International Journal of Modern Physics A

The energy level where the best values of the three fundamental gauge couplings $({\alpha }_1,{\alpha }_2,{\alpha }_3)$ converge is at least two orders of magnitude below the Planck energy level. The existence of this Gap could imply that the gravitational force ‘comes into being’ before QED, QFD and QCD. The most interesting consequence of the Gap would then be the existence of matter whose charge is only the gravitational charge. If this is so, events should be detected where only gravitational waves are produced. Primordial black holes (PBHs) would be produced much more frequently than the standard black holes (SBHs) since SBHs would be ‘derivative’ effects produced later, after matter made with protons, electrons, neutrons, and stars can exist. Collisions between PBHs generating only gravitational waves should be more frequent than SBHs collisions.

The conceptual foundation of the Englert–Brout–Higgs (EBH) mechanism (understood as a set of a scalar field’s couplings to a gauge system and a fermion system) is clarified (as being provided by broken symmetry solution of the scalar field and broken symmetry solutions of the gauge and fermion systems induced by the scalar field’s couplings to these systems, which are manifested in massive scalar and vector bosons as a result of reorganizing the physical degrees of freedom in the scalar and gauge sectors, whose original organization renders possible the broken symmetry solution to the scalar sector and symmetrical solutions to the gauge sector); its ontological status, as a physically real mechanism or merely an instrumental device, is examined, and a new ontologically primary entity, the symbiont of scalar–vector moments is suggested to replace the old ontology of scalar field and vector (gauge) field as the physical underpinning for a realistic understanding of the EBH mechanism; with a conclusion that two puzzles, the transmutation of the Goldstone modes’ dynamic identity and the fixity in reorganizing the physical degrees of freedom within the symbiont, have to be properly addressed before a consistent realist understanding of the mechanism can be developed.

The elastic scattering phase shifts to the two-particle energy levels in a finite cubic box is related by the Lüscher’s formula. In this paper, based on the nonrelativistic quantum mechanics model which is usually assumed to be the low energy scattering case in lattice simulations, we confirmed the generalized Lüscher’s formula for the case of two-particle scattering with arbitrary spin in Ref. 1. In particular, Lüscher’s formula is synthesized for two-spin-3/2-particle scattering, i.e. $\mathrm{\Omega }-\mathrm{\Omega }$ scattering on lattice that may help us study the promising dibaryon states.

Multiplicity fluctuation provides enough information concerning the dynamics of particle production process and even signature of phase transition from hadronic to QGP phase expected in ultrarelativistic nuclear collision. Numerous analyses reported on the fluctuation pattern of pions have been studied from theoretical and phenomenological approaches. Also the fractal properties have been explored to characterize quantitative degree of fluctuation. The present work reports a study of pion fluctuation from a radically different perspective, using science of complexity. For this we have taken two different interactions — one hadron–nucleus and other nucleus–nucleus, namely ${\pi }^{-}$-AgBr (350 GeV) and ${}^{32}$S-AgBr (200 AGeV). We have analyzed both data in the light of complex network analysis, viz. visibility graph method. The data reveal that power of the scale-freeness in visibility graph (PSVG), a quantitative parameter related to Hurst exponent, may provide information on the degree of fluctuation. Further, in a recent work, it was shown that phase transition can also be studied using the same methodology. Based on the result of the present study we further propose to use this methodology, where critical phenomena are to be assessed — even in case of pion fluctuation, for obtaining the QGP like phase transition.

The fermionic fields constructed from Elko have several unexpected properties. They satisfy the Klein–Gordon but not the Dirac equation and are of mass dimension one instead of three-half. Starting with the Klein–Gordon Lagrangian, we initiate a careful study of the symmetries and interactions of these fermions and their higher-spin generalizations. We find, although the fermions are of mass dimension one, the four-point fermionic self-interaction violates unitarity at high-energy so it cannot be a fundamental interaction of the theory. Using the optical theorem, we derive an explicit bound on energy for the fermion–scalar interaction. It follows that for the spin-half fermions, the demand of renormalizability and unitarity forbids four-point interactions and only allows for the Yukawa interaction. For fermions with spin $j>\frac{1}{2}$, they have no renormalizable or unitary interactions. Since the theory is described by a Klein–Gordon Lagrangian, the interaction generated by the local $U(1)$ gauge symmetry which contains a four-point interaction, is excluded by the demand of renormalizability. In the context of the Standard Model, these properties make the spin-half fermions natural dark matter candidates. Finally, we discuss the recent developments on the introduction of new adjoint and spinor duals which may allow us to circumvent the unitarity constraints on the interactions.

