We present measurements of elliptic and triangular azimuthal anisotropy of charged particles detected at forward rapidity $1<|\eta|<3$ in Au$+$Au collisions at $\sqrt{s_{_{NN}}}=200$ GeV, as a function of centrality. The multiparticle cumulant technique is used to obtain the elliptic flow coefficients $v_2\{2\}$, $v_2\{4\}$, $v_2\{6\}$, and $v_2\{8\}$, and triangular flow coefficients $v_3\{2\}$ and $v_3\{4\}$. Using the small-variance limit, we estimate the mean and variance of the event-by-event $v_2$ distribution from $v_2\{2\}$ and $v_2\{4\}$. In a complementary analysis, we also use a folding procedure to study the distributions of $v_2$ and $v_3$ directly, extracting both the mean and variance. Implications for initial geometrical fluctuations and their translation into the final state momentum distributions are discussed.
Centrality dependence of (a) $v_2${2} and (b) $v_2${4}. (a) The red points indicate no pseudorapidity gap whereas the magenta points indicate a pseudorapidity gap of |$\Delta\eta$| > 2.0. (b) The black points indicate $v_2${4} with no pseudorapidity gap, the blue points indicate a two-subevent method with |$\Delta\eta$| > 2.0 but where some short-range pairs are allowed, and the red points indicate a two-subevent method with |$\Delta\eta$| > 2.0 where no short-range pairs are allowed.
Centrality dependence of (a) $v_2${2} and (b) $v_2${4}. (a) The red points indicate no pseudorapidity gap whereas the magenta points indicate a pseudorapidity gap of |$\Delta\eta$| > 2.0. (b) The black points indicate $v_2${4} with no pseudorapidity gap, the blue points indicate a two-subevent method with |$\Delta\eta$| > 2.0 but where some short-range pairs are allowed, and the red points indicate a two-subevent method with |$\Delta\eta$| > 2.0 where no short-range pairs are allowed.
Centrality dependence of (a) $v_2${2} and (b) $v_2${4}. (a) The red points indicate no pseudorapidity gap whereas the magenta points indicate a pseudorapidity gap of |$\Delta\eta$| > 2.0. (b) The black points indicate $v_2${4} with no pseudorapidity gap, the blue points indicate a two-subevent method with |$\Delta\eta$| > 2.0 but where some short-range pairs are allowed, and the red points indicate a two-subevent method with |$\Delta\eta$| > 2.0 where no short-range pairs are allowed.
We have measured the cross section and single spin asymmetries from forward $W^{\pm}\rightarrow\mu^{\pm}\nu$ production in longitudinally polarized $p$$+$$p$ collisions at $\sqrt{s}=510$ GeV using the PHENIX detector at the Relativistic Heavy Ion Collider. The cross sections are consistent with previous measurements at this collision energy, while the most forward and backward longitudinal single spin asymmetries provide new insights into the sea quark helicities in the proton. The charge of the W bosons provides a natural flavor separation of the participating partons.
Single-spin asymmetries at forward $A^{FW}_L$ and backward $A^{BW}_L$ rapidities for $p$+$p$ collisions at $\sqrt{s}$ = 510 GeV for results in 2013 and 2012, plus combined results for both years.
The total $W$ boson production cross sections for $p$+$p$ collisions at $\sqrt{s}$ = 510 GeV for $\sigma$($W^+$ $\rightarrow$ $\mu^+$) and $\sigma$($W^-$ $\rightarrow$ $\mu^-$).
