Roy-Steiner equations for pion-nucleon scattering

Ditsche, Christoph; Hoferichter, Martin; Kubis, Bastian; Meißner, Ulf‐G.

doi:10.22323/1.172.0064

Cited by 5 publications

(6 citation statements)

References 89 publications

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“…In particular, the corresponding factor F V π (q 2 1 )F V π (q 2 2 ) can be moved out of the integrals in (4.13), so that one can simply calculate a reduced amplitude, with the dependence on the pion form factors fully factorized. Further, in the solution of Roy-Steiner equations, a MO representation similar to (4.13) is often required for the low-energy region only, in order to match to some known high-energy input, and to this end a finite matching point is introduced [55,[132][133][134][135]. In case the amplitudes are assumed to vanish above the matching point, it effectively acts as a cutoff both in (4.13) and in the Omnès function.…”

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.

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385

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%

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

Colangelo

Hoferichter

Procura

et al. 2017

J. High Energ. Phys.

Self Cite

385

257

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“…The size of the pion-nucleon term can be determined from the pion-nucleon scattering data. It requires a subtle subthreshold extrapolation of the scattering data [60]. Despite the long history of the sigma-term physics, the precise determination is still highly controversial (for one of the first reviews see e.g.…”

Section: Pion and Strangeness Baryon Sigma Termsmentioning

confidence: 99%

Finite volume effects in the chiral extrapolation of baryon masses

et al. 2014

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We perform an analysis of the QCD lattice data on the baryon octet and decuplet masses based on the relativistic chiral Lagrangian. The baryon self energies are computed in a finite volume at next-to-next-to-next-to leading order (N 3 LO), where the dependence on the physical meson and baryon masses is kept. The number of free parameters is reduced significantly down to 12 by relying on large-N c sum rules. Altogether we describe accurately more than 220 data points from six different lattice groups, BMW, PACS-CS, HSC, LHPC, QCDSF-UKQCD and NPLQCD.Values for all counter terms relevant at N 3 LO are predicted. In particular we extract a pion-nucleon sigma term of 39

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“…At one-loop order the pion decay constant F π is given via [19] 14) which is renormalized in the standard way, i.e. 4 = 4R − R/(16π 2 ).…”

Section: Pion Decay Constant F πmentioning

confidence: 99%

“…[6][7][8][9][10][11][12][13]). Roy-Steiner equations for the pion-nucleon scattering have been also analysed recently [14][15][16][17]. In the low-energy region a systematic and powerful tool to study πN scattering is provided by chiral perturbation theory (ChPT) [18][19][20][21].…”

Section: Introductionmentioning

confidence: 99%

Pion-nucleon scattering in covariant baryon chiral perturbation theory with explicit Delta resonances

Yao

Siemens

Bernard

et al. 2016

J. High Energ. Phys.

100

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We present the results of a third order calculation of the pion-nucleon scattering amplitude in a chiral effective field theory with pions, nucleons and delta resonances as explicit degrees of freedom. We work in a manifestly Lorentz invariant formulation of baryon chiral perturbation theory using dimensional regularization and the extended on-mass-shell renormalization scheme. In the delta resonance sector, the on mass-shell renormalization is realized as a complex-mass scheme. By fitting the low-energy constants of the effective Lagrangian to the S-and P -partial waves a satisfactory description of the phase shifts from the analysis of the Roy-Steiner equations is obtained. We predict the phase shifts for the D and F waves and compare them with the results of the analysis of the George Washington University group. The threshold parameters are calculated both in the delta-less and delta-full cases. Based on the determined low-energy constants, we discuss the pion-nucleon sigma term. Additionally, in order to determine the strangeness content of the nucleon, we calculate the octet baryon masses in the presence of decuplet resonances up to next-to-next-to-leading order in SU(3) baryon chiral perturbation theory. The octet baryon sigma terms are predicted as a byproduct of this calculation.

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Roy-Steiner equations for pion-nucleon scattering

Cited by 5 publications

References 89 publications

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

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

Finite volume effects in the chiral extrapolation of baryon masses

Pion-nucleon scattering in covariant baryon chiral perturbation theory with explicit Delta resonances

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