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

Charmonium and e+e−e^+e^- pair photoproduction at mid-rapidity in ultra-peripheral Pb-Pb collisions at sNN\sqrt{s_{NN}} = 2.76 TeV

The ALICE Collaboration at the LHC has measured the $J/\psi$ and $\psi$' photoproduction at mid-rapidity in ultra-peripheral Pb-Pb collisions at $\sqrt{s_{NN}}$ = 2.76 TeV. The charmonium is identified via its leptonic decay for events where the hadronic activity is required to be minimal. The analysis is based on an event sample corresponding to an integrated luminosity of about 23 ${\mu}b^{-1}$, The cross section for coherent and incoherent $J/\psi$ production in the rapidity interval -0.9 < y < 0.9, are $d\sigma_{J/\psi}^{coh}/dy = 2.38^{+0.34}_{-0.24}(sta+sys)$ mb and $d\sigma_{J/\psi}^{inc}/dy = 0.98^{+0.19}_{-0.17}(sta+sys)$ mb, respectively. The results are compared to theoretical models for $J/\psi$ production and the coherent cross section is found to be in good agreement with those models which include nuclear gluon shadowing consistent with EPS09 parametrization. In addition the cross section for the process $\gamma\gamma \to e^+e^-$ has been measured and found to be in agreement with the STARLIGHT Monte Carlo predictions.publishedVersio

Production of charged pions, kaons and protons at large transverse momenta in pp and Pb-Pb collisions at sNN\sqrt{s_{NN}} = 2.76 TeV

Transverse momentum spectra of $\pi^{\pm}, K^{\pm}$ and $p(\bar{p})$ up to $p_T$ = 20 GeV/c at mid-rapidity, |y| $\le$ 0.8, in pp and Pb-Pb collisions at $\sqrt{s_{NN}}$ = 2.76 TeV have been measured using the ALICE detector at the LHC. At intermediate $p_T$ (2-8 GeV/c) an enhancement of the proton-to-proton ratio, (p + \bar{p})/(\pi^+ + \pi^-\(), with respect to pp collisions is observed and the ratio reaches 0.80 in central Pb-Pb collisions. The measurement of the nuclear modification factors for \(\pi^{\pm}, K^{\pm} and $p(\bar{p})$ indicates that within the systematic and statistical uncertainties they are the same at high $p_T$ (> 10 GeV/c), suggesting that the chemical composition of leading particles from jets in the medium is similar to that of vacuum jets.publishedVersio

Measurement of the Cross Section for Electromagnetic Dissociation with Neutron Emission in Pb-Pb Collisions at √sNN = 2.76 TeV

The first measurement of neutron emission in electromagnetic dissociation of 208Pb nuclei at the LHC is presented. The measurement is performed using the neutron Zero Degree Calorimeters of the ALICE experiment, which detect neutral particles close to beam rapidity. The measured cross sections of single and mutual electromagnetic dissociation of Pb nuclei at √sNN = 2.76 TeV with neutron emission are σ_single EMD = 187.2±0.2 (stat.) +13.8−12.0 (syst.) b and σ_mutual EMD = 6.2 ± 0.1 (stat.) ±0.4 (syst.) b respectively. The experimental results are compared to the predictions from a relativistic electromagnetic dissociation model.publishedVersio

Mid-rapidity anti-baryon to baryon ratios in pp collisions at s\sqrt{s} = 0.9, 2.76 and 7 TeV measured by ALICE

The ratios of yields of anti-baryons to baryons probes the mechanisms of baryon-number transport. Results for anti-proton/proton, anti-$\Lambda/\Lambda$, anti-$\Xi^{+}/\Xi^{-}$ and anti-$\Omega^{+}/\Omega^{-}$ in pp collisions at $\sqrt{s}$ = 0.9, 2.76 and 7 TeV, measured with the ALICE detector at the LHC, are reported. Within the experimental uncertainties and ranges covered by our measurement, these ratios are independent of rapidity, transverse momentum and multiplicity for all measured energies. The results are compared to expectations from event generators, such as PYTHIA and HIJING/B, that are used to model the particle production in pp collisions. The energy dependence of anti-proton/proton, anti-$\Lambda/\Lambda$, anti-$\Xi^{+}/\Xi^{-}$ and anti-$\Omega^{+}/\Omega^{-}$, reaching values compatible with unity for $\sqrt{s}$ = 7 TeV, complement the earlier anti-proton/proton measurement of ALICE. These dependencies can be described by exchanges with the Regge-trajectory intercept of $\alpha_J$ ≈ 0.5, which are suppressed with increasing rapidity interval $\Delta y$, Any significant contribution of an exchange not suppressed at large $\Delta y$ (reached at LHC energies) is disfavoured.publishedVersio

Centrality dependence of the pseudorapidity density distribution for charged particles in Pb-Pb collisions at sNN\sqrt{s_{NN}} = 2.76 TeV

We present the first wide-range measurement of the charged-particle pseudorapidity density distribution, for different centralities (the 0-5%, 5-10%, 10-20%, and 20-30% most central events) in Pb-Pb collisions at $\sqrt{s_{NN}}$ = 2.76 TeV at the LHC. The measurement is performed using the full coverage of the ALICE detectors, -5.0 < $\eta$ < 5.5, and employing a special analysis technique based on collisions arising from LHC ' satellite' bunches. We present the pseudorapidity density as a function of the number of participating nucleons as well as an extrapolation to the total number of produced charged particles $N_{ch}$ = 17165 +/- 772 for the 0-5% most central collisions). From the measured d\)._{ch}\).d\).eta\) distribution we derive the rapidity density distribution, d\)._{ch}\).dy, under simple assumptions. The rapidity density distribution is found to be significantly wider than the predictions of the Landau model, which reproduce data well at RHIC energies. We assess the validity of longitudinal scaling by comparing to lower energy results from RHIC. Finally the mechanisms of the underlying particle production are discussed based on a comparison with various theoretical models.publishedVersio

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