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

Underlying Event measurements in pp collisions at root s=0.9 and 7 TeV with the ALICE experiment at the LHC

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)We present measurements of Underlying Event observables in pp collisions at root s = 0 : 9 and 7 TeV. The analysis is performed as a function of the highest charged-particle transverse momentum p(T),L-T in the event. Different regions are defined with respect to the azimuthal direction of the leading (highest transverse momentum) track: Toward, Transverse and Away. The Toward and Away regions collect the fragmentation products of the hardest partonic interaction. The Transverse region is expected to be most sensitive to the Underlying Event activity. The study is performed with charged particles above three different p(T) thresholds: 0.15, 0.5 and 1.0 GeV/c. In the Transverse region we observe an increase in the multiplicity of a factor 2-3 between the lower and higher collision energies, depending on the track p(T) threshold considered. Data are compared to PYTHIA 6.4, PYTHIA 8.1 and PHOJET. On average, all models considered underestimate the multiplicity and summed p(T) in the Transverse region by about 10-30%.7Calouste Gulbenkian Foundation from LisbonSwiss Fonds Kidagan, ArmeniaConselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Financiadora de Estudos e Projetos (FINEP)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)National Natural Science Foundation of China (NSFC)Chinese Ministry of Education (CMOE)Ministry of Science and Technology of China (MSTC)Ministry of Education and Youth of the Czech RepublicDanish Natural Science Research CouncilCarlsberg FoundationDanish National Research FoundationEuropean Research Council under European CommunityHelsinki Institute of PhysicsAcademy of FinlandFrench CNRS-IN2P3Region Pays de LoireRegion AlsaceRegion AuvergneCEA, FranceGerman BMBFHelmholtz AssociationGeneral Secretariat for Research and Technology, Ministry of Development, GreeceHungarian OTKANational Office for Research and Technology (NKTH)Department of Atomic EnergyDepartment of Science and Technology of the Government of IndiaIstituto Nazionale di Fisica Nucleare (INFN) of ItalyMEXT, JapanJoint Institute for Nuclear Research, DubnaNational Research Foundation of Korea (NRF)CONACYTDGAPA, MexicoALFA-ECHELEN Program (High-Energy physics Latin-American-European Network)Stichting voor Fundamenteel Onderzoek der Materie (FOM)Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO), NetherlandsResearch Council of Norway (NFR)Polish Ministry of Science and Higher EducationNational Authority for Scientific Research - NASR (Autoritatea Nationala pentru Cercetare Stiintifica - ANCS)Federal Agency of Science of the Ministry of Education and Science of Russian FederationInternational Science and Technology Center, Russian Academy of SciencesRussian Federal Agency of Atomic EnergyRussian Federal Agency for Science and InnovationsCERN-INTASMinistry of Education of SlovakiaDepartment of Science and Technology, South AfricaCIEMATEELAMinisterio de Educacion y Ciencia of SpainXunta de Galicia (Conselleria de Educacion)CEADENCubaenergia, CubaIAEA (International Atomic Energy Agency)Swedish Reseach Council (VR)Knut & Alice Wallenberg Foundation (KAW)Ukraine Ministry of Education and ScienceUnited Kingdom Science and Technology Facilities Council (STFC)The United States Department of EnergyUnited States National Science FoundationState of TexasState of OhioFundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq

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