A.I. Vainshtein

QCD and resonance physics. theoretical foundations

A systematic study is made of the non-perturbative effects in quantum chromodynamics. The basic object is the two-point functions of various currents. At large Euclidean momenta q the non-perturbative contributions induce a series in (μ2/q2) where μ is some typical hadronic mass. The terms of this series are shown to be of two distinct types. The first few of them are connected with vacuum fluctuations of large size, and can be consistently accounted for within the Wilson operator expansion. On the other hand, in high orders small-size fluctuations show up and the high-order terms do not reduce (generally speaking) to the vacuum-to-vacuum matrix elements of local operators. This signals the breakdown of the operator expansion. The corresponding critical dimension is found. We propose a Borel improvement of the power series. On one hand, it makes the two-point functions less sensitive to high-order terms, and on the other hand, it transforms the standard dispersion representation into a certain integral representation with exponential weight functions. As a result we obtain a set of the sum rules for the observable spectral densities which correlate the resonance properties to a few vacuum-to-vacuum matrix elements. As the last bid to specify the sum rules we estimate the matrix elements involved and elaborate several techniques for this purpose.

QCD and resonance physics. applications

Abstract Resonance properties are investigated within the QCD-based approach to resonance physics developed earlier. We extend first the dispersion charmonium theory to include power terms due to the non-perturbative effects of QCD. As a byproduct, an estimate for the gluonic vacuum expectation value, 〈0| G μν a G μν a |0〉, emerges. The main emphasis is made on the analysis of the ϱ, ω, ϕ, K ∗ mesons. Predictions are formulated for integrals of the type ∫ Im Π e − s / M 2 d s where Im Π is aan appropriate spectral density. It is shown that there exist such M 2 that the integrals are dominated by a single resonance, on one hand, and are calculable in a reliable way, on the other. As a result we are able to calculate the resonance coupling constants and masses. The typical accuracy achieved is about 10%. The power terms considered explain both the π - ϱ -A 1 mass splittings and the observed pattern of the SU(3) symmetry breaking in the vector nonet. We discuss, also, the relation between our approach and more traditional ones. A few original remarks concerning the MIT bag model, instanton calculus, etc. are included.

Can confinement ensure natural CP invariance of strong interactions

Abstract P - and T -invariance violation in quantum chromodynamics due to the so-called θ-term is discussed. It is shown that irrespectively of how the confinement works there emerge observable P - and T -odd effects. The proof is based on the assumption that QCD resolves the U(1) problem, i.e., the mass of the singlet pseudoscalar meson does not vanish in the chiral limit. We suggest a modification of the axion scheme which restores the natural P and T invariance of the theory and cannot be ruled out experimentally.

Exact Gell-Mann-Low Function of Supersymmetric Yang-Mills Theories from Instanton Calculus

Abstract The instanton contribution to the vacuum energy in supersymmetric Yang-Mills theories is considered. Using the renormalizability of the theory we find the exact beta function for n -extended supersymmetry ( n = 1, 2, 4). The coefficients of the beta function have a geometrical meaning: they are associated with the number of boson and fermion zero modes in the instanton field. If extra matter superfields are added our method allows one to fix the first two coefficients. We prove a non-renormalization theorem which extends the cancellation of vacuum loops to the case of the external instanton field.

Charmonium and gluons

Afther the discovery of J/ψ and ψ′ mesons many other narrow resonances were found which represent various levels of a system called charmonium. In this review theoretical interpretation of charmonium properties is given. The classification of charmonium levels and their electromagnetic and strong decays are discussed. The basic assumption is that strong interaction between charmed quark and charmed antiquark in charmonium is mediated by coloured gluons as described by Quantum Chromodynamics (QCD). It is argued that charmonium is an ideal object to test the basic ideas of QCD. Both the traditional nonrelativistic approach to charmonium and the dispersion one are presented. The latter approach is free from many additional assumptions inherent to potential calculations. Other applications of QCD to the charmed world are briefly reviewed. Different parts of the review are addressed to different readers. It could, in particular, be of interest to students, specializing in elementary particle physics, experimentalists and theoreticians who are active in this field. The final results are presented in such a form as to follow for a direct comparison with corresponding experimental data.

