348 research outputs found
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
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
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
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
Optimal space of linear classical observables for Maxwell k-forms via spacelike and timelike compact de Rham cohomologies
Being motivated by open questions in gauge field theories, we consider non-standard de Rham cohomology groups for timelike compact and spacelike compact support systems. These cohomology groups are shown to be isomorphic respectively to the usual de Rham cohomology of a spacelike Cauchy surface and its counterpart with compact support. Furthermore, an analog of the usual Poincar\ue9 duality for de Rham cohomology is shown to hold for the case with non-standard supports as well. We apply these results to find optimal spaces of linear observables for analogs of arbitrary degree k of both the vector potential and the Faraday tensor. The term optimal has to be intended in the following sense: The spaces of linear observables we consider distinguish between different configurations; in addition to that, there are no redundant observables. This last point in particular heavily relies on the analog of Poincar\ue9 duality for the new cohomology groups
The Radiative Decays B -> V gamma at Next-to-Leading Order in QCD
We provide a model-independent framework for the analysis of the radiative
B-meson decays B -> K* gamma and B -> rho gamma. In particular, we give a
systematic discussion of the various contributions to these exclusive processes
based on the heavy-quark limit of QCD. We propose a novel factorization formula
for the consistent treatment of B -> V gamma matrix elements involving charm
(or up-quark) loops, which contribute at leading power in Lambda_QCD/m_B to the
decay amplitude. Annihilation topologies are shown to be power suppressed. In
some cases they are nevertheless calculable. The approach is similar to the
framework of QCD factorization that has recently been formulated for two-body
non-leptonic B decays. These results allow us, for the first time, to compute
exclusive b -> s(d) gamma decays systematically beyond the leading logarithmic
approximation. We present results for these decays complete to next-to-leading
order in QCD and to leading order in the heavy-quark limit. Phenomenological
implications for various observables of interest are discussed, including
direct CP violation, and isospin and U-spin breaking effects.Comment: discussion on power corrections and references added, otherwise
unchanged, version published in NP
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
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 -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
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
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