We report the measurement of cumulants ($C_n, n=1\ldots4$) of the net-charge distributions measured within pseudorapidity ($|\eta|<0.35$) in Au$+$Au collisions at $\sqrt{s_{_{NN}}}=7.7-200$ GeV with the PHENIX experiment at the Relativistic Heavy Ion Collider. The ratios of cumulants (e.g. $C_1/C_2$, $C_3/C_1$) of the net-charge distributions, which can be related to volume independent susceptibility ratios, are studied as a function of centrality and energy. These quantities are important to understand the quantum-chromodynamics phase diagram and possible existence of a critical end point. The measured values are very well described by expectation from negative binomial distributions. We do not observe any nonmonotonic behavior in the ratios of the cumulants as a function of collision energy. The measured values of $C_1/C_2 = \mu/\sigma^2$ and $C_3/C_1 = S\sigma^3/\mu$ can be directly compared to lattice quantum-chromodynamics calculations and thus allow extraction of both the chemical freeze-out temperature and the baryon chemical potential at each center-of-mass energy.
Efficiency corrected cumulants of net-charge distributions as a function of $\langle N_{part} \rangle$ from Au+Au collisions at different collision energies.
Efficiency corrected cumulants of net-charge distributions as a function of $\langle N_{part} \rangle$ from Au+Au collisions at different collision energies.
Efficiency corrected cumulants of net-charge distributions as a function of $\langle N_{part} \rangle$ from Au+Au collisions at different collision energies.
A three-dimensional (3D) correlation function obtained from mid-rapidity, low pT pion pairs in central Au+Au collisions at sqrt(s_NN)=200 GeV is studied. The extracted model-independent source function indicates a long range tail in the directions of the pion pair transverse momentum (out) and the beam (long). Model comparisons to these distensions indicate a proper breakup time \tau_0 ~ 9 fm/c and a mean proper emission duration \Delta\tau ~ 2 fm/c, leading to sizable emission time differences (<|\Delta \tau_LCM |> ~ 12 fm/c), partly due to resonance decays. They also suggest an outside-in 'burning' of the emission source reminiscent of many hydrodynamical models.
Source function comparison between Therminator calculation and image for $S(r_x)$ in PCMS.
Source function comparison between Therminator calculation and image for $S(r_x)$ in PCMS.
Detailed differential measurements of the elliptic flow for particles produced in Au+Au and Cu+Cu collisions at sqrt(s_NN) = 200 GeV are presented. Predictions from perfect fluid hydrodynamics for the scaling of the elliptic flow coefficient v_2 with eccentricity, system size and transverse energy are tested and validated. For transverse kinetic energies KE_T ~ m_T-m up to ~1 GeV, scaling compatible with the hydrodynamic expansion of a thermalized fluid is observed for all produced particles. For large values of KE_T, the mesons and baryons scale separately. A universal scaling for the flow of both mesons and baryons is observed for the full transverse kinetic energy range of the data when quark number scaling is employed. In both cases the scaling is more pronounced in terms of KE_T rather than transverse momentum.
$v_2$ vs. $p_T$ for charged hadrons for Au+Au collisions.
$v_2$ vs. $p_T$ for charged hadrons for Cu+Cu collisions.
$v_2$ vs. $p_T$ for charged hadrons. divided by $k$ times ($k = 3.1$) the $p_T$-integrated $v_2$ (centrality) for Au+Au and Cu+Cu collisions.
Differential elliptic flow (v_2) for phi mesons and (anti)deuterons (d^bar)d is measured for Au+Au collisions at sqrt(s_NN) = 200 GeV. The v_2 for phi mesons follows the trend of lighter pi^+/- and K^+/- mesons, suggesting that ordinary hadrons interacting with standard hadronic cross sections are not the primary driver for elliptic flow development. The v_2 values for (d^bar)d suggest that elliptic flow is additive for composite particles. This further validation of the universal scaling of v_2 per constituent quark for baryons and mesons suggests that partonic collectivity dominates the transverse expansion dynamics.
$m_{inv}$ distributions for foreground and background $K^+ K^-$ pairs for 20-60% central Au+Au collisions.
Comparison of differential $v_2(p_T)$ for $\pi^{\pm}$. Results are shown for 20-60% central Au+Au collisions.
Comparison of differential $v_2(p_T)$ for $K^{\pm}$. Results are shown for 20-60% central Au+Au collisions.
