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

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

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