Calculating the energy spectra of magnetic molecules: application of real- and spin-space symmetries

The determination of the energy spectra of small spin systems as for instance given by magnetic molecules is a demanding numerical problem. In this work we review numerical approaches to diagonalize the Heisenberg Hamiltonian that employ symmetries; in particular we focus on the spin-rotational symmetry SU(2) in combination with point-group symmetries. With these methods one is able to block-diagonalize the Hamiltonian and thus to treat spin systems of unprecedented size. In addition it provides a spectroscopic labeling by irreducible representations that is helpful when interpreting transitions induced by Electron Paramagnetic Resonance (EPR), Nuclear Magnetic Resonance (NMR) or Inelastic Neutron Scattering (INS). It is our aim to provide the reader with detailed knowledge on how to set up such a diagonalization scheme.Comment: 29 pages, many figure

Measurements of branching fraction ratios and CP-asymmetries in suppressed B^- -> D(-> K^+ pi^-)K^- and B^- -> D(-> K^+ pi^-)pi^- decays

We report the first reconstruction in hadron collisions of the suppressed decays B^- -> D(-> K^+ pi^-)K^- and B^- -> D(-> K^+ pi^-)pi^-, sensitive to the CKM phase gamma, using data from 7 fb^-1 of integrated luminosity collected by the CDF II detector at the Tevatron collider. We reconstruct a signal for the B^- -> D(-> K^+ pi^-)K^- suppressed mode with a significance of 3.2 standard deviations, and measure the ratios of the suppressed to favored branching fractions R(K) = [22.0 \pm 8.6(stat)\pm 2.6(syst)]\times 10^-3, R^+(K) = [42.6\pm 13.7(stat)\pm 2.8(syst)]\times 10^-3, R^-(K)= [3.8\pm 10.3(stat)\pm 2.7(syst]\times 10^-3, as well as the direct CP-violating asymmetry A(K) = -0.82\pm 0.44(stat)\pm 0.09(syst) of this mode. Corresponding quantities for B^- -> D(-> K^+ pi^-)pi^- decay are also reported.Comment: 8 pages, 1 figure, accepted by Phys.Rev.D Rapid Communications for Publicatio

Search for B_s --> mu+mu- and B_d --> mu+mu- Decays with CDF II

A search has been performed for B_s --> mu+mu- and B_d --> mu+mu- decays using 7/fb of integrated luminosity collected by the CDF II detector at the Fermilab Tevatron collider. The observed number of B_d candidates is consistent with background-only expectations and yields an upper limit on the branching fraction of BF(B_d-->mu+mu-) < 6.0E-9 at 95% confidence level. We observe an excess of B_s candidates. The probability that the background processes alone could produce such an excess or larger is 0.27%. The probability that the combination of background and the expected standard model rate of B_s --> mu+mu- could produce such an excess or larger is 1.9%. These data are used to determine BF(B_s-->mu+mu-) = (1.8^{+1.1}_{-0.9})E-8 and provide an upper limit of BF(B_s -->mu+mu-) < 4.0E-8 at 95% confidence level.Comment: 7 pages, 1 figure; version accepted by PR