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These notes contain the written version of lectures given at the 2009 Les Houches Summer School "Modern perspectives in lattice QCD: Quantum field theory and high performance computing." The goal is to provide a pedagogical introduction to…
We present a concise review of the theoretical status of the rare semileptonic B -> X_s l^+ l^- decays in the standard model. Particular attention is thereby devoted to the recent theoretical progress concerning, on the one hand the…
We review recent progress in the study of the large $N_c$ limit of gauge theories from lattice simulations. The focus is not only the planar limit but also the size of ${\mathcal O}(N_c^{-1})$ corrections for values of $N_c\gtrsim 3$. Some…
In the past decades, significant improvements have been made on standard-model predictions on kaon decays using lattice quantum chromodynamics. In these proceedings, I review selected works on long-distance contributions to kaon decays and…
The conventional view is that a solution of the strong CP problem lies beyond QCD. A strong argument supporting this view is that the chiral expansion shows that observables depend on theta (unless a quark mass is zero); this eliminates the…
The talk summarises a calculation of the two-point functions for $\Delta S=1$ current-current and QCD-penguin operators, as well as for the $\Delta S=2$ operator, at the next-to-leading order. The size of the gluonic corrections to…
These lectures are an introduction to the subject of chiral effective Lagrangians of the Standard Model and their applications, mostly in the sector of non--leptonic kaon decays, with special emphasis on CP--violation. The first lecture…
Current and future colliders will provide high precision experimental data. In order to use the high experimental precision it has to be matched with theoretical predictions at the same level of accuracy or better. This involves the…
Chiral dynamics makes definitive predictions for the electromagnetic polarizabilities of hadrons near the chiral limit; but, agreement with experiment is tenuous in some cases. We provide an overview of lattice QCD methods to compute the…
After decades of intensive efforts, lattice methods finally revealed one clear source of the large enhancement of the ratio $Re A_0/Re A_2$ \cite{RBC_UKQCD_PRL13}, which has been a puzzle in particle physics for about sixty years. Lattice…
I review recent results on phase structure and equation of state of strong interaction matter from lattice QCD. Particular emphasis is given to the axes where direct simulations are possible and results are obtained with sufficient control…
Nucleon electric dipole moments originating from strong CP-violation are being calculated by several groups using lattice QCD. We revisit the finite volume corrections to the CP-odd nucleon matrix elements of the electromagnetic current,…
During the last fifteen years B_{s,d} decays, B_{s,d}^0-\bar B^0_{s,d} mixings, CP-violating asymmetries S_{\psi K_S} and S_{\psi\phi} provided the dominant information about the pattern of flavour violation within the SM and its…
We present a calculation of the standard model \Delta S=2 matrix element relevant to indirect CP violation in K->\pi\pi decays which uses Neuberger's chiral formulation of lattice fermions. The computation is performed in the quenched…
We discuss a simple method to evaluate the QCD corrections to $\Delta\rho$. It assumes that the perturbative expansion in terms of $\ms$ parameters is meaningful and, unlike other studies, exploits significant available information…
Electromagnetic effects in the leptonic decay rates $\pi^+ \to \mu^+ \nu$ and $K^+ \to \mu^+ \nu$ are evaluated for the first time on the lattice. Following a method recently proposed in Ref. [1] the emission of virtual photons at leading…
We describe a first-principles method to apply lattice QCD to compute the order $\alpha_{\mathrm{EM}}$ corrections to $K\to\pi\ell\nu_\ell$ decay. This method formulates the calculation in infinite volume with the conventional…
In the last century the non-perturbative regularization of chiral fermions was a long-standing problem. We review how this problem was finally overcome by the formulation of a modified but exact form of chiral symmetry on the lattice. This…
This talks contains a short introduction to Chiral Perturbation Theory and the existing calculations to two-loop order in the mesonic sector. I include a discussion on which quantities the expansion can be organized in. The present best…
I review recent progress achieved on the lattice in the quantitative comprehension of chiral symmetry breaking in QCD. Emphasis is given to the recent precise computations of the spectral density of the Dirac operator in the continuum…