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

ϒ production in p–Pb collisions at √sNN=8.16 TeV

ϒ production in p–Pb interactions is studied at the centre-of-mass energy per nucleon–nucleon collision √sNN = 8.16 TeV with the ALICE detector at the CERN LHC. The measurement is performed reconstructing bottomonium resonances via their dimuon decay channel, in the centre-of-mass rapidity intervals 2.03 < ycms < 3.53 and −4.46 < ycms < −2.96, down to zero transverse momentum. In this work, results on the ϒ(1S) production cross section as a function of rapidity and transverse momentum are presented. The corresponding nuclear modification factor shows a suppression of the ϒ(1S) yields with respect to pp collisions, both at forward and backward rapidity. This suppression is stronger in the low transverse momentum region and shows no significant dependence on the centrality of the interactions. Furthermore, the ϒ(2S) nuclear modification factor is evaluated, suggesting a suppression similar to that of the ϒ(1S). A first measurement of the ϒ(3S) has also been performed. Finally, results are compared with previous ALICE measurements in p–Pb collisions at √sNN = 5.02 TeV and with theoretical calculations.publishedVersio

First proton-proton collisions at the LHC as observed with the ALICE detector: measurement of the charged-particle pseudorapidity density at root s=900 GeV

-On 23rd November 2009, during the early commissioning of the CERN Large Hadron Collider (LHC), two counter-rotating proton bunches were circulated for the first time concurrently in the machine, at the LHC injection energy of 450 GeV per beam. Although the proton intensity was very low, with only one pilot bunch per beam, and no systematic attempt was made to optimize the collision optics, all LHC experiments reported a number of collision candidates. In the ALICE experiment, the collision region was centred very well in both the longitudinal and transverse directions and 284 events were recorded in coincidence with the two passing proton bunches. The events were immediately reconstructed and analyzed both online and offline. We have used these events to measure the pseudorapidity density of charged primary particles in the central region. In the range vertical bar eta vertical bar S collider. They also illustrate the excellent functioning and rapid progress of the LHC accelerator, and of both the hardware and software of the ALICE experiment, in this early start-up phase

Coherent ψ(2S) photo-production in ultra-peripheral PbPb collisions at √sNN=2.76 TeV

We have performed the first measurement of the coherent ψ(2S) photo-production cross section in ultra-peripheral PbPb collisions at the LHC. This charmonium excited state is reconstructed via the ψ(2S)→l+l− and ψ(2S)→J/ψπ+π− decays, where the J/ψ decays into two leptons. The analysis is based on an event sample corresponding to an integrated luminosity of about 22 μb−1. The cross section for coherent ψ(2S) production in the rapidity interval −0.9<y<0.9 is dσψ(2S)coh/dy=0.83±0.19(stat+syst) mb. The ψ(2S) to J/ψ coherent cross section ratio is 0.34−0.07+0.08(stat+syst). The obtained results are compared to predictions from theoretical models

Hypertriton production in p–Pb collisions at √sNN = 5.02 TeV

The study of nuclei and antinuclei production has proven to be a powerful tool to investigate the formation mechanism of loosely bound states in high-energy hadronic collisions. The first measurement of the production of 3ΛH in p-Pb collisions at sNN−−−√ = 5.02 TeV is presented in this Letter. Its production yield measured in the rapidity interval −1<y<0 for the 40% highest multiplicity p-Pb collisions is dN/dy=[6.3±1.8(stat.)±1.2(syst.)]×10−7. The measurement is compared with the expectations of statistical hadronisation and coalescence models, which describe the nucleosynthesis in hadronic collisions. These two models predict very different yields of the hypertriton in charged particle multiplicity environments relevant to small collision systems such as p-Pb and therefore the measurement of dN/dy is crucial to distinguish between them. The precision of this measurement leads to the exclusion with a significance larger than 6.9σ of some configurations of the statistical hadronization model, thus constraining the theory behind the production of loosely bound states at hadron colliders

Inclusive quarkonium production in pp collisions at √s = 5.02 TeV

This article reports on the inclusive production cross section of several quarkonium states, J/ψ, ψ(2S), Υ(1S), Υ(2S), and Υ(3S), measured with the ALICE detector at the LHC, in pp collisions at s√=5.02 TeV. The analysis is performed in the dimuon decay channel at forward rapidity (2.5<y<4). The integrated cross sections and transverse-momentum (pT) and rapidity (y) differential cross sections for J/ψ, ψ(2S), Υ(1S), and the ψ(2S)-to-J/ψ cross section ratios are presented. The integrated cross sections, assuming unpolarized quarkonia, are: σJ/ψ(pT<20 GeV/c) = 5.88 ± 0.03 ± 0.34 μb, σψ(2S)(pT<12 GeV/c) = 0.87 ± 0.06 ± 0.10 μb, σΥ(1S)(pT<15 GeV/c) = 45.5 ± 3.9 ± 3.5 nb, σΥ(2S)(pT<15 GeV/c) = 22.4 ± 3.2 ± 2.7 nb, and σΥ(3S)(pT<15 GeV/c) = 4.9 ± 2.2 ± 1.0 nb, where the first (second) uncertainty is the statistical (systematic) one. For the first time, the cross sections of the three Υ states, as well as the ψ(2S) one as a function of pT and y, are measured at s√=5.02 TeV at forward rapidity. These measurements also significantly extend the J/ψ pT reach and supersede previously published results. A comparison with ALICE measurements in pp collisions at s√=2.76, 7, 8, and 13 TeV is presented and the energy dependence of quarkonium production cross sections is discussed. Finally, the results are compared with the predictions from several production models

