Showing papers on "Mass formula published in 2020"

Gluon propagator and three-gluon vertex with dynamical quarks

Abstract: We present a detailed analysis of the kinetic and mass terms associated with the Landau gauge gluon propagator in the presence of dynamical quarks, and a comprehensive dynamical study of certain special kinematic limits of the three-gluon vertex. Our approach capitalizes on results from recent lattice simulations with ($2+1$) domain wall fermions, a novel nonlinear treatment of the gluon mass equation, and the nonperturbative reconstruction of the longitudinal three-gluon vertex from its fundamental Slavnov–Taylor identities. Particular emphasis is placed on the persistence of the suppression displayed by certain combinations of the vertex form factors at intermediate and low momenta, already known from numerous pure Yang–Mills studies. One of our central findings is that the inclusion of dynamical quarks moderates the intensity of this phenomenon only mildly, leaving the asymptotic low-momentum behavior unaltered, but displaces the characteristic “zero crossing” deeper into the infrared region. In addition, the effect of the three-gluon vertex is explored at the level of the effective gauge coupling, whose size is considerably reduced with respect to its counterpart obtained from the ghost-gluon vertex. The main upshot of the above considerations is the further confirmation of the tightly interwoven dynamics between the two- and three-point sectors of QCD.

Reexamining the relation between the binding energy of finite nuclei and the equation of state of infinite nuclear matter

Abstract: The volume term of the semi-empirical mass formula (16 MeV) is usually assumed to be the binding energy per nucleon in symmetric nuclear matter---a considerable extrapolation from finite nuclei. The authors use the dispersive optical model to estimate the nucleon self-energy by fitting a wide range of cross sections for nucleon elastic scattering and ground-state properties. The binding energy per nucleon obtained for saturated matter in the interior of ${}^{208}$Pb is 13--14 MeV, which casts doubt on the widely used 16 MeV from symmetric nuclear matter.

The role of mass, equation of state, and superfluid reservoir in large pulsar glitches

Abstract: Observations of pulsar glitches may provide insights on the internal physics of neutron stars and recent studies show how it is in principle possible to constrain pulsar masses with timing observations. The reliability of these estimates depend on the current uncertainties about the structure of neutron stars and on our ability to model the dynamics of the superfluid neutrons in the internal layers. We assume a simplified model for the rotational dynamics of a neutron star and estimate an upper bound to the mass of 25 pulsars from their largest glitch and average activity: the aim is to understand to which extent the mass constraints are sensitive to the choice of the unknown structural properties of neutron stars, like the extension of the superfluid region and the equation of state. Reasonable values, within the range measured for neutron star masses, are obtained only if the superfluid domain extends for at least a small region inside the outer core, which is compatible with calculations of the neutron S-wave pairing gap. Moreover, the mass constraints stabilise when the superfluid domain extends to densities over nuclear saturation, irrespective of the equation of state tested.

Relativistic Landau levels for a fermion-antifermion pair interacting through Dirac oscillator interaction.

Abstract: We introduce a unique model for a fermion antifermion pair interacting through Dirac oscillator interaction in the presence of external uniform magnetic field. In order to acquire a non perturbative energy spectrum for such a system we solve the corresponding form of a fully covariant two body Dirac equation. The dynamic symmetry of the system allows to study in three dimensions and the corresponding equation leads a $4\times4$ dimensional matrix equation for such a static and spinless composite system. We can obtain an exact solution of the matrix equation and arrive at a spectrum (in closed form) in energy domain. The obtained energy spectrum shows that the composite system that under scrutiny behaves like a single relativistic quantum oscillator. As a result, we obtain relativistic Landau levels of a fermion antifermion pair interacting through Dirac oscillator interaction and determine the components of the corresponding bi-spinor. We think that our results can provide enlightening informations about the quark antiquark systems and thus mass formula for mesons.

Mass of asymptotically flat 3-manifolds with boundary

Abstract: We study the mass of asymptotically flat $3$-manifolds with boundary using the method of Bray-Kazaras-Khuri-Stern. More precisely, we derive a mass formula on the union of an asymptotically flat manifold and fill-ins of its boundary, and give new sufficient conditions guaranteeing the positivity of the mass. Motivation to such consideration comes from studying the quasi-local mass of the boundary surface. If the boundary isometrically embeds in the Euclidean space, we apply the formula to obtain convergence of the Brown-York mass along large surfaces tending to $\infty$ which include the scaling of any fixed coordinate-convex surface.

