Survival, extinction and approximation of discrete-time branching random walks

We consider a general discrete-time branching random walk on a countable set X. We relate local, strong local and global survival with suitable inequalities involving the first-moment matrix M of the process. In particular we prove that, while the local behavior is characterized by M, the global behavior cannot be completely described in terms of properties involving M alone. Moreover we show that locally surviving branching random walks can be approximated by sequences of spatially confined and stochastically dominated branching random walks which eventually survive locally if the (possibly finite) state space is large enough. An analogous result can be achieved by approximating a branching random walk by a sequence of multitype contact processes and allowing a sufficiently large number of particles per site. We compare these results with the ones obtained in the continuous-time case and we give some examples and counterexamples.Comment: 32 pages, a few misprints have been correcte

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

Study of the D^0 \to pi^-pi^+pi^-pi^+ decay

Using data from the FOCUS (E831) experiment at Fermilab, we present new measurements for the Cabibbo-suppressed decay mode $D^0 \to \pi^-\pi^+\pi^-\pi^+$. We measure the branching ratio $\Gamma(D^0 \to\pi^+\pi^- \pi^+\pi^-)/\Gamma(D^0 \to K^-\pi^+\pi^-\pi^+) = 0.0914 \pm 0.0018 \pm 0.0022$. An amplitude analysis has been performed, a first for this channel, in order to determine the resonant substructure of this decay mode. The dominant component is the decay $D^0 \to a_1(1260)^+ \pi^-$, accounting for 60% of the decay rate. The second most dominant contribution comes from the decay $D^0 \to \rho(770)^0\rho(770)^0$, with a fraction of 25%. We also study the $a_1(1260)$ line shape and resonant substructure. Using the helicity formalism for the angular distribution of the decay $D^0 \to \rho(770)^0\rho(770)^0$, we measure a longitudinal polarization of $P_L = (71 \pm 4\pm 2)$%.Comment: 38 pages, 8 figures. accepted for publication in Physical Review

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

Measurement of the branching ratio of the decay D^0 -> \pi^-\mu^+\nu relative to D^0 -> K^-\mu^+\nu

We present a new measurement of the branching ratio of the Cabibbo suppressed decay D^0\to \pi^-\mu^+\nu relative to the Cabibbo favored decay D^0\to K^-\mu^+\nu and an improved measurement of the ratio |\frac{f_+^{\pi}(0)}{f_+^{K}(0)}|. Our results are 0.074 \pm 0.008 \pm 0.007 for the branching ratio and 0.85 \pm 0.04 \pm 0.04 \pm 0.01 for the form factor ratio, respectively.Comment: 13pages, 3 figure

A Non-parametric Approach to Measuring the \kpi{} Amplitudes in \dpkkpi{} Decay

Using a large sample of \dpkkpi{} decays collected by the FOCUS photoproduction experiment at Fermilab, we present the first non-parametric analysis of the \kpi{} amplitudes in \dpkkpi{} decay. The technique is similar to the technique used for our non-parametric measurements of the \krzmndk{} form factors. Although these results are in rough agreement with those of E687, we observe a wider S-wave contribution for the \ksw{} contribution than the standard, PDG \cite{pdg} Breit-Wigner parameterization. We have some weaker evidence for the existence of a new, D-wave component at low values of the $K^- \pi^+$ mass.Comment: 13 pages 3 figure

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.

Study of the decay asymmetry parameter and CP violation parameter in the Lambdac+ --> Lambda pi+ decay

Using data from the FOCUS (E831) experiment at Fermilab, we present a new measurement of the weak decay-asymmetry parameter alpha(Lambdac) in Lambdac --> Lambda pi decay. Comparing particle with antiparticle decays, we obtain the first measurement of the CP violation parameter : A = [alpha(Lambdac)+alpha(antiLambda_c)]/[alpha(Lambdac)-alpha(antiLambda_c)]. We obtain alpha(Lambdac)=-0.78+-0.16+-0.13 and A = -0.07+-0.19+-0.12 where errors are statistical and systematic.Comment: 18 pages, to be submitted to Phys. Lett. B For a list of the FOCUS collaboration, see http://www-focus.fnal.gov/authors.htm

Application of Genetic Programming to High Energy Physics Event Selection

We review genetic programming principles, their application to FOCUS data samples, and use the method to study the doubly Cabibbo suppressed decay D+ -> K+ pi+ pi- relative to its Cabibbo favored counterpart, D+ -> K- pi+ pi+. We find that this technique is able to improve upon more traditional analysis methods. To our knowledge, this is the first application of the genetic programming technique to High Energy Physics data.Comment: 39 page