Bose-Einstein correlations of charged kaons are measured for Au+Au collisions at sqrt(s_NN) = 200 GeV and are compared to charged pion probes, which have a larger hadronic scattering cross section. Three dimensional Gaussian source radii are extracted, along with a one-dimensional kaon emission source function. The centrality dependences of the three Gaussian radii are well described by a single linear function if N_part^1/3 with zero intercept. Imaging analysis shows a deviation from a Gaussian tail at r >~ 10 fm, although the bulk emission at lower radius is well-described by a Gaussian. The presence of a non-Gaussian tail in the kaon source reaffirms that the particle emission region in a heavy ion collision is extended, and that similar measurements with pions are not solely due to the decay of long-lived resonances.
3D correlation function of charged kaon pairs measured for 0.3 < $k_T$ < 1.5 GeV/$c$ at 0-30% centrality in Au+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV.
3D Gaussian HBT radius parameters for charged kaon pairs as a function of $N_{part}^{1/3}$ measured for 0.3 < $k_T$ < 1.5 GeV/$c$ and $m_T$ measured for 0-30% centrality in Au+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV.
3D Gaussian HBT radius parameters for charged kaon pairs as a function of $N_{part}^{1/3}$ measured for 0.3 < $k_T$ < 1.5 GeV/$c$ and $m_T$ measured for 0-30% centrality in Au+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV.
The PHENIX experiment at RHIC has measured the centrality dependence of the direct photon yield from Au$+$Au collisions at $\sqrt{s_{_{NN}}}=200$ GeV down to $p_T=0.4$ GeV/$c$. Photons are detected via photon conversions to $e^+e^-$ pairs and an improved technique is applied that minimizes the systematic uncertainties that usually limit direct photon measurements, in particular at low $p_T$. We find an excess of direct photons above the $N_{\rm coll}$-scaled yield measured in $p$$+$$p$ collisions. This excess yield is well described by an exponential distribution with an inverse slope of about 240 MeV/$c$ in the $p_T$ range from 0.6--2.0 GeV/$c$. While the shape of the $p_T$ distribution is independent of centrality within the experimental uncertainties, the yield increases rapidly with increasing centrality, scaling approximately with $N_{\rm part}^\alpha$, where $\alpha=1.48{\pm}0.08({\rm stat}){\pm}0.04({\rm syst})$.
Ratio $R_{\gamma}$ as function of photon $p_T$ from the 2007 and 2010 data sets in minimum-bias Au+Au collisions, and the $R_{\gamma}$ in the combined 2007+2010 measurement.
Fast parton probes produced by hard scattering and embedded within collisions of large nuclei have shown that partons suffer large energy loss and that the produced medium may respond collectively to the lost energy. We present measurements of neutral pion trigger particles at transverse momenta p^t_T = 4-12 GeV/c and associated charged hadrons (p^a_T = 0.5-7 GeV/c) as a function of relative azimuthal angle Delta Phi at midrapidity in Au+Au and p+p collisions at sqrt(s_NN) = 200 GeV. These data lead to two major observations. First, the relative angular distribution of low momentum hadrons, whose shape modification has been interpreted as a medium response to parton energy loss, is found to be modified only for p^t_T < 7 GeV/c. At higher p^t_T, the data are consistent with unmodified or very weakly modified shapes, even for the lowest measured p^a_T. This observation presents a quantitative challenge to medium response scenarios. Second, the associated yield of hadrons opposite to the trigger particle in Au+Au relative to that in p+p (I_AA) is found to be suppressed at large momentum (IAA ~ 0.35-0.5), but less than the single particle nuclear modification factor (R_AA ~0.2).
Average away-side $I^{head}_{AA}$ above 2 GeV/$c$ for various $\pi^0$ trigger momenta in central and midcentral collisions where $|\Delta\phi - \pi| < \pi/6$. Note: a 6% scale uncertainty applies to all $I_{AA}$ values.
Away-side jet widths from a Gaussian fit by $h^{\pm}$ partner momentum for various $\pi^0$ trigger momenta in $p+p$ collisions.
Away-side jet widths from a Gaussian fit by $h^{\pm}$ partner momentum for various $\pi^0$ trigger momenta in Au+Au collisions.
We present inclusive charged hadron elliptic flow v_2 measured over the pseudorapidity range |\eta| < 0.35 in Au+Au collisions at sqrt(s_NN) = 200 GeV. Results for v_2 are presented over a broad range of transverse momentum (p_T = 0.2-8.0 GeV/c) and centrality (0-60%). In order to study non-flow effects that are not correlated with the reaction plane, as well as the fluctuations of v_2, we compare two different analysis methods: (1) event plane method from two independent sub-detectors at forward (|\eta| = 3.1-3.9) and beam (|\eta| > 6.5) pseudorapidities and (2) two-particle cumulant method extracted using correlations between particles detected at midrapidity. The two event-plane results are consistent within systematic uncertainties over the measured p_T and in centrality 0-40%. There is at most 20% difference of the v_2 between the two event plane methods in peripheral (40-60%) collisions. The comparisons between the two-particle cumulant results and the standard event plane measurements are discussed.
