b -> d Penguins: CP Violation, General Lower Bounds on the Branching Ratios and Standard Model Tests

With the wealth of new data from the B-factories, b -> d penguin decays become available for study, in addition to their b -> s counterparts that have proven an indespensable tool for the exploration of new-physics effects in flavour physics. A prominent example of the b -> d penguin transitions is $\bar B^0_d \to K^0 \bar K^0$. We show that this decay can be charaterized in the Standard Model by a surface in the observable space of the direct and mixing-induced CP asymmetries and the branching ratio. The form of this surface, which is theoretically clean, implies a lower bound for the branching ratio that has recently been confirmed experimentally. If future measurements of the CP asymmetries yield a point away from the SM surface, this would be an interesting signal of new physics. We point out that the hadronic parameters in $\bar B^0_d \to K^0 \bar K^0$ that parameterize the position on the SM surface are related to hadronic parameters in the B -> pi K system. The fact that the branching ratio of $\bar B^0_d \to K^0 \bar K^0$ is very close to its lower bound yields interesting implications for B -> pi K even without knowledge of the CP asymmetries of $\bar B^0_d \to K^0 \bar K^0$. The mechanism that produces the lower bound for $\bar B^0_d \to K^0 \bar K^0$ is actually much more general; we derive lower bounds for various other b -> d penguin-induced processes, including B -> rho gamma and $B^\pm \to K^{(\ast)\pm} K^{(\ast)}$. Some of these theoretical lower bounds are very close to the current experimental upper bounds.Comment: 4 pages, 2 figures. Contribution to the proceedings of EPS-HEP200

Comparing the QCD potential in Perturbative QCD and Lattice QCD at large distances

We compare the perturbatively calculated QCD potential to that obtained from lattice calculations in the theory without light quark flavours. We examine E_tot(r) = 2 m_pole + V_QCD(r) by re-expressing it in the MSbar mass m = m^MSbar(m^MSbar) and by choosing specific prescriptions for fixing the scale mu (dependent on r and m). By adjusting m so as to maximise the range of convergence, we show that perturbative and lattice calculations agree up to 3*r_0 ~ 7.5 GeV^-1 (r_0 is the Sommer scale) within the uncertainty of order Lambda^3 r^2.Comment: Version to appear in Eur.J.Phys; 16 pages, 7 figure