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Barenboim, G. (2022). Some Aspects About Pushing the CPT and Lorentz Invariance Frontier With Neutrinos. Front. Physics, 10, 813753–7pp.
Abstract: The CPT symmetry, which combines Charge Conjugation, Parity, and Time Reversal, is a cornerstone of our model-building method, and its probable violation will endanger the most extended tool we presently utilize to explain physics, namely local relativistic quantum fields. However, the kaon system's conservation constraints appear to be rather severe. We will show in this paper that neutrino oscillation experiments can enhance this limit by many orders of magnitude, making them an excellent instrument for investigating the basis of our understanding of Nature. As a result, verifying CPT invariance does not evaluate a specific model, but rather the entire paradigm. Therefore, as the CPT's status in the neutrino sector, linked or not to Lorentz invariance violation, will be assessed at an unprecedented level by current and future long baseline experiments, distinguishing it from comparable experimental fingerprints coming from non-standard interactions is critical. Whether the entire paradigm or simply the conventional model of neutrinos is at jeopardy is significantly dependent on this.
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Bernabeu, J. (2020). Symmetries and Their Breaking in the Fundamental Laws of Physics. Symmetry-Basel, 12(8), 1316–27pp.
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.
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Morisi, S., & Peinado, E. (2011). Admixture of quasi-Dirac and Majorana neutrinos with tri-bimaximal mixing. Phys. Lett. B, 701(4), 451–457.
Abstract: We propose a realization of the so-called bimodal/schizophrenic model proposed recently. We assume 54, the permutation group of four objects as flavor symmetry giving tri-bimaximal lepton mixing at leading order. In these models the second massive neutrino state is assumed quasi-Dirac and the remaining neutrinos are Majorana states. In the case of inverse mass hierarchy, the lower bound on the neutrinoless double beta decay parameter m(ee) is about two times that of the usual lower bound, within the range of sensitivity of the next generation of experiments.
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Meloni, D., Morisi, S., & Peinado, E. (2011). Neutrino phenomenology and stable dark matter with A(4). Phys. Lett. B, 697(4), 339–342.
Abstract: We present a model based on the A(4) non-Abelian discrete symmetry leading to a predictive five-parameter neutrino mass matrix and providing a stable dark matter candidate. We found an interesting correlation among the atmospheric and the reactor angles which predicts theta(23) similar to pi/4for very small reactor angle and deviation from maximal atmospheric mixing for large theta(13). Only normal neutrino mass spectrum is possible and the effective mass entering the neutrinoless double beta decay rate is constrained to be vertical bar m(ee)vertical bar > 4 x 10(-4) eV.
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Flores-Tlalpa, A., Lopez Castro, G., & Roig, P. (2016). Five-body leptonic decays of muon and tau lepton. J. High Energy Phys., 04(4), 185–21pp.
Abstract: We study the five-body decays u(-) -> e(-)e(+)e(-)nu u (nu) over bar (e) and tau(-) -> l(-)l'+l'-nu(tau)(nu) over bar (l) for l, l' = e, u within the Standard Model (SM) and in a general effective field theory description of the weak interactions at low energies. We compute the branching ratios and compare our results with two previous – mutually discrepan – SM calculations. By assuming a general structure for the weak currents we derive the expressions for the energy and angular distributions of the three charged leptons when the decaying lepton is polarized, which will be useful in precise tests of the weak charged current at Belle II. In these decays, leptonic T-odd correlations in triple products of spin and momenta – which may signal time reversal violation in the leptonic sector – are suppressed by the tiny neutrino masses. Therefore, a measurement of such T-violating observables would be associated to neutrinoless lepton flavor violating (LFV) decays, where this effect is not extremely suppressed. We also study the backgrounds that the SM five-lepton lepton decays constitute to searches of LFV L- -> ? l(-)l'+l'(-) decays. Searches at high values of the invariant mass of the l'(+)l'(-) pair look the most convenient way to overcome the background.
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Chen, M. C., King, S. F., Medina, O., & Valle, J. W. F. (2024). Quark-lepton mass relations from modular flavor symmetry. J. High Energy Phys., 02(2), 160–28pp.
Abstract: The so-called Golden Mass Relation provides a testable correlation between charged-lepton and down-type quark masses, that arises in certain flavor models that do not rely on Grand Unification. Such models typically involve broken family symmetries. In this work, we demonstrate that realistic fermion mass relations can emerge naturally in modular invariant models, without relying on ad hoc flavon alignments. We provide a model-independent derivation of a class of mass relations that are experimentally testable. These relations are determined by both the Clebsch-Gordan coefficients of the specific finite modular group and the expansion coefficients of its modular forms, thus offering potential probes of modular invariant models. As a detailed example, we present a set of viable mass relations based on the Gamma 4 approximately equal to S4 symmetry, which have calculable deviations from the usual Golden Mass Relation.
