Narrow Results

A careful ab initio construction of the finite-mass (1/2, 1/2) representation space of the Lorentz group reveals it to be a spin-parity multiplet. In general, it does not lend itself to a single-spin interpretation. We find that the (1/2, 1/2) representation space for massive particles naturally bifurcates into a triplet and a singlet of opposite relative intrinsic parties. The textbook separation into spin-1 and spin-0 states occurs only for certain limited kinematical settings. We construct a wave equation for the (1/2, 1/2) multiplet, and show that the particles and antiparticles in this representation space do not carry a definite spin but only a definite relative intrinsic parity. In general, both spin-1 and spin-0 are covariantly inseparable inhabitants of massive vector fields. This last observation suggests that scalar particles, such as the Higgs, are natural inhabitants of massive (1/2, 1/2) representation space.

We review the role of R symmetries in models of supersymmetric unification in four and more dimensions, and in string theory. We show that, if one demands anomaly freedom and fermion masses, only R symmetries can forbid the supersymmetric Higgs mass term μ. We then review the proof that R symmetries are not available in conventional grand unified theories (GUTs) and argue that this prevents natural solutions to the doublet–triplet splitting problem in four dimensions. On the other hand, higher-dimensional GUTs do not suffer from this problem. We briefly comment on an explicit string-derived model in which the μ and dimension-5 proton decay problems are solved simultaneously by an order four discrete R symmetry. We also comment on the higher-dimensional origin of this symmetry.

We propose a new D₄ flavor model based on SU(3)_C⊗SU(3)_L ⊗U(1)_X gauge symmetry responsible for fermion masses and mixings in which all fermion fields act only as singlets under D₄ which differs from our previous work. The neutrinos get small masses from two SU(3)_L anti-sextets and one SU(3)_L triplet which are all in singlets under D₄. If a SU(3)_L Higgs triplet, lying in under D₄, is considered as a perturbation the corresponding neutrino mass mixing matrix gets the most general form. In this case, the model can fit the most recent data on neutrino masses and mixing with nonzero θ₁₃. Our results show that the neutrino masses are naturally small. The sum of three light neutrino masses and the effective mass governing neutrinoless double beta decay are obtained that are consistent with the recent data.

We construct a new version for the 3-3-1 model based on T₇ flavor symmetry where the left-handed leptons under T₇ differ from those of our previous work while the SU(3)_C ⊗SU(3)_L ⊗U(1)_X gauge symmetry is retained. The flavor mixing patterns and mass splitting are obtained without perturbation. The realistic lepton mixing can be obtained if both the direction of breakings T₇ →Z₃ and Z₃ →{Identity} are taken place in neutrino sector. Maximal CP violation is predicted and Cabibbo–Kobayashi–Maskawa (CKM) matrix is the identity matrix at the tree-level.

We investigate the possibility of expressing the charged leptons and neutrino mass matrices as linear combinations of elements of a single finite group. Constraints imposed on the resulting mixing matrix by current data restrict the group types, but allow a nonzero value for the θ₁₃ mixing angle.

We discuss a possible solution to the strong CP problem which is based on spontaneous CP violation and discrete symmetries. At the same time we predict in a simple way the almost right-angled quark unitarity triangle angle $(\alpha \simeq 90^{\circ })$ by making the entries of the quark mass matrices either real or imaginary. To prove the viability of our strategy we present a toy flavour model for the quark sector.

We construct a renormalizable $\mathrm{\text{SU}}{(3)}_C\otimes \mathrm{\text{SU}}{(3)}_L\otimes \mathrm{\text{U}}{(1)}_X\otimes \mathrm{\text{U}}{(1)}_{{ℒ}}$ model with $Q_4$ symmetry accommodating the observed pattern of fermion masses and mixings with Dirac CP violation phase. The smallness of the active neutrino masses arises from a combination of type I and type II seesaw mechanisms. Both normal and inverted neutrino mass ordering are viable in our model in which the obtained physical observables of the lepton sector are well consistent with the global fit of neutrino oscillation data [P. F. de Salas et al., Phys. Lett. B 782, 633 (2018)] while the CKM matrix is unity at tree level and the quark masses are in good agreement with the experimental data [Particle Data Group (M. Tanabashi et al.), Phys. Rev. D 98, 030001 (2018)]. Furthermore, the model also predicts an effective Majorana neutrino mass parameter of $m_{\beta \beta }=3.38449\times 10^{-3}$ eV for normal hierarchy and $m_{\beta \beta }=4.94679\times 10^{-2}$ for inverted hierarchy which are consistent with the constraints given in [P. F. de Salas et al., Phys. Lett. B 782, 633 (2018)].

