SUPERLINEAR ELLIPTIC PROBLEMS WITH SIGN CHANGING COEFFICIENTS

Via variational methods, we study multiplicity of solutions for the problem {-Delta u = lambda b(x)vertical bar u vertical bar(q-2)u + au + g(x, u) in Omega, u - 0 on partial derivative Omega, where a simple example for g( x, u) is |u|(p-2)u; here a, lambda are real parameters, 1 < q < 2 < p <= 2* and b(x) is a function in a suitable space L-sigma. We obtain a class of sign changing coefficients b(x) for which two non-negative solutions exist for any lambda > 0, and a total of five nontrivial solutions are obtained when lambda is small and a >= lambda(1). Note that this type of results are valid even in the critical case.

Asymptotic integral kernel for ensembles of random normal matrices with radial potentials

The method of steepest descent is used to study the integral kernel of a family of normal random matrix ensembles with eigenvalue distribution P-N (z(1), ... , z(N)) = Z(N)(-1)e(-N)Sigma(N)(i=1) V-alpha(z(i)) Pi(1 <= i<j <= N) vertical bar z(i) - z(j)vertical bar(2), where V-alpha(z) = vertical bar z vertical bar(alpha), z epsilon C and alpha epsilon inverted left perpendicular0, infinity inverted right perpendicular. Asymptotic formulas with error estimate on sectors are obtained. A corollary of these expansions is a scaling limit for the n-point function in terms of the integral kernel for the classical Segal-Bargmann space. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.3688293]

MULTIPLICITY OF NONRADIAL SOLUTIONS FOR A CLASS OF QUASILINEAR EQUATIONS ON ANNULUS WITH EXPONENTIAL CRITICAL GROWTH

In this paper, we establish the existence of many rotationally non-equivalent and nonradial solutions for the following class of quasilinear problems (p) {-Delta(N)u = lambda f(vertical bar x vertical bar, u) x is an element of Omega(r), u > 0 x is an element of Omega(r), u = 0 x is an element of Omega(r), where Omega(r) = {x is an element of R-N : r < vertical bar x vertical bar < r + 1}, N >= 2, N not equal 3, r >0, lambda > 0, Delta(N)u = div(vertical bar del u vertical bar(N-2)del u) is the N-Laplacian operator and f is a continuous function with exponential critical growth.

Evolution of pi(0) Suppression in Au plus Au Collisions from root s(NN)=39 to 200 GeV

Neutral-pion pi(0) spectra were measured at midrapidity (vertical bar y vertical bar < 0.35) in Au + Au collisions at root s(NN) = 39 and 62.4 GeV and compared with earlier measurements at 200 GeV in a transverse-momentum range of 1 < p(T) < 10 GeV/c. The high-p(T) tail is well described by a power law in all cases, and the powers decrease significantly with decreasing center-of-mass energy. The change of powers is very similar to that observed in the corresponding spectra for p + p collisions. The nuclear modification factors (RAA) show significant suppression, with a distinct energy, centrality, and p(T) dependence. Above p(T) = 7 GeV/c, R-AA is similar for root sNN = 62.4 and 200 GeV at all centralities. Perturbative-quantum-chromodynamics calculations that describe R-AA well at 200 GeV fail to describe the 39 GeV data, raising the possibility that, for the same p(T) region, the relative importance of initial-state effects and soft processes increases at lower energies. The p(T) range where pi(0) spectra in central Au + Au collisions have the same power as in p + p collisions is approximate to 5 and 7 GeV/c for root sNN = 200 and 62.4 GeV, respectively. For the root sNN = 39 GeV data, it is not clear whether such a region is reached, and the x(T) dependence of the x(T)-scaling power-law exponent is very different from that observed in the root sNN = 62 and 200 GeV data, providing further evidence that initial-state effects and soft processes mask the in-medium suppression of hardscattered partons to higher p(T) as the collision energy decreases.

