Existence of diproton-like particles in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mn>3</mml:mn><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:math>lattice QCD with two flavors and strong coupling

Veiga, Paulo A. Faria da; O’Carroll, Michael; Neto, Antônio Francisco

doi:10.1103/physrevd.83.034506

Phys. Rev. D

2011

DOI: 10.1103/physrevd.83.034506

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Existence of diproton-like particles in3+1lattice QCD with two flavors and strong coupling

Paulo A. Faria da Veiga¹,

Michael O’Carroll²,

Antônio Francisco Neto

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Cited by 3 publications

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“…Some of the models are lattice approximations to continuum quantum field theory ones [1, 2], such as those of ferromagnetic scalar and vector spin, Gross-Neveu, gauge and gauge-matter (QCD) [3]. The excitations correspond to particles and there may be excitations below the two-particle threshold corresponding to bound states.…”

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Analytic Perturbation Theory for Bound States in the Transfer Matrix Spectrum of Weakly Correlated Lattice Ferromagnetic Spin Systems

O’Carroll

2012

J Stat Phys

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We consider general d-dimensional lattice ferromagnetic spin systems with nearest neighbor interactions in the high temperature region (β 1). Each model is characterized by a single site apriori spin distribution taken to be even. We also take the parameter α = s 4 − 3 s 2 2 > 0, i.e. in the region which we call Gaussian subjugation, where s k denotes the kth moment of the apriori distribution. Associated with the model is a lattice quantum field theory known to contain a particle of asymptotic mass − ln β and a bound state below the two-particle threshold. We develop a β analytic perturbation theory for the binding energy of this bound state. As a key ingredient in obtaining our result we show that the Fourier transform of the two-point function is a meromorphic function, with a simple pole, in a suitable complex spectral parameter and the coefficients of its Laurent expansion are analytic in β.Keywords Transfer matrix spectrum · Decay of correlations · Bound states · High-temperature ferromagnetic spin systems · Binding energy analyticity Low lying excitations in lattice models have been the subject of much study in statistical mechanics. Some of the models are lattice approximations to continuum quantum field theory ones [1, 2], such as those of ferromagnetic scalar and vector spin, Gross-Neveu, gauge and gauge-matter (QCD) [3]. The excitations correspond to particles and there may be excitations below the two-particle threshold corresponding to bound states. Particularly in the region of parameters where the variables at different sites are weakly correlated there are a wide variety of methods available to determine the excitations.In this paper we develop an analytic perturbation theory for the two-particle binding energy of one of the simplest models, the weakly correlated (high temperature) ferromagnetic scalar spin model. It is expected that these methods can be adapted to treat other models.

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Analytic Perturbation Theory for Bound States in the Transfer Matrix Spectrum of Weakly Correlated Lattice Ferromagnetic Spin Systems

O’Carroll

2012

J Stat Phys

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On the Energy-Momentum Spectrum and One-Meson Dispersion Curves in (3 + 1)-Dimensional Strongly Coupled Lattice QCD with three Flavors

Veiga¹,

O’Carroll²,

Alvites³

2019

Reports on Mathematical Physics

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Isospin–spin Interchange Symmetry and Two-Baryon Bound States in (3+1)-Dimensional Lattice QCD With Two-Flavors and Strong Coupling

Veiga¹,

O’Carroll²,

Neto

2011

Int. J. Mod. Phys. A

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We determine two-baryon bound states in a 3+1 lattice QCD model with improved Wilson action and two flavors. We work in the strong coupling regime: small hopping parameter κ > 0 and much smaller plaquette coupling β > 0. In this regime, it is known that the low-lying energy–momentum spectrum is comprised of baryons and mesons with asymptotic masses -3 ln κ and -2 ln κ, respectively. We show that the dominant baryon–baryon interaction is an order κ2 space-range-one [Formula: see text]-exchange potential. We also show that this interaction has an important and novel isospin–spin interchange symmetry relating the various possible bound states, and then governing the two-baryon spectral structure. Letting S(I) denote the total spin (total isospin) of the two-baryon bound states, S, I = 0, 1, 2, 3, we find bound states with asymptotic binding energy κ2/4, for I+S = 1, 3, and 4 (here, with I = S = 2); κ2/12, for I+S = 0, 2, 4 and 3 (here, with I = 1, 2). In particular, we show that the two-baryon spectrum contains deuteron (I = 0), diproton (I = 1) and dineutron (I = 1)-like bound states. Using the isospin–spin symmetry, we can circumvent the lack of spin symmetry of the lattice action and show they all have the same asymptotic binding energy, namely κ2/4. Our analysis uses convenient two and four-baryon correlations, their spectral representations and a lattice Bethe–Salpeter equation, which is solved in a ladder approximation. For the isospin, spin part of the interaction, we obtain a permanent representation which describes the interaction of the individual spins and isospins of the quarks of one baryon with those of the other baryon.

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Existence of diproton-like particles in3+1lattice QCD with two flavors and strong coupling

Cited by 3 publications

References 26 publications

Analytic Perturbation Theory for Bound States in the Transfer Matrix Spectrum of Weakly Correlated Lattice Ferromagnetic Spin Systems

Analytic Perturbation Theory for Bound States in the Transfer Matrix Spectrum of Weakly Correlated Lattice Ferromagnetic Spin Systems

On the Energy-Momentum Spectrum and One-Meson Dispersion Curves in (3 + 1)-Dimensional Strongly Coupled Lattice QCD with three Flavors

Isospin–spin Interchange Symmetry and Two-Baryon Bound States in (3+1)-Dimensional Lattice QCD With Two-Flavors and Strong Coupling

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