Showing papers on "Mass formula published in 2015"

Area product and mass formula for Kerr–Newman–Taub–NUT spacetime

Abstract: We derive area product, entropy product, area sum and entropy sum of the event horizon and Cauchy horizons for Kerr–Newman–Taub–NUT (Newman–Unti–Tamburino) black hole in four-dimensional Lorentzian geometry. We observe that these thermodynamic products are not universal (mass-independence) for this black hole (BH), whereas for Kerr–Newman (KN) BH such products are universal (mass-independence). We also examine the entropy sum and area sum. It is shown that they all depend on mass, charge and NUT parameter of the background spacetime. Thus, we can conclude that the universal (mass-independence) behavior of area product and entropy product, area sum and entropy sum for Kerr–Newman–Taub–NUT (KNTN) BH fails and which is also quite different from KN BH. We further show that the KNTN BH do not possess first law of BH thermodynamics and Smarr–Gibbs–Duhem relations, and that such relations are unlikely in the KN case. The failure of these aforementioned features are due to presence of the nontrivial NUT charge which makes the spacetime to be asymptotically non-flat, in contrast with KN BH. The other reason of the failure is that Lorentzian KNTN geometry contains Dirac–Misner type singularity, which is a manifestation of a nontrivial topological twist of the manifold. The BH mass formula and Christodoulou–Ruffini mass formula for KNTN BHs are also derived. Finally, we compute the area bound which is just Penrose like inequality for event horizon. From area bound we derive entropy bound. These thermodynamic products on the multi-horizon play a crucial role in BH thermodynamics to understand the microscopic nature of BH entropy.

Mass Formulas for Local Galois Representations and Quotient Singularities. I: A Comparison of Counting Functions

Abstract: We study a relation between the Artin conductor and the weight coming from the motivic integration over wild Deligne-Mumford stacks. As an application, we prove some version of the McKay correspondence, which relates Bhargava's mass formula for extensions of a local field and the Hilbert scheme of points.

On static Poincaré-Einstein metrics

Abstract: The classification of solutions of the static vacuum Einstein equations, on a given closed manifold or an asymptotically flat one, is a long-standing and much-studied problem. Solutions are characterized by a complete Riemannian n-manifold (M, g) and a positive function N, called the lapse. We study this problem on Asymptotically Poincare-Einstein n-manifolds, n ≥ 3, when the conformal boundary-at-infinity is either a round sphere, a flat torus or smooth quotient thereof, or a compact hyperbolic manifold. Such manifolds have well-defined Wang mass, and are time-symmetric slices of static, vacuum, asymptotically anti-de Sitter spacetimes. By integrating a mildly generalized form of an identity used by Lindblom, Shen, Wang, and others, we give a mass formula for such manifolds. There are no solutions with positive mass. In consequence, we observe that either the lapse is trivial and (M, g) is Poincare-Einstein or the Wang mass is negative, as in the case of time symmetric slices of the AdS soliton. As an application, we use the mass formula to compute the renormalized volume of the warped product (X, γ) ≃ (M 3 , g) × N 2 (S 1 , dt 2). We also give a mass formula for the case of a metric that is static in the region exterior to a horizon on which the lapse function is zero. Then the manifold (X, γ) is said to have a “bolt” where the S 1 factor shrinks to zero length. The renormalized volume of (X, γ) is expected on physical grounds to have the form of the free energy per unit temperature for a black hole in equilibrium with a radiation bath at fixed temperature. When M is 3-dimensional and admits a horizon, we apply this mass formula to compute the renormalized volume of (X, γ) and show that it indeed has the expected thermodynamically motivated form. We also discuss several open questions concerning static vacuum asymptotically Poincare-Einstein manifolds.

Group schemes and local densities of quadratic lattices in residue characteristic 2

Abstract: The celebrated Smith–Minkowski–Siegel mass formula expresses the mass of a quadratic lattice .

Revalidation of the isobaric multiplet mass equation for the A = 20 quintet

Abstract: An unexpected breakdown of the isobaric multiplet mass equation in the A = 20, T = 2 quintet was recently reported, presenting a challenge to modern theories of nuclear structure. In the present work, the excitation energy of the lowest T = 2 state in Na-20 has been measured to be 6498.4 +/- 0.2stat ± 0.4syst keV by using the superallowed 0+ → 0+ beta decay of Mg-20 to access it and an array of high-purity germanium detectors to detect its gamma-ray deexcitation. This value differs by 27 keV (1.9 standard deviations) from the recommended value of 6525 ± 14 keV and is a factor of 28 more precise. The isobaric multiplet mass equation is shown to be revalidated when the new value is adopted.

