Measurement of the charged pion mass using X-ray spectroscopy of exotic atoms

The $5g-4f$ transitions in pionic nitrogen and muonic oxygen were measured simultaneously by using a gaseous nitrogen-oxygen mixture at 1.4\,bar. Due to the precise knowledge of the muon mass the muonic line provides the energy calibration for the pionic transition. A value of (139.57077\,$\pm$\,0.00018)\,MeV/c$^{2}$ ($\pm$\,1.3ppm) is derived for the mass of the negatively charged pion, which is 4.2ppm larger than the present world average

Line shape of the muH(3p - 1s) hyperfine transitions

The (3p - 1s) X-ray transition to the muonic hydrogen ground state was measured with a high resolution crystal spectrometer. A Doppler effect broadening of the X-ray line was established which could be attributed to different Coulomb de-excitation steps preceding the measured transition. The assumption of a statistical population of the hyperfine levels of the muonic hydrogen ground state was directly confirmed by the experiment and measured values for the hyperfine splitting can be reported. The results allow a decisive test of advanced cascade model calculations and establish a method to extract fundamental strong-interaction parameters from pionic hydrogen experiments.Comment: Submitted to Physical Review Letter

Pionic Deuterium

The strong interaction shift and broadening in pionic deuterium have been remeasured with high statistics by means of the (3p-1s) X-ray transition using the cyclotron trap and a high-resolution crystal spectrometer. Preliminary results are (-2325+/-31) meV (repulsive) for the shift and (1171+23/-49} meV for the width, which yields precise values for the pion-deuteron scattering length and the threshold parameter for pion production.Comment: Conf. Proc. Few Body 19 (FB19), August 31 - September 5, 2009, Bonn, Germany 9 pages, 13 figure

Precision determination of the dpi -> NN transition strength at threshold

An unusual but effective way to determine at threshold the dpi -> NN transition strength is to exploit the hadronic ground-state broadening in pionic deuterium, accessible by x-ray spectroscopy. The broadening is dominated by the true absorption channel dpi- -> nn, which is related to s-wave pion production pp -> dpi+ by charge symmetry and detailed balance. Using the exotic atom circumvents the problem of Coulomb corrections to the cross section as necessary in the production experiments. Our dedicated measurement finds (1171+23/-49) meV for the broadening yielding (252+5/-11) \mub.Comment: 4 pages, 2 figures, 1 tabl

Relativistic calculations of pionic and kaonic atoms hyperfine structure

We present the relativistic calculation of the hyperfine structure in pionic and kaonic atoms. A perturbation method has been applied to the Klein-Gordon equation to take into account the relativistic corrections. The perturbation operator has been obtained \textit{via} a multipole expansion of the nuclear electromagnetic potential. The hyperfine structure of pionic and kaonic atoms provide an additional term in the quantum electrodynamics calculation of the energy transition of these systems. Such a correction is required for a recent measurement of the pion mass

Hadronic shift in pionic hydrogen

The hadronic shift in pionic hydrogen has been redetermined to be $\epsilon_{1s}=7.086\,\pm\,0.007(stat)\,\pm\,0.006(sys)$\,eV by X-ray spectroscopy of ground state transitions applying various energy calibration schemes. The experiment was performed at the high-intensity low-energy pion beam of the Paul Scherrer Institut by using the cyclotron trap and an ultimate-resolution Bragg spectrometer with bent crystals.Comment: 10 pages, 6 figure

A new perspective on matter coupling in 2d quantum gravity

We provide compelling evidence that a previously introduced model of non-perturbative 2d Lorentzian quantum gravity exhibits (two-dimensional) flat-space behaviour when coupled to Ising spins. The evidence comes from both a high-temperature expansion and from Monte Carlo simulations of the combined gravity-matter system. This weak-coupling behaviour lends further support to the conclusion that the Lorentzian model is a genuine alternative to Liouville quantum gravity in two dimensions, with a different, and much `smoother' critical behaviour.Comment: 24 pages, 7 figures (postscript

Line shape analysis of the Kβ\beta transition in muonic hydrogen

The K$\beta$ transition in muonic hydrogen was measured with a high-resolution crystal spectrometer. The spectrum is shown to be sensitive to the ground-state hyperfine splitting, the corresponding triplet-to-singlet ratio, and the kinetic energy distribution in the $3p$ state. The hyperfine splitting and triplet-to-singlet ratio are found to be consistent with the values expected from theoretical and experimental investigations and, therefore, were fixed accordingly in order to reduce the uncertainties in the further reconstruction of the kinetic energy distribution. The presence of high-energetic components was established and quantified in both a phenomenological, i.e. cascade-model-free fit, and in a direct deconvolution of the Doppler broadening based on the Bayesian approach.Comment: 22 pages, 21 figure

Portfolio selection problems in practice: a comparison between linear and quadratic optimization models

Several portfolio selection models take into account practical limitations on the number of assets to include and on their weights in the portfolio. We present here a study of the Limited Asset Markowitz (LAM), of the Limited Asset Mean Absolute Deviation (LAMAD) and of the Limited Asset Conditional Value-at-Risk (LACVaR) models, where the assets are limited with the introduction of quantity and cardinality constraints. We propose a completely new approach for solving the LAM model, based on reformulation as a Standard Quadratic Program and on some recent theoretical results. With this approach we obtain optimal solutions both for some well-known financial data sets used by several other authors, and for some unsolved large size portfolio problems. We also test our method on five new data sets involving real-world capital market indices from major stock markets. Our computational experience shows that, rather unexpectedly, it is easier to solve the quadratic LAM model with our algorithm, than to solve the linear LACVaR and LAMAD models with CPLEX, one of the best commercial codes for mixed integer linear programming (MILP) problems. Finally, on the new data sets we have also compared, using out-of-sample analysis, the performance of the portfolios obtained by the Limited Asset models with the performance provided by the unconstrained models and with that of the official capital market indices

Numerical simulations of a non-commutative theory: the scalar model on the fuzzy sphere

We address a detailed non-perturbative numerical study of the scalar theory on the fuzzy sphere. We use a novel algorithm which strongly reduces the correlation problems in the matrix update process, and allows the investigation of different regimes of the model in a precise and reliable way. We study the modes associated to different momenta and the role they play in the ``striped phase'', pointing out a consistent interpretation which is corroborated by our data, and which sheds further light on the results obtained in some previous works. Next, we test a quantitative, non-trivial theoretical prediction for this model, which has been formulated in the literature: The existence of an eigenvalue sector characterised by a precise probability density, and the emergence of the phase transition associated with the opening of a gap around the origin in the eigenvalue distribution. The theoretical predictions are confirmed by our numerical results. Finally, we propose a possible method to detect numerically the non-commutative anomaly predicted in a one-loop perturbative analysis of the model, which is expected to induce a distortion of the dispersion relation on the fuzzy sphere.Comment: 1+36 pages, 18 figures; v2: 1+55 pages, 38 figures: added the study of the eigenvalue distribution, added figures, tables and references, typos corrected; v3: 1+20 pages, 10 eps figures, new results, plots and references added, technical details about the tests at small matrix size skipped, version published in JHE