We suggest a renormalizable standard model (SM) extension based on $D_5$ symmetry which accommodates leptonic mass and mixing parameters with nonzero ${𝜃}_{13}$ and Dirac CP violating phase. Both normal and inverted neutrino mass ordering as well as the smallness of the active neutrino masses are generated at leading order through type-I seesaw mechanism in which the obtained physical parameters are well consistent with the global fit of neutrino oscillation data [P. F. de Salas et al., Phys. Lett. B 782, 633 (2018)], while the quark masses are in good agreement with the recent experimental data [Particle Data Group (M. Tanabashi et al.), Phys. Rev. D 98, 030001 (2018)]. The model also predicts an effective Majorana neutrino mass parameter of $m_{\beta \beta }=8.81123\times 10^{-2}\mathrm{\text{eV}}$ for normal hierarchy and $m_{\beta \beta }=4.90862\times 10^{-2}\mathrm{\text{eV}}$ for inverted hierarchy which are all well below the most current upper limit given [P. F. de Salas et al., Front. Astron. Space Sci. 5, 36 (2018); CUORE Collab. (C. Alduino et al.), Phys. Rev. Lett. 120, 132501 (2018)] and beyond the reach of the present $0\nu \beta \beta$ decay experiments.

We propose a $B-L$ Standard Model (SM) extension based on $\mathrm{\Delta }(27)$ symmetry in which neutrino mass orderings and the tiny neutrino masses are produced by the type-I seesaw mechanism. The obtained physical parameters are well consistent with the global fit of neutrino oscillation.¹ The model is predictive in the sense that it reproduces the experimental values of neutrino parameters. Two of the predicted parameters have little deviations from the best-fit values given in Ref. 1, however they are consistent with the other experimental results.${}^{2,3}$

Quasidegenerate binary systems of neutral mesons of the kaon type are investigated in Quantum Field Theory (QFT). General constraints cast by analyticity and discrete symmetries P, C, CP, TCP on the propagator (and on its spectral function) are deduced. Its poles are the physical masses; this unambiguously defines the propagating eigenstates. It is diagonalized and its spectrum thoroughly investigated. The role of "spurious" states, of zero norm at the poles, is emphasized, in particular for unitarity and for the realization of TCP symmetry. The K_L-K_S mass splitting triggers a tiny difference between their CP violating parameters ∊_L and ∊_S, without any violation of TCP. A constant mass matrix like used in Quantum Mechanics (QM) can only be introduced in a linear approximation to the inverse propagator, which respects its analyticity and positivity properties; it is however unable to faithfully describe all features of neutral mesons as we determine them in QFT, nor to provide any sensible parametrization of eventual effects of TCP violation. The suitable way to diagonalize the propagator makes use of a bi-orthogonal basis; it is inequivalent to a bi-unitary transformation (unless the propagator is normal, which cannot occur here). Problems linked with the existence of different "in" and "out" eigenstates are smoothed out. We study phenomenological consequences of the differences between the QFT and QM treatments; the nonvanishing of the semileptonic asymmetry δ_S - δ_L, does not signal, unlike usually claimed, TCP violation, while A_TCP keeps vanishing when TCP is realized. We provide expressions invariant by the rephasing of K⁰ and .

Basing on the general photon eigenstate and the anomaly cancellation, we have naturally explained the electric charge quantization in two models based on the SU(3)_C ⊗ SU(3)_L ⊗ U(1)_X gauge group, namely in the minimal model and in the model with right-handed neutrinos. In addition, we have shown that the electric charges of the proton and of the electron are opposite; and the same happens with the neutron and the neutrino. We argue that the electric charge quantization in these models is closely related with the generation number problem. In fact, both problems are properly solved as the direct consequences of the fermion content under the anomaly free conditions.

We give an introductory review of quantum physics on the noncommutative space–time called the Groenewold–Moyal plane. Basic ideas like star products, twisted statistics, second quantized fields and discrete symmetries are discussed. We also outline some of the recent developments in these fields and mention where one can search for experimental signals.

The basic motivation of the KLOE-2 experiment is the test of fundamental symmetries and Quantum Mechanics coherence of the neutral kaon system, and the search for phenomena beyond the Standard Model in the hadronic and leptonic decays of ground-state mesons. Perspectives for experimentation by means of the KLOE-2 apparatus equipped with the inner tracker, new scintillation calorimeters, and the γγ taggers at the DAΦNE electron-positron collider upgraded in luminosity and energy are presented.

The technique for representing spinors and the definition of the discrete symmetries is used to illustrate on a toy model properties of massless and massive spinors states, in the first and the second quantized picture. Since in this toy model the number of the starting massless representations is well-defined as well as the origin of masses and charges in d = (3+1) space, this contribution might help to clarify the problem about Dirac, Weyl and Majorana kinds of representations in physically more interesting cases.

