Current correlators to all orders in the quark masses

The contributions to the coefficient functions of the quark and the mixed quark-gluon condensate to mesonic correlators are calculated for the first time to all orders in the quark masses, and to lowest order in the strong coupling constant. Existing results on the coefficient functions of the unit operator and the gluon condensate are reviewed. The proper factorization of short- and long-distance contributions in the operator product expansion is discussed in detail. It is found that to accomplish this task rigorously the operator product expansion has to be performed in terms ofnon-normal-ordered condensates. The resulting coefficient functions are improved with the help of the renormalization group. The scale invariant combination of dimension 5 operators, including mixing with the mass operator, which is needed for the renormalization group improvement, is calculated in the leading order.Supported by the German Bundesministerium für Forschung und Technologie, under the contract 06 TM 761     

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)     

Vector and axial-vector correlators in a non-local chiral quark model

The behavior of the non-perturbative parts of the isovector-vector and isovector and isosinglet axial-vector correlators at Euclidean momenta is studied in the framework of a covariant chiral quark model with non-local quark-quark interactions. The gauge covariance is ensured with the help of the P-exponents, with the corresponding modification of the quark-current interaction vertices taken into account. The low- and high-momentum behavior of the correlators is compared with the chiral perturbation theory and with the QCD operator product expansion, respectively. The V-A combination of the correlators obtained in the model reproduces quantitatively the ALEPH and OPAL data on hadronic decays, transformed into the Euclidean domain via dispersion relations. The predictions for the electromagnetic mass difference and for the pion electric polarizability are also in agreement with the experimental values. The topological susceptibility of the vacuum is evaluated as a function of the momentum, and its first moment is predicted to be . In addition, the fulfillment of the Crewther theorem is demonstrated.Received: 9 May 2003, Revised: 22 September 2003, Published online: 4 November 2003     

Electroweak radiative corrections and quark mass singularities

A consistent method to remove quark mass singularities from physical cross sections is demonstrated. They are factorised into quark and gluon distribution functions. This implies electromagnetic correction terms to theQ ² dependent structure functions. They are calculated in leading order in the fine structure constant α and found to be flat and small overx.     

OPE and sum rules for correlators of pseudoscalar and axial currents

We study the operator product expansion (OPE) and quark-hadron duality for two-and three-point correlators of the axial (A) and pseudoscalar (P) currents of the light quarks. In the chiral limit, these correlators are often dominated by nonperturbative power corrections leading to subtleties of quark-hadron duality relations and of the extraction of properties of light pseudoscalars. For the two-point correlators, we show the sum rule for 〈PP〉 to be sensitive to the excited light pseudoscalar. For the three-point correlators, we derive the Ward identities which provide the normalization of the pion electromagnetic form factor at zero momentum transfer. For large momentum transfer, we demonstrate the way the correct behavior of the pion form factor in agreement with perturbative QCD emerges from condensate terms in the OPE for the 〈PV P〉 and 〈AV P〉 correlators. The local-duality sum rule for 〈AV A〉 is shown to lead to the pion form factor with the required properties for all values of the momentum transfer. The text was submitted by the authors in English. On leave from Institute of Nuclear Physics, Moscow State University, Moscow, Russia.     

Summation bandwidths at threshold in normal and hearing-impaired listeners

The bandwidths for summation at threshold were measured for subjects with normal hearing and subjects with sensorineural hearing loss. Thresholds in quiet and in the presence of a masking noise were measured for complex stimuli consisting of 1 to 40 pure-tone components spaced 20 Hz apart. The single component condition consisted of a single pure tone at 1100 Hz; additional components were added below this frequency, in a replication of the G?ssler [Acustica 4, 408-414 (1954)] procedure. For the normal subjects, thresholds increased approximately 3 dB per doubling of bandwidth for signal bandwidths exceeding the critical bandwidth. This slope was less for the hearing-impaired subjects. Summation bandwidths, as estimated from two-line fits, were wider for the hearing-impaired than for the normal subjects. These findings provide evidence that hearing-impaired subjects integrate sound energy over a wider-than-normal frequency range for the detection of complex signals. A second experiment used stimuli similar to those of Spiegel [J. Acoust. Soc. Am. 66, 1356-1363 (1979)], and added components both above and below the frequency of the initial component. Using these stimuli, the slope of the threshold increase beyond the critical bandwidth was approximately 1.5 dB per doubling of bandwidth, thus replicating the Spiegel (1979) experiment. It is concluded that the differences between the G?ssler (1954) and Spiegel (1979) studies were due to the different frequency content of the stimuli used in each study. Based upon the present results, it would appear that the slope of threshold increase is dependent upon the direction of signal expansion, and the size of the critical bands into which the signal is expanded.     

