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Lattice QCD: testing the standard model of elementary particles from first principles computations


The Standard Model of elementary particles is up to now the accepted framework describing electromagnetic, weak and strong interactions. In particular, Quantum Chromodynamics (QCD) successfully describes strong interactions. Nevertheless, relevant issues are still open and the quantitative predictions from first principles remain a big challenge, mainly due to the non-perturbative nature of many processes involved in strong interactions.

By formulating QCD on a dicretised space-time (lattice) one obtains an important tool to investigate non-perturbative phenomena and to compute the fundamental parameters of the Standard Model in a model-independent way and with a full control on the systematic errors. In particular, this project will focuse on the non-leptonic kaon decays; by considering the transition amplitude of a kaon in a final state with two pions, one observes empirically that the amplitude for a final state with isospin I=0 is considerably enhanced with respect to the case with isospin I=2 (A0/A2=22.1).

This is known as AI=1-2 rule, and the understanding of the underlying mechanism will be the main purpose of the project. This goal will be pursued by determining though lattice QCD computations the low-energy coupling constants of Chiral Perturbation Theory that are directly connected to QCD contributions to the AI=1/2 rule. The key ingredient will be the use of Ginsparg-Wilson fermions; in this formulation, the chiral symmetry is preserved at non-zero lattice spacing and this simplifies considerably the renormalisation of the operators.

The relevant three-point functions will be computed through a numerical Monte Carlo simulation. The physical parameters will be extracted by using recent analytic developments on Chiral Perturbation Theory at finite volume (epsilon expansion). A first principle computation of the AI=1/2 rule is still missing and hence the outcome of the project will be an important step in testing the Standard Model.


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