_{K}/f

_{π}, as well as the zero momentum transfer form factor f

_{+}(0) (which are increasingly so precise that the question of when the precision was enough was raised from the audience after the talk), he proceeded to discuss the general theory of CP violation in neutral Kaon mixing and the ΔI=1/2 rule in K->ππ decays, and the ways in which lattice calculations are needed to understand these topics. A number of recent updates on the Kaon bag parameter B

_{K}were summarized, and the renormalization and mixing of the BSM operators entering neutral Kaon mixing (for which Mauro Papinutto showed some impressive results in one of the parallel sessions) were discussed. Finally, RBC/UKQCD now have results on the ΔI=1/2 and ΔI=3/2 amplitudes in K->ππ decays at the physical pion mass, which strongly support the ΔI=1/2 rule at a level compatible with phenomenology.

This was followed by a talk on a somewhat related topic, namely Stephan Dürr speaking about the question of whether the validity of χPT extends even to the physical pion mass. Contrary to the often-quoted theorem that the answer to any title with a question mark in it is "no", the answer was "yes" in this case. While the chiral expansion breaks down completely at pion masses of around 500 MeV (where NNLO corrections grow to be larger than the NLO ones), two different analyses (one using staggered, and one using Wilson fermions) that Stephan showed indicate that the NLO low-energy constants can be extracted in a reasonably consistent manner from fits in the range M

_{π}=135-400 MeV. However, the low-energy constant l

_{4}showed a significant sensitivity to the range of pion masses used to fit.

The last talk before the coffee break was on Multigrid methods for lattice QCD and was given by Andreas Frommer. Multigrid methods have a long history in applied mathematics, where they are used more commonly in the context of finite-element methods (rather than the finite-difference approach used in lattice field theory). The basic ingredients from the applied mathematics point of view are a smooting operation together with restriction and prolongation operations that allow to reduce the size of the problem to a level where it can be solved directly, and then to retrieve the solution of the original problem from this. Interestingly, this was somewhat reinvented in a way tuned to lattice QCD from the physics side, where Lüscher's inexactly deflated SAP-preconditioned GCR that is part of the DD-HMC and openQCD packages forms a two-level multilevel scheme that leads to a great improvement in runtime behaviour as the quark mass is decreased. The Wuppertal applied mathematics group has extended this to a generic multilevel scheme for QCD (where it is found that three levels are even better than two at small quark masses, but four seem not to help appreciably more). From the mathematical side, most of the existing multigrid theory does not apply to QCD, however, so further mathematical research seems required to fully understand why and when these approaches work for QCD.

After the coffee break, Raul Briceno spoke about few-body physics. In this area, significant theoretical progress seems to have been made recently and still to be under way, extending Lüscher's finite-volume formalism for scattering phase shifts in various directions.

This was followed by a talk on the closely related and somewhat overlapping topic of hadronic interactions by Takeshi Yamazaki, who presented recent results for various scattering lengths and phase shifts, as well as reviewing the alternative HALQCD method, which relies on reconstructing an interaction potential from multi-particle correlators.

In the afternoon there were parallel sessions again. I got to chair the session on renormalization from the Schrödinger functional approach, where there has been significant progress on the chirally rotated SF and on studying the mixing of four-quark operators. Another very interesting session later in the afternoon was concerned with the various methods to get at quark-disconnected contributions to hadron structure observables, and some of the results obtained using them.

In the evening, the poster session took place.

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