Heavy quark currents in ultra-high energy neutrino interactions

We discuss heavy quark contributions to the neutrino-nucleon total cross section at very high energies, well above the real top production threshold. The top-bottom weak current is found to generate strong left-right asymmetry of neutrino-nucleon interactions. We separate contributions of different helicity states and make use of the κ-factorization to derive simple and practically useful formulas for the left-handed (F _L ) and right-handed (F _R ) components of the conventional structure function 2xF ₃ = F _L − F _R in terms of the integrated gluon density. We show that F _L ≫ F _R and, consequently, xF ₃ ≈ F _T , where F _T is the transverse structure function. The conventional structure function F ₂ = F _S + F _T at Q ² ≪ m _t ² appears to be dominated by its scalar (also known as longitudinal) component F _S and the hierarchy F _S ≫ F _L ≫ F _R arises naturally. We evaluate the total neutrino-nucleon cross section at ultra-high energies within the color dipole BFKL-formalism.     

Exchange currents arising from quark degrees of freedom

We investigate the effects of antisymmetrization with respect to valence quarks in nuclei introducing “quark exchange currents”. Their effects in ordinary nuclei are found to be small for lack of contribution from s-wave nucleon pairs owing to spin-isospin symmetry. For example, the Gamow-Teller type β-decay matrix elements for A = 15, 17, 39, 41 and ∞ nuclei are reduced from the single-particle values by 2–8% depending on the baryon size. The effects seem to be larger for Σ-hypernuclei. For example, the magnetic moment of Σ+4Li(1+) is reduced by more than 15%. For Λ-hypernuclei, however, the effects on the magnetic moments tend to cancel each other, and about 1% reduction is obtained for 4ΛHe(1+).     

Moments of heavy quark correlators with two masses: Exact mass dependence to three loops

We compute moments of non-diagonal correlators with two massive quarks. Results are obtained where no restriction on the ratio of the masses is assumed. Both analytical and numerical methods are applied in order to evaluate the two-scale master integrals at three loops. We provide explicit results for the latter which are useful for other calculations. As a by-product we obtain results for the electroweak ρ parameter up to three loops which can be applied to a fourth generation of quarks with arbitrary masses.     

Double logarithmic asymptotics and regge singularities of quark amplitudes with flavour exchange

We derive simple equations in terms of definite signature partial waves for the quark scattering and annihilation amplitudes in the double logarithmic approximation of QCD. We apply the method of isolating the softest virtual particle in the graphs which is based on gauge invariance and unitarity. Besides the particle Regge trajectories and corresponding cuts, there are further singularities in the angular momentum plane generated by perturbative double logarithmic contributions and which may be of phenomenological relevance. We also consider amplitudes with external currents and discuss how to include ultraviolet single logarithms and non-perturbative contributions.     

Grand unification of quark and lepton flavor changing neutral currents

In the context of supersymmetric grand unified theories with soft breaking terms arising at the Planck scale, it is generally possible to link flavor changing neutral current and CP violating processes occurring in the leptonic and hadronic sectors. We study the correlation between flavor changing squark and slepton mass insertions in models à la SU(5). We show that the constraints coming from lepton flavor violation exhibit a strong impact on CP-violating B decays.     

A comment on form factor mass singularities in flavor-changing neutral currents

Flavor-changing effective verticesq _l q _h V ⁰, whereV ⁰ represents a neutral gauge boson (,Z ⁰,g), involving a heavy external quark, are discussed within the standard model at one-loop level and second-order approximation in external momenta and masses: the logarithmic singular terms in the form factors at vanishing mass of the internal quark in the loop have to be replaced by pieces coming from next order in external momenta. Implications in thebd+X penguin transitions are commented.     

Supersymmetric correction to top quark pair production near threshold

We studied the leading supersymmetric contribution to top–antitop threshold production using the NRQCD framework. The one-loop matching to the potential and the Wilson coefficient of the leading ³S₁ production current were considered. We point out that the leading correction to the potential is zero due to SU(3)_c gauge invariance. This is true in general for any new physics that enters above the electroweak scale. The shape of the top quark pair production cross section is therefore almost unaffected near threshold, allowing a precise determination of the top quark mass based on the Standard Model calculations. The supersymmetric correction to the Wilson coefficient c₁ of the production current decouples for heavy super particles. Its contribution is smaller than the Standard Model next-to-next-leading-log results.     

Charm and bottom quark production cross sections near threshold

The cross sections for charm and bottom quark production in the threshold region are discussed. We consider the effects of an all order resummation of initial state soft-plus-virtual gluon radiation on the total cross sections compared to the order $←pha_{s}^{3}$ results.