Spinor Structure and Internal Symmetries

Abstract: Spinor structure and internal symmetries are considered within one theoretical framework based on the generalized spin and abstract Hilbert space. Complex momentum is understood as a generating kernel of the underlying spinor structure. It is shown that tensor products of biquaternion algebras are associated with the each irreducible representation of the Lorentz group. Space-time discrete symmetries P, T and their combination PT are generated by the fundamental automorphisms of this algebraic background (Clifford algebras). Charge conjugation C is presented by a pseudoautomorphism of the complex Clifford algebra. This description of the operation C allows one to distinguish charged and neutral particles including particle-antiparticle interchange and truly neutral particles. Spin and charge multiplets, based on the interlocking representations of the Lorentz group, are introduced. A central point of the work is a correspondence between Wigner definition of elementary particle as an irreducible representation of the Poincare group and SU(3)-description (quark scheme) of the particle as a vector of the supermultiplet (irreducible representation of SU(3)). This correspondence is realized on the ground of a spin-charge Hilbert space. Basic hadron supermultiplets of SU(3)-theory (baryon octet and two meson octets) are studied in this framework. It is shown that quark phenomenologies are naturally incorporated into presented scheme. The relationship between mass and spin is established. The introduced spin-mass formula and its combination with Gell-Mann–Okubo mass formula allows one to take a new look at the problem of mass spectrum of elementary particles.

Baryon resonances in large Nc QCD

Abstract: We review the current status and present open challenges of large $N_c$ QCD baryon spectroscopy. After introducing the $1/N_c$ expansion method we first shortly revisit the latest achievements for the ground state properties. Next we discuss the applicability of this method to excited states, presenting two different approaches with their advantages and disadvantages. Selected results for the spectrum and strong and electromagnetic decays are described. We also show further developments supported by the qualitative compatibility between the quark excitation picture and the meson-nucleon scattering picture. We give a quantitative comparison between results obtained from the mass formula of the $1/N_c$ expansion method and quark models and shortly discuss the implications of different large $N_c$ limits.

Weizsäcker–Skyrme-type mass formula by considering radial basis function correction

Abstract: By incorporating with the radial basis function correction, the Weizsacker-Skyrme-type nuclear mass formula was further improved. The root-mean-square (rms) deviation of the binding energies between the theoretical calculations and 2267 experimental masses has been significantly reduced from 493 keV to 323 keV. The alpha-decay energies Q(alpha) obtained from the binding energy by this hybrid formula also become more precise, i.e. the rms deviations for the Z = 74-118 even-even isotopes and for the 46 superheavy nuclei fall from 420 keV to 161 keV and from 501 keV to 230 keV, respectively. With the above calculated Q(alpha) values as inputs, the calculated alpha-decay half-lives for the even-even (Z = 74-118) nuclei agree with the experimental ones very well, especially for the superheavy nuclei. Thus the further improved Weizsacker-Skyrme-type nuclear mass formula is useful for predicting nuclear properties associated with mass evaluation systematically.

On static Poincaré-Einstein metrics

Abstract: The classification of solutions of the static vacuum Einstein equations, on a given closed manifold or an asymptotically flat one, is a long-standing and much-studied problem. Solutions are characterized by a complete Riemannian n-manifold (M, g) and a positive function N, called the lapse. We study this problem on Asymptotically Poincare-Einstein n-manifolds, n ≥ 3, when the conformal boundary-at-infinity is either a round sphere, a flat torus or smooth quotient thereof, or a compact hyperbolic manifold. Such manifolds have well-defined Wang mass, and are time-symmetric slices of static, vacuum, asymptotically anti-de Sitter spacetimes. By integrating a mildly generalized form of an identity used by Lindblom, Shen, Wang, and others, we give a mass formula for such manifolds. There are no solutions with positive mass. In consequence, we observe that either the lapse is trivial and (M, g) is Poincare-Einstein or the Wang mass is negative, as in the case of time symmetric slices of the AdS soliton. As an application, we use the mass formula to compute the renormalized volume of the warped product (X, γ) ≃ (M 3 , g) × N 2 (S 1 , dt 2). We also give a mass formula for the case of a metric that is static in the region exterior to a horizon on which the lapse function is zero. Then the manifold (X, γ) is said to have a “bolt” where the S 1 factor shrinks to zero length. The renormalized volume of (X, γ) is expected on physical grounds to have the form of the free energy per unit temperature for a black hole in equilibrium with a radiation bath at fixed temperature. When M is 3-dimensional and admits a horizon, we apply this mass formula to compute the renormalized volume of (X, γ) and show that it indeed has the expected thermodynamically motivated form. We also discuss several open questions concerning static vacuum asymptotically Poincare-Einstein manifolds.

