6533b851fe1ef96bd12a8e6e
RESEARCH PRODUCT
Linear confinement in momentum space: singularity-free bound-state equations
Elmar P. BiernatAlfred StadlerAlfred StadlerSofia LeitãoSofia LeitãoM. T. Peñasubject
PhysicsNuclear and High Energy PhysicsBethe–Salpeter equationIntegrable systemNuclear Theory010308 nuclear & particles physicsSpectrum (functional analysis)FOS: Physical sciencesPosition and momentum space16. Peace & justice01 natural sciencesNuclear Theory (nucl-th)High Energy Physics - PhenomenologySingularityHigh Energy Physics - Phenomenology (hep-ph)Linear potentialQuantum mechanics0103 physical sciencesPrincipal valueBound stateCauchy principal valueMomentum space010306 general physicsConfinementMathematical physicsdescription
Relativistic equations of Bethe-Salpeter type for hadron structure are most conveniently formulated in momentum space. The presence of confining interactions causes complications because the corresponding kernels are singular. This occurs not only in the relativistic case but also in the nonrelativistic Schr\"odinger equation where this problem can be studied more easily. For the linear confining interaction the singularity reduces to one of Cauchy principal value form. Although this singularity is integrable, it still makes accurate numerical solutions difficult. We show that this principal value singularity can be eliminated by means of a subtraction method. The resulting equation is much easier to solve and yields accurate and stable solutions. To test the method's numerical efficiency, we performed a three-parameter least-squares fit of a simple linear-plus-Coulomb potential to the bottomonium spectrum.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2014-08-08 |