The discrete family symmetries as the possible solution to the flavour problem

In order to explain the fermions’ masses and mixing parameters appearing in the lepton sector of the Standard Model, one proposes the extension of its symmetry. A discrete, non-Abelian subgroup of U(3) is added to the gauge group SU(3) _C × SU(2) _L × U(1) _Y . Apart from that, one assumes the existence of one extra Higgs doublet. This article focuses mainly on the mathematical theorems and computational techniques which brought us to the results.     

Rare kaon decay $$K^ + \to \pi ^ + \nu \bar \nu $$ in S U(3)C ⊗ S U(3)L ⊗ U(1)N models

The rare kaon decay \(K^ + \to \pi ^ + \nu \bar \nu \) is considered in the framework of models based on the SU(3) _C ? SU(3) _L ? U(1) _N (3-3-1) gauge group. In the 3-3-1 model with right-handed neutrinos, the lower bound of the Z’ mass is derived at 3 TeV, and that in the minimal version, at 1.7 TeV.     

Twin-unified <Emphasis Type="Italic">SU</Emphasis>(5) × <Emphasis Type="Italic">SU</Emphasis>(5)′ GUT and phenomenology

In this article, after a short introduction, grand unified SU(5)×SU(5)^′ model augmented by D₂ parity has been discussed. The latter turns out to be important for phenomenology. Specific pattern of the GUT symmetry breaking causes new strong dynamics at low energies. Consequently, the Standard Model leptons, along with right-handed /sterile neutrinos, come out as composite states. Issues of the gauge coupling unification, generation of the charged fermion and neutrino masses will be presented. Also, various phenomenological implications and constraints will be discussed.     

A modification of Einstein–Schrödinger theory that contains Einstein–Maxwell–Yang–Mills theory

The Lambda-renormalized Einstein–Schrödinger theory is a modification of the original Einstein–Schrödinger theory in which a cosmological constant term is added to the Lagrangian, and it has been shown to closely approximate Einstein– Maxwell theory. Here we generalize this theory to non-Abelian fields by letting the fields be composed of d × d Hermitian matrices. The resulting theory incorporates the U(1) and SU(d) gauge terms of Einstein–Maxwell–Yang–Mills theory, and is invariant under U(1) and SU(d) gauge transformations. The special case where symmetric fields are multiples of the identity matrix closely approximates Einstein–Maxwell–Yang–Mills theory in that the extra terms in the field equations are < 10^?13 of the usual terms for worst-case fields accessible to measurement. The theory contains a symmetric metric and Hermitian vector potential, and is easily coupled to the additional fields of Weinberg–Salam theory or flipped SU(5) GUT theory. We also consider the case where symmetric fields have small traceless parts, and show how this suggests a possible dark matter candidate.     

Dynamical generation of flavour

We propose the generation of Standard Model fermion hierarchy by the extension of renormalizable SO(10) GUT with O(N_g) family gauge symmetry. In this scenario, Higgs representations of SO(10) also carry family indices and are called Yukawons. Vacuum expectation values of these Yukawon fields break GUT and family symmetry and generate MSSM Yukawa couplings dynamically. We have demonstrated this idea using \({\mathbf {10}}\oplus {\mathbf {210}} \oplus {\mathbf {126}} \oplus {\overline {\mathbf {126}}}\) Higgs irrep, ignoring the contribution of 120-plet which is, however, required for complete fitting of fermion mass-mixing data. The effective MSSM matter fermion couplings to the light Higgs pair are determined by the null eigenvectors of the MSSM-type Higgs doublet superfield mass matrix \(\mathcal {H}\). A consistency condition on the doublet ([1,2,±1]) mass matrix (\(\text {Det}(\mathcal {H})=\) 0) is required to keep one pair of Higgs doublets light in the effective MSSM. We show that the Yukawa structure generated by null eigenvectors of \(\mathcal {H}\) are of generic kind required by the MSSM. A hidden sector with a pair of (S_ab; ?_ab) fields breaks supersymmetry and facilitates \(D_{O(N_{g})}\hspace *{-1pt}=\) 0. SUSY breaking is communicated via supergravity. In this scenario, matter fermion Yukawa couplings are reduced from 15 to just 3 parameters in MSGUT with three generations.     

