Modern Physics Letters A

The in-medium physics of heavy quarkonium is an ideal proving ground for our ability to connect knowledge about the fundamental laws of physics to phenomenological predictions. One possible route to take is to attempt a description of heavy quark bound states at finite temperature through a Schrödinger equation with an instantaneous potential. Here we review recent progress in devising a comprehensive approach to define such a potential from first principles QCD and extract its, in general complex, values from non-perturbative lattice QCD simulations. Based on the theory of open quantum systems we will show how to interpret the role of the imaginary part in terms of spatial decoherence by introducing the concept of a stochastic potential. Shortcomings as well as possible paths for improvement are discussed.

The recently observed lepton mixing angle θ₁₃ of the MNS mixing matrix is well incorporated in a universal mixing hypothesis between quark and lepton sectors. This hypothesis asserts that, in the charged lepton diagonal base, all other mass matrices for up- and down-type quarks and light neutrinos are diagonalized by the same unitary matrix except for the phase elements. It is expressed as V_CKM = U_MNS(δ′)^†PU_MNS(δ) for quark mixing matrix V_CKM and lepton mixing matrix U_MNS(δ) in the phenomenological level. Here P is a diagonal phase mass matrix. δ′ is a slightly different phase parameter from the Dirac CP-violating phase δ = 1.1π (best fit) in the MNS lepton mixing matrix.

Neutrinoless double beta decay has been the subject of intensive theoretical work as it represents the only practical approach to discovering whether neutrinos are Majorana particles or not, and whether lepton number is a conserved quantum number. Available calculations of matrix elements and phase-space factors are reviewed from the perspective of a future large-scale experimental search for 0νββ decay. Somewhat unexpectedly, a uniform inverse correlation between phase-space and the square of the nuclear matrix element emerges. As a consequence, no isotope is either favored or disfavored; all have qualitatively the same decay rate per unit mass for any given value of the Majorana mass.

We show the way of dark matter and dark energy presentation via ansatzs on the kinetic energies of the fields in the two-component chiral cosmological model (CCM). To connect a kinetic interaction of dark matter and dark energy with observational data the reconstruction procedure for the chiral metric component h₂₂ and the potential of (self-)interaction V has been developed. The reconstruction of h₂₂ and V for the early and later inflation have been performed. The proposed model is confronted to ΛCDM model as well.

We present a class of extensions of the MSSM characterized by a fully chiral field content (no μ-terms) and no baryon or lepton number violating term in the superpotential due to an extra U′(1) gauge symmetry. The minimal model consists of the usual matter sector with family dependent U′(1) charges, six Higgs weak doublets, and three singlets required to give masses to the Higgsinos and cancel anomalies. We discuss its main features such as the tree level mass spectrum and the constraints on flavor changing processes.

We propose an alternative formulation of the supersymmetric quantum mechanics and Euclidean Dirac and Dirac–Yang–Mills (DYM) operators in terms of complexified quaternions. 4×4 matrix representations of the complexified quaternions are used to express the Euclidean–Dirac operator and Yang–Mills gauge field.

We first review the spontaneous Lorentz symmetry breaking in the presence of massless gauge fields and infraparticles. This result was obtained long time ago in the context of rigorous quantum field theory (QFT) by Fröhlich, Morchio and Strocchi [Ann. Phys.119, 241 (1979); Phys. Lett. B89, 61 (1979)] and reformulated by Balachandran and Vaidya (arXiv:1302.3406) using the notion of superselection sectors and direction-dependent test functions at spatial infinity for gauge transformations. Inspired by these developments and under the assumption that the spectrum of the electric charge is quantized (in units of a fundamental charge e), we construct a family of vertex operators which create winding number k, electrically charged Abelian vortices from the vacuum (zero winding number sector) and/or shift the winding number by k units. Vortices created by this vertex operator may be viewed both as a source and as a probe for inducing and detecting the breaking of spontaneous Lorentz symmetry.

We find that for rotating vortices, the vertex operator at level k shifts the angular momentum of the vortex by , where is the electric charge of the quantum state of the vortex and q is the charge of the vortex scalar field under the U(1) gauge field. We also show that, for charged-particle-vortex composites, angular momentum eigenvalues shift by being the electric charge of the charged-particle-vortex composite. This leads to the result that for half-odd integral and for odd k, our vertex operators flip the statistics of charged-particle-vortex composites from bosons to fermions and vice versa. For fractional values of , application of vertex operator on charged-particle-vortex composite leads in general to composites with anyonic statistics.