Showing papers on "Mass formula published in 2019"

Manifestly finite derivation of the quantum kink mass

Abstract: In 1974 Dashen, Hasslacher and Neveu calculated the leading quantum correction to the mass of the kink in the scalar ϕ4 theory in 1+1 dimensions. The derivation relies on the identification of the perturbations about the kink as solutions of the Poschl-Teller (PT) theory. They regularize the theory by placing it in a periodic box, although the kink is not itself periodic. They also require an ad hoc identification of plane wave and PT states which is difficult to interpret in the decompactified limit. We rederive the mass using the kink operator to recast this problem in terms of the PT Hamiltonian which we explicitly diagonalize using its exact eigenstates. We normal order from the beginning, rendering our theory finite so that no compactification is necessary. In our final expression for the kink mass, the form of the PT potential disappears, suggesting that our mass formula applies to other quantum solitons.

Thermodynamical hairs of the four-dimensional Taub-Newman-Unti-Tamburino spacetimes

Abstract: It is demonstrated that the generic four-dimensional Taub-Newman-Unti-Tamburino (Taub-NUT) spacetimes can be perfectly described in terms of three or four different kinds of thermodynamic hairs: the Komar mass ($M=m$), the ``angular momentum'' (${J}_{n}=mn$), the gravitomagnetic charge ($N=n$), and/or the dual (magnetic) mass ($\stackrel{\texttildelow{}}{M}=n$). In other words, the NUT charge is a thermodynamic multihair which means that it simultaneously has both rotation-like and electromagnetic charge-like characteristics; this is in sharp contrast with the previous knowledge that it has only one physical feature, or that it is purely a single solution parameter. To arrive at this novel result, we put forward a simple, systematic way to investigate the consistent thermodynamic first law and Bekenstein-Smarr mass formulas of all four-dimensional spacetimes that contain a nonzero NUT charge, facilitated by first deriving a meaningful Christodoulou-Ruffini-type squared-mass formula. In this way, not only can the elegant Bekenstein-Hawking one-quarter area-entropy relation be naturally restored in the Lorentzian and Euclidian sectors of generic Taub-NUT-type spacetimes without imposing any constraint condition, but also the physical meaning of the NUT parameter as a poly-facet can be completely clarified in the thermodynamic sense for the first time.

Manifestly Finite Derivation of the Quantum Kink Mass

Abstract: In 1974 Dashen, Hasslacher and Neveu calculated the leading quantum correction to the mass of the kink in the scalar $\phi^4$ theory in 1+1 dimensions. The derivation relies on the identification of the perturbations about the kink as solutions of the Poschl-Teller (PT) theory. They regularize the theory by placing it in a periodic box, although the kink is not itself periodic. They also require an ad hoc identification of plane wave and PT states which is difficult to interpret in the decompactified limit. We rederive the mass using the kink operator to recast this problem in terms of the PT Hamiltonian which we explicitly diagonalize using its exact eigenstates. We normal order from the beginning, rendering our theory finite so that no compactification is necessary. In our final expression for the kink mass, the form of the PT potential disappears, suggesting that our mass formula applies to other quantum solitons.

Thermodynamics and phase transition in rotational Kiselev black hole

Abstract: In this paper, we investigate the thermodynamic properties of rotational Kiselev black holes (KBH). Specifically, we use the first-order approximation of the event horizon (EH) to calculate thermodynamic properties for general equations of state ω. These thermodynamic properties include areas, entropies, horizon radii, surface gravities, surface temperatures, Komar energies and irreducible masses at the Cauchy horizon (CH) and EH. We study the products of these thermodynamic quantities, we find that these products are determined by the equation of state ω and strength parameter α. In the case of the quintessence matter (ω = −2/3), radiation (ω = 1/3) and dust (ω = 0), we discuss their properties in detail. We also generalize the Smarr mass formula and Christodoulou–Ruffini mass formula to rotational KBH. Finally, we study the phase transition and thermodynamic geometry for rotational KBH with radiation (ω = 1/3). Through analysis, we find that this phase transition is a second-order phase transition. Furthermore, we also obtain the scalar curvature in the thermodynamic geometry framework, indicating that the radiation matter may change the phase transition condition and properties for Kerr black hole.

