Discrete Mass Spectrum Research Articles

On black holes as topological defects

In this paper, the gravitational field is revisited as a manifestation of defects in continuum media. The Schwarzschild solution is then interpreted as a permanent plastic deformation of space-time and we conjecture that a discrete dislocation leads to a discrete mass spectrum. The dislocation of this black hole is considered as a quasi-local defect, once it vanishes at the spatial infinity. The C-metric is also considered under this viewpoint. The dislocations in such a space-time reveal how the quasi-local defect interacts with a global defect due to the semi-infinite cosmic string. The disclinations are obtained in agreement at certain limits with the literature.

The Higgs mechanism and geometrical flows for two-manifolds

Using Perelman’s approach for geometrical flows in terms of an entropy functional, the Higgs mechanism is studied dynamically along flows defined in the space of parameters and in fields space. The model corresponds to two-dimensional gravity that incorporates torsion as the gradient of a Higgs field, and with the reflection symmetry to be spontaneously broken. The results show a discrete mass spectrum and the existence of a mass gap between the Unbroken Exact Symmetry and the Spontaneously Broken Symmetry scenarios. In the latter scenario, the geometries at the degenerate vacua correspond to conformally flat manifolds without torsion; twisted two-dimensional geometries are obtained by building perturbation theory around a ground state; the tunneling quantum probability between vacua is determined along the flows.

Horizons and the wave function of Planckian quantum black holes

At the Planck scale the distinction between elementary particles and black holes becomes fuzzy. The very definition of a “quantum black hole” (QBH) is an open issue. Starting from the idea that, at the Planck scale, the radius of the event horizon undergoes quantum oscillations, we introduce a black hole mass-radius Generalized Uncertainty Principle (GUP) and derive a corresponding gravitational wavelength. Next we recover a GUP encoding effective geometry. This semi-classical gravitational description admits black hole configurations only for masses higher than the Planck mass. Quantum corrections lead to a vanishing Hawking temperature when the Planck mass is approached from above. Finally we replace our semi-classical model by a relativistic wave equation for the “horizon wave function”. The solution admits a discrete mass spectrum which is bounded from below by a stable ground state with energy close to the Planck mass. Interestingly higher angular momentum states fit onto Regge trajectories indicating their stringy nature.

Soliton solution for the central dark mass in 47-Tuc globular cluster and implications for the axiverse

We offer a standing wave explanation for the rising proper motions of stars at the center of the globular cluster 47-Tucanae, amounting to $\ensuremath{\simeq}0.44%$ of the total mass. We show that this can be explained as a solitonic core of dark matter composed of light bosons, $m\ensuremath{\ge}{10}^{\ensuremath{-}18}\text{ }\text{ }\mathrm{eV}$, corresponding to $\ensuremath{\le}0.27\text{ }\text{ }\mathrm{pc}$, as an alternative to a single black hole (BH) or a concentration of stellar BH remnants proposed recently. This is particularly important because having a concentrated stellar BH remnant with the above radii is very challenging without the heavy core since the three-body encounters would prevent the BHs from being that concentrated. We propose that this core develops from dark matter captured in the deep gravitational potential of this globular cluster as it orbits the dark halo of our Galaxy. This boson may be evidence for a second light axion, additional to a lighter boson of ${10}^{\ensuremath{-}22}\text{ }\text{ }\mathrm{eV}$, favored for the dominant dark matter implied by the large dark cores of dwarf spheroidal galaxies. The identification of two such light bosonic mass scales favors the generic string theory prediction of a wide, discrete mass spectrum of axionic scalar fields.

Hadron Resonance Gas EoS and the Fluidity of Matter Produced in HIC

We study the equation of state (EoS) of hot and dense hadron gas by incorporating the excluded volume corrections into the ideal hadron resonance gas (HRG) model. The total hadron mass spectrum of the model is the sum of the discrete mass spectrum consisting of all the experimentally known hadrons and the exponentially rising continuous Hagedorn states. We confront the EoS of the model with lattice quantum chromodynamics (LQCD) results at finite baryon chemical potential. We find that this modified HRG model reproduces the LQCD results up to T=160 MeV at zero as well as finite baryon chemical potential. We further estimate the shear viscosity within the ambit of this model in the context of heavy-ion collision experiments.

