Showing papers on "Mass formula published in 2012"

Expanding the concept of in-hadron condensates

Abstract: The in-pseudoscalar-meson condensate can be represented through the pseudoscalar meson's scalar form factor at zero-momentum transfer With the aid of a mass formula for scalar mesons, revealed herein, the analog is shown to be true for in-scalar-meson condensates The concept is readily extended to all hadrons so that, via the zero-momentum-transfer value of any hadron's scalar form factor, one can readily extract the value for a quark condensate in that hadron which is a measure of dynamical chiral symmetry breaking

All-order equation of the effective gluon mass

Abstract: We present the general derivation of the full non-perturbative equation that governs the momentum evolution of the dynamically generated gluon mass, in the Landau gauge. The entire construction hinges crucially on the inclusion of longitudinally coupled vertices containing massless poles of non-perturbative origin, which preserve the form of the fundamental Slavnov-Taylor identities of the theory. The mass equation is obtained from a previously unexplored version of the Schwinger-Dyson equation for the gluon propagator, particular to the PT-BFM formalism, which involves a reduced number of "two-loop dressed" diagrams, thus simplifying the calculational task considerably. The two-loop contributions turn out to be of paramount importance, modifying the qualitative features of the full mass equation, and enabling the emergence of physically meaningful solutions. Specifically, the resulting homogeneous integral equation is solved numerically, subject to certain approximations, for the entire range of physical momenta, yielding positive-definite and monotonically decreasing gluon masses.

Hybrid quark-diquark baryon model

Abstract: A simple hybrid quark-diquark model for the baryons is constructed as a partial solution to the well-known ``missing resonances'' problem. In this model, the quark-diquark approach is merged with the usual constituent three-quark model. The underlying idea is that the quark-diquark approach describes the excited states while the three-quark model the ground states. The spectrum is calculated through a mass formula, a generalization of the G\"ursey-Radicati formula, built to reproduce the rotational and vibrational Regge trajectories. Using the quark-diquark scheme, we were also able to describe the spin-flavor degrees of freedom in the framework of an algebraic model. Moreover, we have constructed a complete classifications of the possible quark-diquark states only based on group theory and thus it can be useful both for other model builders and for experimentalists.

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 (L, Q) as a product of local factors, called the local densities of (L,Q). This mass formula is an essential tool for the classification of integral quadratic lattices. In this paper, we will describe the local density formula explicitly, by constructing a smooth integral group scheme model for an appropriate orthogonal group. Our method works for any unramified finite extension of Q_2. Therefore, we give a long awaited proof for the local density formula of Conway and Sloane and discover its generalization to unramified finite extensions of Q_2. As an example, we give the mass formula for the integral quadratic form Q_n(x_1, ..., x_n)=x_1^2 + ... + x_n^2 associated to a number field k which is totally real and such that the ideal (2) is unramified over k.

The Koide Lepton Mass Formula and Geometry of Circles

Abstract: A remarkable formal similarity between Koide's Lepton mass formula and a generalized Descartes circle formula is reported.

Determination of the effective atomic and mass numbers for mixture and compound materials in high energy photon interactions

Abstract: In consideration the radiological properties of materials and studying the scattering processes in atomic and nuclear physics, the effective atomic and mass numbers is widely employed. These numbers have been calculated for any mixed or composite materials in interaction with high energy photons (Linac in radiation therapy). A pair equation in terms of these numbers is obtained. The first equation has been derived from the conservation of mass energy law and the second by minimizing the binding energy from the semiempirical mass formula (Myers and Swiatecki formula) that gives a relation between atomic and mass numbers for stable nuclei approximately. By these equations one can obtain the effective atomic and mass numbers for any compound or mixed materials uniquely. These numbers are calculated for some materials and compared with the other studies.

A new method for obtaining the spectrum of baryon resonances in the Killingbeck potential

Abstract: In this paper, we investigate the spin- and flavor-dependent SU(6) violations in the baryon resonances spectrum using a simple approach based on the G?rsey?Radicati (GR) mass formula. The relativistic energy spectrum has some very important features that makes it vastly superior to the nonrelativistic one; so, in order to obtain the average energy value of each SU(6) multiplet, we have exactly solved the Dirac equation for the Killingbeck potential analytically by using the wave function ansatz method. The results of our model (the combination of our proposed hypercentral potential and the generalized GR mass formula for the description of the spectrum) show that the strange and nonstrange baryon spectra are, in general, fairly well reproduced. The overall good description of the spectrum which we obtain shows that our model can also be used to give a fair description of the energies of the excited multiplets with more than 2?GeV mass and negative-parity resonance. Moreover, we have shown that our model reproduces the position of the Roper resonance of the nucleon. Finally, we compare the results obtained by the Dirac equation for the Killingbeck potential with the corresponding results of the Schr?dinger equation for the Cornell potential and we find that our model has improved the results of the nonrelativistic model.

