Mikhail A. Shifman

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.

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.

Domain Walls in Strongly Coupled Theories

Abstract Domain walls in strongly coupled gauge theories are discussed. A general mechanism is suggested automatically leading to massless gauge bosons localized on the wall. In one of the models considered, outside the wall the theory is in the non-Abelian confining phase, while inside the wall it is in the Abelian Coulomb phase. The confining property of the non-Abelian theories is a key ingredient of the mechanism which may be of practical use in the context of the dynamic compactification scenarios. In supersymmetric (N = 1) Yang-Mills theories the energy density of the wall can be exactly calculated in the strong coupling regime. This calculation presents a further example of non-trivial physical quantities that can be found exactly by exploiting specific properties of supersymmetry. A key observation is the fact that the wall in this theory is a BPS-saturated state.

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.

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.

QCD predictions for lepton spectra in inclusive heavy flavor decays

We derive the lepton spectrum in semileptonic [ital b] decays from a nonperturbative treatment of QCD; it is based on an expansion in 1/[ital m][sub [ital Q]] with [ital m][sub [ital Q]] being the heavy flavor quark mass. The leading corrections arising on the 1/[ital m][sub [ital Q]] level are completely expressed in terms of the difference in the mass of the heavy hadron and the quark. Nontrivial effects appear in 1/[ital m][sub [ital Q]][sup 2] terms affecting mainly the end-point region; they are different for meson and baryon decays as well as for bottom and charm decays.