Improved lattice QCD with quarks: The two-dimensional case

Jq, Jiang; Luo, Xq; Zh, Mei; Jirari, H.; Kröger, H.; Wu, CM; 吴济民,

doi:10.1103/physrevd.60.014501

“…Applying the same procedure to the mass of the pseudoscalar excitation the extrapolated value of m P is m P /g = 0.6655 which agrees within 16% with the result obtained in [5] in the continuum for N c = 3 and with the lattice numerical calculations of Ref. [6].…”

Section: Discussionsupporting

confidence: 87%

Strongly coupled ’t Hooft model on the lattice

Berruto

¹

,

Grignani

²

,

Sodano

³

2000

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We study the strong coupling limit of the one-flavor and two-flavor massless 't Hooft models, large − N c -color QCD 2 , on a lattice. We use staggered fermions and the Hamiltonian approach to lattice gauge theories. We show that the one-flavor model is effectively described by the antiferromagnetic Ising model, whose ground state is the vacuum of the gauge model in the infinite coupling limit; expanding around this ground state we derive a strong coupling expansion and compute the lowest lying hadron masses as well as the chiral condensate of the gauge theory. Our lattice computation well reproduces the results of the continuum theory. Baryons are massless in the infinite coupling limit; they acquire a mass already at the second order in the strong coupling expansion in agreement with the Witten argument that baryons are the QCD solitons.The spectrum and chiral condensate of the two-flavor model are effectively described in terms of observables of the quantum antiferromagnetic Heisenberg model. We explicitly write the lowest lying hadron masses and chiral condensate in terms of spin-spin correlators on the ground state of the spin model. We show that the planar limit (N c −→ ∞) of the gauge model corresponds to the large spin limit (S −→ ∞) of the antiferromagnet and compute the hadron mass spectrum in this limit finding that, also in this model, the pattern of chiral symmetry breaking of the continuum theory is well reproduced on the lattice.

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“…(7.177), expanding for small z and then taking the limit z −→ ∞, one gets m P g = 0.6655 , (7.179) which agrees within 16% with the result obtained in [22] in the continuum for N c = 3 and with the lattice numerical calculation of Ref. [46]. If one extrapolates to the continuum the scalar meson mass given in Eq.…”

Section: Lattice Versus Continuumsupporting

confidence: 77%

Strongly coupled 't Hooft model on the lattice

Berruto¹

2000

Nuclear Physics B - Proceedings Supplements

1

0

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We study the strong coupling limit of the one-flavor and two-flavor massless 't Hooft models, large − N c -color QCD 2 , on a lattice. We use staggered fermions and the Hamiltonian approach to lattice gauge theories. We show that the one-flavor model is effectively described by the antiferromagnetic Ising model, whose ground state is the vacuum of the gauge model in the infinite coupling limit; expanding around this ground state we derive a strong coupling expansion and compute the lowest lying hadron masses as well as the chiral condensate of the gauge theory. Our lattice computation well reproduces the results of the continuum theory. Baryons are massless in the infinite coupling limit; they acquire a mass already at the second order in the strong coupling expansion in agreement with the Witten argument that baryons are the QCD solitons.The spectrum and chiral condensate of the two-flavor model are effectively described in terms of observables of the quantum antiferromagnetic Heisenberg model. We explicitly write the lowest lying hadron masses and chiral condensate in terms of spin-spin correlators on the ground state of the spin model. We show that the planar limit (N c −→ ∞) of the gauge model corresponds to the large spin limit (S −→ ∞) of the antiferromagnet and compute the hadron mass spectrum in this limit finding that, also in this model, the pattern of chiral symmetry breaking of the continuum theory is well reproduced on the lattice.

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“…For the SU (2)-color QCD 2 , setting t = 1, one gets m P = 1.093, which is 37% higher than the result obtained in [6] in the continuum for N c = 2 and is consistent with the lattice numerical calculations of ref. [7]. For m S one gets m S = 1.133, this mass has not been computed in the continuum.…”

Section: Discussionmentioning

confidence: 98%

Lattice gauge theories and the Heisenberg antiferromagnetic chain

Berruto

¹

,

Coletti

²

,

Grignani

³

et al. 2000

Nuclear Physics B - Proceedings Supplements

0

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We study the strongly coupled 2-flavor lattice Schwinger model and the SU (2)-color QCD2. The strong coupling limit, even with its inherent nonuniversality, makes accurate predictions of the spectrum of the continuum models and provides an intuitive picture of the gauge theory vacuum. The massive excitations of the gauge model are computable in terms of spin-spin correlators of the quantum Heisenberg antiferromagnetic spin-1/2 chain.

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Improved lattice QCD with quarks: The two-dimensional case

Cited by 8 publications

References 38 publications

Strongly coupled ’t Hooft model on the lattice

Strongly coupled ’t Hooft model on the lattice

Strongly coupled 't Hooft model on the lattice

Lattice gauge theories and the Heisenberg antiferromagnetic chain

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