We present measurements of azimuthal correlations of charged hadron pairs in $\sqrt{s_{_{NN}}}=200$ GeV Au$+$Au collisions after subtracting an underlying event using a model that includes higher-order azimuthal anisotropy $v_2$, $v_3$, and $v_4$. After subtraction, the away-side ($\Delta\phi\sim\pi)$ of the highest transverse-momentum trigger ($p_T>4$ GeV/$c$) correlations is suppressed compared to that of correlations measured in $p$$+$$p$ collisions. At the lowest associated particle $p_T$, the away-side shape and yield are modified. These observations are consistent with the scenario of radiative-jet energy loss. For the lowest-$p_T$ trigger correlations, an away-side yield exists and we explore the dependence of the shape of the away-side within the context of an underlying-event model. Correlations are also studied differentially versus event-plane angle $\Psi_n$. The angular correlations show an asymmetry when selecting the sign of the trigger-particle azimuthal angle with respect to the $\Psi_2$ event plane. This asymmetry and the measured suppression of the pair yield out of plane is consistent with a path-length-dependent energy loss. No $\Psi_3$ dependence can be resolved within experimental uncertainties.
Higher-order flow harmonics for charged hadrons at midrapidity in Au$+$Au collisions at $\sqrt{s_{NN}}$ and their systematics: $v_2$, $v_3$, $v_4$, and $v_4\{\Psi_2\}$. The source of systematic uncertainties are difference among RXN event-planes, matching cut width for CNT hadron tracks, and difference between $v_n$ measured with RXN and BBC event planes .
Per-trigger yields $Y(\Delta\phi)$ of dihadrons pairs measured in Au$+$Au collisions at$\sqrt{s_{NN}}$ after subtracting the underlying event model with several $p_T$ selections and centralities. Systematic uncertainties are due to track matching and the $v_n$ and due to ZYAM.
Per-trigger yields $Y(\Delta\phi)$ of dihadron pairs measured in Au$+$Au collisions after subtracting the underlying event-model with several $p_T$ selections of the trigger and associated particles ($p_T^{t,a}$ and several centralities. Systematic uncertainties are due to track matching and the $v_n$ and due to ZYAM.
We present measurements of two-particle angular correlations between high-transverse-momentum ($2<p_T<11$ GeV/$c$) $\pi^0$ observed at midrapidity ($|\eta|<0.35$) and particles produced either at forward ($3.1<\eta<3.9$) or backward ($-3.7<\eta<-3.1$) rapidity in $d$$+$Au and $p$$+$$p$ collisions at $\sqrt{s_{_{NN}}}=200$ GeV. The azimuthal angle correlations for particle pairs with this large rapidity gap in the Au-going direction exhibit a ridge-like structure that persists up to $p_T{\approx}6$ GeV/$c$ and which strongly depends on collision centrality, which is a similar characteristic to the hydrodynamical particle flow in A+A collisions. The ridge-like structure is absent in the $d$-going direction as well as in $p$$+$$p$ collisions, in the transverse-momentum range studied. The results indicate that the ridge-like structure is shifted in the Au-going direction toward more central collisions, similar to the charged-particle pseudorapidity distributions.
Fourier fit coefficients for CNT-MPCS (Au-going) correlations, as a function of collision system and $\pi^0$ $p_T$: (a) the negative of the dipole coefficient, $-c_1$; (b) the quadrupole coefficient $c_2$; (c) the ratio ${-c_2}/{c_1}$.
Fourier fit coefficients for CNT-MPCS (Au-going) correlations, as a function of collision system and $\pi^0$ $p_T$: Fractional systematic uncertainty on the quadrupole coefficient $c_2$ for $d$+Au.
Fourier fit coefficients for CNT-MPCS (Au-going) correlations, as a function of collision system and $\pi^0$ $p_T$: Fractional systematic uncertainty on the quadrupole coefficient $c_2$ for $p$+$p$.