Some Characteristic Functions for the Eigen Solution of Nonlinear Spinor

In this paper, we solve the eigen solutions to some nonlinear spinor equations, and compute several functions reflecting their characteristics. The numerical results show that, the nonlinear spinor equation has only finite meaningful eigen solutions, which have positive discrete mass spectra and anomalous magnetic moment. The nonlinear potential and interactions yield different contributions to the total energy, and these components of the energy lead to different energy-speed relation. The magnitude of these components can be detected by elaborate experiments. The weird properties of the nonlinear spinors might be closely related with the elementary particles and their interactions, so some deeper investigations on them are significant.

Model of quark–antiquark interaction in quantum chromodynamics on the light front

We formulate a model of quark–antiquark interaction related to the limit transition to the light-front Hamiltonian in quantum chromodynamics. As ultraviolet regularization, we use a lattice in the space of transverse coordinates, and we additionally introduce a longitudinal light-front coordinate cutoff and also corresponding periodic boundary conditions. We regard the zero mode with respect to this coordinate as an independent dynamical variable. The state space of the model is limited to a quark and an antiquark that interact only via the zero mode of the gluon field on the light front. In this framework, we obtain a discrete mass spectrum of bound states. This spectrum is determined by an equation that with respect to the longitudinal coordinate turns out to be analogous to the’ t Hooft equation in two-dimensional quantum chromodynamics. The equation also contains a quark–antiquark potential that ensures confinement in the transverse space.

Matching the Hagedorn mass spectrum with lattice QCD results

Based on recent Lattice QCD (LQCD) results obtained at finite temperature, we discuss modeling of the hadronic phase of QCD in the framework of Hadron Resonance Gas (HRG) with discrete and continuous mass spectra. We focus on fluctuations of conserved charges, and show how a common limiting temperature can be used to constrain the Hagedorn exponential mass spectrum in different sectors of quantum number, through a matching of HRG and LQCD. For strange baryons, the extracted spectra are found to be consistent with all known and expected states listed by the Particle Data Group (PDG). The strange-mesonic sector, however, requires additional states in the intermediate mass range beyond that embodied in the database.

Fermions with a bounded and discrete mass spectrum

A mechanism for determining fermion masses in four spacetime dimensions is presented, which uses a scalar-field domain wall extending in a fifth spacelike dimension and a special choice of Yukawa coupling constants. A bounded and discrete fermion mass spectrum is obtained analytically for spinors localized in the fifth dimension. These particular mass values depend on a combination of the absolute value of the Yukawa coupling constant and the parameters of the scalar potential. A similar mechanism for a finite mass spectrum may apply to $(1+1)$--dimensional fermions relevant to condensed matter physics.

Semiclassical geons at particle accelerators

We point out that in certain four-dimensional extensions of general relativity constructed within the Palatini formalism stable self-gravitating objects with a discrete mass and charge spectrum may exist. The incorporation of nonlinearities in the electromagnetic field may effectively reduce their mass spectrum by many orders of magnitude. As a consequence, these objects could be within (or near) the reach of current particle accelerators. We provide an exactly solvable model to support this idea.

Holographic Screens in Ultraviolet Self-Complete Quantum Gravity

This paper studies the geometry and the thermodynamics of aholographic screenin the framework of the ultraviolet self-complete quantum gravity. To achieve this goal we construct a new static, neutral, nonrotating black hole metric, whose outer (event) horizon coincides with the surface of the screen. The spacetime admits an extremal configuration corresponding to the minimal holographic screen and having both mass and radius equalling the Planck units. We identify this object as the spacetime fundamental building block, whose interior is physically unaccessible and cannot be probed even during the Hawking evaporation terminal phase. In agreement with the holographic principle, relevant processes take place on the screen surface. The area quantization leads to a discrete mass spectrum. An analysis of the entropy shows that the minimal holographic screen can store only one byte of information, while in the thermodynamic limit the area law is corrected by a logarithmic term.

