Study of chiral symmetry restoration in linear and nonlinear<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>O</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>N</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math>models using the auxiliary-field method

Seel, Elina; Strüber, Stefan; Giacosa, Francesco; Rischke, Dirk H.

doi:10.1103/physrevd.86.125010

Cited by 16 publications

(27 citation statements)

References 53 publications

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“…4. The system does not undergo a first-order phase transition since there are not jump discontinuities in the order parameter; the latter behavior is seen for instance when considering auxiliar field methods to analyze finite-temperature effects in an Oð4Þ nonlinear model [32]. This second-order critical behavior is confirmed by our analysis of the scalar susceptibility below.…”

Section: Quark Condensate and Scalar Susceptibility: Results And supporting

confidence: 64%

Chiral symmetry restoration for the large-Npion gas

2016

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We analyze chiral restoration within the OðN þ 1Þ=OðNÞ nonlinear sigma model for large N as an effective theory for low-energy QCD at finite temperature T. The free energy is constructed diagrammatically to OðTM 3 Þ in the pion mass expansion, which allows us to derive the quark condensate and the scalar susceptibility in the chiral limit. At this order, we do not have to deal with renormalization, either from divergences from mass tadpoles or from those of higher order loop contributions. Our results for the critical behavior are consistent with expectations from lattice analysis and with previous works where the susceptibility is saturated by the thermal f 0 ð500Þ pole.

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Section: Quark Condensate and Scalar Susceptibility: Results And supporting

confidence: 64%

Chiral symmetry restoration for the large-Npion gas

2016

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“…12=", we recover the equations derived in Ref. [10]. There, however, the equations were neither renormalized nor solved.…”

Section: A Relevant Equationsmentioning

confidence: 50%

Thermodynamics and phase transition of theO(N)model from the two-loopΦ-derivable approximation

2013

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We discuss the thermodynamics of the OðNÞ model across the corresponding phase transition using the two-loop È-derivable approximation of the effective potential and compare our results to those obtained in the literature within the Hartree-Fock approximation. In particular, we find that in the chiral limit the transition is of the second order, whereas it was found to be of the first order in the Hartree-Fock case. These features are manifest at the level of the thermodynamical observables. We also compute the thermal sigma and pion masses from the curvature of the effective potential. In the chiral limit, this guarantees that Goldstone's theorem is obeyed in the broken phase. A realistic parametrization of the model in the N ¼ 4 case, based on the vacuum values of the curvature masses, shows that a sigma mass of around 450 MeV can be obtained. The equations are renormalized after extending our previous results for the N ¼ 1 case by means of the general procedure described in Ref. [8]. When restricted to the Hartree-Fock approximation, our approach reveals that certain problems raised in the literature concerning the renormalization are completely lifted. Finally, we introduce a new type of È-derivable approximation in which the gap equation is not solved at the same level of accuracy as the accuracy at which the potential is computed. We discuss the consistency and applicability of these types of ''hybrid'' approximations and illustrate them in the two-loop case by showing that the corresponding effective potential is renormalizable and that the transition remains of the second order.

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“…In particular, for the case of global O(N ) symmetries that we will be studying here, a naive truncation of the CJT effective action violates the Goldstone theorem [7,8] by higher-order terms, giving rise to a massive Goldstone boson in the Spontaneous Symmetry Breaking (SSB) phase of the theory [9][10][11][12]. Thus far, several studies have been presented in the literature, attempting to provide a satisfactory solution to this problem [11][12][13][14][15][16][17][18][19][20].…”

Section: Introductionmentioning

confidence: 99%

“…A recent approach was to introduce an auxiliary field in the CJT effective action [19], but this was found to lead to physical non-tachyonic solutions, only in the large-N limit. Finally, there has been an attempt to formulate the CJT effective action using a non-linear representation of the background fields in polar coordinates [20].…”

Section: Introductionmentioning

confidence: 99%

Symmetry-improved CJT effective action

2013

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The formalism introduced by Cornwall, Jackiw and Tomboulis (CJT) provides a systematic approach to consistently resumming non-perturbative effects in Quantum Thermal Field Theory. One major limitation of the CJT effective action is that its loopwise expansion introduces residual violations of possible global symmetries, thus giving rise to massive Goldstone bosons in the spontaneously broken phase of the theory. In this paper we develop a novel symmetry-improved CJT formalism for consistently encoding global symmetries in a loopwise expansion. In our formalism, the extremal solutions of the fields and propagators to a loopwise truncated CJT effective action are subject to additional constraints given by the Ward identities due to global symmetries. By considering a simple O(2) scalar model, we show that, unlike other methods, our approach satisfies a number of important field-theoretic properties. In particular, we find that the Goldstone boson resulting from spontaneous symmetry breaking of O (2) is massless and the phase transition is a second order one, already in the Hartree-Fock approximation. After taking the sunset diagrams into account, we show how our approach properly describes the threshold properties of the massless Goldstone boson and the Higgs particle in the loops. Finally, assuming minimal modifications to the Hartree-Fock approximated CJT effective action, we calculate the corresponding symmetryimproved CJT effective potential and discuss the conditions for its uniqueness for scalar-field values away from its minimum.

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Study of chiral symmetry restoration in linear and nonlinearO(N)models using the auxiliary-field method

Cited by 16 publications

References 53 publications

Chiral symmetry restoration for the large-Npion gas

Chiral symmetry restoration for the large-Npion gas

Thermodynamics and phase transition of theO(N)model from the two-loopΦ-derivable approximation

Symmetry-improved CJT effective action

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