Facets of chiral perturbation theory

Ecker, Gerhard

doi:10.1016/j.nuclphysbps.2013.10.002

Cited by 5 publications

(3 citation statements)

References 67 publications

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“…the chiral limit value [32], and l 1 + l 2 is saturated by the f 0 (983), with |c d | 3.2 × 10 −2 GeV and M f 0 = 0.983 GeV [30]. Within errors, these values compare rather well with the phenomenological determinations above.…”

Section: Jhep03(2014)107supporting

confidence: 76%

Asymptotic behaviour of pion-pion total cross-sections

Greynat¹,

Rafael

Vulvert

2014

J. High Energ. Phys.

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We derive a sum rule which shows that the Froissart-Martin bound for the asymptotic behaviour of the ππ total cross sections at high energies, if modulated by the Lukaszuk-Martin coefficient of the leading log 2 s behaviour, cannot be an optimal bound in QCD. We next compute the total cross sections for π + π − , π ± π 0 and π 0 π 0 scattering within the framework of the constituent chiral quark model (CχQM) in the limit of a large number of colours N c and discuss their asymptotic behaviours. The same ππ cross sections are also discussed within the general framework of Large-N c QCD and we show that it is possible to make an Ansatz for the isospin I = 1 and I = 0 spectrum which satisfy the FroissartMartin bound with coefficients which, contrary to the Lukaszuk-Martin coefficient, are not singular in the chiral limit and have the correct Large-N c counting. We finally propose a simple phenomenological model which matches the low energy behaviours of the σ total π ± π 0 (s) cross section predicted by the CχQM with the high energy behaviour predicted by the Large-N c Ansatz. The magnitude of these cross sections at very high energies is of the order of those observed for the pp and pp scattering total cross sections.

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Section: Jhep03(2014)107supporting

confidence: 76%

Asymptotic behaviour of pion-pion total cross-sections

Greynat¹,

Rafael

Vulvert

2014

J. High Energ. Phys.

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“…The values of F π and L 10 are quite reasonable face with our model hypothesis, if one admits the usual 30% error coming from Large-N c QCD limit, compared to the range of variation of F π in the chiral limit, 66 < F π < 84 MeV, and compared to the value 10 3 −5.3 ± 0.13 according to [43] and references therein. We can also notice here that the value of F π is strongly related to the value of κ 2 and then to σ = 4κ 2 as illustrated on figure 6.…”

Section: Predictions For the Chiral Constantssupporting

confidence: 80%

Assuming Regge trajectories in holographic QCD: from OPE to chiral perturbation theory

2015

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The soft wall model in holographic QCD has Regge trajectories but wrong operator product expansion (OPE) for the two-point vectorial QCD Green function. We modify the dilaton potential to comply with the OPE. We study also the axial two-point function using the same modified dilaton field and an additional scalar field to address chiral symmetry breaking. OPE is recovered adding a boundary term and low energy chiral parameters, F π and L 10 , are well described analytically by the model in terms of Regge spacing and QCD condensates. The model nicely supports and extends previous theoretical analyses advocating Digamma function to study QCD two-point functions in different momentum regions.

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“…The values of F π and L 10 are quite reasonable face with our model hypothesis, if one admits the usual 30% error coming from Large-N c QCD limit, compared to the range of variation of F π in the chiral limit, 66 < F π < 84 MeV, and compared to the value 10 3 L 10 = −5.3 ± 0.13 according to [35] and references therein.…”

Section: Analytic Continuation In the Chiral Sector: The Left-right Csupporting

confidence: 79%

From OPE to chiral perturbation theory in holographic QCD

2016

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Abstract. The soft wall model in holographic QCD has Regge trajectories but wrong operator product expansion (OPE) for the two-point vectorial QCD Green function. We modify the dilaton potential to comply with the OPE. We study also the axial two-point function using the same modified dilaton field and an additional scalar field to address chiral symmetry breaking. OPE is recovered adding a boundary term and low energy chiral parameters, F π and L 10 , are well described analytically by the model in terms of Regge spacing and QCD condensates. The model nicely supports and extends previous theoretical analyses advocating Digamma function to study QCD two-point functions in different momentum regions.

show abstract

Facets of chiral perturbation theory

Cited by 5 publications

References 67 publications

Asymptotic behaviour of pion-pion total cross-sections

Asymptotic behaviour of pion-pion total cross-sections

Assuming Regge trajectories in holographic QCD: from OPE to chiral perturbation theory

From OPE to chiral perturbation theory in holographic QCD

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