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Title: 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:
;  [1]
  1. 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}
}
  • No abstract prepared.
  • 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.more » 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.« less
  • We consider baryon-baryon bound states in SU(3) lattice QCD with two flavors, 2x2 spin matrices in 2+1 dimensions, and in an imaginary time formulation. For small hopping parameter 0<{kappa}<<1 and large glueball mass, we show the existence of an isospin 3/2 baryon, with asymptotic mass -3ln{kappa} and isolated dispersion curve. Baryon-baryon bound states of isospin zero and one are found with approximate binding energy {kappa}{sup 2}/8 and {kappa}{sup 2}/24, respectively, using a ladder approximation to a Bethe-Salpeter equation. The baryon-baryon interaction associated with the ladder approximation is an energy independent spatial range-one attractive potential with an O({kappa}{sup 2}) strength. Themore » attractive potential does not have a meson exchange interpretation. Six-point gauge field correlations give rise to attraction and counterbalance the Pauli repulsion to give a vanishing zero-range potential. The overall range-one potential results from a complicated interaction between the isospin components of the constituent quarks of the baryons.« less
  • We study QCD at nonzero quark density, zero temperature, infinite coupling using the Glasgow algorithm. An improved complex zero analysis gives a critical point {mu}{sub c} in agreement with that of chiral symmetry restoration computed with strong coupling expansions, and monomer-dimer simulations. We observe, however, two unphysical critical points: the onset for the number density {mu}{sub 0}, and {mu}{sub s} the saturation threshold, coincident with pathological onsets observed in past quenched QCD calculations. An analysis of the probability distributions for particle number supports our physical interpretation of the critical point {mu}{sub c}, and offers a new intepretation of {mu}{sub 0},more » which confirms its unphysical nature. The perspectives for future lattice QCD calculations of the properties of dense baryonic matter are briefly discussed. {copyright} {ital 1997} {ital The American Physical Society}« less
  • We consider a 3+1 lattice QCD model with three quark flavors, local SU(3){sub c} gauge symmetry, global SU(3){sub f} flavor symmetry, in an imaginary-time formulation and with strong coupling (a small hopping parameter {kappa}>0 and a plaquette coupling {beta}>0, 0<{beta}<<{kappa}<<1). Associated with the model there is an underlying physical quantum mechanical Hilbert space H which, via a Feynman-Kac formula, enables us to derive spectral representations for correlations and obtain the low-lying energy-momentum spectrum exactly. Using the decoupling of hyperplane method and concentrating on the subspace H{sub e} subset of H of vectors with an even number of quarks, we obtainmore » the one-particle spectrum showing the existence of 36 meson states from dynamical first principles, i.e. directly from the quark-gluon dynamics. The particles are detected by isolated dispersion curves w(p-vector) in the energy-momentum spectrum. Besides the SU(3){sub f} quantum numbers (total hypercharge, quadratic Casimir C{sub 2}, total isospin and its 3rd component), the basic excitations also carry spin labels. The total spin operator J and its z-component J{sub z} are defined using {pi}/2 rotations about the spatial coordinate axes and agree with the infinitesimal generators of the continuum for improper zero-momentum meson states. The eightfold way meson particles are given by linear combinations of these 36 states and can be grouped into three SU(3){sub f} nonets associated with the vector mesons (J=1, J{sub z}=0, {+-}1) and one nonet associated with the pseudoscalar mesons (J=0). Each nonet admits a further decomposition into a SU(3){sub f} singlet (C{sub 2}=0) and an octet (C{sub 2}=3). For {beta}=0, the particle dispersion curves are all of the form w(p-vector)=-2ln{kappa}-3{kappa}{sup 2}/2+(1/4){kappa}{sup 2}{sub j=1}{sup 3}2(1-cosp{sup j})+{kappa}{sup 4}r({kappa},p-vector), with p-vector(set-membership sign)(-{pi},{pi}]{sup 3} and |r({kappa},p-vector)|{<=}const. For the pseudoscalar mesons, r({kappa},p-vector) is jointly analytic in {kappa} and p{sup j}, for |{kappa}| and |Imp{sup j}| small. At {beta}=0 the meson masses are given by m({kappa})=-2ln{kappa}-3{kappa}{sup 2}/2+{kappa}{sup 4}r({kappa}), with r(0){ne}0 and r({kappa}) real analytic; for {beta}{ne}0 the nonsingular part of the mass, m({kappa},{beta})+2ln{kappa}, is jointly analytic in {kappa} and {beta}. For a fixed nonet, the mass of the vector mesons are independent of J{sub z} and are all equal within each octet. All singlet masses are also equal for the vector mesons. For {beta}=0, up to and including O({kappa}{sup 4}), for each nonet, the masses of the octet and the singlet are found to be equal. All members of each octet have identical dispersions. Other dispersion curves may differ. Indeed, there is a pseudoscalar, vector meson mass splitting (between J=0 and J=1) given by 2{kappa}{sup 4}+O({kappa}{sup 6}) at {beta}=0, analytic in {beta} and the splitting persists for {beta}<<{kappa}. Using a correlation subtraction method, we show the 36 meson states give the only spectrum in H{sub e} up to near the two-meson threshold of {approx_equal}-4ln{kappa}. Combining our present result with a similar one for baryons (of asymptotic mass -3ln{kappa}) shows that the model does exhibit confinement up to near the two-meson threshold.« less