The 3-3-1 model proposed in 2011 based on discrete symmetry $S_4$ responsible for the neutrino and quark masses is updated, in which the nonzero ${\theta }_{13}$ is focused. Neutrino masses and mixings are consistent with the most recent data on neutrino oscillations without perturbation. The new feature is adding a new $SU{(3)}_L$ anti-sextet lying in doublet under $S_4$ which can result the nonzero ${\theta }_{13}$ without perturbation, and consequently, the number of Higgs multiplets required is less than those of other models based on non-Abelian discrete symmetries and the 3-3-1 models. The exact tribimaximal form obtained with the breaking $S_4\to Z_3$ in charged lepton sector and $S_4\to {𝒦}$ in neutrino sector. If both breakings $S_4\to {𝒦}$ and ${𝒦}\to Z_2$ are taken place in neutrino sector, the realistic neutrino spectrum is obtained without perturbation. The upper bound on neutrino mass and the effective mass governing neutrinoless double beta decay at the tree level are presented. The model predicts the Dirac CP violation phase $\delta =292.45°$ in the normal spectrum (with ${\theta }_{23}\ne \frac{\pi }{4}$) and $\delta =303.14°$ in the inverted spectrum.

We propose a 3-3-1 model with neutral fermions based on $A_4$ flavor symmetry responsible for fermion masses and mixings with nonzero ${\theta }_{13}$. To get realistic neutrino mixing, we just add a new $\mathrm{\text{SU}}{(3)}_L$ triplet being in $\underline{3}$ under $A_4$. The neutrinos get small masses from two $\mathrm{\text{SU}}{(3)}_L$ antisextets and one $\mathrm{\text{SU}}{(3)}_L$ triplet. The model can fit the present data on neutrino masses and mixing as well as the effective mass governing neutrinoless double beta decay. Our results show that the neutrino masses are naturally small and a little deviation from the tri-bimaximal neutrino mixing form can be realized. The Dirac CP violation phase $\delta$ is predicted to either $5.41^{\circ }$ or $354.59^{\circ }$ with ${\theta }_{23}\ne \frac{\pi }{4}$.

We study a neutrino mass model based on $S_4$ flavor symmetry which accommodates lepton mass, mixing with nonzero ${\theta }_{13}$ and CP violation phase. The spontaneous symmetry breaking in the model is imposed to obtain the realistic neutrino mass and mixing pattern at the tree-level with renormalizable interactions. Indeed, the neutrinos get small masses from one $SU{(2)}_L$ doublet and two $SU{(2)}_L$ singlets in which one being in $\underline{2}$ and the two others in $\underline{3}$ under $S_4$ with both the breakings $S_4\to S_3$ and $S_4\to Z_3$ are taken place in charged lepton sector and $S_4\to {𝒦}$ in neutrino sector. The model also gives a remarkable prediction of Dirac CP violation ${\delta }_{\mathrm{\text{CP}}}=\frac{\pi }{2}$ or $-\frac{\pi }{2}$ in both the normal and inverted spectrum which is still missing in the neutrino mixing matrix. The relation between lepton mixing angles is also represented.

The KLOE detector at the DA$\mathrm{\Phi }$NE $\varphi$-factory has been operating in two periods from 2001–2006 and from 2014–2018 collecting a large sample of $\varphi$-meson decays. This allowed to perform precision measurements and studies of fundamental symmetries, and searches of New Physics phenomena. In this overview, the results of KLOE and KLOE-2 Collaborations are presented. The most recent results from the KLOE experiment are discussed, covering: the measurement of the running fine-structure constant ${\alpha }_{\mathrm{\text{em}}}$, the Dalitz plot measurement of $\eta \to {\pi }^{+}{\pi }^{-}{\pi }^0$, the search of a $U$ boson, tests of discrete symmetries and quantum decoherence.

We argue that quaternions form a natural language for the description of quantum-mechanical wave functions with spin. We use the quaternionic spinor formalism which is in one-to-one correspondence with the usual spinor language. No unphysical degrees of freedom are admitted, in contrast to the majority of literature on quaternions. In this paper, we first build a Dirac Lagrangian in the quaternionic form, derive the Dirac equation and take the nonrelativistic limit to find the Schrödinger’s equation. We show that the quaternionic formalism is a natural choice to start with, while in the transition to the noninteracting nonrelativistic limit, the quaternionic description effectively reduces to the regular complex wave function language. We provide an easy-to-use grammar for switching between the ordinary spinor language and the description in terms of quaternions. As an illustration of the broader range of the formalism, we also derive the Maxwell’s equation from the quaternionic Lagrangian of Quantum Electrodynamics. In order to derive the equations of motion, we develop the variational calculus appropriate for this formalism.

We investigate an alternative CPT-odd Lorentz-breaking QED which includes the Carroll–Field–Jackiw (CFJ) term of the Standard Model Extension (SME), writing the gauge sector in the action in a Palatini-like form, in which the vectorial field and the field-strength tensor are treated as independent entities. Interestingly, this naturally induces a Lorentz-violating mass term in the classical action. We study physical consistency aspects of the model both at classical and quantum levels.