A Lagrangian scheme for the solution of nonlinear diffusion equations using moving simplex meshes

A Lagrangian numerical scheme for solving nonlinear degenerate Fokker{Planck equations in space dimensions d>2 is presented. It applies to a large class of nonlinear diffusion equations, whose dynamics are driven by internal energies and given external potentials, e.g. the porous medium equation and the fast diffusion equation. The key ingredient in our approach is the gradient ow structure of the dynamics. For discretization of the Lagrangian map, we use a finite subspace of linear maps in space and a variational form of the implicit Euler method in time. Thanks to that time discretisation, the fully discrete solution inherits energy estimates from the original gradient ow, and these lead to weak compactness of the trajectories in the continuous limit. Consistency is analyzed in the planar situation, d = 2. A variety of numerical experiments for the porous medium equation indicates that the scheme is well-adapted to track the growth of the solution's support

Search for CP Violation in the decays D+ -> K_S pi+ and D+ -> K_S K+

A high statistics sample of photo-produced charm from the FOCUS(E831) experiment at Fermilab has been used to search for direct CP violation in the decays D+->K_S pi+ and D+ -> K_S K+. We have measured the following asymmetry parameters relative to D+->K-pi+pi+: A_CP(K_S pi+) = (-1.6 +/- 1.5 +/- 0.9)%, A_CP(K_S K+) = (+6.9 +/- 6.0 +/- 1.5)% and A_CP(K_S K+) = (+7.1 +/- 6.1 +/- 1.2)% relative to D+->K_S pi+. The first errors quoted are statistical and the second are systematic. We also measure the relative branching ratios: \Gamma(D+->\bar{K0}pi+)/\Gamma(D+->K-pi+pi+) = (30.60 +/- 0.46 +/- 0.32)%, \Gamma(D+->\bar{K0}K+)/\Gamma(D+->K-pi+pi+) = (6.04 +/- 0.35 +/- 0.30)% and \Gamma(D+->\bar{K0}K+)/\Gamma(D+->\bar{K0}pi+) = (19.96 +/- 1.19 +/- 0.96)%.Comment: 4 pages, 3 figure

A Measurement of the Ds+ Lifetime

A high statistics measurement of the Ds+ lifetime from the Fermilab fixed-target FOCUS photoproduction experiment is presented. We describe the analysis of the two decay modes, Ds+ -> phi(1020)pi+ and Ds+ -> \bar{K}*(892)0K+, used for the measurement. The measured lifetime is 507.4 +/- 5.5 (stat.) +/- 5.1 (syst.) fs using 8961 +/- 105 Ds+ -> phi(1020)pi+ and 4680 +/- 90 Ds+ -> \bar{K}*(892)0K+ decays. This is a significant improvement over the present world average.Comment: 5 pages, 3 figures, 2 tables, submitted to PR

A measurement of branching ratios of D+D^+ and Ds+D^+_s hadronic decays to four-body final states containing a KSK_S

We have studied hadronic four-body decays of $D^+$ and $D^+_s$ mesons with a $K_S$ in the final state using data recorded during the 1996-1997 fixed-target run at Fermilab high energy photoproduction experiment FOCUS. We report a new branching ratio measurement of $\Gamma(D^+\to K_S K^-\pi^+\pi^+)/\Gamma(D^+\to K_S \pi^+\pi^+\pi^-)=0.0768\pm0.0041\pm0.0032$. We make the first observation of three new decay modes with branching ratios $\Gamma(D^+\to K_S K^+\pi^+\pi^-)/\Gamma(D^+\to K_S \pi^+\pi^+\pi^-)=0.0562\pm0.0039\pm0.0040$, \Gamma(D^+\to\K_S K^+ K^-\pi^+)/\Gamma(D^+\to K_S \pi^+\pi^+\pi^-)=0.0077\pm0.0015\pm0.0009, and $\Gamma(D^+_s\to K_S K^+\pi^+\pi^-)/\Gamma(D^+_s\to K_S K^-\pi^+\pi^+)=0.586\pm0.052\pm0.043$, where in each case the first error is statistical and the second error is systematic.Comment: 4 pages, 1 table, 2 figures, submitted to Physical Review Letter

