# One-baryon spectrum and analytical properties of one-baryon dispersion curves in 3 + 1 dimensional strongly coupled lattice QCD with three flavors

## Abstract

Considering a 3 + 1 dimensional lattice quantum chromodynamics (QCD) model defined with the improved Wilson action, three flavors, and 4 × 4 Dirac spin matrices, in the strong coupling regime, we reanalyze the question of the existence of the eightfold way baryons and complete our previous work where the existence of isospin octet baryons was rigorously solved. Here, we show the existence of isospin decuplet baryons which are associated with isolated dispersion curves in the subspace of the underlying quantum mechanical Hilbert space with vectors constructed with an odd number of fermion and antifermion basic quark and antiquark fields. Moreover, smoothness properties for these curves are obtained. The present work deals with a case for which the traditional method to solve the implicit equation for the dispersion curves, based on the use of the analytic implicit function theorem, cannot be applied. We do not have only one but two solutions for each one-baryon decuplet sector with fixed spin third component. Instead, we apply the Weierstrass preparation theorem, which also provides a general method for the general degenerate case. This work is completed by analyzing a spectral representation for the two-baryon correlations and providing the leading behaviors of the fieldmore »

- Authors:

- Publication Date:

- OSTI Identifier:
- 22597050

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Mathematical Physics

- Additional Journal Information:
- Journal Volume: 57; Journal Issue: 3; Other Information: (c) 2016 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0022-2488

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ANTIQUARKS; BARYON DECUPLETS; BARYONS; FLAVOR MODEL; HILBERT SPACE; ISOSPIN; MATHEMATICAL SOLUTIONS; OCTET MODEL; QUANTUM CHROMODYNAMICS; QUANTUM MECHANICS; STRONG-COUPLING MODEL

### Citation Formats

```
Faria da Veiga, Paulo A., E-mail: veiga@icmc.usp.br, O’Carroll, Michael, and Valencia Alvites, José C., E-mail: cien.mat@hotmail.com.
```*One-baryon spectrum and analytical properties of one-baryon dispersion curves in 3 + 1 dimensional strongly coupled lattice QCD with three flavors*. United States: N. p., 2016.
Web. doi:10.1063/1.4944585.

```
Faria da Veiga, Paulo A., E-mail: veiga@icmc.usp.br, O’Carroll, Michael, & Valencia Alvites, José C., E-mail: cien.mat@hotmail.com.
```*One-baryon spectrum and analytical properties of one-baryon dispersion curves in 3 + 1 dimensional strongly coupled lattice QCD with three flavors*. United States. doi:10.1063/1.4944585.

```
Faria da Veiga, Paulo A., E-mail: veiga@icmc.usp.br, O’Carroll, Michael, and Valencia Alvites, José C., E-mail: cien.mat@hotmail.com. Tue .
"One-baryon spectrum and analytical properties of one-baryon dispersion curves in 3 + 1 dimensional strongly coupled lattice QCD with three flavors". United States. doi:10.1063/1.4944585.
```

```
@article{osti_22597050,
```

title = {One-baryon spectrum and analytical properties of one-baryon dispersion curves in 3 + 1 dimensional strongly coupled lattice QCD with three flavors},

author = {Faria da Veiga, Paulo A., E-mail: veiga@icmc.usp.br and O’Carroll, Michael and Valencia Alvites, José C., E-mail: cien.mat@hotmail.com},

abstractNote = {Considering a 3 + 1 dimensional lattice quantum chromodynamics (QCD) model defined with the improved Wilson action, three flavors, and 4 × 4 Dirac spin matrices, in the strong coupling regime, we reanalyze the question of the existence of the eightfold way baryons and complete our previous work where the existence of isospin octet baryons was rigorously solved. Here, we show the existence of isospin decuplet baryons which are associated with isolated dispersion curves in the subspace of the underlying quantum mechanical Hilbert space with vectors constructed with an odd number of fermion and antifermion basic quark and antiquark fields. Moreover, smoothness properties for these curves are obtained. The present work deals with a case for which the traditional method to solve the implicit equation for the dispersion curves, based on the use of the analytic implicit function theorem, cannot be applied. We do not have only one but two solutions for each one-baryon decuplet sector with fixed spin third component. Instead, we apply the Weierstrass preparation theorem, which also provides a general method for the general degenerate case. This work is completed by analyzing a spectral representation for the two-baryon correlations and providing the leading behaviors of the field strength normalization and the mass of the spectral contributions with more than one-particle. These are needed results for a rigorous analysis of the two-baryon and meson-baryon particle spectra.},

doi = {10.1063/1.4944585},

journal = {Journal of Mathematical Physics},

issn = {0022-2488},

number = 3,

volume = 57,

place = {United States},

year = {2016},

month = {3}

}