Miniversal deformations of chains of linear mappings

V.I. Arnold [Russian Math. Surveys, 26 (no. 2), 1971, pp. 29–43] gave a miniversal deformation of matrices of linear operators; that is, a simple canonical form, to which not only a given square matrix A, but also the family of all matrices close to A, can be reduced by similarity transformations smoothly depending on the entries of matrices. We study miniversal deformations of quiver representations and obtain a miniversal deformation of matrices of chains of linear mappings V₁ V₂ · · · Vt , where all Vi are complex or real vector spaces and each line denotes −→ or ←−

Measurements of azimuthal anisotropy and charged-particle multiplicity in dd++Au collisions at sNN=\sqrt{s_{_{NN}}}=200, 62.4, 39, and 19.6 GeV

International audienceWe present measurements of the elliptic flow (v2) as a function of transverse momentum (pT), pseudorapidity (η), and centrality in d+Au collisions at sNN=200, 62.4, 39, and 19.6 GeV. The beam-energy scan of d+Au collisions provides a testing ground for the onset of flow signatures in small collision systems. We measure a nonzero v2 signal at all four collision energies, which, at midrapidity and low pT, is consistent with predictions from viscous hydrodynamic models. Comparisons with calculations from parton transport models (based on the ampt Monte Carlo generator) show good agreement with the data at midrapidity to forward (d-going) rapidities and low pT. At backward (Au-going) rapidities and pT>1.5GeV/c, the data diverges from ampt calculations of v2 relative to the initial geometry, indicating the possible dominance of nongeometry related correlations, referred to as nonflow. We also present measurements of the charged-particle multiplicity (dNch/dη) as a function of η in central d+Au collisions at the same energies. We find that in d+Au collisions at sNN=200 GeV the v2 scales with dNch/dη over all η in the PHENIX acceptance. At sNN=62.4, and 39 GeV, v2 scales with dNch/dη at midrapidity and forward rapidity, but falls off at backward rapidity. This departure from the dNch/dη scaling may be a further indication of nonflow effects dominating at backward rapidity

Single-spin asymmetry of J/ψJ/\psi production in p+pp+p, p+p+Al, and p+p+Au collisions with transversely polarized proton beams at sNN=200\sqrt{s_{_{NN}}}=200 GeV

International audienceWe report the transverse single-spin asymmetries of J/ψ production at forward and backward rapidity, 1.2<|y|<2.2, as a function of J/ψ transverse momentum (pT) and Feynman-x (xF). The data analyzed were recorded by the PHENIX experiment at the Relativistic Heavy Ion Collider in 2015 from p+p, p+Al, and p+Au collisions with transversely polarized proton beams at sNN=200  GeV. At this collision energy, single-spin asymmetries for heavy-flavor particle production of p+p collisions provide access to the spin-dependent gluon distribution and higher-twist correlation functions inside the nucleon, such as the gluon Qiu-Sterman and trigluon correlation functions. Proton+nucleus collisions offer an excellent opportunity to study nuclear effects on the correlation functions. The data indicate a positive asymmetry at the two-standard-deviation level in the p+p data for 2  GeV/c<pT<10  GeV/c at backward rapidity and negative asymmetries at the two-standard-deviation level in the p+Au data for pT<2  GeV/c at both forward and backward rapidity, while in p+Al collisions the asymmetries are consistent with zero within the range of experimental uncertainties

Measurements of μμ\mu\mu pairs from open heavy flavor and Drell-Yan in p+pp+p collisions at s=200\sqrt{s}=200 GeV

International audiencePHENIX reports differential cross sections of μμ pairs from semileptonic heavy-flavor decays and the Drell-Yan production mechanism measured in p+p collisions at s=200  GeV at forward and backward rapidity (1.2<|η|<2.2). The μμ pairs from cc¯, bb¯, and Drell-Yan are separated using a template fit to unlike- and like-sign muon pair spectra in mass and pT. The azimuthal opening angle correlation between the muons from cc¯ and bb¯ decays and the pair-pT distributions are compared to distributions generated using pythia and powheg models, which both include next-to-leading order processes. The measured distributions for pairs from cc¯ are consistent with pythia calculations. The cc¯ data present narrower azimuthal correlations and softer pT distributions compared to distributions generated from powheg. The bb¯ data are well described by both models. The extrapolated total cross section for bottom production is 3.75±0.24(stat)±0.500.35(syst)±0.45(global)  [μb], which is consistent with previous measurements at the Relativistic Heavy Ion Collider in the same system at the same collision energy and is approximately a factor of 2 higher than the central value calculated with theoretical models. The measured Drell-Yan cross section is in good agreement with next-to-leading-order quantum-chromodynamics calculations

Correlations of μμ\mu\mu, eμe\mu, and eeee pairs in pp+pp collisions at s=200\sqrt{s}=200 GeV and implications for ccˉc\bar{c} and bbˉb\bar{b} production mechanisms

PHENIX has measured the azimuthal correlations of muon pairs from charm and bottom semi-leptonic decays in $p$+$p$ collisions at $\sqrt{s}=200$ GeV, using a novel analysis technique utilizing both unlike- and like-sign muon pairs to separate charm, bottom and Drell-Yan contributions. The dimuon measurements combined with the previous electron-muon and dielectron measurements span a wide range in rapidity, and are well described by PYTHIA Tune A. Through a Bayesian analysis based on PYTHIA Tune A, we show that leading order pair creation is the dominant $(76\%\pm^{14}_{19}\%)$ contribution for $b\bar{b}$ production, whereas the data favor the scenario in which next-to-leading-order processes dominate $c\bar{c}$ production. The small contribution of next-to-leading-order processes in $b\bar{b}$ production at the collision energies of the Relativistic Heavy Ion Collider contrasts with the case at Large-Hadron-Collider energies, where next-to-leading-order processes are expected to dominate

