Scattering approach to fidelity decay in closed systems and parametric level correlations

This paper is based on recent work which provided an exact analytical description of scattering fidelity experiments with a microwave cavity under the variation of an antenna coupling [K\"ober et al., Phys. Rev. E 82, 036207 (2010)]. It is shown that this description can also be used to predict the decay of the fidelity amplitude for arbitrary Hermitian perturbations of a closed system. Two applications are presented: First, the known result for global perturbations is re-derived, and second, the exact analytical expression for the perturbation due to a moving S-wave scatterer is worked out. The latter is compared to measured data from microwave experiments, which have been reported some time ago. Finally, we generalize an important relation between fidelity decay and parametric level correlations to arbitrary perturbations.Comment: 20 pages, 2 figures, research article, (v2: stylistic changes, ref. added

CP violation in semileptonic tau lepton decays

The leading order contribution to the direct CP asymmetry in tau^{+/-} -> K^{+/-} pi^0 nu_{tau} decay rates is evaluated within the Standard Model. The weak phase required for CP violation is introduced through an interesting mechanism involving second order weak interactions, which is also responsible for tiny violations of the Delta S= Delta Q rule in K_{l3} decays. The calculated CP asymmetry turns out to be of order 10^{-12}, leaving a large window for studying effects of non-standard sources of CP violation in this observable.Comment: 5 pages, 3 figures, version published in Phys.Rev.

Generalizing the relativistic quantization condition to include all three-pion isospin channels

We present a generalization of the relativistic, finite-volume, three-particle quantization condition for non-identical pions in isosymmetric QCD. The resulting formalism allows one to use discrete finite-volume energies, determined using lattice QCD, to constrain scattering amplitudes for all possible values of two- and three-pion isospin. As for the case of identical pions considered previously, the result splits into two steps: The first defines a non-perturbative function with roots equal to the allowed energies, $E_n(L)$, in a given cubic volume with side-length $L$. This function depends on an intermediate three-body quantity, denoted $\mathcal{K}_{\mathrm{df},3}$, which can thus be constrained from lattice QCD input. The second step is a set of integral equations relating $\mathcal{K}_{\mathrm{df},3}$ to the physical scattering amplitude, $\mathcal M_3$. Both of the key relations, $E_n(L) \leftrightarrow \mathcal{K}_{\mathrm{df},3}$ and $\mathcal{K}_{\mathrm{df},3}\leftrightarrow \mathcal M_3$, are shown to be block-diagonal in the basis of definite three-pion isospin, $I_{\pi \pi \pi}$, so that one in fact recovers four independent relations, corresponding to $I_{\pi \pi \pi}=0,1,2,3$. We also provide the generalized threshold expansion of $\mathcal{K}_{\mathrm{df},3}$ for all channels, as well as parameterizations for all three-pion resonances present for $I_{\pi\pi\pi}=0$ and $I_{\pi\pi\pi}=1$. As an example of the utility of the generalized formalism, we present a toy implementation of the quantization condition for $I_{\pi\pi\pi}=0$, focusing on the quantum numbers of the $\omega$ and $h_1$ resonances.Comment: 46 pages, 4 figures. Updated to match erratum published in JHEP. Main conclusions and results unchange

Understanding co-operative R&D activity: evidence from four European countries

This paper investigates co-operative research activity by firms using data from the 3rd Community Innovation Survey for four countries, France, Germany, Spain and the UK. We build on the Cassiman and Veugelers (CV) (2002) study of Belgian manufacturing firms, by incorporating information on the service sector, and considering the role of public support in affecting firms’ decisions to co-operate. Our results support those in CV, in that we find a positive relationship between the likelihood of undertaking co-operative R&D and both incoming knowledge spillovers and the extent to which firms find strategic methods important in appropriating the returns to innovative activity. We find that public support is positively related to the probability of undertaking co-operative agreements particularly with regard to the likelihood of co-operation with the research base. We find some evidence, in particular for Spain, that firms carry out co-operative R&D to overcome excessive perceived risks and financial constraints