J/psi suppression at forward rapidity in Au plus Au collisions at root s(NN)=39 and 62.4 GeV

We present measurements of the J/psi invariant yields in root s(NN) = 39 and 62.4 GeV Au + Au collisions at forward rapidity (1.2 < vertical bar y vertical bar < 2.2). Invariant yields are presented as a function of both collision centrality and transverse momentum. Nuclear modifications are obtained for central relative to peripheral Au + Au collisions (R-CP) and for various centrality selections in Au + Au relative to scaled p + p cross sections obtained from other measurements (R-AA). The observed suppression patterns at 39 and 62.4 GeV are quite similar to those previously measured at 200 GeV. This similar suppression presents a challenge to theoretical models that contain various competing mechanisms with different energy dependencies, some of which cause suppression and others enhancement. DOI: 10.1103/PhysRevC.86.064901

Measurements of D-0 and D* production in p plus p collisions at root s=200 GeV

We report measurements of charmed-hadron (D-0, D*) production cross sections at midrapidity in p + p collisions at a center-of-mass energy of 200 GeV by the STAR experiment. Charmed hadrons were reconstructed via the hadronic decays D-0 -> K- pi(+), D*(+) -> D-0 pi(+) -> K-pi(+)pi(+) and their charge conjugates, covering the p(T) range of 0.6-2.0 and 2.0-6.0 GeV/c for D-0 and D*(+), respectively. From this analysis, the charm-pair production cross section at midrapidity is d sigma/dy vertical bar(c (c) over bar)(y-0) = 170+/-45(stat)(-59)(+38()sys) mu b. The extracted charm-pair cross section is compared to perturbative QCD calculations. The transverse momentum differential cross section is found to be consistent with the upper bound of a fixed-order next-to-leading logarithm calculation.

Ground and excited state charmonium production in p plus p collisions at root s=200 GeV

We report on charmonium measurements [J/psi (1S), psi' (2S), and chi(c) (1P)] in p + p collisions at root s = 200 GeV. We find that the fraction of J/psi coming from the feed-down decay of psi' and chi(c) in the midrapidity region (vertical bar y vertical bar < 0: 35) is 9.6 +/- 2.4% and 32 +/- 9%, respectively. We also present the p(T) and rapidity dependencies of the J/psi yield measured via dielectron decay at midrapidity (vertical bar y vertical bar < 0.35) and via dimuon decay at forward rapidity (1.2 < vertical bar y vertical bar < 2.2). The statistical precision greatly exceeds that reported in our previous publication [Phys. Rev. Lett. 98, 232002 (2007)]. The new results are compared with other experiments and discussed in the context of current charmonium production models.

Inclusive charged hadron elliptic flow in Au+Au collisions at root s(NN)=7.7-39 GeV

A systematic study is presented for centrality, transverse momentum (p(T)), and pseudorapidity (eta) dependence of the inclusive charged hadron elliptic flow (v(2)) at midrapidity (vertical bar eta vertical bar < 1.0) in Au + Au collisions at root s(NN) = 7.7, 11.5, 19.6, 27, and 39 GeV. The results obtained with different methods, including correlations with the event plane reconstructed in a region separated by a large pseudorapidity gap and four-particle cumulants (v(2){4}), are presented to investigate nonflow correlations and v(2) fluctuations. We observe that the difference between v(2){2} and v(2){4} is smaller at the lower collision energies. Values of v(2), scaled by the initial coordinate space eccentricity, v(2)/epsilon, as a function of p(T) are larger in more central collisions, suggesting stronger collective flow develops in more central collisions, similar to the results at higher collision energies. These results are compared to measurements at higher energies at the Relativistic Heavy Ion Collider (root s(NN) = 62.4 and 200 GeV) and at the Large Hadron Collider (Pb + Pb collisions at root s(NN) = 2.76 TeV). The v(2)(pT) values for fixed pT rise with increasing collision energy within the pT range studied (<2 GeV/c). A comparison to viscous hydrodynamic simulations is made to potentially help understand the energy dependence of v(2)(pT). We also compare the v(2) results to UrQMD and AMPT transport model calculations, and physics implications on the dominance of partonic versus hadronic phases in the system created at beam energy scan energies are discussed.

