International Journal of Modern Physics A

Classical results and recent developments on the theoretical description of elementary particles with “continuous” spin are reviewed. At free level, these fields are described by unitary irreducible representations of the isometry group (either Poincaré or anti-de Sitter group) with an infinite number of physical degrees of freedom per space–time point. Their basic group-theoretical and field-theoretical descriptions are reviewed in some details. We mention a list of open issues which are crucial to address for assessing their physical status and potential relevance.

We consider the model of modified gravity with dynamical torsion. This model was previously found to have promising stability properties about various backgrounds. Here, we study the stability of linear perturbations about the self-accelerating solution. We apply the (3+1)-decomposition and consider the scalar sector of perturbations. We find that the number of degrees of freedom is equal to 2, which is the same as in Minkowski background. However, there is at least one instability in the scalar sector, if the value of background torsion is large enough. This does not rule out the possibility of stable self-acceleration with torsion of the order of the effective cosmological constant.

One of the interesting portals linking a dark sector and the Standard Model (SM) is the kinetic mixing between the SM $U{(1)}_Y$ field with a new dark photon $A^{\prime }$ from a $U{(1)}_{A^{\prime }}$ gauge interaction. Stringent limits have been obtained for the kinetic mixing parameter $𝜖$ through various processes. In this work, we study the possibility of searching for a dark photon interaction at a circular $e^{+}{e}^{-}$ collider through the process $e^{+}{e}^{-}\to \gamma A^{\prime }\to \gamma {\mu }^{+}{\mu }^{-}$. We find that the constraint on ${𝜖}^2$ for dark photon mass in the few tens of GeV range, assuming that the ${\mu }^{+}{\mu }^{-}$ invariant mass can be measured to an accuracy of 0.5% $m_{A^{\prime }}$, can be better than $3\times 10^{-6}$ for the proposed CEPC with a 10-year running at $3\sigma$ (statistic) level, and better than $2\times 10^{-6}$ for FCC-ee with even just one-year running at $\sqrt{s}=240\mathrm{\text{GeV}}$, better than the LHCb, ATLAS, CMS experiments and other facilities can do in a similar dark photon mass range. For FCC-ee, running at $\sqrt{s}=160\mathrm{\text{GeV}}$, the constraint can be even better.

Under the assumption of Abelian dominance in QCD, we have shown that chiral condensate is locally present around each QCD monopole. The essence is that either charge or chirality of a quark is not conserved, when the low energy massless quark collides with QCD monopole. In reality, the charge is conserved so that the chirality is not conserved. Reviewing the presence of the local chiral condensate, we show by using chiral anomaly that chiral nonsymmetric quark pair production takes place when a color charge is putted in a vacuum with monopole condensation, while chiral symmetric pair production takes place in a vacuum with no monopole condensation. Our results strongly indicate that the chiral symmetry is broken by the monopole condensation.

We investigate the scattering of a relativistic scalar quantum particle induced by a scattering-like potential that arises from the effects of the violation of the Lorentz symmetry. We then obtain the scattering phase shift caused by the influence of such a potential and use it to calculate the exact expressions for the scattering amplitude as well as for the total scattering cross-section through the optical theorem. In addition, we estimate an upper bound for the Lorentz symmetry violation parameters.

We discuss the modified top quark condensation model proposed in Ref. 54. This construction was inspired by the top-seesaw scenario, in which the extra heavy fermion $\chi$ that may be paired with the top quark is added. Besides, this model incorporates the ideas of the little Higgs scenario, in which the 125 GeV scalar particle appears as a pseudo-Goldstone boson. This model admits (in addition to the 125 GeV scalar boson $H$) the heavier scalar excitation $H^{\prime }$. We consider the region of parameters, where its mass is $M_{H^{\prime }}\sim 1\mathrm{\text{TeV}}$, the width of $H^{\prime }$ is ${\mathrm{\Gamma }}_{H^{\prime }}\sim 0.3M_{H^{\prime }}$, while the mass of the heavy fermion is $m_{\chi }\sim 1\mathrm{\text{TeV}}$. We find that in this model the value of the cross-section ${\sigma }_{pp\to H^{\prime }+X\to \gamma +\gamma +X}$ for $\sqrt{s}=13\mathrm{\text{TeV}}$ is essentially smaller than the present experimental upper bound. Besides, we find that for the chosen values of parameters there should exist the CP-even scalar boson with mass $\approx 2m_{\chi }$ and very small width. In addition, the model predicts the existence of the extra neutral CP-even scalar boson and the charged scalar boson with masses of the order of 1 TeV.