Scalar spectrum in a graviton soft wall model.

Abstract: In this study we present a unified phenomenological analysis of the scalar glueball and scalar meson spectra within an AdS/QCD framework in the bottom up approach. For this purpose we generalize the recently developed graviton soft-wall (GSW) model, which has shown an excellent agreement with the lattice QCD glueball spectrum, to a description of glueballs and mesons with a unique energy scale. In this scheme, dilatonic effects, are incorporated in the metric as a deformation of the AdS space. We apply the model also to the heavy meson spectra with success. We obtain quadratic mass equations for all scalar mesons while the glueballs satisfy an almost linear mass equation. Besides their spectra, we also discuss the mixing of scalar glueball and light scalar meson states within a unified framework: the GSW model. To this aim, the light-front holographic approach, which connects the mode functions of AdS/QCD to the light-front wave functions, is applied. This relation provides the probabilistic interpretation required to properly investigate the mixing conditions.

Measuring mass via coordinate cubes

Abstract: Inspired by a formula of Stern that relates scalar curvature to harmonic functions, we evaluate the mass of an asymptotically flat 3-manifold along faces and edges of a large coordinate cube. In terms of the mean curvature and dihedral angle, the resulting mass formula relates to Gromov’s scalar curvature comparison theory for cubic Riemannian polyhedra. In terms of the geodesic curvature and turning angle of slicing curves, the formula realizes the mass as integration of the angle defect detected by the boundary term in the Gauss–Bonnet theorem.

Genus of vertex algebras and mass formula

Abstract: We introduce the notion of a genus and its mass for vertex algebras. For lattice vertex algebras, their genera are the same as those of lattices, which plays an important role in the classification of lattices. We derive a formula relating the mass for vertex algebras to that for lattices, and then give a new characterization of some holomorphic vertex operator algebras.

Heavy baryons in holographic QCD with higher dimensional degrees of freedom

Abstract: We try to introduce heavy flavors to Sakai-Sugimoto model by regarding higher dimensional components of gauge fields as heavy mesons. Using the Forg\'acs and Manton approach, we obtain a theory composed of heavy mesons and the instanton of light flavors. Applying the collective coordinate quantization method, we derived a mass formula of heavy baryons. In the leading order of $1/{m}_{H}$ expansion (${m}_{H}$ the mass of a heavy quark), we find singlet and doublet states in the heavy quark symmetry (HQS). Also, we obtain the degenerate Roper like and odd parity excitations. By virtue of heavy meson degrees of freedom, our mass formula reproduces the mass ordering of ${\mathrm{\ensuremath{\Sigma}}}_{c}^{*}$ and ${\mathrm{\ensuremath{\Lambda}}}_{c}^{*}$ correctly.

The Origin of Hadron Masses

Abstract: The color confinement can be decently explained by assuming the global $SU(3)$ color symmetry. A hadron is viewed as a bag of a finite size, whose energy is contributed by the color fields within the hadron. In the large momentum frame, the mass of a hadron can be quantized and can be expressed as the sum of the current masses of quarks involved plus a flavor independent term which depends on a universal parameter and can be identified to be the contribution from the QCD trace anomaly. This term depicts the Regge's trajectories of light hadron masses, from which the parameter can be determined and gives the minimal vector meson mass and baryon mass to be 761 MeV and 935 MeV, respectively. The mass formula can explain many features of the hadron spectroscopy.