NONTHERMAL QUANTUM BLACK HOLES WITH QUANTIZED MASSES

In this paper, we discuss nonthermal quantum black holes with a discrete mass spectrum and their possible new signatures at the LHC. We calculate the inclusive cross-sections for the production of quantum black holes with discrete masses at the LHC as well as some exclusive cross-sections for particularly interesting decay modes.

Localizing gauge fields on a topological Abelian string and the Coulomb law

The confinement of electromagnetic field is studied in axial symmetrical, warped, 6D World Brane, using a recently proposed topological abelian string vortex solution as background. It was found, that the massless gauge field fluctuations follow 4D Maxwell equations in the Lorenz gauge. The massless zero mode is localized when the thickness of the string-vortex is less than 5% $\beta/4\pi e^{2}$ there are not others localized massless modes. There is also an infinite of non localized massive Fourier modes, that follow 4 dimensional Proca equations with a continuous spectrum. To compute the corrections to the Coulomb potential, a radial cutoff was introduced, in order to achieve a discrete mass spectrum. As main result, a $\frac{1}{R^{2}}$ correction was found for the 4D effective Coulomb law. Although, this correction is milder than the $% \frac{1}{R^{3}}$ expected for flat 5+1 dimensional electromagnetism, the result is in correspondence with the observed behavior of the Coulomb potential at nowadays measurable distances.

BLACK HOLE AS AN INFORMATION ERASER

We discuss the identity of black hole entropy and show that the first law of black hole thermodynamics, in the case of a Schwarzschild black hole, can be derived from Landauer's principle by assuming that the black hole is one of the most efficient information erasers. The term "most efficient" implies that maximal information will be erased for a given amount of work. We calculate the discrete mass spectra and the entropy of a Schwarzschild black hole assuming that the black hole processes information in unit of bits. The black hole entropy acquires a subleading contribution proportional to the logarithm of its mass-squared in addition to the usual mass-squared term without an artificial cutoff. We also argue that the minimum of the black hole mass is [Formula: see text]

Localization of matters on Anti-de Sitter thick branes

By presenting the mass-independent potentials of the Kaluza-Klein (KK) modes in the corresponding Schr\"{o}dinger equations, we investigate the localization and mass spectra of various bulk matter fields on an AdS thick brane. For a spin 0 scalar $\Phi$ coupled with itself and the domain-wall-forming field $\phi$ via a coupling potential $V=(\lambda \phi^{2}-u^{2})\Phi^{2}+\tau\Phi^{4}$, the localization and spectrum are decided by a critical coupling constant $\lambda_{0}$. When $\lambda>\lambda_0$, the potential of the scalar KK modes in the corresponding Schr\"{o}dinger equation tends to infinite when far away from the brane, which results in that there exist infinite discrete scalar bound KK states, and the massless modes could be trapped on the AdS brane by fine-tuning of parameters. When $\lambda<\lambda_0$, the potential of the scalar KK modes tends to negative infinite when far away from the brane, hence there does not exist any scalar bound KK state. For a spin 1 vector, the situation is same like the scalar with a coupling constant $\lambda>\lambda_0$, but the zero mode can not be localized on the brane. For a spin 1/2 fermion, we introduce the usual Yukawa coupling $\eta\bar{\Psi}\phi\Psi$, and find that the localization of the fermion is decided by a critical coupling constant $\eta_0$. For $\eta > \eta_0$, the four-dimensional massless left chiral fermion and massive Dirac fermions consisted of the pairs of coupled left-hand and right-hand KK modes could be localized on the AdS brane, and the massive Dirac fermions have a set of discrete mass spectrum. While for the case $0<\eta < \eta_{0}$, no four-dimensional Dirac fermion can be localized on the AdS brane.

