Infinitesimal and local convexity of a hypersurface in a semi-Riemannian manifold

Given a Riemannian manifold M and a hypersurface H in M, it is well known that infinitesimal convexity on a neighborhood of a point in H implies local convexity. We show in this note that the same result holds in a semi-Riemannian manifold. We make some remarks for the case when only timelike, null or spacelike geodesics are involved. The notion of geometric convexity is also reviewed and some applications to geodesic connectedness of an open subset of a Lorentzian manifold are given.Comment: 14 pages, AMSLaTex, 2 figures. v2: typos fixed, added one reference and several comments, statement of last proposition correcte

On the energy functional on Finsler manifolds and applications to stationary spacetimes

In this paper we first study some global properties of the energy functional on a non-reversible Finsler manifold. In particular we present a fully detailed proof of the Palais--Smale condition under the completeness of the Finsler metric. Moreover we define a Finsler metric of Randers type, which we call Fermat metric, associated to a conformally standard stationary spacetime. We shall study the influence of the Fermat metric on the causal properties of the spacetime, mainly the global hyperbolicity. Moreover we study the relations between the energy functional of the Fermat metric and the Fermat principle for the light rays in the spacetime. This allows us to obtain existence and multiplicity results for light rays, using the Finsler theory. Finally the case of timelike geodesics with fixed energy is considered.Comment: 23 pages, AMSLaTeX. v4 matches the published versio

Nuclear Stopping in Au+Au Collisions at sqrt(sNN) = 200 GeV

Transverse momentum spectra and rapidity densities, dN/dy, of protons, anti-protons, and net--protons (p-pbar) from central (0-5%) Au+Au collisions at sqrt(sNN) = 200 GeV were measured with the BRAHMS experiment within the rapidity range 0 < y < 3. The proton and anti-proton dN/dy decrease from mid-rapidity to y=3. The net-proton yield is roughly constant for y<1 at dN/dy~7, and increases to dN/dy~12 at y~3. The data show that collisions at this energy exhibit a high degree of transparency and that the linear scaling of rapidity loss with rapidity observed at lower energies is broken. The energy loss per participant nucleon is estimated to be 73 +- 6 GeV.Comment: 5 pages, 4 figure

Evolution of the nuclear modification factors with rapidity and centrality in d+Au collisions at $\sqrt{s_{NN}} = 200 GeV

We report on a study of the transverse momentum dependence of nuclear modification factors $R_{dAu}$ for charged hadrons produced in deuteron + gold collisions at $\sqrt{s_{NN}}= 200$GeV, as a function of collision centrality and of the pseudorapidity ($\eta = 0,1,2.2,3.2$) of the produced hadrons. We find significant and systematic decrease of $R_{dAu}$ with increasing rapidity. The midrapidity enhancement and the forward rapidity suppression are more pronounced in central collisions relative to peripheral collisions. These results are relevant to the study of the possible onset of gluon saturation at RHIC energies.Comment: Four pages, four figures. Published in PRL. Figures 1 and 2 have been updated, and several changes made to the tex

Recent Results from the BRAHMS Experiment

We present recent results obtained by the BRAHMS experiment at the Relativistic Heavy Ion Collider (RHIC) for the systems of Au + Au and Cu + Cu at \rootsnn{200} and at 62.4 GeV, and p + p at \rootsnn{200}. Nuclear modification factors for Au + Au and Cu + Cu collisions are presented. Analysis of anti-particle to particle ratios as a function of rapidity and collision energy reveal that particle populations at the chemical freeze-out stage for heavy-ion reactions at and above SPS energies are controlled by the baryon chemical potential. From the particle spectra we deduce significant radial expansion ($\beta \approx$ 0.75), as expected for systems created with a large initial energy density. We also measure the elliptic flow parameter $v_2$ versus rapidity and \ptn. We present rapidity dependent $p/\pi$ ratios within $0 < y < 3$ for Au + Au and Cu + Cu at \rootsnn{200}. \Raa is found to increase with decreasing collision energy, decreasing system size, and when going towards more peripheral collisions. However, \Raa shows only a very weak dependence on rapidity (for $0 < y < 3.2$), both for pions and protons.Comment: 16 pages and 14 figures, proceedings for plenary talk at Quark Matter 2005, Budapest, Hungar

