The first speaker of the day was Chris Kelly, who spoke about CP violation in the kaon sector from lattice QCD. As I hardly need to tell my readers, there are two sources of CP violation in the kaon system, the indirect CP-violation from neutral kaon-antikaon mixing, and the direct CP-violation from K->ππ decays. Both, however, ultimately stem from the single source of CP violation in the Standard Model, i.e. the complex phase e

^{iδ}in the CKM matrix, which gives the area of the unitarity triangle. The hadronic parameter relevant to indirect CP-violation is the kaon bag parameter B

_{K}, which is a "gold-plated" quantity that can be very well determined on the lattice; however, the error on the CP violation parameter ε

_{K}constraining the upper vertex of the unitarity triangle is dominated by the uncertainty on the CKM matrix element V

_{cb}. Direct CP-violation is particularly sensitive to possible BSM effects, and is therefore of particular interest. Chris presented the recent efforts of the RBC/UKQCD collaboration to address the extraction of the relevant parameter ε'/ε and associated phenomena such as the ΔI=1/2 rule. For the two amplitudes A

_{0}and A

_{2}, different tricks and methods were required; in particular for the isospin-zero channel, all-to-all propagators are needed. The overall errors are still large: although the systematics are dominated by the perturbative matching to the MSbar scheme, the statistical errors are very sizable, so that the 2.1σ tension with experiment observed is not particularly exciting or disturbing yet.

The second speaker of the morning was Gunnar Bali, who spoke about the topic of renormalons. It is well known that the perturbative series for quantum field theories are in fact divergent asymptotic series, whose typical term will grow like

*n*for large orders

^{k}z^{n}n!*n*. Using the Borel transform, such series can be resummed, provided that there are no poles (IR renormalons) of the Borel transform on the positive real axis. In QCD, such poles arise from IR divergences in diagrams with chains of bubbles inserted into gluon lines, as well as from instanton-antiinstanton configurations in the path integral. The latter can be removed to infinity by considering the large-

*N*limit, but the former are there to stay, making perturbatively defined quantities ambiguous at higher orders. A relevant example are heavy quark masses, where the different definitions (pole mass, MSbar mass, 1S mass, ...) are related by perturbative conversion factors; in a heavy-quark expansion, the mass of a heavy-light meson can be written as

_{c}*M=m+Λ+O(1/m)*, where

*m*is the heavy quark mass, and Λ a binding energy of the order of some QCD energy scale. As

*M*is unambiguous, the ambiguities in

*m*must correspond to ambiguities in the binding energy Λ, which can be computed to high orders in numerical stochastic perturbation theory (NSPT). After dealing with some complications arising from the fact that IR divergences cannot be probed directly in a finite volume, it is found that the minimum term in the perturbative series (which corresponds to the perturbative ambiguity) is of order 180 MeV in the quenched theory, meaning that heavy quark masses are only defined up to this accuracy. Another example is the gluon condensate (which may be of relevance to the extraction of α

_{s}from τ decays), where it is found that the ambiguity is of the same size as the typically quoted result, making the usefulness of this quantity doubtful.

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