We present measurements of the transverse-momentum dependence of elliptic flow $v_2$ for identified pions and (anti)protons at midrapidity ($|\eta|<0.35$), in 0%--5% central $p$$+$Au and $^3$He$+$Au collisions at $\sqrt{s_{_{NN}}}=200$ GeV. When taken together with previously published measurements in $d$$+$Au collisions at $\sqrt{s_{_{NN}}}=200$ GeV, the results cover a broad range of small-collision-system multiplicities and intrinsic initial geometries. We observe a clear mass-dependent splitting of $v_2(p_{T})$ in $d$$+$Au and $^3$He$+$Au collisions, just as in large nucleus-nucleus ($A$$+$$A$) collisions, and a smaller splitting in $p$$+$Au collisions. Both hydrodynamic and transport model calculations successfully describe the data at low $p_T$ ($< 1.5$ GeV/$c$), but fail to describe various features at higher $p_T$. In all systems, the $v_2$ values follow an approximate quark-number scaling as a function of the hadron transverse kinetic energy per constituent quark($KE_T/n_q$), which was also seen previously in $A$$+$$A$ collisions.
Values of $v_2$($p_T$) for kaons in central 0-5% $p$+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV.
Values of $v_2$($p_T$) for kaons in central 0-5% $^3$He+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV.
Transverse momentum dependence of $v_2$ for identified pions and protons within $|\eta|$ < 0.35 in 0-5% central $p$+Au collisions.
The PHENIX experiment at the Relativistic Heavy Ion Collider has measured the differential cross section of $\phi$(1020) meson production at forward rapidity in $p$$+$$p$ collisions at $\sqrt{s}=$510 GeV via the dimuon decay channel. The integrated cross section in the rapidity and $p_T$ ranges $1.2<|y|<2.2$ and $2<p_T<7$ GeV/$c$ is $\sigma_\phi=2.79 \pm 0.20\,{\rm (stat)} \pm 0.17\,{\rm (syst)} \pm 0.34\, {\rm (norm)} \times 10^{-2}$~mb. The energy dependence of $\sigma_\phi$ ($1.2<|y|<2.2$; $2<p_T<5$ GeV/$c$) is studied using the PHENIX measurements at $\sqrt{s}=$200 and 510 GeV and the Large-Hadron-Collider measurements at $\sqrt{s}=$2.76 and 7 TeV. The experimental results are compared to various event generator predictions (pythia6, pythia8, phojet, ampt, epos3, and epos-lhc).
The $\phi$-meson-production cross section d$\sigma_{\phi}$/dy in $p$ + $p$ collisions at $\sqrt{s}$ = 510 GeV integrated in the transverse-momentum range 2 < $p_T$ < 7 GeV/$c$.
The $\phi$-meson-production cross section d$\sigma_{\phi}$/dy in $p$ + $p$ collisions at $\sqrt{s}$ = 510 GeV integrated in the transverse-momentum range 2 < $p_T$ < 7 GeV/$c$.
The $\phi$-meson-differential-production cross section d${}^{2}$$\sigma_{\phi}/dp_T dy$ for 1.2 < |y| < 2.2 in $p$ + $p$ collisions at $\sqrt{s}$ = 510 GeV.
We present a detailed measurement of charged two-pion correlation functions in 0%-30% centrality $\sqrt{s_{_{NN}}}=200$ GeV Au$+$Au collisions by the PHENIX experiment at the Relativistic Heavy Ion Collider. The data are well described by Bose-Einstein correlation functions stemming from L\'evy-stable source distributions. Using a fine transverse momentum binning, we extract the correlation strength parameter $\lambda$, the L\'evy index of stability $\alpha$ and the L\'evy length scale parameter $R$ as a function of average transverse mass of the pair $m_T$. We find that the positively and the negatively charged pion pairs yield consistent results, and their correlation functions are represented, within uncertainties, by the same L\'evy-stable source functions. The $\lambda(m_T)$ measurements indicate a decrease of the strength of the correlations at low $m_T$. The L\'evy length scale parameter $R(m_T)$ decreases with increasing $m_T$, following a hydrodynamically predicted type of scaling behavior. The values of the L\'evy index of stability $\alpha$ are found to be significantly lower than the Gaussian case of $\alpha=2$, but also significantly larger than the conjectured value that may characterize the critical point of a second-order quark-hadron phase transition.