A note on large N scalar QCD 2

We review the features of the bound state equation in large N scalar QCD in two dimensions, the 't Hooft model, and compute the discrete hadron mass spectrum in this theory. We make the ansatz that the scalar fields of this model represent spin zero diquarks and we estimate the minimum allowed mass for the first radial excitation of the lowest diquark–antidiquark scalar meson. The discussion is extended to the case of spin one diquarks.

Thermodynamics for a hadronic gas of fireballs with internal color structures and chiral fields

The thermodynamic partition function for a gas of color-singlet bags consisting of fundamental and adjoint particles in both $\mathrm{U}({N}_{c})$ and $\mathrm{SU}({N}_{c})$ group representations is reviewed in detail. The constituent particle species are assumed to satisfy various thermodynamic statistics. The gas of bags is probed to study the phase transition for nuclear matter in extreme conditions. These bags are interpreted as the Hagedorn states, and they are the highly excited hadronic states produced below the phase transition point to the quark-gluon plasma (QGP). The hadronic density of states has the Gross-Witten critical point and exhibits a third-order phase transition from a hadronic phase dominated by the discrete low-lying hadronic mass spectrum particles to another hadronic phase dominated by the continuous Hagedorn states. The Hagedorn threshold production is found just above the highest known experimental discrete low-lying hadronic mass spectrum. The subsequent Hagedorn phase undergoes a first-order deconfinement phase transition to an explosive QGP. The role of the chiral phase transition in the phases of the discrete low-lying mass spectrum and the continuous Hagedorn mass spectrum is also considered. It is found to be crucial in the phase transition diagram. Alternative scenarios are briefly discussed for the Hagedorn gas undergoing a higher order phase transition through multiple processes of internal color-flavor structure modification.

Phenomenology of theSU(3)c⊗SU(3)L⊗U(1)Xmodel with exotic charged leptons

A phenomenological analysis of the three-family model based on the local gauge group $SU(3{)}_{c}\ensuremath{\bigotimes}SU(3{)}_{L}\ensuremath{\bigotimes}U(1{)}_{X}$ with exotic charged leptons, is carried out. Instead of using the minimal scalar sector able to break the symmetry in a proper way, we introduce an alternative set of four Higgs scalar triplets, which combined with an anomaly-free discrete symmetry, produce quark and charged lepton mass spectrum without hierarchies in the Yukawa coupling constants. We also embed the structure into a simple gauge group and show some conditions to achieve a low energy gauge coupling unification, avoiding possible conflict with proton decay bounds. By using experimental results from the CERN-LEP, SLAC linear collider, and atomic parity violation data, we update constraints on several parameters of the model.

Gauge fields, fermions and mass gaps in 6D brane worlds

We study fluctuations about axisymmetric warped brane solutions in 6D minimal gauged supergravity. Much of our analysis is general and could be applied to other scenarios. We focus on bulk sectors that could give rise to Standard Model gauge fields and charged matter. We reduce the dynamics to Schrödinger type equations plus physical boundary conditions, and obtain exact solutions for the Kaluza–Klein wave functions and discrete mass spectra. The power-law warping, as opposed to exponential in 5D, means that zero mode wave functions can be peaked on negative tension branes, but only at the price of localizing the whole Kaluza–Klein tower there. However, remarkably, the codimension two defects allow the Kaluza–Klein mass gap to remain finite even in the infinite volume limit. In principle, not only gravity, but Standard Model fields could ‘feel’ the extent of large extra dimensions, and still be described by an effective 4D theory.

FINITE ACTION KLEIN–GORDON SOLUTIONS ON LORENTZIAN MANIFOLDS

The eigenvalue problem for the square integrable solutions is studied usually for elliptic equations. In this paper we consider such a problem for the hyperbolic Klein–Gordon equation on Lorentzian manifolds. The investigation could help to answer the question why elementary particles have a discrete mass spectrum. An infinite family of square integrable solutions for the Klein–Gordon equation on the Friedman type manifolds is constructed. These solutions have a discrete mass spectrum and a finite action. In particular the solutions on de Sitter space are investigated.