Renormalization of HQET $Delta B=2$ operators: O($a$) improvement and $1/m$ matching with QCD

We determine a basis of dimension-7 operators which arise at O($a$) in the Symanzik expansion of the $Delta B=2$ operators with static heavy quarks. We consider both Wilson-like and Ginsparg-Wilson light quarks. Exact chiral symmetry reduces the number of these O($a$) counterterms by a factor of two. Only a subset of these operators has previously appeared in the literature. We then extend the analysis to the O($1/m$) operators contributing beyond the static approximation.

Solar Neutrinos

The study of solar neutrinos has given since ever a fundamental contribution both to astroparticle and to elementary particle physics, offering an ideal test of solar models and offering at the same time relevant indications on the fundamental interactions among particles. After reviewing the striking results of the last two decades, which were determinant to solve the long standing solar neutrino puzzle and refine the Standard Solar Model, we focus our attention on the more recent results in this field and on the experiments presently running or planned for the near future. The main focus at the moment is to improve the knowledge of the mass and mixing pattern and especially to study in detail the lowest energy part of the spectrum, which represents most of solar neutrino spectrum but is still a partially unexplored realm. We discuss this research project and the way in which present and future experiments could contribute to make the theoretical framemork more complete and stable, understanding the origin of some anomalies that seem to emerge from the data and contributing to answer some present questions, like the exact mechanism of the vacuum to matter transition and the solution of the so called solar metallicity problem.

Determination of the $Delta S = 1$ weak Hamiltonian in the SU(4) chiral limit through topological zero-mode wave functions

A new method to determine the low-energy couplings of the $Delta S=1$ weak Hamiltonian is presented. It relies on a matching of the topological poles in $1/m^2$ of three-point correlators of two pseudoscalar densities and a four-fermion operator, measured in lattice QCD, to the same observables computed in the $epsilon$-regime of chiral perturbation theory. We test this method in a theory with a light charm quark, i.e. with an SU(4) flavour symmetry. Quenched numerical measurements are performed in a 2 fm box, and chiral perturbation theory predictions are worked out up to next-to-leading order. The matching of the two sides allows to determine the weak low-energy couplings in the SU(4) limit. We compare the results with a previous determination, based on three-point correlators containing two left-handed currents, and discuss the merits and drawbacks of the two procedures.

Weak low-energy couplings from topological zero-mode wavefunctions

We discuss a new method to determine the low-energy couplings of the $Delta S=1$ weak Hamiltonian in the $epsilon$-regime. It relies on a matching of the topological poles in $1/m^2$ of three-point functions of two pseudoscalar densities and a four-fermion operator computed in lattice QCD, to the same observables in the Chiral Effective Theory. We present the results of a NLO computation in chiral perturbation theory of these correlation functions together with some preliminary numerical results.