18094742
Exclusive semileptonic decays of heavy mesons
AbstractExclusive semileptonic decays of heavy mesons provide interesting information on systems consisting of quarks of unequal mass. We express the formfactors of the hadronic current in terms of relativistic bound state wave functions for which we take the solutions of a relativistic harmonic oscillator potential. The wave function overlap is determined by the quark mass dependent longitudinal momentum distribution and differs from results based on non relativistic wave functions. The semileptonic widths and lepton spectra are calculated using in addition nearest pole dominance for the momentum transfer dependence of the formfactors. We compare our results with recent experimental data. The formfactor calculation also allows an estimate of special nonleptonic transitions. From the CLEO results on
$$\bar B^0 \to \pi ^ + \pi ^ -$$
 and
$$\bar B^0 \to D^{* + } + \pi ^ -$$
 we find for the corresponding Kobayashi-Maskawa matrix element ratio the limit |Vub/Vcb|≲0.3.
123217667
Polarization effects in heavy meson decays
Exclusive semi-leptonic transitions of {ital D} and {ital B} mesons are investigated within the relativistic quark model approach. The formfactor dependence of decay rates and spectra in semi-leptonic transitions is studied with emphasis on polarization effects in {ital B}{r arrow}{ital D}*{ital l}{bar {nu}} and {ital D}{r arrow}{ital K}*{ital l}{nu} decays.
121411195
Singular vectors of the Virasoro algebra
Abstract We present an explicit construction of the singular (or null) vectors in highest weight Verma modules.
119287711
A dynamical time operator in Dirac's relativistic quantum mechanics
A self-adjoint dynamical time operator is introduced in Dirac's relativistic formulation of quantum mechanics and shown to satisfy a commutation relation with the Hamiltonian analogous to that of the position and momentum operators. The ensuing time-energy uncertainty relation involves the uncertainty in the instant of time when the wave packet passes a particular spatial position and the energy uncertainty associated with the wave packet at the same time, as envisaged originally by Bohr. The instantaneous rate of change of the position expectation value with respect to the simultaneous expectation value of the dynamical time operator is shown to be the phase velocity, in agreement with de Broglie's hypothesis of a particle associated wave whose phase velocity is larger than c. Thus, these two elements of the original basis and interpretation of quantum mechanics are integrated into its formal mathematical structure. Pauli's objection is shown to be resolved or circumvented. Possible relevance to current developments in electron channeling, in interference in time, in Zitterbewegung-like effects in spintronics, graphene and superconducting systems and in cosmology is noted.
118498826
Soft collinear effective theory for heavy WIMP annihilation
A bstractIn a large class of models for Weakly Interacting Massive Particles (WIMPs), the WIMP mass M lies far above the weak scale mW . This work identifies universal Sudakov-type logarithms ∼ α log2(2 M/mW ) that spoil the naive convergence of perturbation theory for annihilation processes. An effective field theory (EFT) framework is presented, allowing the systematic resummation of these logarithms. Another impact of the large separation of scales is that a long-distance wavefunction distortion from electroweak boson exchange leads to observable modifications of the cross section. Careful accounting of momentum regions in the EFT allows the rigorous disentanglement of this so-called Sommerfeld enhancement from the short-distance hard annihilation process. The WIMP is described as a heavy-particle field, while the electroweak gauge bosons are treated as soft and collinear fields. Hard matching coefficients are computed at renormalization scale μ ∼ 2 M , then evolved down to μ ∼ mW , where electroweak symmetry breaking is incorporated and the matching onto the relevant quantum mechanical Hamiltonian is performed. The example of an SU(2)W triplet scalar dark matter candidate annihilating to line photons is used for concreteness, allowing the numerical exploration of the impact of next-to-leading order corrections and log resummation. For M ≃ 3 TeV, the resummed Sommerfeld enhanced cross section is reduced by a factor of ∼ 3 with respect to the treelevel fixed order result.
121325077
On some relations between local height probabilities and conformal invariance
Abstract We observe that the expressions of order parameters (“local height probabilities”) in the regime III of integrable A, D lattice models are closely related to the partition functions of the associated minimal critical theories in a finite box with appropriate boundary conditions. This is more precisely stated in terms of corner transfer matrix properties. Our work thus points out a relation between integrable systems off critically and in the thermodynamic limit with models at critically but in a finite box, once the nome which parametrizes the elliptic Boltzmann weights in the former case is identified with the modular parameter in the latter. As an application we are able to obtain some new properties of the LHP for D N or E 6 , E 7 , E 8 models using conformal invariance techniques only.
121423772
The branching rules of conformal embeddings
After recalling the main properties of a conformal embedding of Lie algebrasg⊃p, which is defined by the equality of the Sugawara central charges on both sides, we launch a systematic study of their branching rules. The bulk of the paper is devoted to the proof of a general formula in the casesu(mn)1⊃su(m)n⊕su(n)m. At the end we give some applications to the construction of modular invariant partition functions.