Mass formula

About: Mass formula is a research topic. Over the lifetime, 1248 publications have been published within this topic receiving 22043 citations.

Mass varying neutrinos, quintessence, and the accelerating expansion of the Universe

Abstract: We analyze the mass varying neutrino scenario. We consider a minimal model of massless Dirac fermions coupled to a scalar field, mainly in the framework of finite-temperature quantum field theory. We demonstrate that the mass equation we find has nontrivial solutions only for special classes of potentials, and only within certain temperature intervals. We give most of our results for the Ratra-Peebles dark energy (DE) potential. The thermal (temporal) evolution of the model is analyzed. Following the time arrow, the stable, metastable, and unstable phases are predicted. The model predicts that the present Universe is below its critical temperature and accelerates. At the critical point, the Universe undergoes a first-order phase transition from the (meta)stable oscillatory regime to the unstable rolling regime of the DE field. This conclusion agrees with the original idea of quintessence as a force making the Universe roll towards its true vacuum with a zero $\ensuremath{\Lambda}$ term. The present mass varying neutrino scenario is free from the coincidence problem, since both the DE density and the neutrino mass are determined by the scale $M$ of the potential. Choosing $M\ensuremath{\sim}{10}^{\ensuremath{-}3}\text{ }\text{ }\mathrm{eV}$ to match the present DE density, we can obtain the present neutrino mass in the range $m\ensuremath{\sim}{10}^{\ensuremath{-}2}--1\text{ }\text{ }\mathrm{eV}$ and consistent estimates for other parameters of the Universe.

Test of S U ( 3 ) symmetry in hyperon semileptonic decays

Abstract: Existing analyses of baryon semileptonic decays indicate the presence of a small $SU(3)$ symmetry breaking effect in hyperon semileptonic decays. However, to provide evidence for $SU(3)$ symmetry breaking, one needs a relation similar to the Gell-Mann--Okubo baryon mass formula satisfied to within a few percent, showing evidence for $SU(3)$ symmetry breaking in the divergence of the vector current matrix element. In this paper, we shall present a similar Gell-Mann--Okubo relation for the hyperon semileptonic decay axial vector form factors. Using these relations and the measured axial vector current for vector current form factor ratios, we show that the amount of $SU(3)$ symmetry breaking in hyperon semileptonic decaysis 5--11%.

Properties of the baryon antidecuplet

Abstract: We study the group structure of baryon anti-decuplet containing the $\Theta^+$. We derive the SU(3) mass relations among the pentaquark baryons in the anti-decuplet, when there is either no mixing or ideal mixing with the pentaquark octet, as advocated by Jaffe and Wilczek. This constitutes the Gell-Mann--Okubo mass formula for the pentaquark baryons. We also derive SU(3) symmetric Lagrangian for the interactions of the baryons in the anti-decuplet with the meson octet and the baryon octet. Our analysis for the decay widths of the anti-decuplet states suggests that the N(1710) is ruled out as a pure anti-decuplet state, but it may have anti-decuplet component in its wavefunction if the multiplet is mixed with the pentaquark octet.

Mass formula for quasi-black holes

Abstract: A quasi-black hole, either nonextremal or extremal, can be broadly defined as the limiting configuration of a body when its boundary approaches the body's quasihorizon. We consider the mass contributions and the mass formula for a static quasi-black hole. The analysis involves careful scrutiny of the surface stresses when the limiting configuration is reached. It is shown that there exists a strict correspondence between the mass formulas for quasi-black holes and pure black holes. This perfect parallelism exists in spite of the difference in derivation and meaning of the formulas in both cases. For extremal quasi-black holes the finite surface stresses give zero contribution to the total mass. This leads to a very special version of Abraham-Lorentz electron in general relativity in which the total mass has pure electromagnetic origin in spite of the presence of bare stresses.

Exact power series solutions of the structure equations of the general relativistic isotropic fluid stars with linear barotropic and polytropic equations of state

Abstract: Obtaining exact solutions of the spherically symmetric general relativistic gravitational field equations describing the interior structure of an isotropic fluid sphere is a long standing problem in theoretical and mathematical physics. The usual approach to this problem consists mainly in the numerical investigation of the Tolman-Oppenheimer-Volkoff and of the mass continuity equations, which describes the hydrostatic stability of the dense stars. In the present paper we introduce an alternative approach for the study of the relativistic fluid sphere, based on the relativistic mass equation, obtained by eliminating the energy density in the Tolman-Oppenheimer-Volkoff equation. Despite its apparent complexity, the relativistic mass equation can be solved exactly by using a power series representation for the mass, and the Cauchy convolution for infinite power series. We obtain exact series solutions for general relativistic dense astrophysical objects described by the linear barotropic and the polytropic equations of state, respectively. For the polytropic case we obtain the exact power series solution corresponding to arbitrary values of the polytropic index $n$. The explicit form of the solution is presented for the polytropic index $n=1$, and for the indexes $n=1/2$ and $n=1/5$, respectively. The case of $n=3$ is also considered. In each case the exact power series solution is compared with the exact numerical solutions, which are reproduced by the power series solutions truncated to seven terms only. The power series representations of the geometric and physical properties of the linear barotropic and polytropic stars are also obtained.