The minimal axion minimal linear $$\sigma $$ model

The minimal SO(5) / SO(4) linear \(\sigma \) model is extended including an additional complex scalar field, singlet under the global SO(5) and the Standard Model gauge symmetries. The presence of this scalar field creates the conditions to generate an axion à la KSVZ, providing a solution to the strong CP problem, or an axion-like-particle. Different choices for the PQ charges are possible and lead to physically distinct Lagrangians. The internal consistency of each model necessarily requires the study of the scalar potential describing the \(SO(5)\rightarrow SO(4)\), electroweak and PQ symmetry breaking. A single minimal scenario is identified and the associated scalar potential is minimised including counterterms needed to ensure one-loop renormalizability. In the allowed parameter space, phenomenological features of the scalar degrees of freedom, of the exotic fermions and of the axion are illustrated. Two distinct possibilities for the axion arise: either it is a QCD axion with an associated scale larger than \(\sim 10^{5}\) TeV and therefore falling in the category of the invisible axions; or it is a more massive axion-like-particle, such as a 1 GeV axion with an associated scale of \(\sim 200\) TeV, that may show up in collider searches.     

QED with vector and axial vector types of interaction and dynamical generation of particle masses

We consider a model of electrodynamics with two types of interaction, the vector \((e\bar \psi (\gamma ^\mu A_\mu )\psi )\) and axial vector \((e_A \bar \psi (\gamma ^\mu \gamma ^5 B_\mu )\psi )\) interactions, i.e., with two types of vector gauge fields, which corresponds to the local nature of the complete massless-fermion symmetry group U(1) ? U _A (1). We present a phenomenological model with spontaneous symmetry breaking through which the fermion and the axial vector field B_μ acquire masses. Based on an approximate solution of the Dyson equation for the fermion mass operator, we demonstrate the phenomenon of dynamical chiral symmetry breaking when the field B_μ has mass. We show the possibility of eliminating the axial anomalies in the model under consideration when introducing other types of fermions (quarks) within the standard-model fermion generations. We consider the polarization operator for the field B_μ and the procedure for removing divergences when calculating it. We demonstrate the emergence of a mass pole in the propagator of the particles that correspond to the field B_03BC when chiral symmetry is broken and consider the problems of regularizing closed fermion loops with axial vector vertices in connection with chiral symmetry breaking.     

Z–Z' mixing effects in W boson pair production processes at hadron and lepton high-energy colliders

Potential possibilities to detect the effects of Z–Z' mixing in the W-pair production process in proton-proton and electron–positron collisions at the Large Hadron Collider (LHC) and International Linear Collider (ILC) have been studied. It has been established that the processes of W boson pair production are very sensitive to the angle of Z–Z' mixing and their measurements in current and future experiments will make it possible to improve modern restrictions on the angle of Z–Z' mixing in the models with extended gauge sector. At a nominal energy of 14 TeV and an integral luminosity of 100 fb^–1, the LHC collider can offer much more precise information on the parameter of Z–Z' mixing and the mass M ₂ than can be obtained using the ILC leptonic collider (0.5 TeV).     

Massive hyper-Kähler sigma models and BPS domain walls

With the non-Abelian hyper-Kähler quotient by U(M) and SU(M) gauge groups, we give the massive hyper-Kähler sigma models that are not toric in the N=1 superfield formalism. The U(M) quotient gives N!/[M!(N-M)!] (N is the number of flavors) discrete vacua that may allow various types of domain walls, whereas the SU(M) quotient gives no discrete vacua. We derive a BPS domain-wall solution in the case of N = 2 and M = 1 in the U(M) quotient model.     

The <Emphasis Type="Italic">HZZ</Emphasis>′ Coupling and the Higgs-Strahlung Production <Emphasis Type="Italic">pp</Emphasis> → <Emphasis Type="Italic">ZH</Emphasis> at the LHC

The Higgs-strahlung production process pp → Z′ → ZH is an important process for studying the HZZ′ interaction. We take the B ? L model and the nonuniversal S U(2)₁ × S U(2)₂ × U(1) _Y model as two examples and investigate their correction effects on ZH production at the LHC. Our numerical results show that, considering constraints on these two new physics models, the contributions of the B ? L model to the ZH production cross section are very small, while the S U(1)₁ × S U(2)₂ × U(1) _Y model can generate significant contributions.     