Charged hadron $v_2$($p_T$) in Au+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV from the two-particle cumulant method, the BBC event plane, and the ZDC-SMD event plane for the indicated centralities.
Charged hadron $v_2$($p_T$) in Au+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV from the two-particle cumulant method, the BBC event plane, and the ZDC-SMD event plane for the indicated centralities.
Charged hadron $v_2$($p_T$) in Au+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV from the two-particle cumulant method, the BBC event plane, and the ZDC-SMD event plane for the indicated centralities.
Azimuthal angle \Delta\phi correlations are presented for charged hadrons from dijets for 0.4 < p_T < 10 GeV/c in Au+Au collisions at sqrt(s_NN) = 200 GeV. With increasing p_T, the away-side distribution evolves from a broad to a concave shape, then to a convex shape. Comparisons to p+p data suggest that the away-side can be divided into a partially suppressed 'head' region centered at Delta\phi ~ \pi, and an enhanced 'shoulder' region centered at Delta\phi ~ \pi +/- 1.1. The p_T spectrum for the 'head' region softens toward central collisions, consistent with the onset of jet quenching. The spectral slope for the 'shoulder' region is independent of centrality and trigger p_T, which offers constraints on energy transport mechanisms and suggests that the 'shoulder' region contains the medium response to energetic jets.
<p>Per-trigger yield versus $\Delta\phi$ for various trigger and partner $p_T$ ($p_T^A$ $\otimes$ $p_T^B$), in $p$+$p$ and 0-20% Au+Au collisions.</p> <p><i>The systematic errors on $v_2$ are represented by "sys. corr." and are dominated by the reaction plane resolution. The fit that accounts for the overlap of the near- and away-side Gaussians at $\Delta\phi_{min}$ gives systematically lower $b_0$ values that that for ZYAM, and is assigned as the differences as one-sided systematic errors on $b_0$ represented by "sys. uncorr.".
<p>Per-trigger yield versus $\Delta\phi$ for various trigger and partner $p_T$ ($p_T^A$ $\otimes$ $p_T^B$), in $p$+$p$ and 0-20% Au+Au collisions.</p> <p><i>The systematic errors on $v_2$ are represented by "sys. corr." and are dominated by the reaction plane resolution. The fit that accounts for the overlap of the near- and away-side Gaussians at $\Delta\phi_{min}$ gives systematically lower $b_0$ values that that for ZYAM, and is assigned as the differences as one-sided systematic errors on $b_0$ represented by "sys. uncorr.".</p></i>
<p>$R_{HS}$ versus $p_T^B$ for $p$+$p$ and Au+Au collisions for four trigger selections.</p> <p><i>The systematic errors on $v_2$ are represented by "sys. corr." and are dominated by the reaction plane resolution. The fit that accounts for the overlap of the near- and away-side Gaussians at $\Delta\phi_{min}$ gives systematically lower $b_0$ values that that for ZYAM, and is assigned as the differences as one-sided systematic errors on $b_0$ represented by "sys. uncorr.".</p></i>
Differential measurements of the elliptic (v_2) and hexadecapole (v_4) Fourier flow coefficients are reported for charged hadrons as a function of transverse momentum (p_T) and collision centrality or the number of participant nucleons (N_part) for Au+Au collisions at sqrt(s_NN)=200 GeV. The v_{2,4} measurements at pseudorapidity |\eta|<=0.35 obtained with four separate reaction plane detectors positioned in the range 1.0<|\eta|<3.9 show good agreement, indicating the absence of significant \eta-dependent nonflow perturbations. Sizable values for v_4(p_T) are observed with a ratio v_4(p_T,N_part)/v_2^2(p_T,N_part)~0.8 for 50<N_part<200, which is compatible with the combined effects of a finite viscosity and initial eccentricity fluctuations. For N_part>200 this ratio increases up to 1.7 in the most central collisions.
Glauber quantities ($N_{part}$, $N_{coll}$, $b$) for Au+Au collisions at 200 GeV (PHENIX Run 2007)
$p_T$ dependence of $v_2$ for charged hadrons for several centrality selections as indicated.
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