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.

Strongly Interacting Dynamics beyond the Standard Model on a Spacetime Lattice

Strong theoretical arguments suggest that the Higgs sector of the Standard Model of the Electroweak interactions is an effective low-energy theory, with a more fundamental theory that is expected to emerge at an energy scale of the order of the TeV. One possibility is that the more fundamental theory be strongly interacting and the Higgs sector be given by the low-energy dynamics of the underlying theory. We review recent works aimed to determining observable quantities by numerical simulations of strongly interacting theories proposed in the literature for explaining the Electroweak symmetry breaking mechanism. These investigations are based on Monte Carlo simulations of the theory formulated on a spacetime lattice. We focus on the so-called Minimal Walking Technicolour scenario, a SU(2) gauge theory with two flavours of fermions in the adjoint representation. The emerging picture is that this theory has an infrared fixed point that dominates the large distance physics. We shall discuss the first numerical determinations of quantities of phenomenological interest for this theory and analyse future directions of quantitative studies of strongly interacting beyond the Standard Model theories with Lattice techniques. In particular, we report on a finite size scaling determination of the chiral condensate anomalous dimension $\gamma$, for which we find $0.05 \le \gamma \le 0.25$.Comment: Minor corrections and clarifications of some points, conclusions unchange

Evidence for a conformal phase in SU(N) gauge theories

We discuss the existence of a conformal phase in SU(N) gauge theories in four dimensions. In this lattice study we explore the model in the bare parameter space, varying the lattice coupling and bare mass. Simulations are carried out with three colors and twelve flavors of dynamical staggered fermions in the fundamental representation. The analysis of the chiral order parameter and the mass spectrum of the theory indicates the restoration of chiral symmetry at zero temperature and the presence of a Coulomb-like phase, depicting a scenario compatible with the existence of an infrared stable fixed point at nonzero coupling. Our analysis supports the conclusion that the onset of the conformal window for QCD-like theories is smaller than Nf=12, before the loss of asymptotic freedom at sixteen and a half flavors. We discuss open questions and future directions.Comment: 11 pages, 11 figures; extended analysis, conclusions unchanged. (version to appear in PRD

Quenched chiral perturbation theory to one loop

We calculate the divergences of the generating functional of quenched chiral perturbation theory at one loop, and renormalize the theory by an appropriate definition of the counterterms. We show that the quenched chiral logarithms can be accounted for by defining a renormalized B0 parameter which, at lowest order, is proportional to the vacuum expectation value of the scalar quark density. Finally, we calculate several quantities at one loop to better analyze the modifications induced by quenching in the ultraviolet finite part of the one-loop corrections. We point out that some of the finite loop corrections may diverge in the chiral limit.