Research

Standard Model (SM) predictions are in impressive agreement with experimental results from many electroweak and strong interaction processes. However, astrophysical evidence and theoretical arguments suggest that the SM cannot be the ultimate theory.

The main objective of this project is to obtain more stringent theoretical predictions on selected electroweak and strong interaction processes by advancing the theoretical understanding of strongly interacting theories in the SM and beyond. We intend to overcome the current limits in the state of the art with new non-conventional theoretical approaches and novel computational strategies.

The comparison with precision measurements at low energy may give access to information at higher energy scales than direct particle production, thus leading to discoveries of new fundamental phenomena in Nature.

We conduct our research within the lattice field theory regularization, where the dynamics of strongly interacting theories can be studied non-perturbatively from first principles. We aim at computing quantities with a precision at the level of percent or less, which is the accuracy required for the interpretation and the analysis of the wealth of experimental results expected both for sub-nuclear matter and for matter at non-vanishing values of temperature and/or chemical potential.

The results that will be obtained in this project will enable us not only to link experimental findings to the fundamental theory, but also to move beyond what can be measured in experiments and address theoretical questions which may unveil deeper theoretical implications.

The project is organized along the following thematical groups of objectives:

Theme 1: QCD and flavour physics (Milano Bicocca, Parma, Roma Tor Vergata)
The aim is to find new fundamental phenomena in Nature by putting more stringent limits on selected electroweak and strong interaction processes, as well as to improve the precision of the free SM parameters in the quark sector. The goals are  the following: (a) a determination of the hadronic contribution to the muon anomalous magnetic moment α_μ at a few permille level; (b) a precise calculation of the weak matrix elements of four-fermion operators which enter the ΔS = 2 effective weak Hamiltonian in the SM and beyond; (c) extraction of the matrix elements of the first two rows of the CKM matrix from leptonic and semi-leptonic meson decays, through precise computations of weak matrix elements; (d) a computation of the nucleon mass and several nucleon matrix elements of quark bilinears close or at the physical point, i.e. g_A and those necessary for the neutron EDM in the SM and beyond.

Theme 2: QCD at high temperature and finite density (Milano Bicocca, Parma)
The long-term goal is to determine the properties of QCD at finite temperature and baryon chemical potential, and to compute the parameters characterizing the QCD phase diagram in the temperature - chemical potential (T, μ) plane.  The goals are: a) to probe the QCD phase diagram by Taylor expansions, gathering information at μ=0, at imaginary μ (where the sign problem is absent) and possibly at real values of μ (on the dominant Lefschetz thimble),aiming at locating the critical end point; b) a percent-level determination of the equation of state of QCD with 2+1 flavours at μ=0 up to temperatures of O(100) GeV, which were never explored so far; c) to determine to a few permille precision the lightest screening masses of QCD with 2+1 flavours at μ=0 up to temperatures of O(100) GeV; d) to carry out an exploratory computation of the topological susceptibility in thermal QCD to determine the T-dependence of the axion potential, an information needed to quantify the hypothetical relic abundance of axions today in the post-inflation scenario.

Theme 3: Theoretical developments (Milano Bicocca, Parma, Roma Tor Vergata)
The development of non-perturbative improvement, renormalization and running will be key contributions to this theme. We will continue our studies on the Lefschetz thimble approach for regularizing gauge theories at finite density, and on the realization of chiral symmetry breaking in QCD. In particular  we plan to: a) determine non-perturbatively the renormalization and RG-running of the ΔF = 2 four-fermion operators relevant for studying neutral Kaon oscillations in the SM and beyond by using the chirally-rotated Schroedinger-functional scheme; b) implement our recently proposed procedure, based on shifted boundary conditions in the presence of an imaginary chemical potential, to renormalize non-perturbatively the energy-momentum tensor in QCD; c) compute the flavour-singlet renormalisation constants for the three flavour theory; d) study Yang-Mills theories in 2 dimensions, where an analytic solution is known and can be cast into a sum over critical points, as a laboratory to shed light on a possible Thimble regularisation of gauge theories; e) compute the η' mass in QCD at the percent level.

Theme 4: Computational strategies (Milano Bicocca, Parma)
The conception and implementation of algorithms is one of the pillars on which the project rests. Numerical strategies will be developed to benefit from the progress in HPC systems, with an emphasis on efficient exploitation of multi/many-cores architectures. In particular we intend to: a) further develop the multi-boson domain-decomposed Hybrid Monte Carlo (MB-DD-HMC) by integrating it with master-field simulation techniques; b) further explore the possibility of computing Taylor expansions on Lefschetz thimbles so that regions where only the dominant thimble contribute to physical results can be bridged, and multiple thimbles computations can be avoided; c) develop a new multi-level computational strategy based on MB-DD-HMC for a precise study of the string breaking in QCD; d) apply multi-level integration for computing transport coefficients in the thermal theory; e) develop new NSPT computational strategies, aiming at effectively computing expansions around non-trivial vacua and at a reduction of noise in high order fermionic computations.