Nonperturbative transverse-momentum-dependent effects in dihadron and direct photon-hadron angular correlations in p+pp+p collisions at s=200\sqrt{s}=200 GeV

International audienceDihadron and isolated direct photon-hadron angular correlations are measured in p+p collisions at s=200  GeV. The correlations are sensitive to nonperturbative initial-state and final-state transverse momenta kT and jT in the azimuthal nearly back-to-back region Δϕ∼π. To have sensitivity to small transverse momentum scales, nonperturbative momentum widths of pout, the out-of-plane transverse-momentum component perpendicular to the trigger particle, are measured. In this region, the evolution of pout can be studied when several different hard scales are measured. These widths are used to investigate possible effects from transverse-momentum-dependent factorization breaking. When accounting for the longitudinal-momentum fraction of the away-side hadron with respect to the near-side trigger particle, the widths are found to increase with the hard scale; this is qualitatively similar to the observed behavior in Drell-Yan and semi-inclusive deep-inelastic scattering interactions, where factorization is predicted to hold. The momentum widths are also studied as a function of center-of-mass energy by comparing to previous measurements at s=510  GeV. The nonperturbative jet widths also appear to increase with s at a similar xT, which is qualitatively consistent to similar measurements in Drell-Yan interactions. Future detailed global comparisons between measurements of processes where transverse-momentum-dependent factorization is predicted to hold and be broken will provide further insight into the role of color in hadronic interactions

Multiparticle azimuthal correlations for extracting event-by-event elliptic and triangular flow in Au++Au collisions at sNN=200\sqrt{s_{_{NN}}}=200 GeV

International audienceWe present measurements of elliptic and triangular azimuthal anisotropy of charged particles detected at forward rapidity 1<|η|<3 in Au + Au collisions at sNN=200 GeV, as a function of centrality. The multiparticle cumulant technique is used to obtain the elliptic flow coefficients v2{2},v2{4},v2{6}, and v2{8}, and triangular flow coefficients v3{2} and v3{4}. Using the small-variance limit, we estimate the mean and variance of the event-by-event v2 distribution from v2{2} and v2{4}. In a complementary analysis, we also use a folding procedure to study the distributions of v2 and v3 directly, extracting both the mean and variance. Implications for initial geometrical fluctuations and their translation into the final-state momentum distributions are discussed

Measurement of ψ(2S)\psi(2S) nuclear modification at backward and forward rapidity in pp++pp, pp++Al, and pp++Au collisions at sNN=200\sqrt{s_{_{NN}}}=200 GeV

International audienceSuppression of the $J/\psi$ nuclear-modification factor has been seen as a trademark signature of final-state effects in large collision systems for decades. In small systems, the nuclear modification was attributed to cold-nuclear-matter effects until the observation of strong differential suppression of the $\psi(2S)$ state in $p/d$ $+$ $A$ collisions suggested the presence of final-state effects. Results of $J/\psi$ and $\psi(2S)$ measurements in the dimuon decay channel are presented here for $p$ $+$ $p$, $p$ $+$Al, and $p$ $+$Au collision systems at $\sqrt{s_{_{NN}}}=200$ GeV. The results are predominantly shown in the form of the nuclear-modification factor, $R_{pA}$, the ratio of the $\psi(2S)$ invariant yield per nucleon-nucleon collision in collisions of proton on target nucleus to that in $p$ $+$ $p$ collisions. Measurements of the $J/\psi$ and $\psi(2S)$ nuclear-modification factor are compared with shadowing and transport-model predictions, as well as to complementary measurements at Large-Hadron-Collider energies

Transverse single-spin asymmetries of midrapidity π0\pi^0 and η\eta mesons in polarized p+pp+p collisions at s=200\sqrt{s}=200 GeV

International audienceWe present a measurement of the transverse single-spin asymmetry for $\pi^0$ and $\eta$ mesons in $p^\uparrow$ $+$ $p$ collisions in the pseudorapidity range $|\eta|<0.35$ and at a center-of-mass energy of 200 GeV with the PHENIX detector at the Relativistic Heavy Ion Collider. In comparison with previous measurements in this kinematic region, these results have a factor of 3 smaller uncertainties. As hadrons, $\pi^0$ and $\eta$ mesons are sensitive to both initial- and final-state nonperturbative effects for a mix of parton flavors. Comparisons of the differences in their transverse single-spin asymmetries have the potential to disentangle the possible effects of strangeness, isospin, or mass. These results can constrain the twist-3 trigluon collinear correlation function as well as the gluon Sivers function

Transverse-single-spin asymmetries of charged pions at midrapidity in transversely polarized p+pp{+}p collisions at s=200\sqrt{s}=200 GeV

International audienceIn 2015, the PHENIX Collaboration has measured single-spin asymmetries for charged pions in transversely polarized p+p collisions at the center-of-mass energy of s=200  GeV. The pions were detected at central rapidities of |η|&lt;0.35. The single-spin asymmetries are consistent with zero for each charge individually, as well as consistent with the previously published neutral-pion asymmetries in the same rapidity range. However, they show a slight indication of charge-dependent differences which may suggest a flavor dependence in the underlying mechanisms that create these asymmetries