On the $\pi\pi$ π π continuum in the nucleon form factors and the proton radius puzzle

Hoferichter, Martin; Kubis, Bastian; Elvira, J. Ruiz de; Hammer, H.-W.; Meißner, Ulf‐G.

doi:10.1140/epja/i2016-16331-7

Cited by 85 publications

(105 citation statements)

References 119 publications

(182 reference statements)

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“…3 ) 2 4s Im h 0 ++,++ (s ) − (s +q 2 1 −q 2 2 )(s −q 2 1 +q 2 2 )Im h 0 00,++ (s ) , 92) where the dependence of the helicity amplitudes on the virtualities is not written explicitly. This result agrees with [30].…”

Section: Jhep04(2017)161mentioning

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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Section: Jhep04(2017)161mentioning

confidence: 99%

“…and time-like data, and thereby profit from the high-statistics form factor measurements motivated mainly by the two-pion contribution to HVP, we adopt the formalism suggested in [86,87] (similar representations have been used in [88][89][90][91][92][93]), whose essential ingredients will be briefly reviewed in the following.…”

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

View full text Add to dashboard Cite

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“…The lightest hadronic state that couples to electromagnetism is the two-pion state [5]. The dispersive framework [6][7][8][9] that utilizes these interrelations is at the heart of the present work.…”

Section: Introductionmentioning

confidence: 99%

“…It can be used to pin down the subthreshold t-channel p-wave pion-nucleon amplitudes. In turn these subthreshold amplitudes provide the necessary input for the vector-isovector form factors of the nucleon [9].…”

Section: Introductionmentioning

confidence: 99%

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The nucleon as a test case to calculate vector-isovector form factors at low energies

Leupold

2018

Eur. Phys. J. A

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Abstract. Extending a recent suggestion for hyperon form factors to the nucleon case, dispersion theory is used to relate the low-energy vector-isovector form factors of the nucleon to the pion vector form factor. The additionally required input, i.e. the pion-nucleon scattering amplitudes are determined from relativistic next-to-leading-order (NLO) baryon chiral perturbation theory including the nucleons and optionally the Delta baryons. Two methods to include pion rescattering are compared: a) solving the MuskhelishviliOmnès (MO) equation and b) using an N/D approach. It turns out that the results differ strongly from each other. Furthermore the results are compared to a fully dispersive calculation of the (subthreshold) pion-nucleon amplitudes based on Roy-Steiner (RS) equations. In full agreement with the findings from the hyperon sector it turns out that the inclusion of Delta baryons is not an option but a necessity to obtain reasonable results. The magnetic isovector form factor depends strongly on a low-energy constant of the NLO Lagrangian. If it is adjusted such that the corresponding magnetic radius is reproduced, then the results for the corresponding pion-nucleon scattering amplitude (based on the MO equation) agree very well with the RS results. Also in the electric sector the Delta degrees of freedom are needed to obtain the correct order of magnitude for the isovector charge and the corresponding electric radius. Yet quantitative agreement is not achieved. If the subtraction constant that appears in the solution of the MO equation is not taken from nucleon+Delta chiral perturbation theory but adjusted such that the electric radius is reproduced, then one obtains also in this sector a pion-nucleon scattering amplitude that agrees well with the RS results.

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Untitled

Alarcón¹,

Blin²,

Weiß³

2018

Light Cone 2016

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Transverse densities describe the distribution of charge and current at fixed light-front time and provide a frame-independent spatial representation of hadrons as relativistic systems. We calculate the transverse densities of the octet baryons at peripheral distances b = O(M −1 π ) in an approach combining chiral effective field theory (χEFT) and dispersion analysis. The densities are represented as dispersive integrals of the imaginary parts of the baryon electromagnetic form factors in the timelike region (spectral functions). The spectral functions on the two-pion cut at t > 4M 2 π are computed using relativistic χEFT with octet and decuplet baryons in the EOMS renormalization scheme. The calculations are extended into the ρ-meson mass region, using a dispersive method that incorporates the timelike pion form-factor data. The approach allows us to construct densities at distances b > 1 fm with controlled uncertainties. Our results provide insight into the peripheral structure of nucleons and hyperons and can be compared with empirical densities and lattice-QCD calculations.

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On the $\pi\pi$ π π continuum in the nucleon form factors and the proton radius puzzle

Cited by 85 publications

References 119 publications

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

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

The nucleon as a test case to calculate vector-isovector form factors at low energies

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