Inverse amplitude method in ππ scattering in chiral perturbation theory to two loops

Nieves, J.; Valderrama, Manuel Pavón; Arriola, E. Ruiz

doi:10.1103/physrevd.65.036002

Cited by 57 publications

(61 citation statements)

References 50 publications

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“…The two-loop ChPT was thoroughly studied in [235,262]. As a matter of fact, the updated IAM pole commented above and listed in Table 5 corresponds to a NNLO IAM fit [235].…”

Section: The Elastic Inverse Amplitude Methodsmentioning

confidence: 99%

From controversy to precision on the sigma meson: A review on the status of the non-ordinary f0(500) resonance

2016

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The existence and properties of the sigma meson have been controversial for almost six decades, despite playing a central role in the spontaneous chiral symmetry of QCD or in the nucleonnucleon attraction. This controversy has also been fed by the strong indications that it is not an ordinary quark-antiquark meson. Here we review both the recent and old experimental data and the model independent dispersive formalisms which have provided precise determinations of its mass and width, finally settling the controversy and leading to its new name: f 0 (500). We then provide a rather conservative average of the most recent and advanced dispersive determinations of its pole position √ s σ = 449 +22−16 −i(275±12). In addition, after comprehensive introductions, we will review within the modern perspective of effective theories and dispersion theory, its relation to chiral symmetry, unitarization techniques, its quark mass dependence, popular models, as well as the recent strong evidence, obtained from the QCD 1/N c expansion or Regge theory, for its non ordinary nature in terms of quarks and gluons.

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“…The two-loop ChPT was thoroughly studied in [235,262]. As a matter of fact, the updated IAM pole commented above and listed in Table 5 corresponds to a NNLO IAM fit [235].…”

Section: The Elastic Inverse Amplitude Methodsmentioning

confidence: 99%

From controversy to precision on the sigma meson: A review on the status of the non-ordinary f0(500) resonance

2016

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“…In contrast, as we will see next, it appears in a rather natural way in the two-loop analysis Now let us move to two loop order in χPT [21] and see if this situation changes. The IAM to two loops for pion-pion scattering was first formulated in [15], and first analysed in [19]. With a larger number of LECs appearing, we clearly have more freedom.…”

Section: Nc Dependence Of ππ Scattering To One Loop Uchpt: Dominmentioning

confidence: 99%

“…Consequently, the fact that χPT satisfies unitarity orderby-order is not sufficiently fast for these key low energy resonances to be described beyond their near threshold tails. Much effort has been devoted to accelerating the process of unitarisation [13][14][15][16][17][18][19]. Low orders in χPT must already contain information about key components at all orders for unitarisation to be achieved.…”

mentioning

confidence: 99%

Chiral perturbation theory, the1/Ncexpansion and Regge behavior determine the structure of the lightest scalar meson

et al. 2011

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The leading 1/Nc behaviour of Unitarised Chiral Perturbation Theory distinguishes the nature of the ρ and the σ: The ρ is a qq meson, while the σ is not. However, semi-local duality between resonances and Regge behaviour cannot be satisfied for larger Nc, if such a distinction holds. While the σ at Nc = 3 is inevitably dominated by its di-pion component, Unitarised Chiral Perturbation Theory also suggests that as Nc increases above 6-8, the σ may have a sub-dominant qq fraction up at 1.2 GeV. Remarkably this ensures semi-local duality is fulfilled for the range of Nc 15 − 30, where the unitarisation procedure adopted applies

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“…Furthermore, the input on γ * γ ( * ) → ππ is available in the form of helicity partial waves: these are in principle observable quantities, even though given the absence of double-virtual data they will have to be reconstructed dispersively by means of the solution of a system of Roy-Steiner equations [28,31,55]. In section 4, we will provide a first estimate of the two-pion rescattering contribution by solving the Roy-Steiner equations for S-waves, using a pion-pole LHC and ππ phase shifts based on the inverse-amplitude method [64][65][66][67][68][69].…”

Section: Helicity Amplitudes and Partial-wave Expansionmentioning

confidence: 99%

“…4.1 γ * γ * → ππ helicity partial waves from the inverse-amplitude method Unitarization within the inverse-amplitude method (IAM) [64][65][66][67][68][69] is based on the observation that elastic unitarity…”

Section: Jhep04(2017)161mentioning

confidence: 99%

Dispersion relation for hadronic light-by-light scattering: two-pion contributions

Colangelo

Hoferichter

Procura

et al. 2017

J. High Energ. Phys.

374

257

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In this third paper of a series dedicated to a dispersive treatment of the hadronic light-by-light (HLbL) tensor, we derive a partial-wave formulation for two-pion intermediate states in the HLbL contribution to the anomalous magnetic moment of the muon (g − 2) µ , including a detailed discussion of the unitarity relation for arbitrary partial waves. We show that obtaining a final expression free from unphysical helicity partial waves is a subtle issue, which we thoroughly clarify. As a by-product, we obtain a set of sum rules that could be used to constrain future calculations of γ * γ * → ππ. We validate the formalism extensively using the pion-box contribution, defined by two-pion intermediate states with a pion-pole left-hand cut, and demonstrate how the full known result is reproduced when resumming the partial waves. Using dispersive fits to high-statistics data for the pion vector form factor, we provide an evaluation of the full pion box, a π-box µ = −15.9(2)×10 −11 . As an application of the partial-wave formalism, we present a first calculation of ππ-rescattering effects in HLbL scattering, with γ * γ * → ππ helicity partial waves constructed dispersively using ππ phase shifts derived from the inverse-amplitude method. In this way, the isospin-0 part of our calculation can be interpreted as the contribution of the f 0 (500) to HLbL scattering in (g − 2) µ . We argue that the contribution due to charged-pion rescattering implements corrections related to the corresponding pion polarizability and show that these are moderate. Our final result for the sum of pion-box contribution and its S-wave rescattering corrections reads a π-box µ + a ππ,π-pole LHC µ,J=0 = −24(1) × 10 −11 .

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Inverse amplitude method in ππ scattering in chiral perturbation theory to two loops

Cited by 57 publications

References 50 publications

From controversy to precision on the sigma meson: A review on the status of the non-ordinary f0(500) resonance

From controversy to precision on the sigma meson: A review on the status of the non-ordinary f0(500) resonance

Chiral perturbation theory, the1/Ncexpansion and Regge behavior determine the structure of the lightest scalar meson

Dispersion relation for hadronic light-by-light scattering: two-pion contributions

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