Abstract: Symmetry transformations have been proven a bedrock tool for understanding the nature of particle interactions, formulating, and testing fundamental theories. Based on the up to now unbroken CPT symmetry, the violation of the CP symmetry between matter and antimatter by weak interactions, discovered in the decay of kaons in 1964 and observed more recently in 2001 in B mesons, strongly suggests that the behavior of these particles under weak interactions must also be asymmetric under time reversal T. However, until recent years there has not been a direct detection of the expected time-reversal violation in the time evolution of any system. This Colloquium examines the field of time-reversal symmetry breaking in the fundamental laws of physics. For transitions, its observation requires an asymmetry with exchange of initial and final states. A discussion is given of the conceptual basis for such an exchange with unstable particles, using the quantum properties of Einstein-Podolsky-Rosen entanglement available at B meson factories combined with the decay as a filtering measurement. The method allows a clear-cut separation of different transitions between flavor and CP eigenstates in the decay of neutral B mesons. These ideas have been implemented for the experiment by the BABAR Collaboration at SLAC's B factory. The results, presented in 2012, prove beyond any doubt the violation of time-reversal invariance in the time evolution between these two states of the neutral B meson.

Abstract: We discuss the eight independent spin observables for the W boson in terms of its vector and tensor polarizations and identify the angular distributions and asymmetries able to separate them in collider experiments. The results are applied to the study of polarized top quark decays and diboson resonances. These novel observables are of great value for disentangling new physics mechanisms in W boson production.

Abstract: The precise connection between the theoretical T, CP, CPT asymmetries, in terms of transition probabilities between the filtered neutral meson B-d states, and the experimental asymmetries, in terms of the double decay rate intensities for Flavour-CP eigenstate decay products in a B-d-factory of entangled states, is established. This allows the identification of genuine Asymmetry Parameters in the time distribution of the asymmetries and their measurability by disentangling genuine and possible fake terms. We express the nine asymmetry parameters three different observables for each one of the three symmetries in terms of the ingredients of the Weisskopf-Wigner dynamical description of the entangled B-d-meson states and we obtain a global fit to their values from the BaBar collaboration experimental results. The possible fake terms are all compatible with zero and the information content of the nine asymmetry parameters is indeed different. The non -vanishing Delta l(c)(T) = 0.687 +/- 0.020 and Delta l(c)(CP) = 0.680 +/- 0.021 are impressive separate direct evidence of Time -Reversal -violation and CP-violation in these transitions and compatible with Standard Model expectations. An intriguing 2 sigma effect for the Re(theta) parameter responsible of CPT -violation appears which, interpreted as an upper limit, leads to vertical bar M (B) over baro (B) over baro vertical bar MBoBo < 4.0 x 10(-5) eV at 95% C.L. for the diagonal flavour terms of the mass matrix. It contributes to the CP-violating Delta l(c)(CP) asymmetry parameter in an unorthodox manner – in its cos(Delta M t) time dependence-, and it is accessible in facilities with non-entangled B-d's, like the LHCb experiment.

Abstract: In the presence of quantum-gravity fluctuations (space-time foam), the CPT operator may be ill-defined. Its perturbative treatment leads to a modification of the Einstein-Podolsky- Rosen correlation of the neutral meson system by adding an entanglement-weakening term of the wrong exchange symmetry, the omega-effect. In the current paper we identify how to probe the complex omega in the entangled B-d system using the flavour (f)-CP(g) eigenstate decay channels: the connection between the intensities for the two timeordered decays (f, g) and (g, f) is lost. Appropriate observables are constructed allowing independent experimental determinations of Re(omega) and Im(omega), disentangled from CPT violation in the evolution Hamiltonian Re(theta) and Im(theta). 2 sigma tensions for both Re(theta) and Im(omega) are shown to be uncorrelated.

Abstract: Massive neutrinos demand to ask whether they are Dirac or Majorana particles. Majorana neutrinos are an irrefutable proof of physics beyond the Standard Model. Neutrinoless double electron capture is not a process but a virtual Delta L = 2 mixing between a parent (A)Z atom and a daughter (A)(Z – 2) excited atom with two electron holes. As a mixing between two neutral atoms and the observable signal in terms of emitted two-hole X-rays, the strategy, experimental signature and background are different from neutrinoless double beta decay. The mixing is resonantly enhanced for almost degeneracy and, under these conditions, there is no irreducible background from the standard two-neutrino channel. We reconstruct the natural time history of a nominally stable parent atom since its production either by nature or in the laboratory. After the time periods of atom oscillations and the decay of the short-lived daughter atom, at observable times the relevant 'stationary" states are the mixed metastable long-lived state and the non-orthogonal short-lived excited state, as well as the ground state of the daughter atom. We find that they have a natural population inversion which is most appropriate for exploiting the bosonic nature of the observed atomic transitions radiation. Among different observables of the atom Majorana mixing, we include the enhanced rate of stimulated X-ray emission from the long-lived metastable state by a high-intensity X-ray beam: a gain factor of 100 can be envisaged at current XFEL facilities. On the other hand, the historical population of the daughter atom ground state can be probed by exciting it with a current pulsed optical laser, showing the characteristic absorption lines: the whole population can be excited in a shorter time than typical pulse duration.