Example fits of Bose-Einstein correlation functions of (a) $\pi^{-}\pi^{-}$ pair with $m_{T}$ between 0.331 and 0.349 GeV/$c^2$ and of (b) $\pi^{+}\pi^{+}$ pair with $m_T$ between 0.655 and 0.675 GeV/$c^2$, as a function $Q$ ≡ |$q_{LCMS}$|, defined in Eq. (26). Both fits show the measured correlation function and the complete fit function (described in VI A), while a Bose-Einstein fit function $C^{(0)}_{2} (Q)$ is also shown, with the Coulomb-corrected data, i.e. the raw data multiplied by $C^{(0)}_{2} (Q)/C_{2}(Q)$. In this analysis we measured 62 such correlation functions (for ++ and -- pairs, in 31 $m_T$ bins), and fitted all of them with the method described in VIA. The first visible point on both panels corresponds to $Q$ values below the accessible range (based on an evaluation of the two-track cuts), these were not taken into account in the fitting.
Example fits of Bose-Einstein correlation functions of (a) $\pi^{-}\pi^{-}$ pair with $m_{T}$ between 0.331 and 0.349 GeV/$c^2$ and of (b) $\pi^{+}\pi^{+}$ pair with $m_T$ between 0.655 and 0.675 GeV/$c^2$, as a function $Q$ ≡ |$q_{LCMS}$|, defined in Eq. (26). Both fits show the measured correlation function and the complete fit function (described in VI A), while a Bose-Einstein fit function $C^{(0)}_{2} (Q)$ is also shown, with the Coulomb-corrected data, i.e. the raw data multiplied by $C^{(0)}_{2} (Q)/C_{2}(Q)$. In this analysis we measured 62 such correlation functions (for ++ and -- pairs, in 31 $m_T$ bins), and fitted all of them with the method described in VIA. The first visible point on both panels corresponds to $Q$ values below the accessible range (based on an evaluation of the two-track cuts), these were not taken into account in the fitting.
Correlation strength parameter $\lambda$ versus average $m_T$ of the pair, for 0%-30% centrality collisions. Statistical and systematic uncertainties are shown as bars and boxes.
Recently, multiparticle-correlation measurements of relativistic $p/d/^3$He$+$Au, $p$$+$Pb, and even $p$$+$$p$ collisions have shown surprising collective signatures. Here we present beam-energy-scan measurements of 2-, 4-, and 6-particle angular correlations in $d$$+$Au collisions at $\sqrt{s_{_{NN}}}$=200, 62.4, 39, and 19.6 GeV. We also present measurements of 2- and 4-particle angular correlations in $p$$+$Au collisions at $\sqrt{s_{_{NN}}}$=200 GeV. We find the 4-particle cumulant to be real-valued for $d$$+$Au collisions at all four energies. We also find that the 4-particle cumulant in $p$$+$Au has the opposite sign as that in $d$$+$Au, indicating that the correlations are geometrical and therefore collective in origin. Further we find that the 6-particle cumulant agrees with the 4-particle cumulant in $d$$+$Au collisions at 200 GeV, which indicates that nonflow effects are subdominant and provides strong evidence of collectivity.
Components $\langle\langle$4$\rangle\rangle$ and 2$\langle\langle$2$\rangle\rangle^{2}$ and cumulant $c_2${4} = $\langle\langle$4$\rangle\rangle$ - 2$\langle\langle$2$\rangle\rangle^{2}$ as a function of $N^{FVTX}_{tracks}$. (a) and (b) show the components and cumulant, respectively, in $p$+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV. (c) and (d) show the components and cumulant, respectively, in $d$+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV. (b) and (d) also show the cumulant as measured in AMPT for $p$+Au and $d$+Au, respectively, indicated by the green line. The shaded green band indicates the statistical uncertainty on the AMPT values.