Investigation of the process <Emphasis Type="Italic">J/ψ</Emphasis> → <Emphasis Type="Italic">e</Emphasis><Superscript>+</Superscript><Emphasis Type="Italic">e</Emphasis><Superscript>−</Superscript> with the KEDR detector

The product of the electron width of the J/ψ meson and the probability for its decay to an electron-positron pair was measured by using data from the KEDR experiment at the VEPP-4M electron-positron collider. The result was Γ _ee × Γ _ee /Γ = 0.3392 ± 0.0068(stat.) ± 0.0063(syst.) keV.     

Interplay between grand unification and supersymmetry in <Emphasis Type="BoldItalic">SU</Emphasis>(5) and <Emphasis Type="BoldItalic">E</Emphasis> <Subscript> <Emphasis Type="Bold">6</Emphasis> </Subscript>

Some aspects of minimal supersymmetric renormalizable grand unified theories are reviewed here. These include some constraints on the model parameters from the Higgs and light fermion masses in SU(5), and the issues of symmetry breaking, doublet–triplet splitting and fermion masses in E₆.     

Effect of the neutrino magnetic moment on the properties of the muon

The effect of the neutrino dipole magnetic moment on the properties of the muon is investigated within the standard model of electroweak interactions and a model based on the SU(2) _L × SU(2) _R × U(1) _B-L gauge group (left-right model). In the case of the Dirac neutrino, muon decay through the channel µ^? → e ^?γ is studied with allowance for the neutrino dipole magnetic moment. It is shown that, both in the standard model supplemented with an SU(2) _L right-handed neutrino singlet and in the standard model featuring two doublets of Higgs fields, radiative muon decay is unobservable. In the left-right model, the contributions of diagrams associated with the neutrino dipole magnetic moment become significant only in the case of a mutual compensation of the contributions of diagrams involving the electromagnetic vertices of charged gauge bosons and singly charged Higgs bosons. At specific values of the parameters of the left-right model, one can then obtain an experimental upper limit on the branching fraction of this reaction. The contributions of the neutrino dipole magnetic moment to the muon anomalous magnetic moment are found for the Dirac and the Majorana neutrino. It is established that, both in the standard model and in the left-right model, values of the neutrino anomalous magnetic moment that are required for explaining the (g ? 2)_µ anomaly are in excess of the theoretical predictions for this moment.     

Winkelkorrelationsmessungen an >30y Holmium 166 und Bestimmung desg R -Faktors des 4+-Rotationsniveaus von Erbium 166

The spins of several excited states of Er¹⁶⁶ have been investigated byγγ-angular correlation measurements. The spin sequence 0+, 2+, 4+, 6+ for the ground state rotational band was presumed to be correct. Unique assignments were derived for the states of 1076 keV, 1377 keV and 1785 keV asI=5, 7 and 6 respectively. These results are in agreement with the spins proposed byGallagher jr. andSoloviev. The multipolarities of theγ-transitions of 408 keV, 709 keV, 811 keV and 831 keV were derived as 95%E1+(5±1)%M2, 99·6%E1+(0·4±0·5)%M2, 99·1%E2+(0·9±0·3)%M1, and 96·1%E2+(3·9±1)%M1 respectively. The unusual mixing ratios of the transitions of 811 keV and 831 keV can be understood as a consequence of theK-selection rule. Eachγ-transition from the 1785 keV state should be stronglyK-forbidden and one expects a half-life ofT _1/2≈3·10^?9s. A measurement of the time spectrum of the coincidences between theβ-radiation and the high energyγ-lines gave however:T _1/2(1785 keV state)≦3·10^?10s. The rotation of the angular correlation between the 184 keV line and theγ-group at 820 keV has been measured in an external magnetic field of 53000 gauss as:ω·τ(4+)=0·083±0·006. This value contains small corrections for an additional rotation of the angular correlation of the 831 keV–184 keV triple cascade in the 6+state and for a small attenuation by internal fields. WithT _1/2(4+state)=1·23·10^?10s, andβ=7·08 one gets for theg-factorg _R=+0·266±0·024 in good agreement with recent results for the 2+ state.     

