Next was a review of progress in light flavour physics by Andreas Jüttner, who likewise gave an excellent overview of this also phenomenologically very important core field. Besides the "standard" quantities, such as the leptonic pion and kaon decay constants and the semileptonic K-to-pi form factors, more difficult light-flavour quantities are now being calculated, including the bag parameter B

_{K}and other quantities related to both Standard Model and BSM neutral kaon mixing, which require the incorporation of long-distance effects, including those from charm quarks. Given the emergence of lattice ensembles at the physical pion mass, the analysis strategies of groups are beginning to change, with the importance of global ChPT fits receding. Nevertheless, the lattice remains important in determining the low-energy constants of Chiral Perturbation Theory. Some groups are also using newer theoretical developments to study quantities once believed to be outside the purview of lattice QCD, such as final-state photon corrections to meson decays, or the timelike pion form factor.

After the coffee break, the Ken Wilson Award for Excellence in Lattice Field Theory was announced. The award goes to Stefan Meinel for his substantial and timely contributions to our understanding of the physics of the bottom quark using lattice QCD. In his acceptance talk, Stefan reviewed his recent work on determining |V

_{ub}|/|V

_{cb}| from decays of Λ

_{b}baryons measured by the LHCb collaboration. There has long been a discrepancy between the inclusive and exclusive (from B -> πlν) determinations of V

_{ub}, which might conceivably be due to a new (BSM) right-handed coupling. Since LHCb measures the decay widths for Λ

_{b}to both pμν and Λ

_{c}μν, combining these with lattice determinations of the corresponding Λ

_{b}form factors allows for a precise determination of |V

_{ub}|/|V

_{cb}|. The results agree well with the exclusive determination from B -> πlν, and fully agree with CKM unitarity. There are, however, still other channels (such as b -> sμ

^{+}μ

^{-}and b -> cτν) in which there is still potential for new physics, and LHCb measurements are pending.

This was followed by a talk by Maxwell T. Hansen (now a postdoc at Mainz) on three-body observables from lattice QCD. The well-known Lüscher method relates two-body scattering amplitudes to the two-body energy levels in a finite volume. The basic steps in the derivation are to express the full momentum-space propagator in terms of a skeleton expansion involving the two-particle irreducible Bethe-Salpeter kernel, to express the difference between the two-particle reducible loops in finite and infinite volume in terms of two-particle cuts, and to reorganize the skeleton expansion by the number of cuts to reveal that the poles of the propagator (i.e. the energy levels) in finite volume are related to the scattering matrix. For three-particle systems, the skeleton expansion becomes more complicated, since there can now be situations involving two-particle interactions and a spectator particle, and intermediate lines can go on-shell between different two-particle interactions. Treating a number of other technical issues such as cusps, Max and collaborators have been able to derive a Lüscher-like formula three-body scattering in the case of scalar particles with a Z

_{2}symmetry forbidding 2-to-3 couplings. Various generalizations remain to be explored.

The day's plenary programme ended with a talk on the Standard Model prediction for direct CP violation in K-> ππ decays by Christopher Kelly. This has been an enormous effort by the RBC/UKQCD collaboration, who have shown that the ΔI=1/2 rule comes from low-energy QCD by way of strong cancellations between the dominant contributions, and have determined ε' from the lattice for the first time. This required the generation of ensembles with an unusual set of boundary conditions (G-parity boundary conditions on the quarks, requiring complex conjugation boundary conditions on the gauge fields) in space to enforce a moving pion ground state, as well as the precise evaluation of difficult disconnected diagrams using low modes and stochastic estimators, and treatment of finite-volume effects in the Lellouch-Lüscher formalism. Putting all of this together with the non-perturbative renormalization (in the RI-sMOM scheme) of ten operators in the electroweak Hamiltonian gives a result which currently still has three times the experimental error, but is systematically improvable, with better-than-experimental precision expected in maybe five years.

In the afternoon there were parallel sessions again, and in the evening, the poster session took place. Food ran out early, but it was pleasant to see free-form smearing begin improved upon and used to very good effect by Randy Lewis, Richard Woloshyn and students.

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