Heavy Ion results from RHIC-BNL

Recent results from heavy ion collision experiments from RHIC at BNL are presented and discussed in terms of Quark Gluon Plasm properties, such as partonic collectivity and partonic energy loss. The experimental results with direct photons and heavy quarks have given important additional insights of the plasma on top of what has been known with light hadrons. Higher order event anisotropies and the related results have provided the geometrical, temporal and dynamical information of the plasma. The beam energy dependence of the various measurements could reveal the structure of QCD phase diagram and possibly the critical point in the diagram, where the properties of phase transition are expected to change drastically.


Introduction
Quark Gluon Plasma (QGP), which is supposed to exist in early universe or inside neutron stars, is currently being studied with high energy nucleus-nucleus collisions at √ s NN = 200 AGeV in Relativistic Heavy Ion Collider (RHIC) at Brookhaven National Laboratory (BNL) and at 2.76 AT eV in Large Hadron Collider (LHC) at European Organization for Nuclear Study (CERN).A large elliptic event anisotropy and its quark number scaling as well as a large partonic energy loss of high p T hadrons and jets have been observed at RHIC energies and they are considered as possible indications of QGP.The properties of QGP at higher temperature region in QCD phase diagram are further investigated at the highest energy in the world at LHC, while the beam energy scan program is also in progress at RHIC in order to find a signature from the critical point, which is expected at higher density in the phase diagram.
The recent results from RHIC (STAR and PHENIX experiments) with direct photons and heavy quarks are discussed in Sect.2, the higher order event anisotropies and their related topics are discussed in Sect.3 and some selected results from beam energy scan program are discussed in Sect.4.

Plasma properties probed by direct photons and heavy quarks
Jet quenching and large elliptic flow of hadrons are the two major discoveries as signatures of QGP at RHIC experiments, several controlled measurements have provided further insights of the discoveries using the penetrating probes like direct photons and leptons as well as with a e-mail: esumi.shinichi.gn@u.tsukuba.ac.jp  d+Au collisions to disentangle the possible additional effect from the cold nuclear matter.Striking difference between strong suppression of π 0 and no suppression of direct γ are shown in the top panel of Fig. 1, which are attributed to the large energy loss of parton inside QGP and the penetration of high p T direct prompt γ from the initial hard scattering.The high p T direct γ is used as trigger particle to study the correlated hadron distribution in opposite azimuthal angle region with respect to the triggered direct γ, where the penetration property of direct γ provides a measure of initial energy of recoil jet, which is observed as the correlated final hadrons, therefore this gives us the modification of the fragmentation function of jet inside the QGP.The presented I AA data in the bottom panel of Fig. 1 show a suppression of fragmentation function at high p T and an enhancement at low p T especially at wide angle, which tells us the partonic energy loss and re-distribution of lost energy.
On the other hand at low p T region, direct thermal γ from the hot and dense matter have been clearly observed to be enhanced in heavy ion collision above the QCD prompt γ expected from the measured p+p data as shown in left panel of Fig. 2. The measured temperature of thermal γ is slightly above the expected phase transition temperature, however the extracted initial temperature from this measurement can be much higher according to the extrapolation by hydro-dynamic calculation.The difference of elliptic event anisotropy parameters v 2 between π 0 and inclusive γ, shown in the right-top panel of Fig. 2, as well as the relative direct γ yield over total inclusive γ, have been used to extract the elliptic event anisotropy v 2 of direct γ as shown in the right-bottom panel of Fig. 2. The high p T direct γ v 2 is small as expected from the penetration property (R AA ∼ 1) of direct prompt γ at high p T , however v 2 of direct thermal γ at low p T has been found to be comparable to the hadron v 2 .This would tell us the thermal photons are dominated from the later stage of collision, after the elliptic expansion has already been developed, surprisingly without any significant contribution from the early stage.heavy quarks, the strongly interacting sQGP is considered as the property of the hot and dense matter created at RHIC energy.However, since the J/ψ v 2 is found to be much smaller than the light hadrons and open-charms, the recombination scenario for J/ψ production is disfavored at RHIC energies, which could be different with enhanced charm production at LHC energies.

