The B -> pi K Puzzle and its Relation to Rare B and K Decays

The Standard-Model interpretation of the ratios of charged and neutral B-> pi K rates, R_c and R_n, respectively, points towards a puzzling picture. Since these observables are affected significantly by colour-allowed electroweak (EW) penguins, this ``B -> pi K puzzle'' could be a manifestation of new physics in the EW penguin sector. Performing the analysis in the R_n-R_c plane, which is very suitable for monitoring various effects, we demonstrate that we may, in fact, move straightforwardly to the experimental region in this plane through an enhancement of the relevant EW penguin parameter q. We derive analytical bounds for q in terms of a quantity L, that measures the violation of the Lipkin sum rule, and point out that strong phases around 90 deg are favoured by the data, in contrast to QCD factorisation. The B -> pi K modes imply a correlation between q and the angle gamma that in the limit of negligible rescattering effects and colour suppressed EW penguins depends only on the value of L. Concentrating on a minimal flavour-violating new-physics scenario with enhanced Z^0 penguins, we find that the current experimental values on B -> X_s mu^+ mu^- require roughly L pi K data give L = 5.7 +- 2.4, L has either to move to smaller values once the B -> pi K data improve or new sources of flavour and CP violation are needed. In turn, the enhanced values of L seen in the B -> pi K data could be accompanied by enhanced branching ratios for rare decays. Most interesting turns out to be the correlation between the B -> pi K modes and BR(K^+ -> pi^+ nu nu), with the latter depending approximately on a single ``scaling'' variable \bar L= L (|V_{ub}/V_{cb}|/0.086)^2.3.Comment: 19 pages, 7 figures, a few typos corrected and two references adde

Flavour Visions

This decade will allow to improve the resolution of the short distance scales by at least an order of magnitude, extending the picture of fundamental physics down to scales $5\cdot 10^{-20}$m with the help of the LHC. Further resolution down to scales as short as $10^{-21}$m should be possible with the help of high precision experiments in which flavour violating processes will play a prominent role. Will this increase in resolution allow us to see new particles (new animalcula) similarly to what Antoni van Leeuvenhoek saw by discovering bacteria in 1676? The basic question for particle physics is how these new animalcula will look like and which difficulties of the Standard Model (SM) they will help us to solve and which new puzzles and problems they will bring with them. I will describe what role flavour physics will play in these exciting times provided this new world is animalculated.Comment: 18 pages, 1 Figure, Talk given at the 13th International Conference on B-Physics at Hadron Machines, April 4-8 2011 Amsterdam, the Netherland

Two--Loop Anomalous Dimension Matrix for ΔS=1\Delta S=1 Weak Non-Leptonic Decays II: O(αeαs){\cal O}(\alpha_e \alpha_s)

We calculate the $10\times 10$ two--loop anomalous dimension matrix to order \ord(\alpha_e \alpha_s) in the dimensional regularization scheme with anticommuting $\gamma_5$ (NDR) which is necessary for the extension of the $\Delta S=1$ weak Hamiltonian involving electroweak penguins beyond the leading logarithmic approximation. We demonstrate, how a direct calculation of penguin diagrams involving $\gamma_5$ in closed fermion loops can be avoided thus allowing a consistent calculation of two--loop anomalous dimensions in the simplest renormalization scheme with anticommuting $\gamma_5$ in $D$ dimensions. We give the necessary one--loop finite terms which allow to obtain the corresponding two--loop anomalous dimension matrix in the HV scheme with non--anticommuting $\gamma_5$.Comment: 25 page

The B -> pi pi, pi K Puzzles: Implications for Hadron Physics, New Physics and Rare Decays

The B-meson system is an interesting probe for the exploration of strong interactions, the quark-flavour sector of the Standard Model, and the search for new physics. In this programme, non-leptonic B decays, which are particularly challenging from the point of view of QCD, play a key role. After discussing strategies to deal with the corresponding hadronic matrix elements of four-quark operators and popular avenues for new physics to manifest itself in B decays, we focus on puzzling patterns in the B-factory data for B -> pi pi, pi K decays; we explore their implications for hadron physics, new physics and rare K and B decays.Comment: 10 pages, 2 figures, plenary talk at the International Conference on QCD and Hadronic Physics, Peking University, Beijing, China, 16-20 June 2005, to appear in the Proceeding

Flavour Theory and the LHC Era

This decade should make a significant progress towards the Theory of Flavour and the main goal of this talk is to transfer this believe to my colleagues in the particle physics community. Indeed a significant part of this decade could turn out to be the Flavour Era with participation of the LHC, Belle II, Super-Flavour-Facility and dedicated Kaon and lepton flavour violation experiments. Selected superstars of flavour physics listed below will play a prominent role in these events. In this writeup the leading role is played by the prima donna of 2010: CP violation in B_s system.Comment: 17 Pages, 1 Figure, Plenary talk presented at the Symposium "Physics at the LHC 2010", DESY, June, 201