The generating functional for hadronic weak interactions and its quenched approximation

We derive the generating functional of $|\Delta S| =1, 2$ hadronic weak interactions at one loop for a generic number of flavours and its counterpart in the quenched approximation. A systematic analysis of the ultraviolet divergences in the full theory (with and without a singlet dynamical field) and in the quenched case is performed. We show that the quenched chiral logarithms in the presence of weak interactions amount to a redefinition of the weak mass term in the $\Delta S=\pm 1$ weak effective Lagrangian at leading order. Finally, we apply the results to $B_K$ and $K\to\pi\pi$ matrix elements with $\Delta I=1/2,3/2$ to analyze the modifications induced by quenching on the coefficients of chiral logarithms in the one-loop corrections.Comment: 44 pages, Latex, uses epsfig.sty, 2 postscript figure

The S parameter in a technicolour model with explicit chiral symmetry breaking

We derive the S parameter of the electroweak radiative corrections in a scaled-QCD technicolour and using a Nambu-Jona Lasinio model for hadronic low energy interactions. In this framework deviations from low energy QCD can be quantitatively deduced. We induce explicit chiral symmetry breaking in the NJL model through the current-quarks mass term. It is shown that the prediction for the S parameter can be sensitively reduced respect to the chiral prediction.Comment: 10 pages (Latex), 3 postscript figures appended, preprint ROM2F/94/3

The mass of the scalar boson beyond the large-Nc limit

Within the framework of the 1/Nc expansion of four-fermion interaction models, we analyse the next to leading 1/Nc corrections to the well known large-Nc result MS = 2MQ where MS is the mass of the scalar boson and MQ is the constituent quark mass. The calculation is performed in the Extended Nambu-Jona Lasinio (ENJL) model which is suitable for describing low energy hadron properties. We treat the model as fully non renormalizable and discuss the comparison with approaches based on the equivalence with renormalizable Yukawa type models. We consider both the GV = 0 and the GV ≠ 0 cases with nf = 2 flavours and study the dependence upon the regularization scheme. We find that pure next-to-leading 1/Nc corrections are large and negative, while a partially resummed treatment can induce positive and smaller corrections. A triplet-singlet states’ splitting is observed.

Topology, the meson spectrum and the scalar glueball: three probes of conformality and the way it is lost

We discuss properties of non-Abelian gauge theories that change significantly across the lower edge of the conformal window. Their probes are the topological observables, the meson spectrum and the scalar glueball operator. The way these quantities change tells about the way conformal symmetry is lost.Comment: 16 pages, 3 figures, contribution to Sakata Memorial KMI Workshop on "Origin of Mass and Strong Coupling Gauge Theories (SCGT15)", 3-6 March 2015, Nagoya Universit

On K→ππK\to\pi\pi Decays in Quenched and Unquenched Chiral Perturbation Theory

We calculate the logarithmic corrections to the matrix elements for $K^+\to\pi^+$ and $K\to$vacuum (which are used on the lattice to determine $K\to\pi\pi$ amplitudes), in one-loop quenched and unquenched Chiral Perturbation Theory. We find that these corrections can be large. We also discuss, and present some results for, the direct determination of $K\to\pi\pi$ amplitudes. In particular, we address effects from choosing $m_s=m_d$ and vanishing external spatial momenta, finite volume and quenching. In the quenched octet case, we find enhanced finite-volume contributions which may make numerical estimates of this matrix element unreliable for large volumes.Comment: LATTICE99(Matrix Elements), LaTeX(espcrc2.sty), 3p, 1 ps figur

Pion loops in quenched Quantum Chromodynamics

We calculate the divergences of the generating functional of quenched Chiral Perturbation Theory to one loop for a generic number of flavours. The flavour number dependence of our result enlightens the mechanism of quark loop cancellation in the quenched effective theory for any Green function or S matrix element. We also apply our results to $\pi \pi$ scattering and evaluate the coefficient of the chiral log in the S-wave scattering lengths for the quenched case.Comment: Latex, 10 pages, 1 figur