Nuclear matter as a liquid phase of spontaneously broken semi-classical $SU(2)_L \times SU(2)_R$ chiral perturbation theory: Static chiral nucleon liquids

Abstract: We study effective field theories (EFT) of nuclear structure based on spontaneously broken global $SU(2)_L\times SU(2)_R$ chiral symmetry of QCD with two massless quarks, i.e. $SU(2)\chi PT$. For ground-state nuclei, this EFT enables expansion and truncation in inverse powers of $\Lambda_{\chi SB}\simeq 1 GeV$, with analytic operators renormalized to all loop orders. We derive the EFT Lagrangian to order $\Lambda^0_{\chi SB}$. We show that $SU(2)\chi PT$ of protons, neutrons and pions admits a semi-classical "Static Chiral Nucleon Liquid" (Static$\chi$NL) phase and that "Pion-less" $SU(2)\chi PT$ emerges in this liquid: far-infrared pions decouple from Static$\chi$NL, vastly simplifying the derivation of saturated nuclear matter (the infinite liquid phase) and of finite microscopic liquid drops (ground-state nuclides). Static$\chi$NL are made entirely of nucleons with even parity, total spin zero, and even $Z$ and $N$; local expectation values for spin and momenta vanish. They explain the power of pion-less $SU(2)\chi PT$ to capture experimental ground-state properties of certain nuclides, this explanation following directly from the global symmetries of QCD with two massless quarks. Mean-field Static$\chi$NL non-topological solitons are true solutions of $SU(2)\chi PT$'s semi-classical symmetries: they obey all CVC and PCAC conservation laws and they have zero internal and external pressure. The nuclear liquid-drop model and the semi-empirical mass formula emerge -- with correct nuclear density and saturation and asymmetry energies -- in an explicit Thomas-Fermi construction. We relate our work to compatible and complementary work in pionless and in halo/ cluster EFTs, also composed entirely of nucleons and applied to light ($A\leq 6$) nuclei, which might provide important (<12.5%) corrections to Static$\chi NL$.

Three Applications of the Siegel Mass Formula

Abstract: We present three applications of the Siegel mass formula, using the explicit upper bounds for densities derived in Bourgain and Demeter (Int Math Res Not 2015(11):3150–3184, 2014).

The Fundament of the Mass and Effects of the Gravitation on a Particle and Light in the Mass, Time, Distance, Velocity, Frequency, Wavelength: Variant Mass for a Particle which emits Gravitational Energy for a Particle Orbiting a large Planet or Sun and for a Binary Star and Variant Frequency for the Light Passing Close a Gravitational Field from a Massive Object (Sun)

Abstract: Albert Einstein wrote in a research article: “Does the inertia of a body depend on its energy content?” (Ist die Tragheit eines Korpers von seimen Energienhalt abhangig?): “If a body emits energy E in the form of radiation, its mass decreases by E/c2”. This is true for any type of radiation emitted (gravitational or electromagnetic energy) which produce a decrease in the mass of the body. Thus, Maxwell's theory shows that electromagnetic waves are radiated whenever charges accelerate as for example for the electron. Then, this electromagnetic radiation (photons) produces decreases in the mass of the electron which is given by the formula of the Variant Mass for an Accelerated Charged Particle which was demonstrated by myself at this research. The objective of this research is to demonstrate by theory, experiment and result the discovery formula which describe exactly the variant mass of a particle which emits gravitational energy. The results of the mass formula are of great relevance for Gravitational Interactions. It is in accordance with the classic result for the emission of the total gravitational energy (bond total energy) for a particle orbiting a large Planet or Sun and for a Binary Star. It is also demonstrated and explained the effects of the gravitation in a particle or light and the Perihelion Precession of Mercury. The formula for the gravitation redshift frequency, the wavelength, the light velocity, time measurement and the decreasing radius for a particle in a gravitational field are demonstrated. The formula of the light velocity is tested for the deflection of light passing close to the sun. The formula for time dilation and decrease distance are used to calculate the Perihelion Precession of Mercury. It is in agreement with the experiment result and with the Theory of General Relativity. The consequences of this research are amazing and in accordance with the same General Theory of Relativity, Newton Theory and with profound Insignia in Quantum Mechanics and for the Unification Theory.

Comments on two papers of Cl\'ement and Gal'tsov

Abstract: We comment on physical inconsistences of the Cl\'ement-Gal'tsov approach to Smarr's mass formula in the presence of magnetic charge. We also point out that the results of Cl\'ement and Gal'tsov involving the NUT parameter are essentially based on the known study (dating back to 2006) of the Demia\'nski-Newman solutions which was not cited by them.