Higher order event anisotropy and related topics
The higher order event anisotropy is supposed to be originated from the initial geometrical shape of the participants region, where the initial overlapped region is mainly dominated as elliptic shape in an non-central heavy ion collision, while the higher harmonic order anisotropies also arise in a central collision, because of statistical fluctuation of initial participant positions followed by hydro-dynamic expansion of the system.Simultaneous description of different order event anisotropies have been found to give a good constraint on determining the hydro-dynamic properties like share viscosity over entropy ratio such as η/S as well as initial conditions like the shape of initial energy density distribution.The measured higher order event anisotropy parameters v  the quark number scaled v n are shown as a function of the quark number scaled transverse kinetic energy, the v n differences in hadron mass and the number of constituent quarks as a function of p T are found to be scaled and minimized for each harmonic order as seen in the Fig. 4, which could be taken as an indication that the higher order harmonic collectivity is already formed during the prehadronic quark phase at top RHIC energy.
The higher order event anisotropy signals v n define the higher order event planes direction Ψ n for each harmonic order, the higher order event plane angles Ψ n have been utilized to measure the geometrical event shape of QGP at the end of freeze-out stage via two-particle quantum interferometry method called as HBT.The measured two transverse sizes as a function of the azimuthal pair angle with respect to the higher order event planes Ψ 2 and Ψ 3 are shown in Fig. 5 for both sideward and outward directions as explained in the figure caption.The phase and magnitude of the measured of oscillation would tell us the orientation and the eccentricity for the 2nd order (the triangularity for the 3rd order) of the geometrical shape with respect to the defined event planes.The measured orientation indicates that the major axis of elliptic event shape is still perpendicular to the reaction plane, even after the strong elliptic expansion in the minor axis from the pressure gradient of initial elliptic density distribution.The similar effects can been seen for the 3rd order plane Ψ 3 dependence.It is also remarkable to observe that the outward radii, which are considered to include the both depth and temporal spread of the freeze-out region, show larger amplitude of oscillation than the sideward radii in central Au+Au collisions at 200 GeV.
The higher order event planes are also used to test the geometrical dependence of jet-medium interaction with two-particle jet-like azimuthal distribution.The twoparticle distributions are separated by the azimuthal angle of trigger particle with respect to the higher order event plane angle Ψ n , the distributions are corrected for the back ground expected from the single particle flow correlation with event planes and the back ground subtracted distributions are shown in Fig. 6 for Ψ 2 dependences in the top panels and for Ψ 3 dependences in the bottom panels.The extracted trigger-associate correlations show rather strong Ψ 2 dependences and left-right asymmetry but weak Ψ 3 dependences.This indicates that there is strong interplay between the jet-medium interaction and elliptic event geometry and/or elliptic expansion.

