A note on comonotonicity and positivity of the control components of decoupled quadratic FBSDE

In this small note we are concerned with the solution of Forward-Backward Stochastic Differential Equations (FBSDE) with drivers that grow quadratically in the control component (quadratic growth FBSDE or qgFBSDE). The main theorem is a comparison result that allows comparing componentwise the signs of the control processes of two different qgFBSDE. As a byproduct one obtains conditions that allow establishing the positivity of the control process.Comment: accepted for publicatio

Search for Neutral Heavy Leptons Produced in Z Decays

Weak isosinglet Neutral Heavy Leptons ($\nu_m$) have been searched for using data collected by the DELPHI detector corresponding to $3.3\times 10^{6}$ hadronic~Z$^{0}$ decays at LEP1. Four separate searches have been performed, for short-lived $\nu_m$ production giving monojet or acollinear jet topologies, and for long-lived $\nu_m$ giving detectable secondary vertices or calorimeter clusters. No indication of the existence of these particles has been found, leading to an upper limit for the branching ratio $BR($Z$^0\rightarrow \nu_m \overline{\nu})$ of about $1.3\times10^{-6}$ at 95\% confidence level for $\nu_m$ masses between 3.5 and 50 GeV/$c^2$. Outside this range the limit weakens rapidly with the $\nu_m$ mass. %Special emphasis has been given to the search for monojet--like topologies. One event %has passed the selection, in agreement with the expectation from the reaction: %$e^+e^- \rightarrow\ell \bar\ell \nu\bar\nu$. The results are also interpreted in terms of limits for the single production of excited neutrinos

Energy dependence of the differences between the quark and gluon jet fragmentation

Three jet events arising from decays of the Z boson, collected by the DELPHI detector, were used to measure differences in quark and gluon fragmentation. Gluon jets were anti-tagged by identifying b quark jets. Unbiased quark jets came from events with two jets plus one photon. Quark and gluon jet properties in different energy ranges were compared for the first time within the same detector. Quark and gluon jets of nearly the same energy in symmetric three jet event topologies were also compared. Using three independent methods, the average value of the ratio of the mean charged multiplicities of gluon and quark jets is $$=1.241\pm 0.015\ (stat.) \pm 0.025\ (syst.).$$ Gluon jets are broader and produce fragments with a softer energy spectrum than quark jets of equivalent energy. The string effect has been observed in fully symmetric three jet events. The measured ratio R_{\gamma} of the charged particle flow in the q\overline{q} inter-jet region of the q\bar{q}g and q\bar{q}\gamma samples agrees with the perturbative QCD expectation. The dependence of the mean charged multiplicity on the hadronic center-of-mass energy was analysed in photon plus n-jet events. The value for \alpha_s(M_Z) determined from these data using a QCD prediction with corrections at leading and next-to-leading order is \[ \alpha_s(M_Z)=0.116 \pm 0.003\ (stat.) \pm 0.009\ (syst.). \

Measurement of inclusive π0\pi^{0} production in hadronic Z0Z^{0} decays

An analysis is presented of inclusive \pi^0 production in Z^0 decays measured with the DELPHI detector. At low energies, \pi^0 decays are reconstructed by \linebreak using pairs of converted photons and combinations of converted photons and photons reconstructed in the barrel electromagnetic calorimeter (HPC). At high energies (up to x_p = 2 \cdot p_{\pi}/\sqrt{s} = 0.75) the excellent granularity of the HPC is exploited to search for two-photon substructures in single showers. The inclusive differential cross section is measured as a function of energy for {q\overline q} and {b \bar b} events. The number of \pi^0's per hadronic Z^0 event is N(\pi^0)/ Z_{had}^0 = 9.2 \pm 0.2 \mbox{(stat)} \pm 1.0 \mbox{(syst)} and for {b \bar b}~events the number of \pi^0's is {\mathrm N(\pi^0)/ b \overline b} = 10.1 \pm 0.4 \mbox{(stat)} \pm 1.1 \mbox{(syst)} . The ratio of the number of \pi^0's in b \overline b events to hadronic Z^0 events is less affected by the systematic errors and is found to be 1.09 \pm 0.05 \pm 0.01. The measured \pi^0 cross sections are compared with the predictions of different parton shower models. For hadronic events, the peak position in the \mathrm \xi_p = \ln(1/x_p) distribution is \xi_p^{\star} = 3.90^{+0.24}_{-0.14}. The average number of \pi^0's from the decay of primary \mathrm B hadrons is found to be {\mathrm N} (B \rightarrow \pi^0 \, X)/\mbox{B hadron} = 2.78 \pm 0.15 \mbox{(stat)} \pm 0.60 \mbox{(syst)}

Search for new phenomena using single photon events in the DELPHI detector at LEP

Data are presented on the reaction \epem~\into~\gamma + no other detected particle at center-of-mass energies, \sqs = 89.48 GeV, 91.26 GeV and 93.08 GeV. The cross section for this reaction is related directly to the number of light neutrino generations which couple to the \zz boson, and to several other phenomena such as excited neutrinos, the production of an invisible `X' particle, a possible magnetic moment of the tau neutrino, and neutral monojets. Based on the observed number of single photon events, the number of light neutrinos which couple to the \zz is measured to be N_\nu = 3.15 \pm 0.34. No evidence is found for anomalous production of energetic single photons, and upper limits at the 95\% confidence level are determined for excited neutrino production (BR < 4-9 \times 10^{-6}), production of an invisible `X' particle (\sigma < 0.1 pb), and the magnetic moment of the tau neutrino (< 5.2 \times 10^{-6} \mu_B). No event with the topology of a neutral monojet is found, and this corresponds to the limit \sigma < 0.044/\epsilon pb at the 95\% confidence level, where \epsilon is the unknown overall monojet detection efficiency

Search for Lepton Flavour Number violating Z0Z^0-Decays

A search for lepton flavour number violating $Z^0$ decays in the channels \begin{center} $Z^0\rightarrow \mu\tau$,\\ $Z^0\rightarrow e\tau$, \\ $Z^0\rightarrow e\mu$, \\ \end{center} using the DELPHI detector with data collected during the 1991--94 LEP runs, is described. No signal was found. Upper limits at 95\% confidence level for the respective branching fractions of $1.2\times 10^{-5}$, $2.2\times 10^{-5}$, and $0.25\times 10^{-5}$, were obtained

Transverse sphericity of primary charged particles in minimum bias proton–proton collisions at √s = 0.9, 2.76 and 7 TeV

Measurements of the sphericity of primary charged particles in minimum bias proton–proton collisions at s√=0.9, 2.76 and 7 TeV with the ALICE detector at the LHC are presented. The observable is measured in the plane perpendicular to the beam direction using primary charged tracks with p T>0.5 GeV/c in |η|<0.8. The mean sphericity as a function of the charged particle multiplicity at mid-rapidity (N ch) is reported for events with different p T scales (“soft” and “hard”) defined by the transverse momentum of the leading particle. In addition, the mean charged particle transverse momentum versus multiplicity is presented for the different event classes, and the sphericity distributions in bins of multiplicity are presented. The data are compared with calculations of standard Monte Carlo event generators. The transverse sphericity is found to grow with multiplicity at all collision energies, with a steeper rise at low N ch, whereas the event generators show an opposite tendency. The combined study of the sphericity and the mean p T with multiplicity indicates that most of the tested event generators produce events with higher multiplicity by generating more back-to-back jets resulting in decreased sphericity (and isotropy). The PYTHIA6 generator with tune PERUGIA-2011 exhibits a noticeable improvement in describing the data, compared to the other tested generators