Keywords: Discrete Symmetries; Flavour Symmetries; Theories of Flavour
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Dong, P. V., Huong, D. T., Queiroz, F. S., Valle, J. W. F., & Vaquera-Araujo, C. A. (2018). The dark side of flipped trinification. J. High Energy Phys., 04(4), 143–31pp.
Abstract: We propose a model which unifies the Left-Right symmetry with the SU(3)L gauge group, called flipped trinification, and based on the SU(3)(C)circle times SU(3)(L)circle times SU(3)(R)circle times U(1)(x) gauge group. The model inherits the interesting features of both symmetries while elegantly explaining the origin of the matter parity, W-p = ( 1)(3(B-L)+/- 2s), and dark matter stability. We develop the details of the spontaneous symmetry breaking mechanism in the model, determining the relevant mass eigenstates, and showing how neutrino masses are easily generated via the seesaw mechanism. Moreover, we introduce viable dark matter candidates, encompassing a fermion, scalar and possibly vector fields, leading to a potentially novel dark matter phenomenology.
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de Medeiros Varzielas, I., King, S. F., Luhn, C., & Neder, T. (2017). Spontaneous CP violation in multi-Higgs potentials with triplets of Delta(3n(2)) and Delta(6n(2)). J. High Energy Phys., 11(11), 136–56pp.
Abstract: Motivated by discrete flavour symmetry models, we analyse Spontaneous CP Violation (SCPV) for potentials involving three or six Higgs fi elds (both electroweak doublets and singlets) which fall into irreducible triplet representations of discrete symmetries belonging to the Delta(3n(2)) and Delta(6n(2)) series, including A(4), S-4, Delta(27) and Delta(54). For each case, we give the potential and fi nd various global minima for di ff erent regions of the parameter space of the potential. Using CP-odd basis Invariants that indicate the presence of Spontaneous CP Violation we separate the VEVs into those that do or do not violate CP. In cases where CP is preserved we reveal a CP symmetry of the potential that is preserved by those VEVs, otherwise we display a non-zero CP-odd Invariant. Finally we identify interesting cases where there is Spontaneous Geometrical CP Violation in which the VEVs have geometrical phases.
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Bernabeu, J., & Segarra, A. (2019). Do T asymmetries for neutrino oscillations in uniform matter have a CP-even component? J. High Energy Phys., 03(3), 103–12pp.
Abstract: Observables of neutrino oscillations in matter have, in general, contributions from the effective matter potential. It contaminates the CP violation asymmetry adding a fake effect that has been recently disentangled from the genuine one by their different behavior under T and CPT. Is the genuine T-odd CPT-invariant component of the CP asymmetry coincident with the T asymmetry? Contrary to CP, matter effects in uniform matter cannot induce by themselves a non-vanishing T asymmetry; however, the question of the title remained open. We demonstrate that, in the presence of genuine CP violation, there is a new non-vanishing CP-even, and so CPT-odd, component in the T asymmetry in matter, which is of odd-parity in both the phase delta of the flavor mixing and the matter parameter a. The two disentangled components, genuine A(alpha beta)(T;CP) and fake A(alpha beta)(T;CPT), could be experimentally separated by the measurement of the two T asymmetries in matter (nu(alpha) <-> nu(beta)) and ((nu) over bar <-> (nu) over bar (beta)). For the (nu(mu) <-> nu(e)) transitions, the energy dependence of the new A(mu e)(T;CPT) component is like the matter-induced term A(mu e)(CP;CPT) of the CP asymmetry which is odd under a change of the neutrino mass hierarchy. We have thus completed the physics involved in all observable asymmetries in matter by means of their disentanglement into the three independent components, genuine A(alpha beta)(CP;T) and fake A(alpha beta)(CP;CPT) and A(alpha beta)(T;CPT).
Keywords: CP violation; Discrete Symmetries; Neutrino Physics
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Bernabeu, J., Di Domenico, A., & Villanueva-Perez, P. (2013). Direct test of time reversal symmetry in the entangled neutral kaon system at a phi-factory. Nucl. Phys. B, 868(1), 102–119.
Abstract: We present a novel method to perform a direct T (time reversal) symmetry test in the neutral kaon system, independent of any CP and/or CPT symmetry tests. This is based on the comparison of suitable transition probabilities, where the required interchange of in <-> out states for a given process is obtained exploiting the Einstein-Podolski-Rosen correlations of neutral kaon pairs produced at a phi-factory. In the time distribution between the two decays, we compare a reference transition like the one defined by the time-ordered decays (l(-), pi pi) with the T-conjugated one defined by (3 pi(0), l(+)). With the use of this and other T-conjugated comparisons, the KLOE-2 experiment at DA Phi NE could make a statistically significant test.
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