On the role of strong interaction in understanding nuclear beta stability line and nuclear binding energy

Abstract: In this paper an attempt is made to fit and understand the nuclear binding energy and proton-neutron beta stability lime in terms of strong interaction. In nuclear physics, generally the semi-empirical mass formula (SEMF) is used to approximate the mass and various other properties of an atomic nucleus [1]. In modern nuclear physics the corresponding semi empirical relation can be expressed as follows. With usual notation,

Relativistic three-body quark model of light baryons based on hypercentral approach

Abstract: In this paper, we have treated the light baryons as a relativistic three-body bound system Inspired by lattice QCD calculations, we treated baryons as a spin-independent three-quark system within a relativistic three-quark model based on the three-particle Klein–Gordon equation We presented the analytical solution of three-body Klein–Gordon equation with employing the constituent quark model based on a hypercentral approach through which two- and three-body forces are taken into account Herewith the average energy values of the up, down and strange quarks containing multiplets are reproduced To describe the hyperfine structure of the baryon, the splittings within the SU(6)-multiplets are produced by the generalized Gursey Radicati mass formula The considered SU(6)-invariant potential is popular "Coulomb-plus-linear" potential and the strange and non-strange baryons spectra are in general well reproduced

Analytical mass formula and nuclear surface properties in the ETF approximation

Abstract: The problem of the determination of the nuclear surface and surface symmetry energy is addressed in the framework of the Extended Thomas Fermi (ETF) approximation using Skyrme functionals. We propose an analytical model for the density profiles with variationally determined diffuseness parameters. For the case of symmetric nuclei, the resulting ETF functional can be exactly integrated, leading to an analytical formula expressing the surface energy as a function of the couplings of the energy functional. The importance of non-local terms is stressed, which cannot be simply deduced from the local part of the functional. In the case of asymmetric nuclei, we propose an approximate expression for the diffuseness and the surface energy. These quantities are analytically related to the parameters of the energy functional. In particular, the influence of the different equation of state parameters can be explicitly quantified. Detailed analyses of the different energy components (local/non-local, isoscalar/isovector, surface/curvature and higher order) are also performed. Our analytical solution of the ETF integral improves over previous models and leads to a precision better than 200 keV per nucleon in the determination of the nuclear binding energy for dripline nuclei.

Mass Formula of a Five-dimensional Almost-BPS Supergravity Soliton with a Magnetic "Bolt"

Abstract: We derive the Smarr formula for a five-dimensional spacetime which has a magnetic “bolt” in its center and is asymptotically R 1,3 ×S 1 . Supersymmetry – and so the BPS-bound – is broken by the holonomy. We show how each topological feature of a space-like hypersurface enters the mass formula and which ones in particular give rise to the violation of the BPS-bound.

Smarr formula for black holes endowed with both electric and magnetic charges

Abstract: The present paper clarifies how to consistently take into account the contribution of magnetic charges in the generalized Smarr mass formula by using properly the Tomimatsu's representation of Komar integrals. It is shown in particular that in all three examples of the dyonic solutions considered by us, the sum of the two electromagnetic terms in Smarr's formula can be cast into the form $\bar{\cal Q}\Phi^H_{ext}$, where ${\cal Q}$ is the complex charge and $\Phi^H_{ext}$ the complex extension of the electric potential.

Remarks on Smarr's mass formula in the presence of both electric and magnetic charges

Abstract: The present paper clarifies how to use correctly Tomimatsu's representation of Komar integrals for consistently taking into account the contribution of magnetic charges in the generalized Smarr mass formula. In all three examples of the dyonic solutions considered by us, the sum of the two electromagnetic terms in that formula can be cast into the form $\bar{\cal Q}\Phi^H_{ext}$, where ${\cal Q}$ is the complex charge and $\Phi^H_{ext}$ the complex extension of the electric potential.