Description of the X(6900) as a Four Charmed Quark State in Terms of a First-Order Tetraquark Mass Formula

Abstract: A recently discovered tetraquark candidate having four charmed quarks is investigated using a first-order mass formula. This mass relationship is based on weakly bound meson clusters and provides a reasonable prediction of 6300 MeV/c2 for the measured X(6900) tetraquark mass.

Alpha clustering preformation probability in even-even and odd-A270 -317 (116 and 117) using cluster formation model and the mass formulae : KTUY05 and WS4

Abstract: The calculations were carried out using an energy-dependent formula, where the superheavy-nuclei mass defect was evaluated by using both the KTUY05 and WS4 nuclear mass formulae. This formula reproduced successfully the value of 212 P o calculated from a combined microscopic shell and cluster model and described satisfactorily the alpha decay of heavy nuclei. The values of the preformation probability and the cluster formation energy, and their dependence on the neutron number, confirmed the shell and subshell closures and the similarities of alpha clustering between heavy and superheavy nuclei. The calculations carried out with the WS4 mass formula showed larger alpha-clustering effects than the KTUY05.

Local Densities of Diagonal Integral Ternary Quadratic Forms at Odd Primes

Abstract: We give formulas for local densities of diagonal integral ternary quadratic forms at odd primes. Exponential sums and quadratic Gauss sums are used to obtain these formulas. These formulas (along with 2-adic densities and Siegel's mass formula) can be used to compute the representation numbers of certain ternary quadratic forms.

Comment on: "Neutron star under homotopy perturbation method" Ann. Phys. 409 (2019) 167918

Abstract: In this comment we discuss the application of homotopy perturbation method to a nonlinear differential mass equation that solves the Tolman-Oppenheimer-Volkoff equation for an isotropic and spherically symmetric system. We show that one obtains the same results, more easily and straightforwardly, by means of a textbook power-series method.

Axion and neutrino mass from a hidden gauge symmetry model

Abstract: We propose a model of dark sector described by gauged hidden $U(1)_H$ symmetry in which neutrino masses are generated at one-loop level and axion is induced by assigning Peccei-Quinn charge to fermions in dark sector relevantly. Then our scenario connects exotic fermion mass generation, neutrino mass matrix and axion through scalar fields associated with $U(1)_H$ and Peccei-Quinn symmetry breaking. We investigate neutrino mass formula, lepton flavor violation, anomalous magnetic moment of muon, dark matter relic density and axion couplings, which are originated from interactions among our dark sector and the standard model particles.

A relaxed version of Koide's mass formula from Yukawaons: classical and SUSY scenarios

Abstract: We present a relaxed version of Koide's mass formula from a nonet Yukawaon scalar in the $\mathrm{SU}(3)$ flavor symmetry. Koide's character $K$, which involves the Standard Model fermion masses, is derived from vacuum expactation values of Yukawaons in both classical and supersymmetric scenarios. Requirements from the flavor symmetry and renormalizability leave two free parameters in the scalar potential or the superpotential of Yukawaons. One of the free parameters provides possible loop-level mass corrections, while the other parameter modulates Koide's character $K$ in the relaxed mass formula from the original formula. The parameter modulating $K$ may also provide quark mixing in a similar Yukawaon model coupled to the quark sector.

Mesons and Glueballs, the Strong Effective Coupling within Analytic Confinement

Abstract: The phenomena of hadron mass generating, strong running coupling and radiative transitions of charmonium excited states have been studied in the framework of a relativistic field model with analytic confinement. A meson mass equation is derived and a specific new behavior of the mass-dependent strong coupling $$\mathop {\bar {\alpha }} olimits_s $$ is revealed in the time-like region. A new infrared fixed point $$\mathop {\bar {\alpha }} olimits_s (0) = 1.032$$ has been found at origin. Independent and new estimates on the scalar glueball mass, radius and gluon condensate value have been performed. The spectrum of conventional mesons have been calculated by introducing a minimal set of parameters with relative errors less than 1.8 percent compared to the latest data. Accurate estimates of the leptonic decay constants of pseudoscalar and vector mesons have also been performed. Partial decay widths of the dominant radiative transitions of the charmonium orbital excitations have been estimated with reasonable accuracy.