Evaluation of the degree of restoration of broken Wigner's SU(4) spin-isospin symmetry in nuclei

Abstract: The Franzini-Radicati factor R was calculated on the basis of experimental data on the masses of nuclei in the mass-number range of 5 ≤ A ≤ 257. The values calculated for this factor made it possible to evaluate the degree of fulfillment of Wigner’s SU(4) spin-isospin symmetry in nuclei. An expression for the factor R was obtained on the basis of Wigner’s mass formula. This expression is isospin-dependent and takes into account odd-even variations in the mass. The formula for the factor R describes the separation of nuclei into threeWigner-type groups. The values calculated for the factor R were analyzed by the method of Student’s t criterion, and it was inferred from the results of this analysis that only for nuclei having odd values of the mass number A and an isospin in the range of Tz ≥ 53/2 is broken Wigner’s SU(4) spin-isospin symmetry restored, the confidence level being α = 0.01.

NEUTRON RICH NUCLEI IN A NEW BINDING ENERGY FORMULA AND THE ASTROPHYSICAL r-PROCESS

Abstract: Neutron rich nuclei has been studied with a new phenomenological mass formula. Predictions of different mass formulas for the location of the neutron drip line are compared with those from the present calculation. The implications of the new mass formula for r-process nucleosynthesis are discussed. It is found that though the neutron drip line obtained from this formula differs substantially from other formulas, the r-process abundance upto mass 200 are unlikely to be significantly different. The errors inherent in the mass formula are found to play an insignificant role beyond mass A = 80.

Group schemes and local densities of ramified hermitian lattices in residue characteristic 2 Part I

Abstract: The obstruction to the local-global principle for a hermitian lattice (L, H) can be quantified by computing the mass of (L, H). The mass formula expresses the mass of (L, H) as a product of local factors, called the local densities of (L, H). The local density formula is known except in the case of a ramified hermitian lattice of residue characteristic 2. Let F be a finite unramified field extension of Q_2. Ramified quadratic extensions E/F fall into two cases that we call Case 1 and Case 2. In this paper, we obtain the local density formula for a ramified hermitian lattice in Case 1, by constructing a smooth integral group scheme model for an appropriate unitary group. Consequently, this paper, combined with the paper of W. T. Gan and J.-K. Yu, allows the computation of the mass formula for a hermitian lattice (L, H) in Case 1.

Endpoint of rp Process Using Relativistic Mean Field Approach and a New Mass Formula

Abstract: Densities from relativistic mean field calculations are applied to construct the optical potential and, hence calculate the endpoint of the rapid proton capture (rp) process. Mass values are taken from a new phenomenological mass formula. Endpoints are calculated for different temperature-density profiles of various X-ray bursters. We find that the rp process can produce significant quantities of nuclei upto around mass 95. Our results differ from existing works to some extent.

Endpoint of $rp$ process using relativistic mean field approach and a new mass formula

Abstract: Densities from relativistic mean field calculations are applied to construct the optical potential and, hence calculate the endpoint of the rapid proton capture ($rp$) process. Mass values are taken from a new phenomenological mass formula. Endpoints are calculated for different temperature- density profiles of various X-ray bursters. We find that the $rp$ process can produce significant quantities of nuclei upto around mass 95. Our results differ from existing works to some extent.

Glueball masses and Regge trajectories for the QCD-inspired potential

Abstract: The bound state of two massive constituent gluons is studied in the potential approach. The relativistic quasi-classical wave equation with the QCD-inspired scalar potential is solved by the quasi-classical method in the complex plane. Glueball masses are calculated with the help of the universal mass formula. The hadron Regge trajectories are given by the complex non-linear function in the whole region of the invariant variable t. The Chew–Frautschi plot of the leading glueball trajectory, α P (t), has the properties of a t-channel Pomeron, which is dual to the glueball states in the s channel. The imaginary part of the Pomeron is also calculated.

Glueball masses and Regge trajectories for the QCD-inspired potential

Abstract: The bound state of two massive constituent gluons is studied in the potential approach. The relativistic quasi-classical wave equation with the QCD-inspired scalar potential is solved by the quasi-classical method in the complex plane. Glueball masses are calculated with the help of the universal mass formula. The hadron Regge trajectories are given by the complex non-linear function in the whole region of the invariant variable t . The Chew–Frautschi plot of the leading glueball trajectory, αP (t), has the properties of a t-channel Pomeron, which is dual to the glueball states in the s channel. The imaginary part of the Pomeron is also calculated.