Nuclear physics from QCD on lattice

Abstract: We have presented a strategy to study nuclei and nuclear matters from first principles, namely, from QCD. We first compute nucleon-nucleon potentials numerically in lattice QCD, and then use them to investigate properties of nuclei and nuclear matter by various methods developed in nuclear physics. As a demonstration that this strategy works, mass and structure of ^4^He, ^16^O and ^40^Ca, and equation of state of nuclear matters are determined with the lattice QCD induced two-nucleon potentials in a heavy quark region as an input. We have found that these nuclei and the symmetric nuclear matter are bound at one quark mass corresponding to the pseudo-scalar meson (pion) mass of 469 MeV (the octet baryon (nucleon) mass of 1161 MeV). The obtained binding energy per nucleon has a uniform mass-number A dependence which is consistent to the Bethe-Weizsacker mass formula qualitatively. The present study demonstrates that our strategy works well to investigate various properties of atomic nuclei and nuclear matter starting from QCD, without depending on models or experimental information about the nuclear force.

Spectrum of light and strange baryon resonances under the decatic potential

Abstract: In this paper, we calculate the light and strange baryons spectrum using a new baryon mass formula. For this purpose we have exactly solved the radial Schrodinger equation in six-dimensional Hilbert space under the decatic potential by power series method via a suitable ansatz to the wave function with parameters those existing in the potential function, possibly for the first time. By applying our model, we find a good agreement for the even and odd parity resonances, the excited multiplets up to 3 GeV and the position of the Roper resonances of the nucleon with the spectrum of the particle data group.

A New Method for Obtaining the Baryons Mass under the Killingbeck Plus Isotonic Oscillator Potentials

Abstract: In this work, the spectrum of ground state and excited baryons (N, {\Delta}, , , and {\Omega} particles) has been investigated by using a non-relativistic quantum mechanics under the Killingbeck plus isotonic oscillator potentials. Using the Jacobi-coordinates, anzast method and generalized Gursey Radicati (GR) mass formula the three body wave equation is solved to calculate the different states of the considered baryons. A comparison between our calculations and the available experimental data shows that the position of the Roper resonances of the nucleon, the ground states and the excited multiplets up to three GeV are in general well reproduced. Also one can conclude that; the interaction between the quark constituents of baryon resonances could be described adequately by using the combination of Killingbeck and isotonic oscillator potentials form.

Weighted Discriminants and Mass Formulas for Number Fields

Abstract: We define the notion of a weighted discriminant and corresponding counting function for number fields, and what it means for these counting functions to have a mass formula for a set of primes. We extend a result of Kedlaya to show that any proper counting function for a finite group $\Gamma$ has a mass formula for the set of primes not dividing $|\Gamma|$. We also prove that if $\Gamma$ is an $\ell$-group for some prime $\ell$, then there are only finitely many weighted discriminant counting functions for $\Gamma$-extensions of $\Q$ that have a mass formula for all primes. Finally, we enumerate all such counting functions for $\Gamma=D_4$ and $\Gamma=Q_8$.

On static Poincar\'e-Einstein metrics

Abstract: The classification of solutions of the static vacuum Einstein equations, on a given closed manifold or an asymptotically flat one, is a long-standing and much-studied problem. Solutions are characterized by a complete Riemannian $n$-manifold $(M,g)$ and a positive function $N$, called the lapse. We study this problem on Asymptotically Poincare-Einstein $n$-manifolds, $n\ge 3$, when the conformal boundary-at-infinity is either a round sphere, a flat torus or smooth quotient thereof, or a compact hyperbolic manifold. Such manifolds have well-defined Wang mass, and are time-symmetric slices of static, vacuum, asymptotically anti-de Sitter spacetimes. By integrating a mildly generalized form of an identity used by Lindblom, Shen, Wang, and others, we give a mass formula for such manifolds. In consequence, we observe that either the lapse is trivial and $(M,g)$ is Poincare-Einstein or the Wang mass is negative, as in the case of time symmetric slices of the AdS soliton. As an application, we use the mass formula to compute the renormalized volume of the warped product $(X,\gamma) = (M^3,g) \times_{N^2} (S^1,dt^2)$. We also give a mass formula for the case of a metric that is static in the region exterior to a horizon on which the lapse function is zero. Then the manifold $(X,\gamma)$ is said to have a "bolt" where the $S^1$ factor shrinks to zero length. The renormalized volume of $(X,\gamma)$ is expected on physical grounds to have the form of the free energy per unit temperature for a black hole in equilibrium with a radiation bath at fixed temperature. When $M$ is 3-dimensional and admits a horizon, we apply this mass formula to compute the renormalized volume of $(X,\gamma)$ and show that it indeed has the expected thermodynamically motivated form.