Components $\langle\langle$4$\rangle\rangle$ and 2$\langle\langle$2$\rangle\rangle^{2}$ and cumulant $c_2${4} = $\langle\langle$4$\rangle\rangle$ - 2$\langle\langle$2$\rangle\rangle^{2}$ as a function of $N^{FVTX}_{tracks}$. (a) and (b) show the components and cumulant, respectively, in $p$+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV. (c) and (d) show the components and cumulant, respectively, in $d$+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV. (b) and (d) also show the cumulant as measured in AMPT for $p$+Au and $d$+Au, respectively, indicated by the green line. The shaded green band indicates the statistical uncertainty on the AMPT values.
$v_2${2}, $v_2${2, |$\Delta\eta$| > 2}, and $v_2${4} as a function of $N^{FVTX}_{tracks}$ in $d$+Au collisions with $\sqrt{s_{NN}}$= (a) 200 GeV, (b) 62.4 GeV, (c) 39 GeV, and (d) 19.6 GeV; also shown in (a) is $v_2${6} for $\sqrt{s_{NN}}$= 200 GeV. The arrowheads on the statistical uncertainties indicate cases where the standard 1$\sigma$ uncertainty on the $c_2${4} crosses zero. For 19.6 GeV, the combined confidence interval for $v_2${4} to be real is 79%.
During 2015 the Relativistic Heavy Ion Collider (RHIC) provided collisions of transversely polarized protons with Au and Al nuclei for the first time, enabling the exploration of transverse-single-spin asymmetries with heavy nuclei. Large single-spin asymmetries in very forward neutron production have been previously observed in transversely polarized $p$$+$$p$ collisions at RHIC, and the existing theoretical framework that was successful in describing the single-spin asymmetry in $p$$+$$p$ collisions predicts only a moderate atomic-mass-number ($A$) dependence. In contrast, the asymmetries observed at RHIC in $p$$+$$A$ collisions showed a surprisingly strong $A$ dependence in inclusive forward neutron production. The observed asymmetry in $p$$+$Al collisions is much smaller, while the asymmetry in $p$$+$Au collisions is a factor of three larger in absolute value and of opposite sign. The interplay of different neutron production mechanisms is discussed as a possible explanation of the observed $A$ dependence.
Forward neutron $A_N$ in $p$+$A$ collisions for $A$ = 1 ($p$), 27 (Al), and 197 (Au), for ZDC inclusive, ZDC $\otimes$ BBC-tag, and ZDC $\otimes$ BBC-veto triggered samples. The 3% scale uncertainty is from the polarization normalization uncertaintiy.
The cross section and transverse single-spin asymmetries of $\mu^{-}$ and $\mu^{+}$ from open heavy-flavor decays in polarized $p$+$p$ collisions at $\sqrt{s}=200$ GeV were measured by the PHENIX experiment during 2012 at the Relativistic Heavy Ion Collider. Because heavy-flavor production is dominated by gluon-gluon interactions at $\sqrt{s}=200$ GeV, these measurements offer a unique opportunity to obtain information on the trigluon correlation functions. The measurements are performed at forward and backward rapidity ($1.4<|y|<2.0$) over the transverse momentum range of $1.25<p_T<7$ GeV/$c$ for the cross section and $1.25<p_T<5$ GeV/$c$ for the asymmetry measurements. The obtained cross section is compared to a fixed-order-plus-next-to-leading-log perturbative-quantum-chromodynamics calculation. The asymmetry results are consistent with zero within uncertainties, and a model calculation based on twist-3 three-gluon correlations agrees with the data.
$A_N$ of negatively-charged muons from open heavy-flavor decays as a function of $p_T$ in the backward ($x_F$ < 0) and forward ($x_F$ > 0) regions.
$A_N$ of positively-charged muons from open heavy-flavor decays as a function of $p_T$ in the backward ($x_F$ < 0) and forward ($x_F$ > 0) regions.
$A_N$ of negatively-charged and positively-charged muons from open heavy-flavor decays as a function of $x_F$, where $x_F$ > 0 is along the direction of the polarized proton.
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