International Journal of Modern Physics A

We review results of recent studies of transitions between bottomonium states obtained from analysis of the large $e^{+}{e}^{-}$ data sample recorded by the Belle detector at various $\mathrm{{\rm Y}}$-resonances and energy scan data in the center-of-mass energy range from $\sqrt{s}=10.63$ GeV to 11.02 GeV.

We discuss the possibility that inflation is driven by supersymmetry breaking with the superpartner of the goldstino (sgoldstino) playing the role of the inflaton. Imposing an R-symmetry allows to satisfy easily the slow-roll conditions, avoiding the so-called $\eta$-problem, and leads to an interesting class of small field inflation models, characterized by an inflationary plateau around the maximum of the scalar potential near the origin, where R-symmetry is restored with the inflaton rolling down to a minimum describing the present phase of the Universe. Inflation can be driven by either an $F$- or a $D$-term, while the minimum has a positive tuneable vacuum energy. The models agree with cosmological observations and in the simplest case predict a rather small tensor-to-scalar ratio of primordial perturbations.

While the QCD Lagrangian as the whole is only chirally symmetric, its electric part has larger chiral-spin $SU{(2)}_{\mathrm{\text{CS}}}$ and $SU(2N_F)$ symmetries. This allows separation of the electric and magnetic interactions in a given reference frame. Artificial truncation of the near-zero modes of the Dirac operator results in the emergence of the $SU{(2)}_{\mathrm{\text{CS}}}$ and $SU(2N_F)$ symmetries in hadron spectrum. This implies that while the confining electric interaction is distributed among all modes of the Dirac operator, the magnetic interaction is located at least predominantly in the near-zero modes. Given this observation one could anticipate that above the pseudocritical temperature, where the near-zero modes of the Dirac operator are suppressed, QCD is $SU{(2)}_{\mathrm{\text{CS}}}$ and $SU(2N_F)$ symmetric, which means absence of deconfinement in this regime. Solution of the $N_F=2$ QCD on the lattice with a chirally symmetric Dirac operator reveals that indeed in the interval $Tc-3Tc$ QCD is approximately $SU{(2)}_{\mathrm{\text{CS}}}$ and $SU(2N_F)$ symmetric which implies that degrees of freedom are chirally symmetric quarks bound by the chromoelectric field into color-singlet objects without the chromomagnetic effects. This regime is referred to as a Stringy Fluid. At larger temperatures this emergent symmetry smoothly disappears and QCD approaches the Quark–Gluon Plasma regime with quasifree quarks. The Hadron Gas, the Stringy Fluid and the Quark–Gluon Plasma differ by symmetries, degrees of freedom and properties.

Landau gauge longitudinal and transverse gluon propagators are studied in lattice QCD with gauge group $SU(2)$ at varying temperature and quark density. In particular, it is found that the longitudinal propagator decreases with increasing quark chemical potential at all temperatures under study, whereas the transverse propagator increases with increasing quark chemical potential at $T<200$ MeV and does not depend on it at higher temperatures. The relative strength of chromoelectric and chromomagnetic interactions is also discussed.

We discuss application of Wigner–Weyl formalism to the lattice models of condensed matter physics and relativistic quantum field theory. For the noninteracting models our technique relates Wigner transformation of the fermionic Green’s function with the Weyl symbol $Q_W$ of lattice Dirac operator. We take as an example of the model defined on rectangular lattice the model of Wilson fermions. It represents the regularization of relativistic quantum field theory and, in addition, describes qualitatively certain topological materials in condensed matter physics. In this model we derive expression for $Q_W$ in the presence of the most general case of external $U(1)$ gauge field. Next, we solve the Groenewold equation to all orders in powers of the derivatives of $Q_W$.

We establish topological nature of Hall conductivity of graphene and other ${\mathbb{Z}}_2$ crystals in 2D and 3D in the presence of inhomogeneous perturbations. To this end the lattice Weyl–Wigner formalism is employed. The nonuniform mechanical stress is considered, along with the spatially varying magnetic field. The relation of the obtained topological invariant to level counting is clarified.

When supersymmetry is spontaneously broken at the tree level, the spectrum of the heterotic string compactified on orbifolds of tori contains an infinite number of potentially tachyonic modes. We show that this implies instabilities of Minkowski space–time, when the scale of supersymmetry breaking is of the order of the string scale. We derive the phase space structure of vacua in the case where the tachyonic spectrum contains a mode with trivial momenta and winding numbers along the internal directions not involved in the supersymmetry breaking.

In this work, we study a warped five-dimensional (5D) model with ultraviolet (UV) and infrared (IR) branes, that solves the hierarchy problem with a fundamental 5D Planck scale $M$, and curvature parameter $k$, of the order of the 4D Planck mass $M_{\mathrm{\text{Pl}}}\equiv 2.4\times 10^{15}$ TeV. The model exhibits a continuum of Kaluza–Klein (KK) modes with different mass gaps, at the TeV scale, for all fields. We have computed Green’s functions and spectral densities, and shown how the presence of a continuum KK spectrum can produce an enhancement in the cross-section of some Standard Model processes. The metric is linear near the IR, in conformal coordinates, as in the linear dilaton (LD) and 5D clockwork models, for which $M\sim$ TeV. We also analyze a pure (continuum) LD scenario, solving the hierarchy problem with more conventional fundamental $M$ and $k$ scales of the order of $M_{\mathrm{\text{Pl}}}$, and a continuum spectrum.

Hubbard-type models on the hexagonal lattice are of great interest, as they provide realistic descriptions of graphene and other related materials. Hybrid Monte Carlo simulations offer a first-principles approach to study their phase structure. Here, we review the present status of our work in this direction.

Topological insulators are materials where current does not flow through the bulk, but along the boundaries, only. They are of particular practical importance, since it is considerably more difficult, by “conventional” means, to affect their transport properties, than for the case of conventional materials. They are, thus, particularly robust to perturbations. One way to accomplish such changes is by engineering defects. The defects that have been the most studied are domain walls; however flux compactifications can also work. We recall the domain wall construction and compare it to the construction from flux compactification. A particular way of engineering the presence of such defects is by introducing anisotropic couplings for the gauge fields. In this case, a new phase appears, where matter is confined along layers and local degrees of freedom cannot propagate through the bulk. It is also possible to take into account the “backreaction” of the dynamics of the gauge fields on the defects and find that a new phase, the layered phase, where, while transport of local degrees of freedom is confined to surfaces, the topological properties can propagate through the bulk, constituting an example of anomaly flow. The anisotropy itself can be understood as emerging from a particular Maxwell-dilaton coupling.

We present new results on the thermal production yield of a hypothetical state made of six quarks $uuddss$ assuming its production in heavy-ion collisions at the CERN Large Hadron Collider (LHC). A state with this quark content and mass low enough to be stable against decay in timescales of the order of the age of the Universe has been hypothesized by one of us (G. Farrar) and has been discussed as a possible dark matter candidate. In this work, we address for the first time the thermal production rate that can be expected for this state in heavy-ion collisions at colliders. For this estimate we use a thermal model which has been shown to describe accurately the production of hadrons and nuclei in heavy-ion collisions at LHC energy. This estimate is of great relevance for sexaquark searches at colliders as well as for its consideration as a dark matter candidate and for the composition of neutron stars.