Determination of absoluteK-internal conversion coefficients of some transitions in Ce140 by the internal-external conversion method

The internalK-conversion coefficients of the 331, 431, 815 and 933 keV transitions following the decay of La¹⁴⁰ have been determined absolutely by the method of comparing internal and external conversion lines measured in a double — focusing beta — ray spectrometers. TheK-internal conversion coefficients of the 4+→2+ 487 keV transition in Ce¹⁴⁰ was used to normalize relativeK-electron and gamma-ray intensities for these transitions. The results obtained are:α _K (331)=0.04432±0.00471,α _K (431)=0.28110±0.02913,α _K (815)=0.00396±0.00043,α _K (933)=0.00282±0.00031. Multipolarity assignments based on these values are suggested. The 815 keV transition is found to be pure magnetic dipole character in good agreement with the theoretical values calculated bySliv andBand. The 331 and 933 keV transitions are proved to have magnetic dipole character withE2/M1 equal 0.2852±0.0143 and 0.1750±0.0088 respectively. The 431 keV transition was found to have magnetic octupole character. The results obtained are most consistent with the assignment 2+, 4+, 2+, 3+ and 1+ for the 1597, 2084, 2184, 2410 and 2515 keV levels respectively.     

Non-Fermi liquid theory of quantum Hall effects

Within the Grassmannian U(2N)/U(N) × U(N) nonlinear σ-model representation of localization, one can study the low-energy dynamics of both a free and interacting electron gas. We study the crossover between these two fundamentally different physical problems. We show how the topological arguments for the exact quantization of the Hall conductance are extended to include the Coulomb interaction problem. We discuss dynamical scaling and make contact with the theory of variable range hopping.     

Niederenergetische Gammalinien vom Neutroneneinfang in Lu 175 und Lu 176

The low energy gamma-rays from neutron-capture in Lu 175 and Lu 176 have been investigated by means of the bent crystal-spectrometer at the DR-3-reactor at Risø. From the transitions in Lu 177 3 rotational bands have been determined. The levels of the (404)K=7/2⁺ groundstate rotational band are: 121,62 keV (I=9/2), 268,79keV (I=11/2), 440,66 keV (I=13/2), 636,22 keV (I=15/2), 854,34 keV (I=17/2). The level-sequence of the (514)K=9/2^?-band is: 150,39 keV (I=9/2), 288,99 keV (I=11/2), 451,49 keV (I=13/2), 637,05 keV (I=15/2) and 844,88 keV (I=17/2). At 457,92 keV is the basis for the (402)K=5/2⁺-band the higher levels of which are 552,05 keV (I=7/2), 671,89 keV (I=9/2), 816,63 keV (I=11/2), 985,23 keV (I=13/2), 1176,73keV (I=15/2) and probably 1389,5 keV (I=17/2). The energies of the levels apart from the 1389 keV-level have an accuracy of 7×10^?5. The energy differences between the 3 bands agree very well with the values expected from the Bohr-Mottelson-formulaE=A·I(I+1)+B·I ²(I+1)². The calculated branching-ratios within the 3 bands are in fairly good agreement with the experimental values. Theg _K -factors have been determined for 2 bands: It was found that for the (514)-bandg _K =1,16±0,04 and for the (402)-bandg _K =1,33±0,07.     

D-brane SM-like and scalar dark matter in type IIA superstring theory

In light of the present LHC Run II at √s = 13 TeV, a SM-like string model is studied. Specifically, a singlet S scalar-extended SM given in terms of four stacks of intersecting D6-branes in a type IIA superstring compactification producing a large gauge symmetry is examined. The scales involved are dealt with. According to the dark matter relic density, the mass of the scalar dark matter beyond the SM m _S ? 10³ GeV and the corresponding Higgs portal couplings λ _SH ? 10^–8 have been obtained.     

Finite Hamiltonian systems: Linear transformations and aberrations

Finite Hamiltonian systems contain operators of position, momentum, and energy, having a finite number N of equally-spaced eigenvalues. Such systems are under the æis of the algebra su(2), and their phase space is a sphere. Rigid motions of this phase space form the group SU(2); overall phases complete this to U(2). But since N-point states can be subject to U(N) ?U(2) transformations, the rest of the generators will provide all N ² unitary transformations of the states, which appear as nonlinear transformations—aberrations—of the system phase space. They are built through the “finite quantization” of a classical optical system.