Production of K*(892)(0) and phi(1020) in pp collisions at root s=7 TeV

The production of K*(892)(0) and phi(1020) in pp collisions at root s = 7 TeV was measured by the ALICE experiment at the LHC. The yields and the transverse momentum spectra d(2)N/dydp(T) at midrapidity vertical bar y vertical bar < 0.5 in the range 0 < p(T) < 6 GeV/c for K*(892)(0) and 0.4 < p(T) < 6 GeV/c for phi(1020) are reported and compared to model predictions. Using the yield of pions, kaons, and Omega baryons measured previously by ALICE at root s = 7 TeV, the ratios K*/K-, phi/K*, phi/ K-, phi/pi(-), and (Omega + <(Omega)over bar>)/phi are presented. The values of the K*/K-, phi/K* and phi/K- ratios are similar to those found at lower centre-of-mass energies. In contrast, the phi/pi(-) ratio, which has been observed to increase with energy, seems to saturate above 200 GeV. The (Omega + (Omega) over bar)/phi ratio in the p(T) range 1-5 GeV/ c is found to be in good agreement with the prediction of the HIJING/B (B) over bar v2.0model with a strong colour field.

Transverse sphericity of primary charged particles in minimum bias proton-proton collisions at root s=0.9, 2.76 and 7 TeV

Measurements of the sphericity of primary charged particles in minimum bias proton-proton collisions at root 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 vertical bar eta vertical bar < 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.

Pion, Kaon, and Proton Production in Central Pb-Pb Collisions at root s(NN)=2.76 TeV

In this Letter we report the first results on pi(+/-), K-+/-, p, and (p) over bar production at midrapidity (vertical bar y vertical bar < 0.5) in central Pb-Pb collisions at root s(NN) = 2.76 TeV, measured by the ALICE experiment at the LHC. The p(T) distributions and yields are compared to previous results at root s(NN) = 200 GeV and expectations from hydrodynamic and thermal models. The spectral shapes indicate a strong increase of the radial flow velocity with root s(NN), which in hydrodynamic models is expected as a consequence of the increasing particle density. While the K/pi ratio is in line with predictions from the thermal model, the p/pi ratio is found to be lower by a factor of about 1.5. This deviation from thermal model expectations is still to be understood.

Measurement of prompt J/psi and beauty hadron production cross sections at mid-rapidity in pp collisions at root s=7 TeV

The ALICE experiment at the LHC has studied J/psi production at mid-rapidity in pp collisions at root s = 7 TeV through its electron pair decay on a data sample corresponding to an integrated luminosity L-int = 5.6 nb(-1). The fraction of J/psi from the decay of long-lived beauty hadrons was determined for J/psi candidates with transverse momentum p(t) > 1,3 GeV/c and rapidity vertical bar y vertical bar < 0.9. The cross section for prompt J/psi mesons, i.e. directly produced J/psi and prompt decays of heavier charmonium states such as the psi(2S) and chi(c) resonances, is sigma(prompt J/psi) (p(t) > 1.3 GeV/c, vertical bar y vertical bar < 0.9) = 8.3 +/- 0.8(stat.) +/- 1.1 (syst.)(-1.4)(+1.5) (syst. pol.) mu b. The cross section for the production of b-hadrons decaying to J/psi with p(t) > 1.3 GeV/c and vertical bar y vertical bar < 0.9 is a sigma(J/psi <- hB) (p(t) > 1.3 GeV/c, vertical bar y vertical bar < 0.9) = 1.46 +/- 0.38 (stat.)(-0.32)(+0.26) (syst.) mu b. The results are compared to QCD model predictions. The shape of the p(t) and y distributions of b-quarks predicted by perturbative QCD model calculations are used to extrapolate the measured cross section to derive the b (b) over bar pair total cross section and d sigma/dy at mid-rapidity.

