# Baryon-baryon bound states in strongly coupled lattice QCD

## Abstract

We determine baryon-baryon bound states in 3+1 dimensional SU(3) lattice QCD with two flavors, 4x4 spin matrices, and in an imaginary-time functional integral formulation. For small hopping parameter, {kappa}>0, and large glueball mass (strong coupling regime), we show the existence of three-quark isospin 1/2 particles (proton and neutron) and isospin 3/2 baryons (delta particles), with asymptotic masses -3ln{kappa} and isolated dispersion curves. We only consider the existence of bound states of total isospin I=0,3. Using a ladder approximation to a lattice Bethe-Salpeter equation, baryon-baryon bound states are found in these two sectors, with asymptotic masses -6ln{kappa} and binding energies of order {kappa}{sup 2}. The dominant baryon-baryon interaction is an energy-independent spatial range-one potential with an O({kappa}{sup 2}) strength. There is also attraction arising from gauge field correlations associated with six overlapping bonds, but it is counterbalanced by Pauli repulsion to give a vanishing zero-range potential. The overall range-one potential results from a quark, antiquark exchange with no meson-exchange interpretation; the repulsive or attractive nature of the interaction does depend on the isospin and spin of the two-baryon state.

- Authors:

- Departamento de Matematica Aplicada e Estatistica, ICMC-USP, C.P. 668, 13560-970 Sao Carlos SP (Brazil)

- Publication Date:

- OSTI Identifier:
- 21020294

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. D, Particles Fields; Journal Volume: 75; Journal Issue: 7; Other Information: DOI: 10.1103/PhysRevD.75.074503; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BARYON-BARYON INTERACTIONS; BETHE-SALPETER EQUATION; BINDING ENERGY; BOSON-EXCHANGE MODELS; BOUND STATE; CORRELATIONS; FLAVOR MODEL; GLUEBALLS; ISOSPIN; LADDER APPROXIMATION; LATTICE FIELD THEORY; MATRICES; NEUTRONS; POTENTIALS; PROTONS; QUANTUM CHROMODYNAMICS; SPIN; STRONG-COUPLING MODEL; SU-3 GROUPS

### Citation Formats

```
Faria da Veiga, Paulo A., and O'Carroll, Michael.
```*Baryon-baryon bound states in strongly coupled lattice QCD*. United States: N. p., 2007.
Web. doi:10.1103/PHYSREVD.75.074503.

```
Faria da Veiga, Paulo A., & O'Carroll, Michael.
```*Baryon-baryon bound states in strongly coupled lattice QCD*. United States. doi:10.1103/PHYSREVD.75.074503.

```
Faria da Veiga, Paulo A., and O'Carroll, Michael. Sun .
"Baryon-baryon bound states in strongly coupled lattice QCD". United States.
doi:10.1103/PHYSREVD.75.074503.
```

```
@article{osti_21020294,
```

title = {Baryon-baryon bound states in strongly coupled lattice QCD},

author = {Faria da Veiga, Paulo A. and O'Carroll, Michael},

abstractNote = {We determine baryon-baryon bound states in 3+1 dimensional SU(3) lattice QCD with two flavors, 4x4 spin matrices, and in an imaginary-time functional integral formulation. For small hopping parameter, {kappa}>0, and large glueball mass (strong coupling regime), we show the existence of three-quark isospin 1/2 particles (proton and neutron) and isospin 3/2 baryons (delta particles), with asymptotic masses -3ln{kappa} and isolated dispersion curves. We only consider the existence of bound states of total isospin I=0,3. Using a ladder approximation to a lattice Bethe-Salpeter equation, baryon-baryon bound states are found in these two sectors, with asymptotic masses -6ln{kappa} and binding energies of order {kappa}{sup 2}. The dominant baryon-baryon interaction is an energy-independent spatial range-one potential with an O({kappa}{sup 2}) strength. There is also attraction arising from gauge field correlations associated with six overlapping bonds, but it is counterbalanced by Pauli repulsion to give a vanishing zero-range potential. The overall range-one potential results from a quark, antiquark exchange with no meson-exchange interpretation; the repulsive or attractive nature of the interaction does depend on the isospin and spin of the two-baryon state.},

doi = {10.1103/PHYSREVD.75.074503},

journal = {Physical Review. D, Particles Fields},

number = 7,

volume = 75,

place = {United States},

year = {Sun Apr 01 00:00:00 EDT 2007},

month = {Sun Apr 01 00:00:00 EDT 2007}

}