Reinterpretation of the Mass Formula for Black Holes

Abstract: Since these elementary considerations about the black hole mass formula were not given in the original articles, nor seem to be found in any reviews since those early days of the renaissance of general relativity, it seems useful to present them now.

A relativistic model for the light baryon masses in hypercentral potential and spin-flavor dependence

Abstract: In this paper, we studied the light baryon resonances spectrum within a relativistically quark model based on Dirac equation and generalized Gursey Radicati mass formula (GR). For exact solving of the Dirac equation for our proposed hypercentral confining potential analytically, we used the Ansatz approach. The results of our model show that the light baryons spectrums are fairly well reproduced, thanks to the flavor-dependent interaction. The overall good description of the spectrums which we obtain shows that our model can also be used to give a fair description of the energies of the negativeparity resonance and excited multiplets, at least up to 3 GeV. Eventually, we compare the results obtained from our model with the corresponding results of the Schrodinger equation for the Coulombiclike term plus a linear confining term and we found out that our model has certainly improved the results of the non-relativistic model.

Black holes with metric and fields of the same form

Abstract: We present two rotating black hole solutions with axion ξ, dilaton \({\phi}\) and two U(1) vector fields. Starting from a non-rotating metric with three arbitrary parameters, which we have found previously, and applying the “Newman–Janis complex coordinate trick” we get a rotating metric gμν with four arbitrary parameters namely the mass M, the rotation parameter a and the charges electric QE and magnetic QM. Then we find a solution of the equations of motion having this gμν as metric. Our solution is asymptotically flat and has angular momentum J = Ma, gyromagnetic ratio g = 2, two horizons, the singularities of the solution of Kerr, axion and dilaton singular only when r = a cos θ = 0 etc. By applying to our solution the S-duality transformation we get a new solution, whose axion, dilaton and vector fields have one more parameter. The metrics, the vector fields and the quantity \({\lambda=\xi+ie^{-2\phi}}\) of our solutions and the solution of: Sen for QE, Sen for QE and QM, Kerr–Newman for QE and QM, Kerr, Reference Kyriakopoulos [Class. Quantum Grav. 23:7591, 2006, Eqs. (54–57)], Shapere, Trivedi and Wilczek, Gibbons–Maeda–Garfinkle–Horowitz–Strominger, Reissner–Nordstrom, Schwarzschild are the same function of a, and two functions ρ2 = r(r + b) + a2 cos2θ and Δ = r(r + b) − 2Mr + a2 + c, of a, b and two functions for each vector field, and of a, b and d respectively, where a, b, c and d are constants. From our solutions several known solutions can be obtained for certain values of their parameters. It is shown that our two solutions satisfy the weak the dominant and the strong energy conditions outside and on the outer horizon and that all solutions with a metric of our form, whose parameters satisfy some relations satisfy also these energy conditions outside and on the outer horizon. This happens to all solutions given in the “Appendix”. Mass formulae for our solutions and for all solutions which are mentioned in the paper are given. One mass formula for each solution is of Smarr’s type and another a differential mass formula. Many solutions with metric, vector fields and λ of the same functional form, which include most physically interesting and well known solutions, are listed in an “Appendix”.

Tadpole cancellation in top-quark condensation

Abstract: We show that quadratic divergences in top-quark condensation are cancelled when the tadpoles cancel. This latter cancellation is naturally implemented as the cancellation among the top-quark, Goldstone and Higgs contributions. We also calculate the bosonic correction terms to Gribov's mass formula for the Higgs boson. These reduce the prediction for M_H from 167 GeV to 132 GeV. The tadpole cancellation condition by itself is an independent condition on the mass of the Higgs boson which, in Gribov's U(1)_Y scenario, yields M_H \approx 117 GeV with large theoretical uncertainty. More generally, we are able to obtain all three masses, M_W, m_t and M_H, in 100 MeV to 10 TeV energy range as a function of the cut-off scale and the gauge couplings only.

Highly excited negative parity baryons in the 1/Nc expansion.

Abstract: The masses of experimentally known highly excited baryons of negative parity supposed to belong to the $[{\bf 70},\ell^-]$ multiplets ($\ell$ = 1,2,3) of the $N = 3$ band are calculated in the $1/N_c$ expansion method to order $1/N_c$ by using a procedure which allows to considerably reduce the number of linearly independent operators entering the mass formula. The numerical fits to present data show that the coefficients encoding the QCD dynamics have large, comparable values, for the flavor and spin operators. It implies that these operators contribute dominantly to the flavor-spin SU(6) symmetry breaking, like for the $[{\bf 70},1^-]$ multiplet of the $N = 1$ band.

