Pion-kaon scattering near the threshold in chiral SU(2) perturbation theory

Abstract

In the context of chiral SU (2) perturbation theory, pion-kaon scattering is analysed near the threshold to fourth chiral order. The scattering amplitude is calculated both in the relativistic framework and by using an approach similar to heavy baryon chiral perturbation theory. Both methods lead to equivalent results. We obtain relations between threshold parameters, valid to fourth chiral order, where all those combinations of low-energy constants which are not associated with chiralsymmetry breaking terms drop out. The remaining low-energy constants can be estimated using chiral SU (3) symmetry. Unfortunately, the experimental information is not precise enough to test our lowenergy theorems.

Hyperons in two-flavor chiral perturbation theory

“…For hyperons, there is a wealth of literature exploring hyperon properties utilizing the SU(3) heavy baryon Lagrangian . On the other hand, an SU(2) treatment of kaons was developed [47] to describe π-K scattering near threshold, which was further explored in [48]. Strange matrix elements of the nucleon were explored with an SU(2) Lagrangian [49], and an SU(2) treatment of spin-1/2 baryons was pursued in [50] to investigate hyper-nuclear interactions and hyperon decays at tree-level.…”

precise SM tests

“…From the practical point of view this difficulty has been overcome in two ways: either by doing an SU(2) chiral analysis of data on kaons (i.e. by considering the strange quark as heavy and expanding only aroundm = 0, an approach pioneered by Roessl [10] This issue is even more urgent for the four-quark K − π matrix elements discussed by Norman Christ in his talk [11], because for those quantities the failure of χPT is quite dramatic. Of course, the main motivation for carrying out such difficult calculations is to get the K → ππ matrix elements which are relevant in the CP-violating decays and play an important role in the calculation of ε ′ /ε, and since it is possible to calculate these directly, this is the route that lattice collaborations interested in these problems will take (as announced in [11]).…”

Observation and investigation ofπKatoms

“…ChPT with L (2) , L (4) , L (6) in 2-loop approximation predicts S-wave scattering length difference [5]:…”

“…ChPT in 1-loop approximation predicts S-wave pion-kaon scattering lengths with isospin 1/2 (a 1/2 0 ) and 3/2 (a 3/2 0 ) to be [3,4]: a 1/2 0 = 0.19 ± 0.2, a 3/2 0 = −0.05 ± 0.02, a 1/2 0 − a 3/2 0 = 0.23 ± 0.01 .…”