Beyond Wigner's isobaric multiplet mass equation: Effect of charge-symmetry-breaking interaction and Coulomb polarization

Abstract: The quadratic form of the isobaric multiplet mass equation (IMME), which was originally suggested by Wigner and has been generally regarded as valid, is seriously questioned by recent high-precision nuclear mass measurements. The usual resolution to this problem is to add empirically the cubic and quartic ${T}_{z}$ terms to characterize the deviations from the IMME, but finding the origin of these terms remains an unsolved difficulty. Based on a strategy beyond Wigner's first-order perturbation, we derive explicitly the cubic and quartic ${T}_{z}$ terms. These terms are shown to be generated by the effective charge-symmetry-breaking and charge-independence-breaking interactions in the nuclear medium combined with the Coulomb polarization effect. Calculations for the $sd$ and lower $fp$ shells explore a systematic emergence of the cubic ${T}_{z}$ term, suggesting a general deviation from the original IMME. Intriguingly, the magnitude of the deviation exhibits an oscillation-like behavior with mass number, modulated by the shell effect.

Upsilon decay widths in magnetized asymmetric nuclear matter

Abstract: The in-medium partial decay widths of $\Upsilon (4S) \rightarrow B\bar B$ in magnetized asymmetric nuclear matter are studied using a field theoretic model for composite hadrons with quark/antiquark constituents. The medium modifications of the decay widths of $\Upsilon (4S)$ to $B\bar B$ pair in magnetized matter, arise due to the mass modifications of the decaying $\Upsilon (4S)$ as well as of the produced $B$ and $\bar B$ mesons. The effects of the anomalous magnetic moments for the proton and neutron are taken into consideration in the present investigation. The presence of the external magnetic field is observed to lead to different mass modifications within the $B (B^+, B^0)$ as well as the $\bar B (B^-, \bar {B^0})$ doublets, even in isospin symmetric nuclear matter, due to the difference in the interactions of the proton and the neutron to the electromagnetic field. This leads to difference in the upsilon decay widths to the neutral ($B^0 \bar {B^0}$) and the charged ($B^+ B^-$) pairs in the magnetized symmetric nuclear matter. The isospin asymmetry is observed to lead to quite different behaviours for the $\Upsilon (4S)$ decay widths to the charged and neutral $B\bar B$. In the presence of the magnetic field, the Landau level contributions give rise to positive shifts in the masses of the charged $B$ and $\bar B$ mesons. This leads to the decay of $\Upsilon(4S)$ to the charged $B^+ B^-$ to be suppressed as compared to the neutral $B\bar B$ pair, especially at low densities. This may lead to suppression in the production of the charged $B^\pm$ mesons as compared to the neutral $B^0$ and $\bar {B^0}$ mesons at LHC and RHIC.

The fourth-order symmetry energy of nuclear matter and symmetry energy coefficients of finite nuclei using extended semi-empirical mass formula

Abstract: An extended nuclear mass formula has been used by considering the bulk, surface and coulomb contributions to the nuclear mass. In this mass formula, the fourth-order symmetry energy coefficient asy...

Strong Effective Coupling, Meson Ground States, and Glueball within Analytic Confinement

Abstract: The phenomena of strong running coupling and hadron mass generating have been studied in the framework of a QCD-inspired relativistic model of quark-gluon interaction with infrared-confined propagators We derived a meson mass equation and revealed a specific new behavior of the mass-dependent strong coupling α ^ s ( M ) defined in the time-like region A new infrared freezing point α ^ s ( 0 ) = 103198 at origin has been found and it did not depend on the confinement scale Λ > 0 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: the masses of constituent quarks and Λ The obtained values are in good agreement with the latest experimental data with relative errors less than 18 percent Accurate estimates of the leptonic decay constants of pseudoscalar and vector mesons have been performed

Mass, Kähler manifolds, and symplectic geometry

Abstract: In the author’s previous joint work with Hein (Commun Math Phys 347:183–221, 2016), a mass formula for asymptotically locally Euclidean Kahler manifolds was proved, assuming only relatively weak fall-off conditions on the metric. However, the case of real dimension 4 presented technical difficulties that led us to require fall-off conditions in this special dimension that are stronger than the Chruściel fall-off conditions that sufficed in higher dimensions. Nevertheless, the present article shows that techniques of four-dimensional symplectic geometry can be used to obtain all the major results of Hein-LeBrun (2016), assuming only Chruściel-type fall-off. In particular, the present article presents a new proof of our Penrose-type inequality for the mass of an asymptotically Euclidean Kahler manifold that only requires this very weak metric fall-off.