Generalized Smarr formula as a local identity for arbitrary dimensional black holes

Abstract: We discuss a method based on Killing symmetries and Komar conserved charges to generalize Smarr mass formula for arbitrary dimensional charged, rotating spacetime. We derive a local identity defined at the event horizon of the rotating black hole in Einstein-Maxwell gravity which reproduces the generalized Smarr formula as a by-product. The advantages of this new identity are the following: (i) unlike Smarr formula, which is non-local, this identity is purely local and hence a switchover between horizon and infinity is unnecessary and (ii) the new identity could be mapped with the recent investigations on emergent gravity.

A new baryonic equation of state at sub-nuclear densities for core-collapse simulations

Abstract: We construct a new equation of state for baryons at sub-nuclear densities for the use in core-collapse simulations of massive stars. The formulation is based on the nuclear statistical equilibrium description and the liquid drop approximation of nuclei. The model free energy to minimize is calculated by using relativistic mean field theory for nucleons and the mass formula for nuclei with atomic number up to ∼ 1000. We have also taken into account the pasta phase. We find that the free energy and other thermodynamical quantities are not very different from those given in the standard EOSs that adopt the single nucleus approximation. On the other hand, the average mass is systematically different, which may have an important effect to the rates of electron captures and coherent neutrino scatterings on nuclei in supernova cores. It is also interesting that the root mean square of the mass number is not very different from the average mass number, since the former is important for the evaluation of coherent ...

Generalized Smarr formula as a local identity for arbitrary dimensional black holes

Abstract: We discuss a method based on Killing symmetries and Komar conserved charges to generalize Smarr mass formula for arbitrary dimensional charged, rotating spacetime. We derive a local identity defined at the event horizon of the rotating black hole in Einstein-Maxwell gravity which reproduces the generalized Smarr formula as a by-product. The advantages of this new identity are the following: (i) unlike Smarr formula, which is non-local, this identity is purely local and hence a switchover between horizon and infinity is unnecessary and (ii) the new identity could be mapped with the recent investigations on emergent gravity.

Volume-averaged Mass Equations for Multiphase Flow in Porous Media for In Situ Combustion

Abstract: The multiphase flow of oil, water, and gas through porous media is presented when the in situ combustion technique is applied in oil reservoirs. This technique implies phenomena such as phase change, chemical reactions, and heat transfer, among others. The mathematical modeling of such a technique requires the deduction of mass, momentum, and energy equations, taking into account the phenomena mentioned. In this work the volume-averaged mass transport equations for gas (g), oil (o), and water (w) flowing simultaneously through a homogeneous, isotropic, rigid, and nonpermeable porous media (s) were obtained. The mass equation for the deposited coke in the porous media was also obtained. To obtain the equations, the local mass equations for phases as well as their corresponding jump conditions were used as starting point. We took the following into account: (a) the gas compressibility, (b) the mass generation of coke due to the chemical reaction of oil, (c) the mass generation of gas due to the com...

Particle mass formulae

Abstract: Important relations among some particle masses are investigated. The eta-prime / eta masses’ ratio is noted to be a fraction of integers with high precision. The masses of muon, kaon, eta, and neutron are observed to fit a linear mass formula within an accuracy of 0.25 MeV.

Glueball masses and Regge trajectories for the QCD-inspired potential

Abstract: Bound state of two massive constituent gluons is studied in the potential approach. Relativistic quasi-classical wave equation with the QCD-inspired scalar potential is solved by the quasi-classical method in the complex plane. Glueball masses are calculated with the help of the universal mass formula. The hadron Regge trajectories are given by the complex non-linear function in the whole region of the invariant variable $t$. The Chew-Frautschi plot of the leading glueball trajectory, $\alpha_P(t)$, has the properties of the t-channel Pomeron, which is dual to the glueball states in the s channel. The imaginary part of the Pomeron is also calculated.

Complex masses of resonances and the Cornell potential

Abstract: Physical properties of the Cornell potential in the complex-mass scheme are investigated. Two exact asymptotic solutions of relativistic wave equation for the coulombic and linear components of the potential are used to derive the resonance complex-mass formula. The centered masses and total widths of the $\rho$-family resonances are calculated.

Neutron rich nuclei in a new binding energy formula and the astrophysical $r-$process

Abstract: Neutron rich nuclei has been studied with a new phenomenological mass formula. Predictions of different mass formulas for the location of the neutron dripline are compared with those from the present calculation. The implications of the new mass formula for r-process nucleosynthesis are discussed. It is found that though the neutron drip line obtained from this formula differs substantially from other formulas, the r-process abundance upto mass 200 are unlikely to be significantly different. The errors inherent in the mass formula are found to play an insignificant role beyond mass A = 80.