Large N, chiral approach to pseudoscalar masses, mixings and decays

Vecchia, P. Di; Nicodemi, F.; Pettorino, R.; Veneziano, G.

doi:10.1016/0550-3213(81)90356-4

Cited by 141 publications

(94 citation statements)

References 22 publications

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“…These decays were also studied in Ref. [35], using an * It has been recently pointed out in Ref. [32] that there can be ambiguities in the definition of χ ′ ch in a lattice regularized theory.…”

Section: Radiative Decays Of the Pseudoscalar Mesonsmentioning

confidence: 99%

“…[35] using an effective Lagrangian which includes only the usual qq chiral condensate (so there is no field η X ! ):…”

Section: Radiative Decays Of the Pseudoscalar Mesonsmentioning

confidence: 99%

“…[35] using an effective Lagrangian which includes only the usual qq chiral condensate (so there is no field η X ! ): Therefore, the introduction of the new condensate (while leaving the π 0 → γγ decay rate unaffected, as it must!)…”

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confidence: 99%

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Reviewing the problem of the U(1) axial symmetry and the chiral transition in QCD

Marchi¹,

Meggiolaro²

2003

Nuclear Physics B

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We discuss the role of the U(1) axial symmetry for the phase structure of QCD at finite temperature. We expect that, above a certain critical temperature, also the U(1) axial symmetry will be (effectively) restored. We will try to see if this transition has (or has not) anything to do with the usual chiral transition: various possible scenarios are discussed. In particular, supported by recent lattice results, we analyse a scenario in which a U(1)-breaking condensate survives across the chiral transition. This scenario can be consistently reproduced using an effective Lagrangian model. The effects of the U(1) chiral condensate on the slope of the topological susceptibility in the full theory with quarks are studied: we find that this quantity (in the chiral limit of zero quark masses) acts as an order parameter for the U(1) axial symmetry above the chiral transition. Further information on the new U(1) chiral order parameter is derived from the study (at zero temperature) of the radiative decays of the "light" pseudoscalar mesons in two photons: a comparison of our results with the experimental data is performed. (PACS codes: 12.38.Aw, 12.39.Fe, 11.15.Pg, 11.30.Rd) IntroductionIt is generally believed that a phase transition which occurs in QCD at a finite temperature is the restoration of the spontaneously broken SU(L) ⊗ SU(L) chiral symmetry in association with L massless quarks. At zero temperature the chiral symmetry is broken spontaneously by the condensation of qq pairs and the L 2 − 1 J P = 0 − mesons are just the Goldstone bosons associated with this breaking [1]. At high temperatures the thermal energy breaks up the qq condensate, leading to the restoration of chiral symmetry. We expect that this property not only holds for massless quarks but also continues for a small mass region. The order parameter for the chiral symmetry breaking is apparently qq ≡ L i=1 q i q i : the chiral symmetry breaking corresponds to the non-vanishing of qq in the chiral limit sup(m i ) → 0. From lattice determinations of the chiral order parameter qq one knows that the SU(L) ⊗ SU(L) chiral phase transition temperature T ch , defined as the temperature at which the chiral condensate qq goes to zero (in the chiral limit sup(m i ) → 0), is nearly equal to the deconfining temperature T c (see, e.g., Ref. [2]). But this is not the whole story: QCD possesses not only an approximate SU(L) ⊗ SU(L) chiral symmetry, for L light quark flavours, but also a U(1) axial symmetry (at least at the classical level) [3,4]. The role of the U(1) symmetry for the finite temperature phase structure has been so far not well studied and it is still an open question of hadronic physics whether the fate of the U(1) chiral symmetry of QCD has or has not something to do with the fate of the SU(L) ⊗ SU(L) chiral symmetry.In the "Witten-Veneziano mechanism" [5,6] for the resolution of the U(1) problem, a fundamental role is played by the so-called "topological susceptibility" in a QCD without quarks, i.e., in a pure Yang-Mills (YM) theory, in...

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Section: Radiative Decays Of the Pseudoscalar Mesonsmentioning

confidence: 99%

“…[35] using an effective Lagrangian which includes only the usual qq chiral condensate (so there is no field η X ! ):…”

Section: Radiative Decays Of the Pseudoscalar Mesonsmentioning

confidence: 99%

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Reviewing the problem of the U(1) axial symmetry and the chiral transition in QCD

Marchi¹,

Meggiolaro²

2003

Nuclear Physics B

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“…(4.3) to be valid, the renormalization conditions for the charge and for the susceptibility need to be chosen so that in presence of fermions the anomalous chiral Ward identities are satisfied [29,30,31]. In this case the value of χ when N c → ∞ corresponds also to a low-energy constant in the simultaneous expansion in momenta and in 1/N c of the U(3) chiral effective theory [58,59,60,61]. We know three families of definitions of the topological charge whose cumulants are ultraviolet finite and unambiguous: the one suggested by Ginsparg-Wilson (GW) fermions [26,27,28,29,30,31], the spectral projector formulas [36], and the naive definition at positive flow time [62].…”

Section: Pos(lattice 2015)001mentioning

confidence: 99%

Recent progress on chiral symmetry breaking in QCD

Giusti¹

2016

Proceedings of the 33rd International Symposium on Lattice Field Theory — PoS(LATTICE 2015)

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“…On the other hand it was already found in ref. [4] that some of the physics of the η ′ , such as the decay η ′ → ηππ, cannot be described, even qualitatively, without going to higher orders in 1/N c .…”

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confidence: 99%