D-S(+) meson production at central rapidity in proton-proton collisions at root s=7 TeV

The P-T-differential inclusive production cross section of the prompt charm-strange meson D-s(+) in the rapidity range vertical bar y vertical bar < 0.5 was measured in proton-proton collisions at root s = 7 TeV at the LHC using the ALICE detector. The analysis was performed on a data sample of 2.98 x 10(8) events collected with a minimum-bias trigger. The corresponding integrated luminosity is L-int = 4.8 nb(-1). Reconstructing the decay D-s(+) -> phi pi(+) with phi -> K-K+, and its charge conjugate, about 480 D-s(+/-) mesons were counted, after selection cuts, in the transverse momentum range 2 < P-T < 12 GeV/c. The results are compared with predictions from models based on perturbative QCD. The ratios of the cross sections of four D meson species (namely D-0, D+, D*+ and D-s(+)) were determined both as a function of p(T) and integrated over p(T)after extrapolating to full p(T) range, together with the strangeness suppression factor in charm fragmentation. The obtained values are found to be compatible within uncertainties with those measured by other experiments in e(+)e(-), ep and pp interactions at various centre-of-mass energies. (C) 2012 CERN. Published by Elsevier By. All rights reserved.

Multi-strange baryon production in pp collisions at root s=7 TeV with ALICE

A measurement of the multi-strange Xi(-) and Omega(-) baryons and their antiparticles by the ALICE experiment at the CERN Large Hadron Collider (LHC) is presented for inelastic proton-proton collisions at a centre-of-mass energy of 7 TeV. The transverse momentum (p(T)) distributions were studied at mid-rapidity (vertical bar y vertical bar < 0.5) in the range of 0.6 < p(T) < 8.5 GeV/c Xi(-) for and Xi(+) baryons, and in the range of 0.8 < P-T < 5 GeV/c for Omega(-) and<(Omega)over bar>(+). Baryons and antibaryons were measured as separate particles and we find that the baryon to antibaryon ratio of both particle species is consistent with unity over the entire range of the measurement. The statistical precision of the current data has allowed us to measure a difference between the mean p(T) of Xi(-) ((Xi) over bar)(+) and Omega(-) ((Omega) over bar (+)). Particle yields, mean pi, and the spectra in the intermediate pi range are not well described by the PYTHIA Perugia 2011 tune Monte Carlo event generator, which has been tuned to reproduce the early LHC data. The discrepancy is largest for Omega(-)((Omega) over bar (+)). This PYTHIA tune approaches the pi spectra of Xi(-) and Xi(+) baryons below p(T) <0.85 GeV/c and describes the Xi(-) and Xi(+) spectra above p(T) > 6.0 GeV/c. We also illustrate the difference between the experimental data and model by comparing the corresponding ratios of (Omega(-) +(Omega) over bar (+))/(Xi(-) + Xi(+)) as a function of transverse mass. (C) 2012 CERN. Published by Elsevier B.V. All rights reserved.

Suppression of high transverse momentum D mesons in central Pb-Pb collisions at root s(NN)=2.76 TeV

The production of the prompt charm mesons D-0, D+, D*(+), and their antiparticles, was measured with the ALICE detector in Pb-Pb collisions at the LHC, at a centre-of-mass energy root s(NN) = 2.76 TeV per nucleon-nucleon collision. The p(t)-differential production yields in the range 2 < p(t) < 16 GeV/c at central rapidity, vertical bar y vertical bar < 0.5, were used to calculate the nuclear modification factor R-AA with respect to a proton-proton reference obtained from the cross section measured at root s = 7 TeV and scaled to root s = 2.76 TeV. For the three meson species, R-AA shows a suppression by a factor 3-4, for transverse momenta larger than 5 GeV/c in the 20% most central collisions. The suppression is reduced for peripheral collisions.