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

Centrality dependence of the charged-particle multiplicity density at mid-rapidity in Pb-Pb collisions at sNN\sqrt{s_{NN}} = 2.76 TeV

The centrality dependence of the charged-particle multiplicity density at mid-rapidity in Pb-Pb collisions at $\sqrt{s_{NN}}$ = 2.76 TeV is presented. The charged-particle density normalized per participating nucleon pair increases by about a factor 2 from peripheral (70-80%) to central (0-5%) collisions. The centrality dependence is found to be similar to that observed at lower collision energies. The data are compared with models based on different mechanisms for particle production in nuclear collisions.The centrality dependence of the charged-particle multiplicity density at mid-rapidity in Pb-Pb collisions at $\sqrt{s_{\rm NN}}$ = 2.76 TeV is presented. The charged-particle density normalized per participating nucleon pair increases by about a factor 2 from peripheral (70-80%) to central (0-5%) collisions. The centrality dependence is found to be similar to that observed at lower collision energies. The data are compared with models based on different mechanisms for particle production in nuclear collisions

Multiplicity dependence of the average transverse momentum in pp, p-Pb, and Pb-Pb collisions at the LHC

The average transverse momentum versus the charged-particle multiplicity $N_{ch}$ was measured in p-Pb collisions at a collision energy per nucleon-nucleon pair $\sqrt{s_{NN}}$ = 5.02 TeV and in pp collisions at collision energies of $\sqrt{s}$ = 0.9, 2.76, and 7 Tev in the kinematic range 0.15 with $N_{ch}$ is observed, which is much stronger than that measured in Pb-Pb collisions. For pp collisions, this could be attributed, within a model of hadronizing strings, to multiple-parton interactions and to a final-state color reconnection mechanism. The data in p-Pb and Pb-Pb collisions cannot be described by an incoherent superposition of nucleon-nucleon collisions and pose a challenge to most of the event generators

Charge correlations using the balance function in Pb?Pb collisions at ?sNN = 2.76 TeV

In high-energy heavy-ion collisions, the correlations between the emitted particles can be used as a probe to gain insight into the charge creation mechanisms. In this article, we report the first results of such studies using the electric charge balance function in the relative pseudorapidity \Delta\eta and azimuthal angle \Delta\phi in Pb-Pb collisions at sqrt{s_{NN}} = 2.76 TeV with the ALICE detector at the Large Hadron Collider. The width of the balance function decreases with growing centrality (i.e. for more central collisions) in both projections. This centrality dependence is not reproduced by HIJING, while AMPT, a model which incorporates strings and parton rescattering, exhibits qualitative agreement with the measured correlations in \Delta\phi but fails to describe the correlations in \Delta\eta. A thermal blast wave model incorporating local charge conservation and tuned to describe the p_T spectra and v_2 measurements reported by ALICE, is used to fit the centrality dependence of the width of the balance function and to extract the average separation of balancing charges at freeze-out. The comparison of our results with measurements at lower energies reveals an ordering with sqrt{s_{NN}}: the balance functions become narrower with increasing energy for all centralities. This is consistent with the effect of larger radial flow at the LHC energies but also with the late stage creation scenario of balancing charges. However, the relative decrease of the balance function widths in \Delta\eta and \Delta\phi with centrality from the highest SPS to the LHC energy exhibits only small differences. This observation cannot be interpreted solely within the framework where the majority of the charge is produced at a later stage in the evolution of the heavy-ion collision