2016/05/05 by K. Pedro, Pedro, Leonardo
Physics and Astronomy · #Particle physics theoretical and experimental studies #Neutrino Physics Research #Black Holes and Theoretical Physics
paper · pdf · doi:10.48550/arxiv.1605.01512
One common way to define spontaneous symmetry breaking involves explicit\nsymmetry breaking. This definition can be used in any approach to Effective\nField Theory, from perturbation theory to lattice simulations. It allows us to\nstudy the spontaneous breakdown of global symmetries without assuming that the\nlocal gauge symmetry is spontaneously broken. This is important since\nperturbation theory is insufficient to study extended Higgs sectors: it is\ninsufficient to predict the physical spectrum of the SU(5) Grand Unified Theory\n(Georgi-Glashow) or to predict the spontaneous breakdown of global symmetries.\n We also study background symmetries: these are symmetries that despite they\nare already explicitly broken, can be still spontaneously broken. We analyse\nexamples where a background CP (charge-parity) symmetry is not spontaneously\nbroken: in the Standard Model, in rephasing symmetries and in geometrical\nCP-violation.\n We show that all fields are real representations of the group of symmetries,\nsince CP is a unitary transformation. There are consequences: to study\naccidental symmetries (e.g. custodial symmetry, pseudo-golstone bosons) we must\nconsider real representations; CP is a symmetry of order 4 if the neutrinos are\nMajorana particles and the notion of CP-violating phases is inconsistent in\nsome Lagrangians; a recent claim that a toy model exhibits physical\nCP-violation while the CP symmetry is conserved by the Lagrangian and the\nvacuum is false.\n