Mass formula

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

Giving up modular invariance constraints in heterotic orbifold vacua

Abstract: We consider D = 6, N = 1, Z M orbifold compactifications of heterotic strings in which the usual modular invariance constraints are violated. It is argued that in the presence of non-perturbative effects many of these vacua are nevertheless consistent. The perturbative massless sector can be computed explicitly from the perturbative mass formula subject to an extra shift in the vacuum energy. The non-perturbative piece is given by five-branes either moving in the bulk or stuck at the fixed points. We also discuss how to carry out this type of construction to the D = 4, N = 1 case and specific examples are presented in which non-perturbative transitions changing the number of chiral generations do occur.

Second order perturbations of a macroscopic string: Covariant approach

Abstract: Using a world-sheet covariant formalism, we derive the equations of motion for second order perturbations of a generic macroscopic string, thus generalizing previous results for first order perturbations. We give the explicit results for the first and second order perturbations of a contracting near-circular string; these results are relevant for the understanding of the possible outcome when a cosmic string contracts under its own tension, as discussed in a series of papers by Vilenkin and Garriga. In particular, second order perturbations are necessary for a consistent computation of the energy. We also quantize the perturbations and derive the mass formula up to second order in perturbations for an observer using world-sheet time {tau}. The high frequency modes give the standard Minkowski result while, interestingly enough, the Hamiltonian turns out to be nondiagonal in oscillators for low-frequency modes. Using an alternative definition of the vacuum, it is possible to diagonalize the Hamiltonian, and the standard string mass spectrum appears for all frequencies. We finally discuss how our results are also relevant for the problems concerning string-spreading near a black hole horizon, as originally discussed by Susskind.

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.

SU(6) $[{\bf 70},1^-]$ baryon multiplet in the $1/N_c$ expansion

Abstract: The masses of excited states of mixed orbital symmetry of nonstrange and strange baryons belonging to the lowest [70,1{sup -}] multiplet are calculated in the 1/N{sub c} expansion to order 1/N{sub c} with a new method which allows one to considerably reduce the number of linearly independent operators entering the mass formula. This study represents an extension to SU(6) of our work on nonstrange baryons, the framework of which was SU(4). The conclusion regarding the role of the flavor operator, neglected in previous SU(6) studies, is reinforced. Namely, both the flavor and spin operators contribute dominantly to the flavor-spin breaking.

Charged lepton mass formula — development and prospect

Abstract: The recent devolopment on the charged lepton mass forumula $m_e + m_{\mu} + m_{\tau} = \frac{2}{3}(\sqrt{m_e} + \sqrt{m_\mu} + \sqrt{m_{\tau}})^2$ is reviewed. An S3 or A4 model will be promising for the mass relation.