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.

A First-Order Mass Formula for Quarks in Terms of Constituent Preons

Abstract: Preon masses are predicted using a first-order mass formula. The model assumes there are six preons (D, U, S, C, B, and T) that combine to form the three generations of quarks. The two lightest preon masses (U and D) and two model parameters (δ and ξ) are derived from the quark vertex and an assumed relation between the U and D preons. The remaining preon masses are determined from the model parameters and the s, c, b, and t quark masses.

Binding, bonding and charge symmetry breaking in Λ-hypernuclei

Abstract: Recent experiments have presented more accurate data on the ΛΛ-binding energies of a few ΛΛ-hypernuclei. This is important as the ΛΛ-bond energies (ΔBΛΛ) of double-Λ hypernuclei provide a measure of the in-medium strength of the ΛΛ-interaction. A mass formula, optimized with the newly available ΛΛ binding energy data, is used to estimate the binding energy and bond energy over a wide range of hypernuclei. The ΔBΛΛ values calculated with this mass formula are in good agreement with the experimental data and the predictions of the quark mean-field (QMF) and relativistic mean-field (RMF) models, except at low mass region where large uncertainties exist in the current experimental data. The ΛΛ-bond energies in ΛΛ-hypernuclei are found to diminish with neutron numbers, approaching zero near the neutron-drip line. In this formalism, the calculated binding energy difference in mirror nuclei arises from the Coulomb contributions and can be utilized to extract the Coulomb-corrected charge symmetry breaking effect in mirror Λ-hypernuclei. Our calculations show the regions where more experimental data are needed for light and neutron-rich Λ and ΛΛ-hypernuclei.

Thermodynamics of Black Holes: Semi-Classical Approaches and Beyond

Abstract: This thesis is focussed to study various aspects of black hole physics. Our approach is a semi-classical type, where the spacetime geometry of black holes is considered to be classical but the fields moving in the background are quantum in nature. Some notable facets of this thesis are the following. We start by looking into the issue of generalized Smarr mass formula for arbitrary dimensional black holes in Einstein-Maxwell gravity. We derive this formula for these black holes and also demonstrate that such a formula can be expressed in the form of a dimension independent identity $K_{\chi^{\mu}}=2ST$ (where the l.h.s is the Komar conserved charge corresponding to the null Killing vector $\chi^{\mu}$ and in the r.h.s $S, T$ are the semi-classical entropy and temperature of a black hole) defined at the black hole event horizon. We highlight the role of exact differentials in computations involving black hole thermodynamics. Some results like the first law of black hole thermodynamics and semi-classical entropy are obtained without using the laws of black hole mechanics as usually done. The blackbody (Hawking) radiation spectrum for higher dimensional black holes is computed by using a density matrix technique of tunneling mechanism by considering both event and cosmological horizons. We also provide the modifications to the semi-classical Hawking temperature and Bekenstein-Hawking entropy due to various effects. These modifications are mainly found due to higher order (in $\hbar$) effects to the WKB ansatz used for the quantum tunneling formalism and non-commutative gravity inspired effects. Finally, in we discuss phase transition phenomena in black holes. We formulate a new methodology based on Clausius-Clapeyron and Ehrenfest's equations to exhibit and classify phase transitions in black holes in analogy to what is done in standard thermodynamics.

