Low-energy expansion of the pion-nucleon Lagrangian

Ecker, Gerhard; Mojžiš, Martin

doi:10.1016/0370-2693(95)01275-3

Cited by 108 publications

(231 citation statements)

References 16 publications

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“…To allow for an easier comparison with the various calculations performed in that basis, we construct here the corresponding third order effective Lagrangian. This extends the work of Ecker and Mojžiš [13] since we explicitely work out the various 1/m corrections to the dimension three terms and do not #5 Note that due to the appearance of odd and even powers in the effective pion-nucleon Lagrangian, the N -loop order consists of terms of order q 2N +1 and q 2N +2 .…”

Section: Introductionsupporting

confidence: 67%

“…While parts of the final result have already been given by Ecker and Mojžiš [13], we fill in the necessary details and also work in the basis of the review [6], which is most convenient for comparison with earlier work on photoproduction, Compton scattering and so on. In particular, in [13] the 1/m corrections appearing at third order were always subsumed in the LECs (whenever possible). While this is a legitimate procedure, we prefer these corrections to be separated, in particular, if one wishes to estimate the corresponding LECs via resonance exchange or some other model.…”

Section: Construction Of the Effective Lagrangianmentioning

confidence: 99%

“…The novel Feynman rules from the dimension three Lagrangian relevant for the problem of pionnucleon scattering are collected in app. C. For an easier comparison with the Lagrangian given in [13], we have ordered the operators in the same way. This means that their b i can be mapped on our d i for i = 1, 2, 3 and their b i+1 onto d i for i = 4, .…”

Section: Effective Lagrangian In the Heavy Fermion Limitmentioning

confidence: 99%

“…absorb them in the corresponding LECs (as done in [13]). We also fill in some details on the construction of the effective Lagrangian which have not yet appeared in the literature.…”

Section: Introductionmentioning

confidence: 99%

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Pion-nucleon scattering in chiral perturbation theory (I): Isospin-symmetric case

1998

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We construct the complete effective chiral pion-nucleon Lagrangian to third order in small momenta based on relativistic chiral perturbation theory. We then perform the so-called heavy baryon limit and construct all terms up-to-and-including order 1/m 2 with fixed and free coefficients. As an application, we discuss in detail pionnucleon scattering. In particular, we show that for this process and to third order, the 1/m expansion of the Born graphs calculated relativistically can be recovered exactly in the heavy baryon approach without any additional momentum-dependent wave function renormalization. We fit various empirical phase shifts for pion laboratory momenta between 50 and 100 MeV. This leads to a satisfactory description of the phase shifts up to momenta of about 200 MeV. We also predict the threshold parameters, which turn out to be in good agreement with the dispersive analysis. In particular, we can sharpen the prediction for the isovector S-wave scattering length, 0.083We also consider the subthreshold parameters and give a short comparison to other calculations of πN scattering in chiral perturbation theory or modifications thereof.

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Section: Introductionsupporting

confidence: 67%

Section: Construction Of the Effective Lagrangianmentioning

confidence: 99%

Section: Effective Lagrangian In the Heavy Fermion Limitmentioning

confidence: 99%

“…absorb them in the corresponding LECs (as done in [13]). We also fill in some details on the construction of the effective Lagrangian which have not yet appeared in the literature.…”

Section: Introductionmentioning

confidence: 99%

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Pion-nucleon scattering in chiral perturbation theory (I): Isospin-symmetric case

1998

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“…A consistent power counting, and thus a systematic treatment of higher-order corrections has become possible within the framework of the heavy-baryon formulation of chiral perturbation theory. For example, the pion-nucleon interaction in the one-nucleon sector can be described in terms of the most general effective Lagrangian [5] …”

Section: Introductionmentioning

confidence: 99%

Chiral dynamics of rare η decays and virtual Compton scattering off the nucleon

Scherer

1997

Nuclear Physics A

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Renormalization of the Chiral Pion–Nucleon Lagrangian beyond Next-to-Leading Order

Meißner¹,

Müller²,

Steininger³

2000

Annals of Physics

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The complete renormalization of the generating functional for Green functions of quark currents between one-nucleon states in two-flavor heavy baryon chiral perturbation theory is performed to order q 4 . We show how the heat-kernel method must be extended for operators orthogonal to the heavy fermion four-velocity. We develop a method of treating the multicoincidence limit arising from insertions of dimension two (and higher) operators on internal baryon propagators in self-energy graphs. As examples, we study the divergences in the isoscalar magnetic moment and the scalar form factor of the nucleon.

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Low-energy expansion of the pion-nucleon Lagrangian

Abstract: The renormalized pion-nucleon Lagrangian is calculated to O(p 3 ) in heavy baryon chiral perturbation theory. By suitably chosen transformations of the nucleon field, the Lagrangian is brought to a standard form.

Cited by 108 publications

References 16 publications

Pion-nucleon scattering in chiral perturbation theory (I): Isospin-symmetric case

Pion-nucleon scattering in chiral perturbation theory (I): Isospin-symmetric case

Chiral dynamics of rare η decays and virtual Compton scattering off the nucleon

Renormalization of the Chiral Pion–Nucleon Lagrangian beyond Next-to-Leading Order

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