Stephan Narison

QCD spectral sum rules

The aim of the book is to give an introduction to the method of QCD Spectral Sum Rules and to review its developments. After some general introductory remarks, Chiral Symmetry, the Historical Developments of the Sum Rules and the necessary materials for perturbative QCD including the MS regularization and renormalization schemes are discussed. The book also gives a critical review and some improvements of the wide uses of the QSSR in Hadron Physics and QSSR beyond the Standard Hadron Phenomenology. The author has participated actively in this field since 1978 just before the expanding success of the SVZ QSSR.

QCD analysis of the tau hadronic width

Abstract The total τ hadronic width can be accurately calculated using analyticity and the operator product expansion. The theoretical analysis of this observable is updated to include all available perturbative and non-perturbative corrections. Experimental measurements of τ decay rates are used to determine with high precision the QCD running coupling constant at the scale of the τ mass. The analysis is also used to study the present discrepancy between the experimental measurements of the leptonic branching fractions of the τ and its total lifetime.

Spectral function sum rules in quantum chromodynamics: (I). Charged currents sector

Abstract The Weinberg sum rules of the algebra of currents are reconsidered in the light of quantum chromodynamics (QCD). We derive new finite-energy sum rules which replace the old Weinberg sum rules. The new sum rules are convergent and the rate of convergence is explicitly calculated in perturbative QCD at the first non-trivial order. Phenomenological applications of these sum rules in the charged current sector are also discussed.

Techniques of dimensional regularization and the two-point functions of QCD and QED☆

Abstract The necessary and useful tools of dimensional regularization (and renormalization), the so-called ϵ-scheme, are reviewed. A survey on a comparison of various renormalization schemes is done. The applications of the ϵ-scheme to the two-point funtions of quantum chromodynamics (QCD) and quantum electrodynamics (QED) are given. In these applications it is shown explicitly how to compute Feynman diagrams and how to use the renormalization group equation (RGE) for the prediction of some terms induced by higher order diagrams. Some phenomenological uses of the two-point functions are briefly discussed. These include the quark mass, the spectral function sum rules in QCD and the control of the asymptotic SU( n )×SU( n ) flavour chiral symmetry, the proton-neutron electromagnetic mass difference in the light of QCD and the running electromagnetic charge of QED. We also confront the operator product expansion (OPE) results of the anomalous dimension of non-singlet operators to the result obtained from the method of factorization of mass singularities.

Short-distance tachyonic gluon mass and 1/Q2 corrections

Abstract We consider the assumption that a tachyonic gluon mass imitates short-distance non-perturbative physics of QCD. The phenomenological implications include modifications of the QCD sum rules for correlators of currents with various quantum numbers. The new 1/ Q 2 terms allow us to resolve in a natural way old puzzles in the pion and scalar-gluonium channels. They lead to a slight reduction of the values of the running light quark masses from the (pseudo)scalar sum rules and of α s ( M τ ) from τ decay data. Analogously such terms only affect slightly the determinations of the running strange quark mass from e + e − and τ decay data. Further tests can be provided by precision measurements of the correlators on the lattice and by the e + e − → hadrons data.

QCD Formulation of the tau Decay and Determination of Lambda (MS)

Abstract We present a simple formulation of the inclusive and exclusive semi-hadronic decays of the tau lepton using QCD-duality finite energy sum rules (FESRs). We find that the tau decay is a good laboratory for measuring the QCD scaleΛ. Within the present experimental accuracy, we obtain Λ M S ¯ ⋍ 100–200 MeV to four loops. This prediction can be sensibly improved once the experimental situation has been clarified.

Masses, decays and mixings of gluonia in QCD

We compute the masses and decay widths of the gluonia using QCD spectral sum rules and low-energy theorems. In the scalar sector, one finds a gluonium having a mass MG = (1.5 ± 0.2) GeV, which decays mainly into the U(1)A channels ηη′ and 4π0. However, for a consistency of the whole approach, one needs broad low-mass gluonia (the σB and its radial excitation), which couple strongly to the quark degrees of freedom similarly to the η′ of the U(1)A sector. Combining these results with the ones for the q¯q quarkonia, we present maximal gluonium-quarkonium mixing schemes, which can provide quite a good description of the complex spectra and various decay widths of the observed scalar mesons σ(1.), f0(0.98), f0(1.37), f0(1.5) and fJ(1.71). In the tensor sector, the gluonium mass is found to be MT ⋍ (2.0±0.1) GeV, which makes the ζ(2.2) a good 2++ gluonium candidate, even though we expect a rich population of 2++ gluonia in this region. In the pseudoscalar channel, the gluonium mass is found to be Mp ⋍ (2.05 ± 0.19) GeV, while we also show that the E/ι(1.44) couples more weakly to the gluonic current than the η′(0.96), which can favour its interpretation as the first radial excitation of the η′(0.96).

On QCD sum rules of the Laplace transform type and light quark masses

Abstract We discuss the relation between the usual dispersion relation sum rules and the Laplace transform type sum rules in QCD. Two specific examples corresponding to the ϱ-coupling constant sum rule and the light quark masses sum rules are considered. An interpretation, within QCD, of Leutwylers formula for the current algebra quark masses is also given.

Heavy quarkonia mass-splittings in QCD: gluon condensate, αs and 1m-expansion

I present a more refined analysis of the mass-splittings between the different heavy quarkonia states, using {\it new double ratios} of exponential moments of different two-point functions. Then, I test the validity of the

Decay constants of the B and D mesons from QCD-duality sum rules

1/m