Pion–nucleon scattering in chiral perturbation theory II: Fourth order calculation

Fettes, Nadia; Meißner, Ulf‐G.

doi:10.1016/s0375-9474(00)00199-8

Cited by 174 publications

(294 citation statements)

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“…Recently, the complete fourth order one-loop analysis of low energy πN-scattering has been performed in ref. [4].…”

Section: To Be Published In: Physical Review Cmentioning

confidence: 99%

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Chiral corrections to kaon-nucleon scattering lengths

Kaiser

2001

Phys. Rev. C

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We calculate the threshold T-matrices of kaon-nucleon and antikaon-nucleon scattering to one loop order in SU(3) heavy baryon chiral perturbation theory. To that order the complex-valued isospin-1 KN threshold T-matrix can be successfully predicted from the isospin-0 and 1 KN threshold T-matrices. As expected perturbation theory fails to explain the isospin-0 KN threshold T-matrix which is completely dominated by the nearby subthreshold Λ * (1405)-resonance. Cancelations of large terms of second and third chiral order are observed as they seem to be typical for SU(3) baryon chiral perturbation theory calculations. We also give the kaon and eta loop corrections to the πN scattering lengths and we investigate πΛ scattering to one-loop order. The second order s-wave low-energy constants are all of natural size and do not exceed 1 GeV −1 in magnitude.PACS: 12.38.Bx, 12.39.Fe, 13.75.Gx, 13.75.Jz To be published in: Physical Review C.Chiral symmetry severely constrains the interaction of the strongly interacting particles at low energies, first formulated in terms of current algebra. One of the most splendid successes of current algebra was the Tomozawa-Weinberg prediction [1] for the s-wave pion-nucleon scattering lengths a ± πN . The tool to systematically investigate the consequences of spontaneous and explicit chiral symmetry breaking in QCD is chiral perturbation theory. Observables are calculated with the help of an effective field theory formulated in terms of the Goldstone bosons (π, K, K, η) and the low-lying baryons (N, Λ, Σ, Ξ). A systematic expansion in small external momenta and meson masses is possible. Pion-loop corrections to a ± πN have been first calculated in ref. [2]. In the case of the isospin-odd πN-scattering length a − πN the chiral loop correction in fact closes the about 15% gap between the lowest order Tomozawa-Weinberg prediction and the empirical value [3]. Recently, the complete fourth order one-loop analysis of low energy πN-scattering has been performed in ref. [4].Kaon-nucleon and antikaon-nucleon scattering are then of interest as a testing ground of the three-flavor chiral dynamics. In comparison to the SU(2) sector of πN-interaction these processes involve several new complications. First, the pertinent expansion parameter is much larger since the pion mass gets replaced by the kaon mass. Secondly, for KN-scattering there exist inelastic channels involving a pion and a hyperon down to threshold, while KN-scattering is purely elastic at low energies. The dynamical differences in KN versus KN-scattering naturally show up in the values of the s-wave scattering lengths or the equivalent threshold T-matrices, T (0,1) KN = 4π(1 + m K /M N )a

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“…Recently, the complete fourth order one-loop analysis of low energy πN-scattering has been performed in ref. [4].…”

Section: To Be Published In: Physical Review Cmentioning

confidence: 99%

“…Recently, the complete fourth order one-loop analysis of low energy πN-scattering has been performed in ref. [4].Kaon-nucleon and antikaon-nucleon scattering are then of interest as a testing ground of the three-flavor chiral dynamics. In comparison to the SU(2) sector of πN-interaction these processes involve several new complications.…”

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confidence: 99%

Chiral corrections to kaon-nucleon scattering lengths

Kaiser

2001

Phys. Rev. C

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“…c 1 denotes a dimension two coupling in the chiral Lagrangian sensitive to the internal structure of the nucleon in close connection to the pion-nucleon sigma term. Most determinations agree about its sign but are uncertain about its precise value (related to the still unsatisfactory situation in the extraction of the pion-nucleon sigma term based on various partial waves analyses of elastic πN scattering data): [31,32,33,34,35,36,37]. Choosing the central value for c 1 and fixing M 0 = 0.88 GeV to reproduce the physical mass of the nucleon for m π = 0.138 GeV one therefore obtains the mass of the nucleon as a function of the mass of the pion as shown in Fig.…”

Section: Third Order Calculation Of the Nucleon Mass In Dimensional Rmentioning

confidence: 99%

Cutoff schemes in chiral perturbation theory and the quark mass expansion of the nucleon mass

2004

Self Cite

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We discuss the use of cutoff methods in chiral perturbation theory. We develop a cutoff scheme based on the operator structure of the effective field theory that allows to suppress high momentum contributions in Goldstone boson loop integrals and by construction is free of the problems traditional cutoff schemes have with gauge invariance or chiral symmetries. As an example, we discuss the chiral expansion of the nucleon mass. Contrary to other claims in the literature we show that the mass of a nucleon in heavy baryon chiral perturbation theory has a well behaved chiral expansion up to effective Goldstone boson masses of 400 MeV when one utilizes standard dimensional regularization techniques. With the help of the here developed cutoff scheme we can demonstrate a well-behaved chiral expansion for the nucleon mass up to 600 MeV of effective Goldstone Boson masses. We also discuss in detail the prize, in numbers of additional short distance operators involved, that has to be paid for this extended range of applicability of chiral perturbation theory with cutoff regularization, which is usually not paid attention to. We also compare the fourth order result for the chiral expansion of the nucleon mass with lattice results and draw some conclusions about chiral extrapolations based on such type of representation.

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“…Elastic pion-nucleon (πN) scattering certainly belongs to the the most extensively studied processes in ChPT [8][9][10][11][12][13][14][15][16]. The πN scattering amplitude enters as a subprocess into the interactions between two and three nucleons at large distances.…”

Section: Elastic Pion-nucleon Scatteringmentioning

confidence: 99%