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Register a new userIsospin Breaking in Low-Energy Charged Pion and Kaon Elastic Scattering
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Authors
A. Nehme
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We use chiral perturbation theory to evaluate the scattering amplitude for the process Pi^+ K^- to Pi^+ K^- at leading and next-to-leading orders in the chiral counting and in the presence of isospin breaking effects. We also discuss the influence of the latter on the combination of the S-wave Pi K scattering lengths which is relevant for the 2S - 2P energy levels shift of K Pi atoms.
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The charged $K_{ell 4}$ decay, $K^+topi^+pi^-ell^+ u_{ell}$ is studied in the framework of chiral perturbation theory based on the effective Lagrangian including mesons, photons, and leptons. We give analytic expressions for the two vectorial form factors, $f$ and $g$, calculated at one-loop level in the presence of Isospin breaking effects. These expressions may then be used to disentangle the Isospin breaking part from the measured form factors and hence improve the accuracy in the determination of $pipi$ scattering parameters from $K_{ell 4}$ experiments.
In recent years, high-accuracy data for pionic hydrogen and deuterium have become the primary source of information on the pion-nucleon scattering lengths. Matching the experimental precision requires, in particular, the study of isospin-breaking corrections both in pion-nucleon and pion-deuteron scattering. We review the mechanisms that lead to the cancellation of potentially enhanced virtual-photon corrections in the pion-deuteron system, and discuss the subtleties regarding the definition of the pion-nucleon scattering lengths in the presence of electromagnetic interactions by comparing to nucleon-nucleon scattering. Based on the pi^{+/-} p channels we find for the virtual-photon-subtracted scattering lengths in the isospin basis a^{1/2}=(170.5 +/- 2.0) x 10^{-3} mpi^{-1} and a^{3/2}=(-86.5 +/- 1.8) x 10^{-3} mpi^{-1}.
The electromagnetic corrections to the low energy scattering amplitude involving charged pions only are investigated at leading and next-to-leading orders in the two-flavour chiral expansion. As an application, the corresponding variation in the strong $2S-2P$ level shift is evaluated. The relative variation is of the order of 5%.
Based on our analysis of the contributions from the connected and disconnected contraction diagrams to the pion-kaon scattering amplitude, we provide the first determination of the low-energy constant $L_0^r$ in SU$(4|1)$ Partially-Quenched Chiral Perturbation Theory from data of the Extended Twisted Mass Collaboration, $L_0^r = 0.51(26)cdot 10^{-3}$ at $mu=1$ GeV.
In the presence of photons, the neutral $K_{ell 4}$ decay, $K^0topi^0pi^-ell^+ u_ell$, can be parameterized in terms of three vectorial, one anomalous, and one tensorial form factors. We present here analytic expressions of two vectorial form factors, $f$ and $g$, calculated at one-loop level in the framework of chiral perturbation theory based on the effective Lagrangian including mesons, photons, and leptons. These expressions may then be used to disentangle the Isospin breaking part from the measured form factors and hence improve the accuracy in the determination of $pipi$ scattering parameters from $K_{ell 4}$ experiments.
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