Centrality dependence of charged-particle pseudorapidity distributions from d+Au collisions at sqrt(s_{NN})=200 GeV

Charged-particle pseudorapidity densities are presented for the d+Au reaction at sqrt{s_{NN}}=200 GeV with -4.2 <= eta <= 4.2$. The results, from the BRAHMS experiment at RHIC, are shown for minimum-bias events and 0-30%, 30-60%, and 60-80% centrality classes. Models incorporating both soft physics and hard, perturbative QCD-based scattering physics agree well with the experimental results. The data do not support predictions based on strong-coupling, semi-classical QCD. In the deuteron-fragmentation region the central 200 GeV data show behavior similar to full-overlap d+Au results at sqrt{s_{NN}}=19.4 GeV.Comment: 4 pages, 3figures; expanded discussion of uncertainties; added 60-80% centrality range; added additional discussion on centrality selection bia

High Pt Hadron Spectra at High Rapidity

We report the measurement of charged hadron production at different pseudo-rapidity values in deuteron+gold as well as proton+proton collisions at $sqrt{s_{NN}}$ = 200GeV at RHIC. The nuclear modification factors $R_{dAu}$ and $R_{cp}$ are used to investigate new behaviors in the deuteron+gold system as function of rapidity and the centrality of the collisions respectively.Comment: Nine pages 4 figures to be published in the QM2004 Proceedings, typos corrected and one reference adde

Scanning the phases of QCD with BRAHMS

BRAHMS has the ability to study relativistic heavy ion collisions from the final freeze-out of hadrons all the way back to the initial wave-function of the gold nuclei. This is accomplished by studying hadrons with a very wide range of momenta and angles. In doing so we can scan various phases of QCD, from a hadron gas, to a quark gluon plasma and perhaps to a color glass condensate.Comment: 8 pages, 6 figures, proceedings of plenary talk at Quark Matter 2004 conferenc

Forward and midrapidity like-particle ratios from p+p collisions at sqrt(s)=200 GeV

We present a measurement of pi-\pi+, K-/K+ and pbar/p from p+p collisions at sqrt(s) = 20 0GeV over the rapidity range 0<y<3.4. For pT < 2.0 GeV/c we see no significant transverse momentum dependence of the ratios. All three ratios are independent of rapidity for y ~< 1.5 and then steadily decline from y ~ 1.5 to y ~ 3. The pi-\pi+ ratio is below unity for y > 2.0. The pbar/p ratio is very similar for p+p and 20% central Au+Au collisions at all rapidities. In the fragmentation region the three ratios seem to be independent of beam energy when viewed from the rest frame of one of the protons. Theoretical models based on quark-diquark breaking mechanisms overestimate the pbar/p ratio up to y ~< 3. Including additional mechanisms for baryon number transport such as baryon junctions leads to a better description of the data.Comment: 15 pages, 4 figures, uses elsart.sty. Changes to references and discussion based on referee comments, resubmitted to Phys. Lett.

Nuclear Modification Factor for Charged Pions and Protons at Forward Rapidity in Central Au+Au Collisions at 200 GeV

We present spectra of charged pions and protons in 0-10% central Au+Au collisions at $\sqrt{s_{NN}}=200$ GeV at mid-rapidity ($y=0$) and forward pseudorapidity ($\eta=2.2$) measured with the BRAHMS experiment at RHIC. The spectra are compared to spectra from p+p collisions at the same energy scaled by the number of binary collisions. The resulting nuclear modification factors for central Au+Au collisions at both $y=0$ and $\eta=2.2$ exhibit suppression for charged pions but not for (anti-)protons at intermediate $p_T$. The $\bar{p}/\pi^-$ ratios have been measured up to $p_T\sim 3$ GeV/$c$ at the two rapidities and the results indicate that a significant fraction of the charged hadrons produced at intermediate $p_T$ range are (anti-)protons at both mid-rapidity and $\eta = 2.2$