Are all hadrons alike

Abstract Using the existing knowledge of the chromodynamic vacuum as a basis we investigate mesons built from u, d, s quarks and/or gluons. A new classification of hadrons is proposed which reflects the strength of interaction of various currents with vacuum fields. It is found that the mass scale intrinsic to the resonance structures in different channels is not universal; a large mass scale is discovered, for instance, in the 0 − , 0 + gluonic channels. Starting from our classification we establish the hierarchy of scales. Regularities of the hadronic phenomenology [Zweigs selection rule, approximate SU(6) symmetry and so on] are naturally explained. The properties of glueballs are discussed in some detail. A few low-energy theorems are derived, which imply, in particular, a new mass relation for the η′ meson.

Solution of the Anomaly Puzzle in SUSY Gauge Theories and the Wilson Operator Expansion

Abstract The present paper completes a series of works on β functions and the anomaly problem in supersymmetric theories. Exact expressions for the β functions are obtained within the framework of standard perturbation theory. The key observation is that the Wilson effective action S W ( μ ) does not coincide with the sum of vacuum loops in the external field Γ(μ). The difference is due to infrared effects. The coefficient 1/ g 2 in front of the operator W 2 in S W is renormalized only at one-loop level (extension of the non-renormalization theorem for F -terms). This fact results in the one-loop form of the anomalous operator equation for the supercurrent (generalization of the Adler-Bardeen theorem). The full Gell-Mann-Low function emerges after passing to matrix elements of the operators. The quantity entering observable amplitudes differs from 1/ g 2 by Σ i ln Z i where the factors Z i describe renormalization of the fields. (In this sense the Z factors of the matter fields become observable.) We discuss the relation with calculations of the instanton type.

Asymptotic freedom, light quarks and the origin of the ΔT = 12 rule in the non-leptonic decays of strange particles

Abstract A dynamical mechanism for the ΔT = 1 2 rule in the non-leptonic decays of strange particles is considered. The weak interactions are described within the Weinberg-Salam model while the strong interactions are assumed to be mediated by the exchange of an octet of colour vector gluons. It is shown that the effect of the strong interactions gives rise to new operators in the effective Hamiltonian of weak interactions which contain both left- and right-handed fermions. These operators satisfy the ΔT = 1 2 rule, and estimates within the relativistic quark model indicate that their contribution dominates the physical amplitudes of the K → 2 π , 3 π decays.

Nonperturbative continuity in graviton mass versus perturbative discontinuity

We address the question whether a graviton could have a small nonzero mass. The issue is subtle for two reasons: there is a discontinuity in the mass in the lowest tree-level approximation, and, moreover, the nonlinear four-dimensional theory of a massive graviton is not defined unambiguously. First, we reiterate the old argument that for the vanishing graviton mass the lowest tree-level approximation breaks down since the higher order corrections are singular in the graviton mass. However, there exist nonperturbative solutions which correspond to the summation of the singular terms and these solutions are continuous in the graviton mass. Furthermore, we study a completely nonlinear and generally covariant five-dimensional model which mimics the properties of the four-dimensional theory of massive gravity. We show that the exact solutions of the model are continuous in the mass, yet the perturbative expansion exhibits the discontinuity in the leading order and the singularities in higher orders as in the four-dimensional case. Based on exact cosmological solutions of the model we argue that the helicity-zero graviton state which is responsible for the perturbative discontinuity decouples from the matter in the limit of vanishing graviton mass in the full classical theory.

Remarks on Higgs Boson Interactions with Nucleons

Low-energy hadronic transitions induced by Higgs or Higgs-like bosons are considered. In particular, it is shown that the Higgs coupling to nucleons is fixed. Implications for the models with muon number nonconservation in the Higgs sector are discussed.