FLAG phase 2: Status and prospects

In this talk I presented the FLAG initiative, discussed the history of the project, its aim and scope. After completing the first review in 2010, we decided to extend the review to more quantities and to involve a larger group of people. I have illustrated the phase 2 of the project, its new structure and the schedule for the release of the next review.

A Dispersive Treatment of Kl4 Decays

K`4 decays are interesting for several reasons: They allow an accurate measurement of a combination of S-wave pp scattering lengths, one form factor of the decay is connected to the chiral anomaly and the decay is the best source for the determination of some low energy constants of ChPT. We present a dispersive approach to K`4 decays, which takes rescattering effects fully into account. Some fits to NA48/2 and E865 measurements and results of the matching to ChPT are shown.

A scrutiny of hard pion chiral perturbation theory

In the recently proposed framework of hard pion chiral perturbation theory, the leading chiral logarithms are predicted to factorize with respect to the energy dependence in the chiral limit. We have scrutinized this assumption in the case of vector and scalar pion form factors FV;S(s) by means of standard chiral perturbation theory and dispersion relations. We show that this factorization property is valid for the elastic contribution to the dispersion integrals for FV;S(s) but it is violated starting at three loops when the inelastic four-pion contributions arise.

Extraction of the s-wave pi N scattering lengths from data on pionic atoms

For many years a combined analysis of pionic hydrogen and deuterium atoms has been known as a good tool to extract information on the isovector and especially on the isoscalar s-wave pN scattering length. However, given the smallness of the isoscalar scattering length, the analysis becomes useful only if the pion–deuteron scattering length is controlled theoretically to a high accuracy comparable to the experimental precision. To achieve the required few-percent accuracy one needs theoretical control over all isospin-conserving three-body pNN !pNN operators up to one order before the contribution of the dominant unknown (N†N)2pp contact term. This term appears at next-to-next-to-leading order in Weinberg counting. In addition, one needs to include isospin-violating effects in both two-body (pN) and three-body (pNN) operators. In this talk we discuss the results of the recent analysis where these isospin-conserving and -violating effects have been carefully taken into account. Based on this analysis, we present the up-to-date values of the s-wave pN scattering lengths.

Improved dispersive analysis of the scalar form factor of the nucleon

We present a coupled system of integral equations for the pp → ¯NN and ¯K K → ¯N N S-waves derived from Roy–Steiner equations for pion–nucleon scattering. We discuss the solution of the corresponding two-channel Muskhelishvili–Omnès problem and apply the results to a dispersive analysis of the scalar form factor of the nucleon fully including ¯KK intermediate states. In particular, we determine the corrections Ds and DD, which are needed for the extraction of the pion– nucleon s term from pN scattering, and show that the difference DD −Ds = (−1.8±0.2)MeV is insensitive to the input pN parameters.