Measurements of the groomed and ungroomed jet angularities in pp collisions at √s = 5.02 TeV

The jet angularities are a class of jet substructure observables which characterize the angular and momentum distribution of particles within jets. These observables are sensitive to momentum scales ranging from perturbative hard scatterings to nonperturbative fragmentation into final-state hadrons. We report measurements of several groomed and ungroomed jet angularities in pp collisions at s√=5.02 TeV with the ALICE detector. Jets are reconstructed using charged particle tracks at midrapidity (|η|<0.9). The anti-kT algorithm is used with jet resolution parameters R=0.2 and R=0.4 for several transverse momentum pch jetT intervals in the 20−100 GeV/c range. Using the jet grooming algorithm Soft Drop, the sensitivity to softer, wide-angle processes, as well as the underlying event, can be reduced in a way which is well-controlled in theoretical calculations. We report the ungroomed jet angularities, λα, and groomed jet angularities, λα,g, to investigate the interplay between perturbative and nonperturbative effects at low jet momenta. Various angular exponent parameters α=1, 1.5, 2, and 3 are used to systematically vary the sensitivity of the observable to collinear and soft radiation. Results are compared to analytical predictions at next-to-leading-logarithmic accuracy, which provide a generally good description of the data in the perturbative regime but exhibit discrepancies in the nonperturbative regime. Moreover, these measurements serve as a baseline for future ones in heavy-ion collisions by providing new insight into the interplay between perturbative and nonperturbative effects in the angular and momentum substructure of jets. They supply crucial guidance on the selection of jet resolution parameter, jet transverse momentum, and angular scaling variable for jet quenching studies

Constraining the magnitude of the Chiral Magnetic Effect with Event Shape Engineering in Pb-Pb collisions at sNN\sqrt{s_{\rm NN}} = 2.76$ TeV

In ultrarelativistic heavy-ion collisions, the event-by-event variation of the elliptic flow $v_2$ reflects fluctuations in the shape of the initial state of the system. This allows to select events with the same centrality but different initial geometry. This selection technique, Event Shape Engineering, has been used in the analysis of charge-dependent two- and three-particle correlations in Pb-Pb collisions at $\sqrt{s_{_{\rm NN}}} =2.76$ TeV. The two-particle correlator $\langle \cos(\varphi_\alpha - \varphi_\beta) \rangle$, calculated for different combinations of charges $\alpha$ and $\beta$, is almost independent of $v_2$ (for a given centrality), while the three-particle correlator $\langle \cos(\varphi_\alpha + \varphi_\beta - 2\Psi_2) \rangle$ scales almost linearly both with the event $v_2$ and charged-particle pseudorapidity density. The charge dependence of the three-particle correlator is often interpreted as evidence for the Chiral Magnetic Effect (CME), a parity violating effect of the strong interaction. However, its measured dependence on $v_2$ points to a large non-CME contribution to the correlator. Comparing the results with Monte Carlo calculations including a magnetic field due to the spectators, the upper limit of the CME signal contribution to the three-particle correlator in the 10-50% centrality interval is found to be 26-33% at 95% confidence level

Charged-particle multiplicity fluctuations in Pb–Pb collisions at √sNN = 2.76 TeV

Measurements of event-by-event fluctuations of charged-particle multiplicities in Pb-Pb collisions at sNN−−−√ = 2.76 TeV using the ALICE detector at the CERN Large Hadron Collider (LHC) are presented in the pseudorapidity range |η|<0.8 and transverse momentum 0.2<pT<2.0 GeV/c. The amplitude of the fluctuations is expressed in terms of the variance normalized by the mean of the multiplicity distribution. The η and pT dependences of the fluctuations and their evolution with respect to collision centrality are investigated. The multiplicity fluctuations tend to decrease from peripheral to central collisions. The results are compared to those obtained from HIJING and AMPT Monte Carlo event generators as well as to experimental data at lower collision energies. Additionally, the measured multiplicity fluctuations are discussed in the context of the isothermal compressibility of the high-density strongly-interacting system formed in central Pb-Pb collisions