Meson loops in the Nambu-Jona-Lasinio model

Nikolov, Emil N.; Broniowski, Wojciech; Christov, C. I.; Ripka, G.; Goeke, K.

doi:10.1016/0375-9474(96)00231-x

Cited by 66 publications

(134 citation statements)

References 30 publications

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“…The situation is more complicated in a nonlocal than a local model [6,8] because there are two kinds of contribution to be considered, arising from the local and nonlocal parts of the symmetry current (see Sec. II).…”

Section: Meson Coupling To a Currentmentioning

confidence: 99%

“…Even if the calculations were of interest for no other reason, a check on this perturbative approach would be very valuable. Encouragingly, there seems to be a general consensus emerging from recent studies that NLO corrections are indeed relatively small for standard choices of the model parameters [6,8,[10][11][12][13][14][15], at least for properties of the ground state and of the pion. A contrary view, however, has been expressed by Kleinert and Van den Bossche [16].…”

Section: Introductionmentioning

confidence: 99%

“…Conventionally two of these parameters are fitted to the pion mass and decay constant, while the third is at least constrained by the value of the quark condensate. However, the regularization of the model must be further specified at NLO since meson and quark loop integrals can be regulated quite independently without affecting chiral symmetry relations [6,8,9,[12][13][14]17]. The parameter space can be limited to some extent because the NLO corrections produce instabilities for large values of the meson cutoff [13,17].…”

Section: Introductionmentioning

confidence: 99%

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Mesonic fluctuations in a nonlocal Nambu–Jona-Lasinio model

Plant

Birse

2002

Nuclear Physics A

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The effects of meson fluctuations are studied in a nonlocal generalization of the Nambu-JonaLasinio model, by including terms of next-to-leading order (NLO) in 1/Nc. In the model with only scalar and pseudoscalar interactions NLO contributions to the quark condensate are found to be very small. This is a result of cancellation between virtual mesons and Fock terms, which occurs for the parameter sets of most interest. In the quark self-energy, similar cancellations arise in the tadpole diagrams, although not in other NLO pieces which contribute at the ∼ 25% level. The effects on pion properties are also found to be small. NLO contributions from real ππ intermediate states increase the sigma meson mass by ∼ 30%. In an extended model with vector and axial interactions, there are indications that NLO effects could be larger.

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Section: Meson Coupling To a Currentmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Mesonic fluctuations in a nonlocal Nambu–Jona-Lasinio model

Plant

Birse

2002

Nuclear Physics A

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“…Other authors have investigated NTL effects in NJL-type frameworks without gauge bosons [28], [35]- [38]. The authors of [28] calculated the NTL effects with an effective action formalism, and those of [35] with diagrammatic methods.…”

Section: Conclusion and Comparison To Other Workmentioning

confidence: 99%

Regularization at the Next-to-Leading Order in the Top-Mode Standard Model without Gauge Bosons

Cvetič

1997

Annals of Physics

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We study Higgs condensation H ∼tt in the top-mode standard model at the next-to-leading (NTL) order in 1/N c , by calculating the effective potential as a function of a hard mass term σ 0 of the top quark. We include the effects of the third generation quarks, the Higgs and the Goldstone fields, and the leading QCD effects, but not the effects of the transverse components of the electroweak gauge bosons. The resulting effective theory contains finite energy cutoff parameters (Λ f , Λ b ) for the fermionic and the bosonic degrees of freedom. Condensation is supposed to take place at energies Λ ∼ Λ f ∼ Λ b . The paper describes how to regularize the integrals over the fermionic momenta in a way free of momentum branching ambiguities and how to treat the terms of 1/N c expansion mutually consistently. This is achieved by the proper time approach, employing specifically the proper time cutoff (PTC) or a Pauli-Villars (PV) regulator. For comparison, we use also the covariant spherical (S) cutoff. On the other hand, for the bosonic momenta we have to use the covariant spherical cutoff.We discuss how to ensure the validity of Goldstone theorem. Demanding that the NTL contributions not "wash out" the leading ones, we obtain rather low bounds for the cutoffs: Λ = O(1TeV). The results for the corresponding cases with PTC, PV and S regularization differ only marginally. Thus, in the described framework, 1/N c expansion approach has a predictive power only if Λ = O(1TeV), a result largely independent of the regularization procedure.

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“…Only a few studies that go beyond the mean field approximation were reported. Nikolov et al [17] extended the mean field approximation to the next-to-leading order in 1/N that includes the meson loop contributions. The extension preserves the symmetry property of the theory.…”

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confidence: 99%

Meson loop effect on high density chiral phase transition

Sakaguchi

Kashiwa

Matsuzaki³

et al. 2008

Open Physics

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Abstract:We test the stability of the mean field solution in the Nambu-Jona-Lasinio model in a semi-quantitative manner. For stable solutions with respect to both the σ and π directions, we investigate effects of the mesonic loop corrections of 1/N , which correspond to the next-to-leading order in the 1/N expansion, on the high density chiral phase transition. The corrections weaken the first order phase transition and shift the critical chemical potential to a lower value. At N = 3, however, instability of the mean field effective potential prevents us from determining the minimum of the corrected one.PACS ( At high temperature and density quantum chromodynamics (QCD) undergoes qualitative changes of great physical interest. Although many works are done, aspects of the transition region are not under full theoretical control. It is mandatory to deepen its understanding in order to understand the structure of compact stars and the history of the early universe, as well as results of ultra relativistic heavy ion experiments. With the aid of the progress in computer power, lattice simulations have become feasible for thermal system with zero or small density. In general, chiral restoration and deconfinement have been expected to occur simultaneously [1]. But a recent lattice simula- * E-mail: matsuza@fukuoka-edu.ac.jp tion results in different critical temperatures [2]. See also Ref.[3] for the order of the high temperature transition. One of the most important recent findings is strong correlations in the deconfined quark gluon plasma just above the critical temperature; on the one hand it appears as the near perfect fluidity [4][5][6] and on the other hand as the mesonic correlations [7,8].As an approach complementary to the first-principle lattice QCD simulation, we can consider effective models. In particular, they are even indispensable at high density where lattice QCD is not applicable due to the sign problem. One of them is the Nambu-Jona-Lasinio (NJL) model. Since it was proposed [9,10], this model has been widely used [11,12] in the mean field approximation, for example, for analyses of the critical end point of chiral transition on the temperature (T )  chemical potential (µ) plane [13][14][15][16].

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Meson loops in the Nambu-Jona-Lasinio model

Cited by 66 publications

References 30 publications

Mesonic fluctuations in a nonlocal Nambu–Jona-Lasinio model

Mesonic fluctuations in a nonlocal Nambu–Jona-Lasinio model

Regularization at the Next-to-Leading Order in the Top-Mode Standard Model without Gauge Bosons

Meson loop effect on high density chiral phase transition

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