Some group theoretical mass formulae

Abstract: A 'mass formula' is a formula involving a sum of reciprocals of automorphism groups orders. We provide several such formulae, e.g. ones involving covering groups of finite groups. Others generalize a formula of P.Hall, repalcing the class of abelian $p$-groups by subclasses, or by isoclinism classes of non-abelian groups, also by replacing automorphism groups by holomorphs, etc. We also note relations with the Rogers-Ramanujan and related identities.

Alternative method for evaluating the pair energy of nucleons in nuclei

Abstract: An alternative method for determining the odd–even effect parameter related to special features of the Casimir operator in Wigner’s mass formula for nuclei is proposed. A procedure for calculating this parameter is presented. The proposed method relies on a geometric interpretation of the Casimir operator, experimental data concerning the contribution of spin–orbit interaction to the nuclear mass for even–even and odd–odd nuclei, and systematics of energy gaps in the spectra of excited states of even–even nuclei.

Comment on "Lattice determination of $\Sigma$-$\Lambda$ mixing"

Abstract: A recent lattice QCD (LQCD) calculation of $\Sigma$-$\Lambda$ mixing by the QCDSF-UKQCD Collaboration [Phys. Rev. D 91, 074512 (2015)] finds a mixing angle about half of that found from the Dalitz-von Hippel (DvH) flavor SU(3) mass formula which relates the $\Sigma$-$\Lambda$ mixing matrix element to known octet baryon mass differences and which has been used widely to evaluate charge symmetry breaking effects in $\Lambda$ hypernuclei. We show that the LQCD-calculated $\Sigma$-$\Lambda$ mixing matrix element and octet baryon masses satisfy the DvH mass formula, concluding thereby that a good LQCD evaluation of $\Sigma$-$\Lambda$ mixing requires an equally good reproduction of octet baryon mass differences which is yet to be demonstrated.

Counting Extensions of $\mathfrak{p}$-Adic Fields with Given Invariants

Abstract: We give two specializations of Krasner's mass formula. The first formula yields the number of extensions of a $\mathfrak{p}$-adic field with given, inertia degree, ramification index, discriminant, and ramification polygon. We then refine this formula further to the case where an additional invariant related to the residual polynomials of the segments of the ramification polygon is given.

Separation energies of light nuclei with atomic number from 1 to 20

Abstract: The 1n and 1p halo nuclei from atomic number 1 to 20 are discussed here to calculate the variation of separation energy with mass defect and binding energy. Semi-empirical mass formula and shell model are the methods applied here. The appearances of p- and r-branches satisfying the selection rules for different isotopes of nuclides are discussed.

The Mass of the Electron (II)

Abstract: A formula for the mass of the electron is derived from a lepton mass factor, a Koidean ratio for quarks and a dimensionless factor based on the fine-structure constant. If this formula were correct it would prove a profound relationship between the masses of leptons and quarks.

Incoherence of the Relativistic Dynamics: e = Mc2 Contradicts Special Relativity!

Abstract: The ‘relativistic” mass concept is rooted in the problematic longitudinal and transverse mass equations emerging from the Lorentz transformation, as presented by Einstein in his 1905 paper on Special Relativity. These equations, although actual outcomes of the Special Relativity, and verified in this paper through both simplified dimensional analyses and conservation of energy principle, had later been implicitly dropped and replaced by an ad-hoc relativistic mass equation, needed to maintain the consistency of the Special Relativity with the conservation of momentum law—although it results in its violation of the law of conservation of energy. Maintaining the latter law, results in the same transverse mass equation as obtained in Einstein’s said paper. The relativistic mass adopted in the literature is but an attempt to conceal contradictions in the Special Relativity, and a convenient means for arriving at the relativistic kinetic energy formula implying the desired mass-energy equivalence equation E = mc2. In this paper, the incoherence of the Special Relativity emerging from its established mass formulae is revealed through simplified physical demonstrations. Depending on the force definition and the “moving” mass equation used, four different formulae for the relativistic kinetic energy are obtained, all validated from the Special Relativity perspective, creating a detrimental incoherence in the theory. All these formulae are reduced to the classical kinetic energy equation for v << c (v = velocity, c = speed of light). It is revealed that the energy equation E = mc2 is not a valid consequence of the Special Relativity.