Abstract: Symmetries in the Physical Laws of Nature lead to observable effects. Beyond the regularities and conserved magnitudes, the last few decades in particle physics have seen the identification of symmetries, and their well-defined breaking, as the guiding principle for the elementary constituents of matter and their interactions. Flavour SU(3) symmetry of hadrons led to the Quark Model and the antisymmetric requirement under exchange of identical fermions led to the colour degree of freedom. Colour became the generating charge for flavour-independent strong interactions of quarks and gluons in the exact colour SU(3) local gauge symmetry. Parity Violation in weak interactions led us to consider the chiral fields of fermions as the objects with definite transformation properties under the weak isospin SU(2) gauge group of the Unifying Electro-Weak SU(2) x U(1) symmetry, which predicted novel weak neutral current interactions. CP-Violation led to three families of quarks opening the field of Flavour Physics. Time-reversal violation has recently been observed with entangled neutral mesons, compatible with CPT-invariance. The cancellation of gauge anomalies, which would invalidate the gauge symmetry of the quantum field theory, led to Quark-Lepton Symmetry. Neutrinos were postulated in order to save the conservation laws of energy and angular momentum in nuclear beta decay. After the ups and downs of their mass, neutrino oscillations were discovered in 1998, opening a new era about their origin of mass, mixing, discrete symmetries and the possibility of global lepton-number violation through Majorana mass terms and Leptogenesis as the source of the matter-antimatter asymmetry in the universe. The experimental discovery of quarks and leptons and the mediators of their interactions, with physical observables in spectacular agreement with this Standard Theory, is the triumph of Symmetries. The gauge symmetry is exact only when the particles are massless. One needs a subtle breaking of the symmetry, providing the origin of mass without affecting the excellent description of the interactions. This is the Brout-Englert-Higgs Mechanism, which produces the Higgs Boson as a remnant, discovered at CERN in 2012. Open present problems are addressed with by searching the New Physics Beyond-the-Standard-Model.

Abstract: We present a new global fit of the 19-dimensional phenomenological Minimal Supersymmetric Standard Model (pMSSM-19) that complies with all the latest experimental results from dark matter indirect, direct and accelerator dark matter searches. We show that the model provides a satisfactory explanation of the excess of gamma rays from the Galactic centre observed by the Fermi Large Area Telescope, assuming that it is produced by the annihilation of neutralinos in the Milky Way halo. We identify two regions that pass all the constraints: the first corresponds to neutralinos with a mass similar to 80 – 100 GeV annihilating into WW with a branching ratio of 95%; the second to heavier neutralinos, with mass similar to 180 – 200 GeV annihilating into (l) over barl with a branching ratio of 87%. We show that neutralinos compatible with the Galactic centre GeV excess will soon be within the reach of LHC run-II – notably through searches for charginos and neutralinos, squarks and light smuons – and of Xenon1T, thanks to its unprecedented sensitivity to spin-dependent cross-section off neutrons.