Expression for SU(4) multiplet and Masses of undiscovered Baryons in Standard Model

Abstract: In particle physics, study of the symmetry plays very important role in order to get useful information about the nature. The classification and arrangements of subatomic particles is also necessary to study particle physics. Particles which are building blocks of nature are quarks, gluons and leptons. Baryons and Mesons composed of quarks were arranged by Gell-Mann and Okubo in their well-known Eight-Fold way up to SU(3) symmetry. Standard model of particles is composed of these particles. Particles in SU(4) also make some multiplets. However all the baryons with spin JP= 3/2+ and 1/2+ in these multiplets have not been observed till date. We have studied properties of the multiplets having spin JP= 3/2+ in an early work. In this paper the SU(4) multiplets with spin JP= 1/2+ have been organized and studied in an easy way. As a result some clues about the masses and iso-spins of the unknown baryons have been obtained. These approximations about the characteristics of the unidentified baryons have been recorded in this article. Mass formula for the baryons having spin JP= 1/2+ in SU(4) multiplets have been extracted.

Improved Numerical Generalization of the Bethe-Weizsäcker Mass Formula for Prediction the Isotope Nuclear Mass, the Mass Excess Including of Artificial Elements 119 and 120

Abstract: George Gamow’s liquid drop model of the nucleus can account for most of the terms in the formula and gives rough estimates for the values of the coefficients. Its semi-numerical equation was first formulated in 1935 by Weizsacker and in 1936 Bethe [1, 2], and although refinements have been made to the coefficients over the years, the structure of the formula remains the same today. Their formula gives a good approximation for atomic masses and several other effects, but does not explain the appearance of magic numbers of protons and neutrons, and the extra binding-energy and measure of stability that are associated with these numbers of nucleons. Mavrodiev and Deliyergiyev [3] formalized the nuclear mass problem in the inverse problem framework. This approach allowed them to infer the underlying model parameters from experimental observation, rather than to predict the observations from the model parameters. They formulated the inverse problem for the numerically generalized semi-empirical mass formula of Bethe and von Weizsacker going step-by-step through the AME2012 [4] nuclear database. The resulting parameterization described the measured nuclear masses of 2564 isotopes with a maximal deviation of less than 2.6 MeV, starting from the number of protons and number of neutrons equal to 1. The unknown functions in the generalized mass formula was discovered in a step-by-step way using the modified procedure realized in the algorithms developed by Aleksandrov [5-7] to solve nonlinear systems of equations via the Gauss-Newton method. In the presented herein article we describe a further development of the obtained by [3] formula by including additional factors,- magic numbers of protons, neutrons and electrons. This inclusion is based the well-known experimental data on the chemically induced polarization of nuclei and the effect of such this polarization on the rate of isotope decay. It allowed taking into account resonant interaction of the spins of nuclei and electron shells. As a result the maximal deviation from the measured nuclear masses of less than 1.9 MeV was reached. This improvement allowed prediction of the nuclear characteristics of the artificial elements 119 and 120.

The Study of Modified Semi-Empirical Mass Formula (SEMF) by Considering Isospin Effects in Liquid Drop Model

Abstract: We do theoretically study of Modified Semi-Empirical Mass Formula (SEMF) based on macroscopic approach in liquid drop model by considering isospin effects. Isospin is one of internal symmetry properties in hadron group, particularly the nucleon multiplet, it represented by isospin group. Hadron is a group of elementary particles take place in the strong interaction. The role of strong interactions represents homogeneous nuclear force, interactions between proton-proton, proton-neutron, and neutron-neutron are same. In other words, protons and neutrons are indistinguishable because mass (energy) between protons and neutrons is almost the same, by removing charge between them (charge independent). The dependence of isospin effects on nuclear symmetry term and oddeven (pairing) term made the formulation of SEMF should be modificated, in order to obtain nuclear mass and binding energy of a nucleus close to the experimental results. We do two accuracy testing. First, by comparing for nuclei using SEMF before and after being modified, the result shows that using SEMF before modification the value of and for modified SEMF we obtained at . The value of for modified SEMF is smaller than before modification, it indicates that Modified SEMF is a good formula to calculate the mass of nuclei. Second, by comparing Modified SEMF with other models such as FRDM, HFB-14, and HFB-17 using accuracy parameter in the form of rms deviation and number of model parameters. The results show that rms deviation decrease 21% to 0,516 and number of model parameters decrease to 15, consists of 13 macroscopic model parameters and two microscopic model parameters and . The value of model parameters was obtained by fitting to experimental results, as a reason it is called semi-empiric.