Chiral corrections to kaon-nucleon scattering lengths

Abstract

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

Pion-nucleon scattering to $\mathcal{O}(p^3)$ in heavy baryon SU(3) chiral perturbation theory

“…In addition, our results from one-loop diagrams are consistent with the threshold T-matrices (t → 0) obtained in Ref. [37,38]. Putting all amplitudes from different one-loop diagrams together, we have…”

On the strangeness -1 S-wave meson-baryon scattering

“…[44,45,46]. Even more, for the case of S-wave I=0KN scattering lengths, the CHPT prediction is a disaster [44]. This is due to the presence of the Λ(1405) resonance below and close to theKN threshold.…”

“…These facts make that cancellations of large contributions at second and third chiral order often happen with still sizable O(p 4 ) contributions, see, e.g., refs. [44,45,46]. Even more, for the case of S-wave I=0KN scattering lengths, the CHPT prediction is a disaster [44].…”

Light pseudoscalar meson and heavy meson scattering lengths to $\mathcal{O}(p^4)$ in heavy meson chiral perturbation theory

“…From refs. [40,41,42,43,44,45,46,47], it turned out that the calculations in SU (3) HBChPT can also lead to reasonable predictions.…”