Exclusive Radiative Decays of B Mesons

We present within the Standard Model the exclusive radiative decays B -> K*/rho gamma and B_(s/d) -> gamma gamma in QCD factorization based on the heavy-quark limit m_b >> Lambda_QCD. For the decays with a vector meson in the final state we give results complete to next-to-leading order in QCD.Comment: 4 pages, contributed to QCD 02: High-Energy Physics International Conference in Quantum Chromodynamics, Montpellier, France, 2-9 July 200

Noncyclic geometric changes of quantum states

Non-Abelian quantum holonomies, i.e., unitary state changes solely induced by geometric properties of a quantum system, have been much under focus in the physics community as generalizations of the Abelian Berry phase. Apart from being a general phenomenon displayed in various subfields of quantum physics, the use of holonomies has lately been suggested as a robust technique to obtain quantum gates; the building blocks of quantum computers. Non-Abelian holonomies are usually associated with cyclic changes of quantum systems, but here we consider a generalization to noncyclic evolutions. We argue that this open-path holonomy can be used to construct quantum gates. We also show that a structure of partially defined holonomies emerges from the open-path holonomy. This structure has no counterpart in the Abelian setting. We illustrate the general ideas using an example that may be accessible to tests in various physical systems.Comment: Extended version, new title, journal reference adde

Graded infinite order jet manifolds

The relevant material on differential calculus on graded infinite order jet manifolds and its cohomology is summarized. This mathematics provides the adequate formulation of Lagrangian theories of even and odd variables on smooth manifolds in terms of the Grassmann-graded variational bicomplex.Comment: 30 page

Manifestations of quantum holonomy in interferometry

Abelian and non-Abelian geometric phases, known as quantum holonomies, have attracted considerable attention in the past. Here, we show that it is possible to associate nonequivalent holonomies to discrete sequences of subspaces in a Hilbert space. We consider two such holonomies that arise naturally in interferometer settings. For sequences approximating smooth paths in the base (Grassmann) manifold, these holonomies both approach the standard holonomy. In the one-dimensional case the two types of holonomies are Abelian and coincide with Pancharatnam's geometric phase factor. The theory is illustrated with a model example of projective measurements involving angular momentum coherent states.Comment: Some changes, journal reference adde

The exclusive \bar{B} --> \pi e^+ e^- and \bar{B} --> \rho e^+ e^- decays in the two Higgs doublet model with flavor changing neutral currents

We calculate the leading logarithmic QCD corrections to the matrix element of the decay b --> d e^+ e^- in the two Higgs doublet model with tree level flavor changing currents (model III). We continue studying the differential branching ratio and the CP violating asymmetry for the exclusive decays B --> \pi e^+ e^- and B --> \rho e^+ e^- and analysing the dependencies of these quantities on the selected model III parameters, \xi^{U,D}, including the leading logarithmic QCD corrections. Further, we present the forward-backward asymmetry of dileptons for the decay B --> \rho e^+ e^- and discuss the dependencies to the model III parameters. We observe that there is a possibility to enhance the branching ratios and suppress the CP violating effects for both decays in the framework of the model III. Therefore, the measurements of these quantities will be an efficient tool to search the new physics beyond the SM.Comment: 27 pages, 14 Figure

SIC-POVMs and the Extended Clifford Group

We describe the structure of the extended Clifford Group (defined to be the group consisting of all operators, unitary and anti-unitary, which normalize the generalized Pauli group (or Weyl-Heisenberg group as it is often called)). We also obtain a number of results concerning the structure of the Clifford Group proper (i.e. the group consisting just of the unitary operators which normalize the generalized Pauli group). We then investigate the action of the extended Clifford group operators on symmetric informationally complete POVMs (or SIC-POVMs) covariant relative to the action of the generalized Pauli group. We show that each of the fiducial vectors which has been constructed so far (including all the vectors constructed numerically by Renes et al) is an eigenvector of one of a special class of order 3 Clifford unitaries. This suggests a strengthening of a conjuecture of Zauner's. We give a complete characterization of the orbits and stability groups in dimensions 2-7. Finally, we show that the problem of constructing fiducial vectors may be expected to simplify in the infinite sequence of dimensions 7, 13, 19, 21, 31,... . We illustrate this point by constructing exact expressions for fiducial vectors in dimensions 7 and 19.Comment: 27 pages. Version 2 contains some additional discussion of Zauner's original conjecture, and an alternative, possibly stronger version of the conjecture in version 1 of this paper; also a few other minor improvement

Geometric Phase in Eigenspace Evolution of Invariant and Adiabatic Action Operators

The theory of geometric phase is generalized to a cyclic evolution of the eigenspace of an invariant operator with $N$-fold degeneracy. The corresponding geometric phase is interpreted as a holonomy inherited from the universal connection of a Stiefel U(N)-bundle over a Grassmann manifold. Most significantly, for an arbitrary initial state, this geometric phase captures the inherent geometric feature of the state evolution. Moreover, the geometric phase in the evolution of the eigenspace of an adiabatic action operator is also addressed, which is elaborated by a pullback U(N)-bundle. Several intriguing physical examples are illustrated.Comment: Added Refs. and corrected typos; 4 page

Geometrical aspects of integrable systems

We review some basic theorems on integrability of Hamiltonian systems, namely the Liouville-Arnold theorem on complete integrability, the Nekhoroshev theorem on partial integrability and the Mishchenko-Fomenko theorem on noncommutative integrability, and for each of them we give a version suitable for the noncompact case. We give a possible global version of the previous local results, under certain topological hypotheses on the base space. It turns out that locally affine structures arise naturally in this setting.Comment: It will appear on International Journal of Geometric Methods in Modern Physics vol.5 n.3 (May 2008) issu

Calculation of two-loop virtual corrections to b --> s l+ l- in the standard model

We present in detail the calculation of the virtual O(alpha_s) corrections to the inclusive semi-leptonic rare decay b --> s l+ l-. We also include those O(alpha_s) bremsstrahlung contributions which cancel the infrared and mass singularities showing up in the virtual corrections. In order to avoid large resonant contributions, we restrict the invariant mass squared s of the lepton pair to the range 0.05 < s/mb^2 < 0.25. The analytic results are represented as expansions in the small parameters s/mb^2, z = mc^2/mb^2 and s/(4 mc^2). The new contributions drastically reduce the renormalization scale dependence of the decay spectrum. For the corresponding branching ratio (restricted to the above s-range) the renormalization scale uncertainty gets reduced from +/-13% to +/-6.5%.Comment: 41 pages including 9 postscript figures; in version 2 some typos and inconsistent notation correcte