International Journal of Modern Physics A

Scalar dark matter (DM) in a theory introduces hierarchy problems, and suffers from the inability to predict the preferred mass range for the DM. In a WIMP-like minimal scalar DM setup we show that the infinite derivative theory can predict the DM mass and its coupling. The scale of nonlocality $(M)$ in such a theory in its lowermost limit (constrained by LHC) implies a DM mass $\sim$ TeV and a coupling with the Standard Model (SM) Higgs ${\lambda }_{\text{HS}}\sim 10^{-2}$. Planned DM direct detection experiments reaching such sensitivity in the DM will effectively translate into lower bounds on the scale at which the nonlocality comes into the play.

We exploit the power and potential of the (anti-)chiral superfield approach (ACSA) to Becchi–Rouet–Stora–Tyutin (BRST) formalism to derive the nilpotent (anti-)BRST symmetry transformations for any arbitrary $D$-dimensional interacting non-Abelian 1-form gauge theory where there is an $SU(N)$ gauge invariant coupling between the gauge field and the Dirac fields. We derive the conserved and nilpotent (anti-)BRST charges and establish their nilpotency and absolute anticommutativity properties within the framework of ACSA to BRST formalism. The clinching proof of the absolute anticommutativity property of the conserved and nilpotent (anti-)BRST charges is a novel result in view of the fact that we consider, in our endeavor, only the (anti-)chiral super expansions of the superfields that are defined on the $(D,1)$-dimensional super-submanifolds of the general $(D,2)$-dimensional supermanifold on which our $D$-dimensional ordinary interacting non-Abelian 1-form gauge theory is generalized. To corroborate the novelty of the above result, we apply the ACSA to an ${𝒩}=2$ supersymmetric (SUSY) quantum mechanical (QM) model of a harmonic oscillator and show that the nilpotent and conserved ${𝒩}=2$ supercharges of this system do not absolutely anticommute.

We construct the $E$ theory analogue of the particles that transform under the Poincaré group, that is, the irreducible representations of the semi-direct product of the Cartan involution subalgebra of $E_{11}$ with its vector representation. We show that one such irreducible representation has only the degrees of freedom of 11-dimensional supergravity. This representation is most easily discussed in the light cone formalism and we show that the duality relations found in $E$ theory take a particularly simple form in this formalism. We explain that the mysterious symmetries found recently in the light cone formulation of maximal supergravity theories are part of $E_{11}$. We also argue that our familiar space–times have to be extended by additional coordinates when considering extended objects such as branes.

In this paper, we study some classical aspects of Podolsky electrodynamics in the static regime. We develop the multipole expansion for the theory in both the electrostatic and the magnetostatic cases. We also address the problem of consistently truncating the infinite series associated with the several kinds of multipoles, yielding approximations for the static Podolskian electromagnetic field to any degree of precision required. Moreover, we apply the general theory of multipole expansion to some specific physical problems. In those problems, we identify the first terms of the series with the monopole, dipole, and quadrupole terms in the generalized theory. We also propose a situation in which Podolsky theory can be experimentally tested.

In the context of Clifford functional integral formalism, we revisit the Nambu–Jona-Lasinio-type dynamical symmetry breaking model and examine the properties of the dynamically generated composite bosons. Given that the model with 4-fermion interactions is nonrenormalizable in the traditional sense, the aim is to gain insight into the divergent integrals without resorting to explicit regularization. We impose a restriction on the linearly divergent primitive integrals, thus resolving the long-standing issue of momentum routing ambiguity associated with fermion–antifermion condensations. The removal of the ambiguity paves the way for the possible calculation of the true ratio of Higgs boson mass to top quark mass in the top condensation model. In this paper, we also investigate the negative vacuum energy resulted from dynamical symmetry breaking and its cosmological implications. In the framework of modified Einstein–Cartan gravity, it is demonstrated that the late-time acceleration is driven by a novel way of embedding the Hubble parameter into the Friedmann equation via an interpolation function, whereas the dynamically generated negative cosmological constant only plays a minor role for the current epoch. Two cosmic scenarios are proposed, with one of which suggesting that the universe may have been evolving from an everlasting coasting state towards the accelerating era characterized by the deceleration parameter approaching −0.5 at low redshift. One inevitable outcome of the modified Friedmannian cosmology is that the directly measured local Hubble parameter should in general be larger than the Hubble parameter calibrated from the conventional Friedmann equation. This Hubble tension becomes more pronounced when the Hubble parameter is comparable or less than a characteristic Hubble scale.

In the extended Nambu–Jona-Lasinio (NJL) model, the decay widths of $\tau \to (K,K(1460)){\nu }_{\tau }$, $(K,K(1460))\to \mu {\nu }_{\mu }$ are calculated. The contributions from intermediate axial-vector mesons $K_1(1270)$, $K_1(1400)$ and the first radially excited state $K_1(1650)$ are taken into account. Estimates for the weak decay constants $F_K$ and $F_{K^{\prime }}$ are given. Predictions are made for the width of $\tau \to K(1460){\nu }_{\tau }$ decay and $F_{K^{\prime }}$ constant.

Asymptotically anti-de Sitter–Kerr black holes (we focus here on the five-dimensional case) are associated holographically with matter at conformal infinity which has a nonzero angular momentum density. It is natural to attempt to associate this angular momentum with the recently discovered vorticity of the plasmas produced in peripheral heavy-ion collisions. We assume that an AdS₅–Kerr black hole with angular momentum to mass ratio ${𝒜}$ is dual to boundary matter with an angular momentum density to energy density ratio also equal to ${𝒜}$. With this assumption, we find that, for collisions corresponding to a given value of ${𝒜}$, there is a maximal possible angular velocity (well below the maximal value permitted by causality) for such matter at infinity, and that this value is in approximate agreement with the experimentally reported value of the average plasma vorticity produced in typical peripheral collisions of heavy ions.