Measurements of Ξc+\Xi_c^{+} Branching Ratios

Using data collected by the fixed target Fermilab experiment FOCUS, we measure the branching ratios of the Cabibbo favored decays $\Xi_c^+ \to \Sigma^+K^-\pi^+$, $\Xi_c^+ \to \Sigma^+ \bar{K}^{*}(892)^0$, and $\Xi_c^+ \to \Lambda^0K^-\pi^+\pi^+$ relative to $\Xi_c^+ \to \Xi^-\pi^+\pi^+$ to be $0.91\pm0.11\pm0.04$, $0.78\pm0.16\pm0.06$, and $0.28\pm0.06\pm0.06$, respectively. We report the first observation of the Cabibbo suppressed decay $\Xi_c^+ \to \Sigma^+K^+K^-$ and we measure the branching ratio relative to $\Xi_c^+ \to \Sigma^+K^-\pi^+$ to be $0.16\pm0.06\pm0.01$. We also set 90% confidence level upper limits for $\Xi_c^+ \to \Sigma^+ \phi$ and $\Xi_c^+ \to \Xi^*(1690)^0(\Sigma^+ K^-) K^+$ relative to $\Xi_c^+ \to \Sigma^+K^-\pi^+$ to be 0.12 and 0.05, respectively. We find an indication of the decays $\Xi_c^+ \to \Omega^-K^{+}\pi^+$ and $\Xi_c^+ \to \Sigma^{*}(1385)^+ \bar{K}^0$ and set 90% confidence level upper limits for the branching ratios with respect to $\Xi_c^+ \to \Xi^-\pi^+\pi^+$ to be 0.12 and 1.72, respectively. Finally, we determine the 90% C.L. upper limit for the resonant contribution $\Xi_c^+ \to \Xi^{*}(1530)^0 \pi^+$ relative to $\Xi_c^+ \to \Xi^-\pi^+\pi^+$ to be 0.10.Comment: 14 pages, 8 figure

Dalitz plot analysis of D_s+ and D+ decay to pi+pi-pi+ using the K-matrix formalism

FOCUS results from Dalitz plot analysis of D_s+ and D+ to pi+pi-pi+ are presented. The K-matrix formalism is applied to charm decays for the first time to fully exploit the already existing knowledge coming from the light-meson spectroscopy experiments. In particular all the measured dynamics of the S-wave pipi scattering, characterized by broad/overlapping resonances and large non-resonant background, can be properly included. This paper studies the extent to which the K-matrix approach is able to reproduce the observed Dalitz plot and thus help us to understand the underlying dynamics. The results are discussed, along with their possible implications on the controversial nature of the sigma meson.Comment: To be submitted to Phys.Lett.B A misprint corrected in formula

A Non-parametric Approach to the D+ to K*0bar mu+ nu Form Factors

Using a large sample of D+ -> K- pi+ mu+ nu decays collected by the FOCUS photoproduction experiment at Fermilab, we present the first measurements of the helicity basis form factors free from the assumption of spectroscopic pole dominance. We also present the first information on the form factor that controls the s-wave interference discussed in a previous paper by the FOCUS collaboration. We find reasonable agreement with the usual assumption of spectroscopic pole dominance and measured form factor ratios.Comment: 14 pages, 5 figures, and 2 tables. We updated the previous version by changing some words, removing one plot, and adding two tables. These changes are mostly stylisti

Search for Λc+→pK+π−\Lambda_c^+ \to p K^+ \pi^- and Ds+→K+K+π−D_s^+ \to K^+ K^+ \pi^- Using Genetic Programming Event Selection

We apply a genetic programming technique to search for the double Cabibbo suppressed decays $\Lambda_c^+ \to p K^+ \pi^-$ and $D_s^+ \to K^+ K^+ \pi^-$. We normalize these decays to their Cabibbo favored partners and find $\text{BR}($\Lambda_c^+ \to p K^+ \pi^-$)/\text{BR}($\Lambda_c^+ \to p K^- \pi^+$) = (0.05 \pm 0.26 \pm 0.02)$ and $\text{BR}($D_s^+ \to K^+ K^+ \pi^-$)/\text{BR}($D_s^+ \to K^+ K^- \pi^+$) = (0.52\pm 0.17\pm 0.11)$ where the first errors are statistical and the second are systematic. Expressed as 90% confidence levels (CL), we find $< 0.46$ and $< 0.78$ respectively. This is the first successful use of genetic programming in a high energy physics data analysis.Comment: 10 page

Measurements of Six-Body Hadronic Decays of the D^0 Charmed Meson

Using data collected by the FOCUS experiment at Fermilab, we report the discovery of the decay modes D^0 --> K- pi+ pi+ pi+ pi- pi- and D^0 --> pi+ pi+ pi+ pi- pi- pi-. With a sample of 48 +/- 10 reconstructed D^0 --> K- pi+ pi+ pi+ pi- pi- decays and 149 +/- 17 reconstructed D^0 --> pi+ pi+ pi+ pi- pi- pi- decays, we measure the following relative branching ratios: ${\Gamma (D^0 \to K^- \pi^+ \pi^+ \pi^+ \pi^- \pi^-) / \Gamma (D^0 \to K^- \pi^+ \pi^+ \pi^-)} = (2.70 \pm 0.58 \pm 0.38) \times 10^{-3}$ ${\Gamma (D^0 \to \pi^+ \pi^+ \pi^+ \pi^- \pi^- \pi^-) / \Gamma (D^0 \to K^- \pi^+ \pi^+ \pi^-)} = (5.23 \pm 0.59 \pm 1.35) \times 10^{-3}$ ${\Gamma (D^0 \to \pi^+ \pi^+ \pi^+ \pi^- \pi^- \pi^-) / \Gamma (D^0 \to K^- \pi^+ \pi^+ \pi^+ \pi^- \pi^-)} = 1.93 \pm 0.47 \pm 0.48$ The first errors are statistical and the second are systematic. The branching fraction of the Cabibbo suppressed six-body decay mode is measured to be a factor of two higher than the branching fraction of the Cabibbo favored six-body decay mode.Comment: To be submitted to Phys. Lett.