In this paper, we discuss Bagger–Witten line bundles over moduli spaces of SCFTs. We review how in general they are “fractional” line bundles, not honest line bundles, twisted on triple overlaps. We discuss the special case of moduli spaces of elliptic curves in detail. There, the Bagger–Witten line bundle does not exist as an ordinary line bundle, but rather is necessarily fractional. As a fractional line bundle, it is nontrivial (though torsion) over the uncompactified moduli stack, and its restriction to the interior, excising corners with enhanced stabilizers, is also fractional. It becomes an honest line bundle on a moduli stack defined by a quotient of the upper half plane by a metaplectic group, rather than $SL(2,\mathbb{Z})$. We review and compare to results of recent work arguing that well-definedness of the worldsheet metric implies that the Bagger–Witten line bundle admits a flat connection (which includes torsion bundles as special cases), and gives general arguments on the existence of universal structures on moduli spaces of SCFTs, in which superconformal deformation parameters are promoted to nondynamical fields ranging over the SCFT moduli space.

Considering the Cornell potential $V(r)=-\frac{4{\alpha }_s}{3r}+br+c$, we have revisited the Dalgarno’s method of perturbation by incorporating two scales $r^{\mathrm{\text{short}}}$ and $r^{\mathrm{\text{long}}}$ as integration limit so that the perturbative procedure can be improved in a potential model. With the improved version of the wave function the ground state masses of the heavy–light mesons $D$, $D_s$, $B$, $B_s$ and $B_c$ are computed. The slopes and curvatures of the form factors of semileptonic decays of heavy–light mesons in both HQET limit and finite mass limit are calculated and compared with the available data.

The spin and pseudospin symmetries in the Dirac Hamiltonian are investigated in the presence of the Hartmann and the Higgs oscillator superintegrable potentials. The Pauli-Dirac representation is used in the Dirac equation with scalar and vector potentials of equal magnitude. Then, the Dirac equation is reduced to a Schrödinger-like equation. The symmetry algebras of the Schrödinger-like equation corresponding to the superintegrable potentials are represented. Also, the associated irreducible representations are shown by means of the quadratic algebras. Finally, the relativistic energy spectra of the Hartmann and the Higgs oscillator superintegrable potentials are calculated.

We study the entanglement entropy (EE) for pure gauge theories in 1+1 dimensions with the lattice regularization. Using the definition of the EE for lattice gauge theories proposed in a previous paper,¹ we calculate the EE for arbitrary pure as well as mixed states in terms of eigenstates of the transfer matrix in (1+1)-dimensional lattice gauge theory. We find that the EE of an arbitrary pure state does not depend on the lattice spacing, thus giving the EE in the continuum limit, and show that the EE for an arbitrary pure state is independent of the real (Minkowski) time evolution. We also explicitly demonstrate the dependence of EE on the gauge fixing at the boundaries between two subspaces, which was pointed out for general cases in the paper. In addition, we calculate the EE at zero as well as finite temperature by the replica method, and show that our result in the continuum limit corresponds to the result obtained before in the continuum theory, with a specific value of the counterterm, which is otherwise arbitrary in the continuum calculation. We confirm the gauge dependence of the EE also for the replica method.

Vertex operators for photo- and electro-production of baryon states with arbitrary spin-parity, $\gamma +N\to B(J^P)$, are constructed. The operators obey gauge invariance and analyticity constraints. Analyticity is realized as a requirement of the generalized Siegert theorem for vertex form factors.

We develop a purely hydrodynamic formalism to describe collisional, anisotropic instabilities in a relativistic plasma, that are usually described with kinetic theory tools. Our main motivation is the fact that coarse-grained models of high particle number systems give more clear and comprehensive physical descriptions of those systems than purely kinetic approaches, and can be more easily tested experimentally as well as numerically. Also they make it easier to follow perturbations from linear to nonlinear regimes. In particular, we aim at developing a theory that describes both a background nonequilibrium fluid configurations and its perturbations, to be able to account for the backreaction of the latter on the former. Our system of equations includes the usual conservation laws for the energy–momentum tensor and for the electric current, and the equations for two new tensors that encode the information about dissipation. To make contact with kinetic theory, we write the different tensors as the moments of a nonequilibrium one-particle distribution function (1pdf) which, for illustrative purposes, we take in the form of a Grad-like ansatz. Although this choice limits the applicability of the formalism to states not far from equilibrium, it retains the main features of the underlying kinetic theory. We assume the validity of the Vlasov–Boltzmann equation, with a collision integral given by the Anderson–Witting prescription, which is more suitable for highly relativistic systems than Marle’s (or Bhatnagar, Gross and Krook) form, and derive the conservation laws by taking its corresponding moments. We apply our developments to study the emergence of instabilities in an anisotropic, but axially symmetric background. For small departures of isotropy we find the dispersion relation for normal modes, which admit unstable solutions for a wide range of values of the parameter space.