A Contraction Theory Approach to Stochastic Incremental Stability

We investigate the incremental stability properties of It\^o stochastic dynamical systems. Specifically, we derive a stochastic version of nonlinear contraction theory that provides a bound on the mean square distance between any two trajectories of a stochastically contracting system. This bound can be expressed as a function of the noise intensity and the contraction rate of the noise-free system. We illustrate these results in the contexts of stochastic nonlinear observers design and stochastic synchronization.Comment: 23 pages, 2 figure

CP asymmetry and branching ratio of B -> pi pi

We investigate the branching ratios and CP asymmetries of the B -> pi pi processes measured in B factory experiments. Fits to the experimental data of this process indicate a large ratio of color-suppressed (C) to color-allowed (T) tree contributions. We investigate whether the large C/T can be explained within the QCD based model computation with i) a large effect from the end-point singularity or with ii) large final-state-interaction phase between two different isospin amplitudes. We show that the current experimental data do not exclude either possibility but we may be able to distinguish these two effects in future measurements of direct CP asymmetry of B -> pi^0 pi^0.Comment: 8 pages, 10 figure

Effective Lagrangian for Two-photon and Two-gluon Decays of PP-wave Heavy Quarkonium χc0,2\chi_{c0,2} and χb0,2\chi_{b0,2} states

In the traditional non-relativistic bound state calculation, the two-photon decay amplitudes of the $P$-wave $\chi_{c0,2}$ and $\chi_{b0,2}$ states depend on the derivative of the wave function at the origin which can only be obtained from potential models. However by neglecting the relative quark momenta, the decay amplitude can be written as the matrix element of a local heavy quark field operator which could be obtained from other processes or computed with QCD sum rules technique or lattice simulation. Following the same line as in recent work for the two-photon decays of the $S$-wave $\eta_{c}$ and $\eta_{b}$ quarkonia, we show that the effective Lagrangian for the two-photon decays of the $P$-wave $\chi_{c0,2}$ and $\chi_{b0,2}$ is given by the heavy quark energy-momentum tensor local operator or its trace, the $\bar{Q}Q$ scalar density and that the expression for $\chi_{c0}$ two-photon and two-gluon decay rate is given by the $f_{\chi_{c0}}$ decay constant and is similar to that of $\eta_{c}$ which is given by $f_{\eta_{c}}$. From the existing QCD sum rules value for $f_{\chi_{c0}}$, we get $5\rm keV$ for the $\chi_{c0}$ two-photon width, somewhat larger than measurement, but possibly with large uncertainties.Comment: v3, LaTeX, 5 pages, 1 figure, minor typos corrected, to appear in Physical Review

Chiral Anomaly Effects and the BaBar Measurements of the γγ∗→π0\gamma\gamma^{*}\to \pi^{0} Transition Form Factor

The recent BaBar measurements of the $\gamma\gamma^{*}\to \pi^{0}$ transition form factor show spectacular deviation from perturbative QCD prediction for large space-like $Q^{2}$ up to $34\,\rm GeV^{2}$. When plotted against $Q^{2}$, $Q^{2}F(Q^{2})$ shows steady increase with $Q^{2}$ in contrast with the flat $Q^{2}$ behavior predicted by perturbative QCD, and at $34\,\rm GeV^{2}$ is more than 50% larger than the QCD prediction. Stimulated by the BaBar measurements, we revisit our previous paper on the cancellation of anomaly effects in high energy processes $Z^{0}\to \pi^{0}\gamma$, $e^{+}e^{-}\to \pi^{0}\gamma$ and apply our results to the $\gamma^{*}\gamma\to \pi^{0}$ transition form factor measured in the $e^{+}e^{-}\to e^{+}e^{-}\pi^{0}$ process with one highly virtual photon. We find that, the transition form factor $F(Q^{2})$ behaves as $(\frac{m^{2}}{Q^{2}})\times (\ln(Q^{2}/m^{2}))^{2}$ and produces a striking agreement with the BaBar data for $Q^{2}F(Q^{2})$ with $m=132\,\rm MeV$ which also reproduces very well the CLEO data at lower $Q^{2}$.Comment: v4, LaTeX, 8 pages, one figure, minor changes(references), to appear in Int. J. Mod. Phys.

