Ruggero Ferrari

Endowing the nonlinear sigma model with a flat connection structure: a way to renormalization

We discuss the quantized theory of a pure-gauge non-abelian vector field (flat connection) as it would appear in a mass term ? la St?ckelberg. However the paper is limited to the case where only the flat connection is present (no field strength term). The perturbative solution is constructed by using only the functional equations and by expanding in the number of loops. In particular we do not use a perturbative approach based on the path integral or on a canonical quantization. It is shown that there is no solution with trivial S-matrix. Then the model is embedded in a nonlinear sigma model. The solution is constructed by exploiting a natural hierarchy in the functional equations given by the number of insertions of the flat connection and of the constraint component of the sigma field. The amplitudes with the sigma field are simply derived from those of the flat connection and of the constraint component. Unitarity is enforced by hand by using Feynman rules. We demonstrate the remarkable fact that in generic dimensions the na?ve Feynman rules yield amplitudes that satisfy the functional equations. This allows a dimensional renormalization of the theory in D = 4 by recursive subtractions of the poles in the Laurent expansion. Thus one gets a finite theory depending only on two parameters. The novelty of the paper is the use of the functional equation associated to the local left multiplication introduced by Faddeev and Slavnov, here improved by adding the external source coupled to the constrained component. It gives a powerful tool to renormalize the nonlinear sigma model.

Weak Power-Counting Theorem for the Renormalization of the Nonlinear Sigma Model in Four Dimensions

The formulation of the non linear σ-model in terms of flat connection allows the construction of a perturbative solution of a local functional equation by means of cohomological techniques which are implemented in gauge theories. In this paper we discuss some properties of the solution at the one-loop level in D = 4. We prove the validity of a weak power-counting theorem in the following form: although the number of divergent amplitudes is infinite only a finite number of counterterms parameters have to be introduced in the effective action in order to make the theory finite at one loop, while respecting the functional equation (fully symmetric subtraction in the cohomological sense). The proof uses the linearized functional equation of which we provide the general solution in terms of local functionals. The counterterms are expressed in terms of linear combinations of these invariants and the coefficients are fixed by a finite number of divergent amplitudes. These latter amplitudes contain only insertions of the composite operators φ0 (the constraint of the non linear σ-model) and Fμ (the flat connection). The structure of the functional equation suggests a hierarchy of the Green functions. In particular once the amplitudes for the composite operators φ0 and Fμ are given all the others can be derived by functional derivatives. In this paper we show that at one loop the renormalization of the theory is achieved by the subtraction of divergences of the amplitudes at the top of the hierarchy. As an example we derive the counterterms for the four-point amplitudes.

Determination of Neutrino mixing parameters after SNO oscillation evidence

An updated analysis of all available neutrino oscillation evidence in solar experiments (SK day and night spectra, global rates from Homestake, SAGE, and GALLEX) including the latest SNO CC and NC data is presented. Assuming that the shape of the SNO CC energy spectrum is undistorted and using the information provided by SNO we obtain, for the fraction of electron neutrinos remaining in the solar beam at energies \ensuremath{\gtrsim}5 MeV,

Massive Yang-Mills theory based on the nonlinearly realized gauge group

{\ensuremath{\varphi}}_{\mathrm{CC}}/{\ensuremath{\varphi}}_{\mathrm{NC}}{=0.34}_{\ensuremath{-}0.04}^{+0.05},

FURTHER COMMENTS ON THE SYMMETRIC SUBTRACTION OF THE NONLINEAR SIGMA MODEL

which is nominally many standard deviations away from the standard value. The fraction of oscillating neutrinos into active ones is computed to be

Physical unitarity for massive non-Abelian gauge theories in the Landau gauge: Stueckelberg and Higgs

({\ensuremath{\Phi}}_{\mathrm{NC}}\ensuremath{-}{\ensuremath{\Phi}}_{\mathrm{CC}})/({\ensuremath{\Phi}}_{\mathrm{SSM}}\ensuremath{-}{\ensuremath{\Phi}}_{\mathrm{CC}}{)=0.92}_{\ensuremath{-}0.20}^{+0.39},

Algebraic Aspects of the Background Field Method

nearly

Constructive algebraic renormalization of the Abelian Higgs-Kibble model

5\ensuremath{\sigma}

Direct algebraic restoration of Slavnov-Taylor identities in the Abelian Higgs-Kibble model

deviations from the pure sterile oscillation case. The data are still compatible with an important fraction of sterile component in the solar beam (up to 20%\char21{}30% of the total). In the framework of two active neutrino oscillations we determine individual neutrino mixing parameters and their errors in the region of no spectrum distortion

Renormalization of the non-linear sigma model in four dimensions. A two-loop example

(\ensuremath{\Delta}〈{T}_{e}〉l1%);