The flavor-changing electromagnetic dipole operator O 7 gives the dominant contribution to the B ! X s decay rate. We calculate two-loop QCD corrections to its matrix element together with the corresponding bremsstrahlung contributions. The optical theorem is applied, and the relevant imaginary parts of three-loop diagrams are computed following the lines of our recent t ! X b W calculation. The complete result allows us to test the validity of the naive non-Abelianization (NNA) approximation that has been previously applied to estimate the next-to-next-to-leading order QCD correction to ÿ B ! X s =ÿ B ! X u e . When both decay widths are normalized to m 5 b;R in the same renormalization scheme R, the calculated O 2 s correction is sizable ( 6%), and the NNA estimate is about 1=3 too large. On the other hand, when the ratio of the decay widths is written as S m 2 b;MS m b =m 2 b;pole , the calculated O 2 s correction to S is at the level of 1% for both the complete and the NNA results.

We derive an analytic result for the pion pole contribution to the light-by-light scattering correction to the anomalous magnetic moment of the muon, aµ = (gµ − 2)/2. Using the vector meson dominance model (VMD) for the pion transition form factor, we obtain a LBL,π 0 µ = +56 × 10 −11 .

We present a determination of a new class of three-loop Feynman diagrams describing heavy-tolight transitions. We apply it to find the O α 2 s corrections to the top quark decay t → bW and to the distribution of lepton invariant mass in the semileptonic b quark decay b → ulν. We also confirm the previously determined total rate of that process as well as the O α 2 corrections to the muon lifetime.PACS numbers: 12.38. Bx,13.35.Bv,14.65.Ha The determination of higher order corrections in perturbative quantum field theory is notoriously difficult, and with the general tendency towards precision measurements in particle physics, each newly-won class of perturbative integrals expands the possibilities for phenomenological analyses. For instance, quantum corrections to decays of neutral particles, such as a virtual photon or a Z boson into hadrons, are known to sixth order in perturbation theory, O α Much less is known about radiative corrections to processes with a charged particle in the initial state. Only relatively recently have first results been obtained in fourth order perturbation theory, O α

Diquarks with J P = 0 ± , 1 ± containing a heavy (charm or bottom) quark and a light quark are investigated using QCD Laplace sum rules. Masses are determined using appropriately constructed gauge invariant correlation functions, including for the first time next-to-leading order perturbative contributions. The J P = 0 + and 1 + charm-light diquark masses are respectively found to be 1.86 ± 0.05 GeV and 1.87 ± 0.10 GeV, while those of the 0 + and 1 + bottom-light diquarks are both determined to be 5.08±0.04 GeV. The sum rules derived for heavy-light diquarks with negative parity are poorly behaved and do not permit unambiguous mass predictions, in agreement with previous results for negative parity light diquarks. The scalar and axial vector heavy-light diquark masses are degenerate within uncertainty, as expected by heavy quark symmetry considerations. Furthermore, these mass predictions are in good agreement with masses extracted in constituent diquark models of the tetraquark candidates X(3872) and Y b (10890). Thus these results provide QCD support for the interpretation of the X(3872) and Y b (10890) as J P C = 1 ++ tetraquark states composed of diquark clusters. Further implications for tetraquarks among the heavy quarkonium-like XYZ states are discussed.