Two-photon decay of pseudoscalar quarkonia

We report on our recent evaluation of the two-photon width of the pseudoscalar quarkonia, eta_c(nS) and eta_b(nS) in an approach based on Heavy-Quark Spin Symmetry (HQSS). To what concerns the 1S state eta_c, our parameter-free computation agrees with experiments, as well as most of other theoretical works. On the other hand, our computation for the 2S-state looks 2S like a confirmation that there may exist an anomaly related to the decay of eta_c(2S), especially in the light of the new preliminary result of the Belle collaboration. We also point out that the essentially model-independent ratio of eta_b two-photon width to the Upsilon leptonic width and the eta_b two-photon width could be used to extract the strong coupling constant alpha_s.Comment: Presented by T.N. Pham at the Joint Meeting Heidelberg-Liege-Paris-Wroclaw (HLPW08), Spa, Belgium, 6-8 March 2008, 9 pages, 2 figures, LaTeX, uses aip-6s.clo, aipproc.cls and aipxfm.sty (included

Interacting Antiferromagnetic Droplets in Quantum Critical CeCoIn_5

The heavy fermion superconductor CeCoIn_5 can be tuned between superconducting and antiferromagnetic ground states by hole doping with Cd. Nuclear magnetic resonance (NMR) data indicate that these two orders coexist microscopically with an ordered moment ~0.7 \mu_B. As the ground state evolves, there is no change in the low frequency spin dynamics in the disordered state. These results suggest that the magnetism emerges locally in the vicinity of the Cd dopants.Comment: 4 pages, 4 figure

Two-photon width of eta_c and eta'_c from Heavy-Quark Spin Symmetry

We evaluate the two-photon width of the pseudoscalar charmonia, Gamma(eta_c -> gamma gamma) and Gamma(eta'_c -> gamma gamma), within a Heavy-Quark Spin-Symmetry setting and show that whereas the former agrees with experiment, the latter is more than twice larger than the recent measurement by CLEO. When binding-energy effects are included in the eta'_c case, the discrepancy is worse, pointing out at a possible anomaly in the eta'_c decay.Comment: 4 pages, 2 figures, Revtex4; v2: discussions enlarged and some references added. The conclusions are unchange

Do nonparametric measures of extreme equity risk change the parametric ordinal ranking? Evidence from Asia

There has been much discussion in the literature about how central measures of equity risk such as standard deviation fail to account for extreme tail risk of equities. Similarly, parametric measures of value at risk (VaR) may also fail to account for extreme risk as they assume a normal distribution which is often not the case in practice. Nonparametric measures of extreme risk such as nonparametric VaR and conditional value at risk (CVaR) have often been found to overcome this problem by measuring actual tail risk without applying any predetermined assumptions. However, this article argues that it is not just the actual risk of equites that is important to investor choices, but also the relative (ordinal) risk of equities compared to each other. Using an applied setting of industry portfolios in a variety of Asian countries (benchmarked to the United States), over crisis and non-crisis periods, this article finds that nonparametric measures of VaR and CVaR may provide only limited new information to investors about relative risk in the portfolios examined as there is a high degree of similarity found in relative industry risk when using nonparametric metrics as compared to central or parametric measures such as standard deviation and parametric VaR

Where neuroscience and dynamic system theory meet autonomous robotics: A contracting basal ganglia model for action selection

International audienceAction selection, the problem of choosing what to do next, is central to any autonomous agent architecture. We use here a multidisciplinary approach at the convergence of neuro-science, dynamical systems theory and autonomous robotics, in order to propose an efficient action selection mechanism based on a new model of the basal ganglia. We first describe new developments of contraction theory regarding locally projected dynamical systems. We exploit these results to design a stable computational model of the cortico-baso-thalamo-cortical loops. Based on recent anatomical data, we include usually neglected neu-ral projections, which participate in performing accurate selection. Finally, the efficiency of this model as an autonomous robot action selection mechanism is assessed in a standard survival task. The model exhibits valuable dithering avoidance and energy-saving properties , when compared with a simple if-then-else decision rule