The chiral extension of lattice QCD

Brower, Richard C.; Orginos, Konstantinos; Tan, C-I

doi:10.1016/0920-5632(95)00185-c

Cited by 10 publications

(7 citation statements)

References 6 publications

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“…From a numerical point of view, the evaluation of the fermionic determinant should be faster in presence of the auxiliary fields, as they already provide the propagation of the pions. Some support to the above can be found in [16].…”

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confidence: 68%

Lattice QCD and chiral mesons

Caracciolo

Palumbo

Scimia

2001

Nuclear Physics B - Proceedings Supplements

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The standard QCD action is improved by the addition of irrelevant operators built with chiral composites. An effective Lagrangian is derived in terms of auxiliary fields, which has the form of the phenomenological chiral Lagrangians. Our improved QCD action appears promising for numerical simulations as the pion physics is explicitely accounted for by the auxiliary fields. QCD in the high energy limit is efficiently described by the perturbative expansion in the gauge coupling constant. For the low energy properties instead, we do not have an equally satisfactory theory.At the phenomenological level a description of the low energy physics related to the symmetry breaking of the chiral invariance is obtained by using the phenomenological chiral Lagrangians [1,2], but a direct derivation from the basic theory of quarks and gluons is still lacking.At a more fundamental level the lattice formulation has allowed us to investigate the quark confinement [3] and the spontaneous breaking of chiral invariance, but due to the complexities related to the definition of chiral fermions [3,4], in numerical simulations the chiral limit is achieved only through a fine-tuning procedure. Even though these difficulties can be overcome, we remain unable to unify the treatment of high energy and low energy properties.For these reasons we have developed an approach based on the use of quark composites as fundamental variables. The idea behind it is that a significant part of the binding of the hadrons can be accounted for in this way, so that the "residual interaction" is sufficiently weak for a perturbative treatment.The quark-composites approach is in principle fairly general, since it allows us to treat all the hadrons composite of quarks, but for technical reasons the composites with the quantum numbers of mesons and barions are treated in a different way. The nucleonic composites, for instance, naturally satisfy the Berezin integration rules and we derived the substitution rules which allow us to replace polynomials of the quark fields by appropriate polynomials of these composites [5] in the partition function. The mesonic composites instead, due to the complexity of the integral over even elements of a Grassmann algebra, are replaced by auxiliary fields [6] by means of the Stratonovich-Hubbard transformation [7]. Even though our effective action is not renormalizable by power counting, due to the renormalizability of QCD only a finite number of free parameters can be generated by the counterterms because of the BRS identities.We assume the modified partition functionwhere S Y M is the Yang-Mills action, S q is the action of the quark field and S C is a four fermions irrelevant operator which provides the kinetic terms for the quark composites with the quantum numbers of the chiral mesons. λ is the quark field while the gluon field is associated to the link variables V . Differentials in square brackets are understood to be the product of the differentials over the lattice sites and the internal indices. All the fields live in a...

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confidence: 68%

Lattice QCD and chiral mesons

Caracciolo

Palumbo

Scimia

2001

Nuclear Physics B - Proceedings Supplements

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“…This makes a big contrast to the previous attempts of simply adding scalar fields to QCD [6][7][8]. Since they are formally different from QCD, and have non-renormalizable four-quark interactions, it is non-trivial to keep the theory in the same universality class of QCD.…”

Section: Xqcd In Four Dimensionsmentioning

confidence: 89%

Renormalization of Extended QCD$_2$

Fukaya,

Yamamura

2015

Preprint

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Extended QCD (XQCD) proposed by Kaplan [1] is an interesting reformulation of QCD with additional bosonic auxiliary fields. While its partition function is kept exactly the same as that of original QCD, XQCD naturally contains properties of low energy hadronic models. We analyze the renormalization group flow of two-dimensional (X)QCD, which is solvable in the limit of large number of colors N c , to understand what kind of roles the auxiliary degrees of freedom play and how the hadronic picture emerges in the low energy region.

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“…As we noted in the introduction this result is almost "obvious", but we are reassured by numerical "proof" and encourage to extend these numerical method to subtler coupled Higgs systems where our plausibility arguments might not be convincing. Our model does serves as an illustration for the key feature of Chirally Extended QCD [4] [5] which, although involves extra degrees of freedom on the lattice, is expected to lead to the same continuum theory as the standard Wilson Lattice QCD. The numerical success of this demonstration gives us hope that more complex coupled systems can be studied by similar techniques.…”

Section: Discussionmentioning

confidence: 99%

“…In these more complicated examples, it is not obvious when they remain in the same universality class as the original theory or if numerical methods can give convincing evidence. We were able to prove that an extended Nambu-Jona Lasino model and a two spin coupled O(N) models are equivalent in large N [4,5]. At large N, the extra degrees of freedom become decoupled in the continuum limit and the low energy spectrum is exactly the same as if no extra degrees of freedom were introduced at the cut-off scale.…”

Section: Introductionmentioning

confidence: 85%

“…Here we wish to consider a different but closely related phenomenon where the same excitation is represented twice in a single Lagrangian by two different fields, yet in the scaling limit the theory is universal to either spin system taken separately. Such a redundant description has recently been advocated as an improved lattice formulation of GCD in the so called chirally extended action (XQCD) [4], [5]. Here an elementary scalar field is coupled to the Wilson lattice QCD action.…”

Section: Introductionmentioning

confidence: 99%

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Monte Carlo study of the Yukawa coupled two-spin Ising model

Brower¹,

Orginos²,

Shen³

et al. 1995

Physica A: Statistical Mechanics and its Applications

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We consider a particular 4 state spin system composed of two Ising spins ( s x , σ x ) with independent hopping parameters κ 1 , κ 2 , coupled by a bilinear Yukawa term, ys x σ x . The Yukawa term is solely responsible for breaking the global Z 2 × Z 2 symmetry down to Z 2 . This model is intended as an illustration of general coupled Higgs system where scalars can arise both as composite and elementary excitations. For the Ising example in 2d, we give convincing numerical evidence of the universality of the two spin system with the one spin Ising model, by Monte Carlo simulations and finite scaling analysis . We also show that as we approach the phase transition, universality arises by a separation of low mass spin waves from an extra set of spin waves with an energy gap that diverges as the correlations length diverges.

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The chiral extension of lattice QCD

Cited by 10 publications

References 6 publications

Lattice QCD and chiral mesons

Lattice QCD and chiral mesons

Renormalization of Extended QCD$_2$

Monte Carlo study of the Yukawa coupled two-spin Ising model

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