a Relativistic Calculation of Baryon Masses
Abstract
We calculate ground state baryon masses using a saddlepoint variational (SPV) method, which permits us the use of fully relativistic 4component Dirac spinors without the need for positive energy projection operators. This variational approach has been shown to work in the relativistic domain for one particle in an external potential (Dirac equation). We have extended its use to the relativistic 3body Breit equation. Our procedure is as follows: we pick a trial wave function having the appropriate spin, flavor and color dependence. This can be accomplished with a nonsymmetric relativistic spatial wave function having two different size parameters if the the first two quarks are always chosen to be identical. We than calculate an energy eigenvalue for the particle state and vary the parameters in our wave function to search for a "saddlepoint". We minimize the energy with respect to the two size parameters and maximize with respect to two parameters that measure the contribution from the negativeenergy states. This gives the baryon's mass as a function of four input parameters: the masses of the up, down and strange quarks (m_{u=d },m_{s}), and the strength of the coupling constants for the potentials ( alpha_{s},mu). We do this for the eight Baryon ground states and fit these to experimental data. This fit gives the values of the input parameters. For the potentials we use a coulombic term to represent onegluon exchange and a linear term for confinement. For both terms we include a retardation term required by relativity. We also add delta function and spinspin terms to account for the large contribution of the coulomb interaction at the origin. The results we obtain from our SPV method are in good agreement with experimental data. The actual search for the saddlepoint parameters and the fitting of the quark masses and the values of the coupling strengths was done on a CDC Cyber 860.
 Publication:

Ph.D. Thesis
 Pub Date:
 January 1990
 Bibcode:
 1990PhDT.......103G
 Keywords:

 SADDLE POINT VARIATIONAL METHOD;
 BREIT EQUATION;
 QUARK POTENTIAL;
 Physics: Elementary Particles and High Energy