An infinite class of $4d$ ${𝒩}=1$ gauge theories can be engineered on the worldvolume of D3-branes probing toric Calabi–Yau 3-folds. This kind of setup has multiple applications, ranging from the gauge/gravity correspondence to local model building in string phenomenology. Brane tilings fully encode the gauge theories on the D3-branes and have substantially simplified their connection to the probed geometries. The purpose of this paper is to push the boundaries of computation and to produce as comprehensive a database of brane tilings as possible. We develop efficient implementations of brane tiling tools particularly suited for this search. We present the first complete classification of toric Calabi–Yau 3-folds with toric diagrams up to area 8 and the corresponding brane tilings. This classification is of interest to both physicists and mathematicians alike.

The influence of the noncommutativity on the average speed of a relativistic electron interacting with a uniform magnetic field within the minimum evolution time is investigated. We find that it is possible for the wave packet of the electron to travel faster than the speed of light in vacuum because of the noncommutativity. It is a clear signature of violating Lorentz invariance in the noncommutative relativistic quantum mechanical region.

The constraints from the measurements of the $B\to X_s\gamma$ decay rate on the parameter space of 3-Higgs Doublet Models (3HDMs), where all the doublets have nonzero vacuum expectation values, are studied at the next-to-leading order in QCD. In order to naturally avoid the presence of flavour changing neutral currents at the tree level, we impose two softly-broken discrete $Z_2$ symmetries. This gives rise to five independent types of 3HDMs that differ in their Yukawa couplings. We show that in all these 3HDMs (including the case of type-II-like Yukawa interactions) both masses of the two charged Higgs bosons $m_{H_1^{\pm }}$ and $m_{H_2^{\pm }}$ can be smaller than the top mass $m_t$ while complying with the constraints from $B\to X_s\gamma$. As an interesting phenomenological consequence, the branching ratios of the charged Higgs bosons decay into the $cb$ final states can be as large as $80\%$ when their masses are taken to be below $m_t$ in two of the five 3HDMs (named as Type-Y and Type-Z). This light charged Higgs boson scenario provides a hallmark 3HDM signature that cannot be realised in $Z_2$ symmetric 2-Higgs doublet models. We find that in the Type-Y and Type-Z 3HDMs the scenario with $90\mathrm{\text{GeV}}<m_{H_1^{\pm }}$, $m_{H_2^{\pm }}<m_t$ is ruled out by the direct searches at the LHC, but in the Type-Y 3HDM $80\text{GeV}<m_{H_1^{\pm }}<90\text{GeV}$ and $90\text{GeV}<m_{H_2^{\pm }}<m_t$ is allowed by $B\to X_s\gamma$ and direct searches at LEP2, Tevatron and LHC due to the reduced sensitivity of these searches to the degenerate case $m_{H_1^{\pm }}\approx m_{W^{\pm }}$. The cases where only one or both charged Higgs bosons are above the top quark mass are also naturally allowed in the both Type-Y and Type-Z 3HDMs.

We investigate the classical Brownian motion of a particle in a two-dimensional noncommutative (NC) space. Using the standard NC algebra embodied by the symplectic Weyl–Moyal formalism we find that noncommutativity induces a nonvanishing correlation between both coordinates at different times. The effect stands out as a signature of spatial noncommutativity and thus could offer a way to experimentally detect the phenomena. We further discuss some limiting scenarios and the trade-off between the scale imposed by the NC structure and the parameters of the Brownian motion itself.

A new model of nonlinear electrodynamics with two parameters is proposed. We study the phenomenon of vacuum birefringence, the causality and unitarity in this model. There is no singularity of the electric field in the center of pointlike charges and the total electrostatic energy is finite. We obtain corrections to the Coulomb law at $r\to \infty$. The weak, dominant and strong energy conditions are investigated. Magnetized charged black hole is considered and we evaluate the mass, metric function and their asymptotic at $r\to \infty$ and $r\to 0$. The magnetic mass of the black hole is calculated. The thermodynamic properties and thermal stability of regular black holes are discussed. We calculate the Hawking temperature of black holes and show that there are first-order and second-order phase transitions. The parameters of the model when the black hole is stable are found.