Space-time and hadrons

Abstract

The hadronic structure is investigated in terms of a recently proposed theory which considers the effect of the strong interaction in the space-time description. From the equations, the masses of the particles may be calculated, and quark confinement appears as a natural result, without the need of confining potentials. Some properties of the considered particles, such as the topponium size, are also estimated.Keywords: Quark confinement; Heavy quarkonium; Space-time curvatureThe effect of space-time in quantum physics, or, semantics apart, the effect of quantum physics in the structure of spacetime are subjects that until today do not have a theory. The efforts made in the attempt of quantizing the gravitational field illustrate this fact.In most of the descriptions of quantum systems and of particle physics, for example, this question is not considered, and the space is the flat Minkowski one, with the metric tensorand no interaction is considered to affect its structure. However a fundamental question that remains is whether the electromagnetic and strong interactions may affect space-time, in a way similar to the role of the gravitational field in general relativity, and if these effects may be observed. With these questions in mind, recently, a theory has been proposed [1]- [3], in which the effects mentioned above have been taken into account, and very interesting results have been obtained. For example, the agreement with the experimental results of the deuterium atom spectrum is improved by one decimal digit, when compared with the Dirac results [4]-[6], a fact that may hardly be considered as a coincidence, and this agreement shows the same pattern for all energy levels. The results of the theory when applied to hadron physics are also very interesting, and quark confinement appears in a natural way.In this work a brief review of this theory will be made, and a special emphasis will be given to its application to the study of hadrons. The fundamental principle of the theory will also be formulated.For simplicity, a first step is to consider a system with spherical symmetry, but the basic ideas can be generalized to systems with arbitrary metrics. In fact, this approach is very illustrative, many systems may be described by spherical symmetry, or at least, investigated in a first approximation. With this procedure, the main results of the theory are obtained and all the results may be obtained analytically.So, if the spherical symmetry is considered, the space-time is described by the metric derived in [1], that is very similar to the Schwarzschild metric [7], [8],where r, θ and φ are the particle coordinates, ξ(r) is determined by the interaction potential V (r) and is a function only of r, for a time independent interaction. The energy relation for this system is [1]withApplying these ideas to the study of one electron atoms, V is the Coulomb potentialα is the fine structure constant and Z is the atomic number. Consequently, the function ξ is given bywhere m is the electron mass. These expressions dete...

Baryons from quarks in curved space and deconfinement

“…R in [24], [36]. Finally, both the Coulomb and the HO problems have been also solved in spaces with a negative constant curvature (Lobachevsky geometry) in the second reference [27], and in [37], [38], to mention only few representative examples of such studies (see also ref. [2] for a recent up-date).…”