Meson-meson scattering within one-loop chiral perturbation theory and its unitarization

Nicola, Á. Gómez; Peláez, J. R.

doi:10.1103/physrevd.65.054009

Cited by 216 publications

(166 citation statements)

References 71 publications

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“…In any case, it is not the purpose of this work to provide a very precise fit to experimental data, as in other unitarized or dispersive approaches [50,53] which can even be compared to lattice results by suitable mass extrapolations [54]. After all, this is just a two-parameter fit in the chiral limit.…”

Section: Partial Wave Analysis and Unitaritymentioning

confidence: 99%

Large-Npion scattering at finite temperature: Thef0(500)and chiral restoration

2016

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We consider the OðN þ 1Þ=OðNÞ nonlinear sigma model for large N as an effective theory for lowenergy QCD at finite temperature T, in the chiral limit. At T ¼ 0 this formulation provides a good description of scattering data in the scalar channel and dynamically generates the f 0 ð500Þ pole, the pole position lying within experimental determinations. Previous T ¼ 0 results with this model are updated using newer analysis of pion scattering data. We calculate the pion scattering amplitude at finite T and show that it exactly satisfies thermal unitarity, which had been assumed but not formally proven in previous works. We discuss the main differences with the T ¼ 0 result, and we show that one can define a proper renormalization scheme with T ¼ 0 counterterms such that the renormalized amplitude can be chosen to depend only on a few parameters. Next, we analyze the behavior of the f 0 ð500Þ pole at finite T, which is consistent with chiral symmetry restoration when the scalar susceptibility is saturated by the f 0 ð500Þ state, in a second-order transition scenario and in accordance with lattice and theoretical analysis.

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Section: Partial Wave Analysis and Unitaritymentioning

confidence: 99%

Large-Npion scattering at finite temperature: Thef0(500)and chiral restoration

2016

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“…By using the null relations (2.58), we subtract zero on the right-hand side and obtain 68) where the second equality follows from the fact that p kj (s) = p kj (q 2 3 ) is constant for j < 7. For j ≥ 7, p kj (s) is linear in s or quadratic for j ∈ {31, .…”

Section: Physical Sum Rulesmentioning

confidence: 99%

“…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%

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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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“…Before summarising a short outlook on the forthcoming η/η programme with the Crystal Ball/TAPS setup at MAMI will be given. Other interesting topics that can be studied with η and η decays as the search for violation of lepton-family numbers, placing limits on the masses and couplings of many proposed lepto-quark familes [2][3][4][5][6], and investigating violations of a e-mail: unvemarc@kph.uni-mainz.de C, CP, and CPT invariance [7] will not be covered by this contribution.…”

Section: Introductionmentioning

confidence: 99%

ηandη′Physics at MAMI

Unverzagt

2014

EPJ Web of Conferences

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Abstract. The Crystal Ball/TAPS setup at MAMI is ideally suited to detect neutral and electromagnetic decays of the η and η mesons. In this contribution recent results on η and η decays from the Crystal Ball/TAPS experiment at MAMI are presented. These are the accurate measruement of η photoproduction cross-sections in the threshold region, the determination of the timelike electromagnetic transition form factors, and a test of low-energy QCD with the η → π 0 γγ decay. Finally, further perspectives are discussed.

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Meson-meson scattering within one-loop chiral perturbation theory and its unitarization

Cited by 216 publications

References 71 publications

Large-Npion scattering at finite temperature: Thef0(500)and chiral restoration

Large-Npion scattering at finite temperature: Thef0(500)and chiral restoration

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

ηandη′Physics at MAMI

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