scalar correlator we consider the single-top-quark production via the process and the decay rate of a charged Higgs boson into hadrons, respectively. In both cases the computed NLO corrections are shown to be numerically much less important than the leading ones. On the contrary, the NLO order QCD corrections to the HQET sum rule for the leptonic decay rate of a heavy-light meson proves to be comparable to the leading one. Received: 19 June 2001 / Published online: 10 August 2001     

Looking at saturation effects with production in pA collisions

We compute the inclusive differential cross section production of the pseudo-scalar meson η^′ in high-energy proton-nucleus (pA) collisions. We use an effective coupling between gluons and η^′ meson to derive a reduction formula that relates the η^′ production to a field-strength tensor correlator. We take into account saturation effects on the nucleus side by using the Color Glass Condensate formalism to evaluate this correlator. We derive new results for Wilson line - color charges correlators in the McLerran-Venugopalan model needed in the computation of η^′ production. The unintegrated parton distribution functions are used to characterize the gluon distribution inside the proton. We show that the cross section is sensitive to saturation effects so it can be utilized to estimate the value of the saturation scale.     

Heavy-to-light transition form factors and their relations in light-cone QCD sum rules

The light-cone QCD sum rules approach improved by using the chiral current correlator is systematically reviewed and applied to the calculation of all the heavy-to-light form factors, including all the semileptonic and penguin ones. By choosing suitable chiral currents, the light-cone sum rules for all the form factors are greatly simplified and depend mainly on one leading-twist distribution amplitude of the light meson. As a result, relations between these form factors arise naturally. At the considered accuracy, these relations reproduce the results obtained in the literature. Moreover, since the explicit dependence on the leading-twist distribution amplitudes is preserved, these relations may be more useful to simulate the experimental data and extract information on the distribution amplitude.     

Recent progress on the chiral unitary approach to meson meson and meson baryon interactions

We report on recent progress on the chiral unitary approach, analogous to the effective range expansion in Quantum Mechanics, which is shown to have a much larger convergence radius than ordinary chiral perturbation theory, allowing one to reproduce data for meson meson interaction up to 1.2 GeV. Applications to physical processes so far unsuited for a standard chiral perturbative approach are presented. Results for the extension of these ideas to the meson baryon sector are discussed, together with applications to kaons in a nuclear medium and K⁻ atoms.     

Low- and high-energy expansion of heavy-quark correlators at next-to-next-to-leading order

We calculate three-loop corrections to correlation functions of heavy-quark currents in the low- and high-energy regions. We present 30 coefficients both in the low-energy and the high-energy expansion of the scalar and the vector correlator with non-diagonal flavour structure. In addition we compute 30 coefficients in the high-energy expansion of the diagonal vector, axial-vector, scalar and pseudo-scalar correlators. Possible applications of our new results are improvements of lattice-based quark-mass determinations and the approximate reconstruction of the full momentum dependence of the correlators.     

Dispersive approach to the axial anomaly,the t'Hooft's principle and QCD sum rules

The dispersive approach to the axial anomaly is revisited. Considering the familiar VVA triangle graph, the anomalous Ward identity is proved in the case of the external momenta corresponding to one real and one virtual photon. We also comment on a recent claim that the anomaly pole in QCD fails to reproduce the pion pole. In this connection, it is emphasized that there is no need to introduce a massless axial meson in the chiral limit. In the framework of QCD sum rules method a constraint for the Borel transform of relevant form factors imposed by the anomaly is considered.     

Anomalous scattered light correlator

The space-time correlation function of the scattered radiation intensity of atoms situated in an external field is investigated. This function includes contributions of the normal +E^–> and anomalous –E–> complex field amplitude correlator. These correlators have components due to scattering by density fluctuations and to collective, diffraction effects. The spatial structure of these correlators is studied and the conditions for the measurement of the anomalous correlator are derived. The temporal properties of the anomalous correlator and the effect of Doppler broadening on the correlation properties of scattered radiation are also considered. The investigation of the anomalous correlator is of interest in high-resolution spectroscopy and may also be useful in the study of nonresonant media.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 70–73, February, 1982.