Beam energy scan program and critical point
Significant high p T suppression of hadron has been observed at Au+Au √ s NN = 200 AGeV, which is taken as an indication of possible QGP signature as partonic energy loss, while the suppression has not been seen at SPS energy around 20 AGeV.Therefore the beam energy scan program has been carried out at RHIC in order to find the onset of suppression as well as any other possible indication of phase transition.The beam energy dependence of charged particle R CP from 7.7 AGeV up to 200 AGeV as a function of p T are presented in Fig. 7.The R CP extracted from central-peripheral ratio clearly shows a strong energy dependence, where the suppression pattern seen in the highest RHIC beam energy changes into the enhance- Figure 8. Beam energy dependence of products of higher moments (top: skewness times sigma, middle: kurtosis times sigma squared, bottom: normalized skewness times sigma relative to the Poisson expectation), where the higher moments are measured by multiplicity distribution of net-proton [7] ment pattern at the low RHIC beam energy.The crossing point from suppression to enhancement is found be around 30 AGeV, where the QGP phase transition could have been occurred, although the transition seems to be gradually monotonic.
The critical point is expected on the QCD phase diagram along the phase boundary, which is somewhat away from the temperature axis into the high density region.However the exact location of the point is not well known, 02007-p.5 Figure 9. Beam energy dependence of v 1 slope with respect to the normalized rapidity for protons, anti-protons and π − in the top panel and for p-pbar in the bottom panel [7] this is also one of the reason of the RHIC beam energy scan program in order to find the existence and the location of the critical point on the phase diagram.The fluctuation of the conserved quantities is suggested as a signal from the critical point, because the correlation length would diverge so that the fluctuation could increase, if the system is very close to the critical point.The high density side of phase boundary beyond the critical point is also expected to be the 1st order (discrete) phase transition in stead of 2nd order (cross over) transition at the low density side close to the temperature axis.The net-proton multiplicity distribution as a measure of conserved net-baryon number is experimentally measured and the higher order moments of the multiplicity distribution are extracted, the products of 2nd (σ: sigma), 3rd (S : skewness) and 4th (κ: kurtosis) order moments are shown in Fig. 8 as a function of beam energy, where the bottom panel is normalized by the expected signal from Poisson fluctuation.There might be some indication of possible non-monotonic behavior around 20 ∼ 30 GeV, however the signal is not yet significant enough to claim the signal from the critical point.
The directed event anisotropy v 1 of protons and antiprotons and their slopes with respect to normalized rapidity dv 1 /dy would reflect the ratio of system compression between transverse and longitudinal directions as well as the system response, therefore the beam energy dependence of the v 1 slope dv 1 /dy is expected to provide a sensitivity on the property of high density matter.The measured v 1 slopes dv 1 /dy from the RHIC beam energy scan are shown in the top panel of Fig. 9 for proton, anti-proton and π − .Since the energy dependence of baryon stopping and transport would play an important role in this measurement, the net-proton data are also shown in the bottom panel of Fig. 9, where there could be an indication of non-monotonic behavior around 10 ∼ 30 GeV, which may be related with the critical point, while there could also be other possible scenarios to explain the observed dependence.

Summary and conclusion
Recent results about the property of hot and dense matter created in high energy heavy ion collisions from RHIC experiments are presented.The several indications of quark gluon plasma have been observed such as partonic collectivity and partonic energy loss especially with probes of direct photons and heavy quarks.Higher order anisotropy and related topics are also shown in order to discuss the geometrical, temporal and dynamical information of QGP.The RHIC beam energy scan program and several selected results are presented with some possible indications of phase transition close to the critical point near the phase boundary.

Figure 1 .
Figure 1.Top: π 0 and direct γ nuclear modification factor R AA as a function of transverse momentum p T in central Au+Au collisions at √ s NN = 200 AGeV [1, 2].Bottom: Ratio I AA Au+Au over p+p, for associate hadron yield per trigger direct γ as a function of z T , which is defined as hadron p T relative to the trigger direct γ p T [3].

Figure 2 .
Figure 2. Left: Direct γ p T spectra at p+p and Au+Au at 200 GeV [4].Right-top: π 0 and inclusive γ v 2 and Right-bottom: direct γ elliptic event anisotropy parameter v 2 as a function of p T in minimum bias Au+Au collisions [5].

R
AA and v 2 of single electron from heavy quarks are shown in left panel of Fig.3.These data indicate that heavy quarks, which are dominated by charm quarks at low p T and bottom quarks at high p T , have similar partonic energy loss and similar elliptic expansion comparable to the other light quarks such as up, down and strangeness quarks in spite of the quite large mass difference.This has been confirmed by the suppression of directly reconstructed Dmeson as shown in right-top panel of Fig.3.Because of these observations of energy loss and collective flow of 02007-p.2

Figure 3 .
Figure 3. Left: R AA and v 2 of single electron from heavy quarks as a function of p T at 200 GeV Au+Au collisions [6] Right-top: D-meson R AA and Right-bottom: J/ψ v 2 as a function of p T at 200 GeV Au+Au collisions[7]

Figure 5 .
Figure 5. Extracted sideward size (left: perpendicular to the pair direction) and outward size (right: parallel to the pair direction) in transverse radius of QGP at freeze-out from two-particle interferometry measurement as a function of azimuthal angle of the pair with respect to the elliptic event plane Ψ 2 and the triangular event plane Ψ 3 .The average radii are fixed at 10 f m 2 and 5 f m 2 , respectively [3].

Figure 7 .
Figure 7. Beam energy dependence of nuclear modification factor R CP measured via central-peripheral yield ratio for charged particles as a function of p T[7]