soft physics at rhic · 2018-02-23 · star, aps2013 phenix, rhic&ags users meeting. h. masui,...
TRANSCRIPT
H. Masui, KPS, Nov/1/2013 /20
Soft physics at RHIC
Hiroshi Masui, University of Tsukuba !Fall KPS meeting, Nov. 2013
!1H. Masui, KPS, Nov/1/2013 /20
/20H. Masui, KPS, Nov/1/2013
RHIC heavy ion collisions
!2
√sNN (GeV) 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012
200
130
62.4
39
27
22.5
19.6
11.5
7.7
5.0
Au+Au Cu+Cu d+Au U+U & Cu+Au
STAR only
Test run
/20H. Masui, KPS, Nov/1/2013
RHIC heavy ion collisions
!2
√sNN (GeV) 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012
200
130
62.4
39
27
22.5
19.6
11.5
7.7
5.0
Au+Au Cu+Cu d+Au U+U & Cu+Au
STAR only
Test run
• Variety of collision systems (d to U), wide range (5-200 GeV) of collision energies
/20H. Masui, KPS, Nov/1/2013
RHIC heavy ion collisions
!2
√sNN (GeV) 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012
200
130
62.4
39
27
22.5
19.6
11.5
7.7
5.0
Au+Au Cu+Cu d+Au U+U & Cu+Au
STAR only
Test run
• Variety of collision systems (d to U), wide range (5-200 GeV) of collision energies
• QGP properties at top RHIC energy
/20H. Masui, KPS, Nov/1/2013
RHIC heavy ion collisions
!2
√sNN (GeV) 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012
200
130
62.4
39
27
22.5
19.6
11.5
7.7
5.0
Au+Au Cu+Cu d+Au U+U & Cu+Au
STAR only
Test run
• Variety of collision systems (d to U), wide range (5-200 GeV) of collision energies
• QGP properties at top RHIC energy
• Search for QCD critical point & phase boundary by Beam Energy Scan (BES) program phase-I
/20H. Masui, KPS, Nov/1/2013
RHIC heavy ion collisions
!2
√sNN (GeV) 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012
200
130
62.4
39
27
22.5
19.6
11.5
7.7
5.0
Au+Au Cu+Cu d+Au U+U & Cu+Au
STAR only
Test run
• Variety of collision systems (d to U), wide range (5-200 GeV) of collision energies
• QGP properties at top RHIC energy
• Search for QCD critical point & phase boundary by Beam Energy Scan (BES) program phase-I
Study structure of QCD phase diagram
/20H. Masui, KPS, Nov/1/2013
Multi-particle correlations
• Powerful tools to study the bulk properties of the system ‣ Azimuthal anisotropy !
!
‣ Femtoscopy (identical bosons) !
‣ Conserved charge fluctuations !
!
• I’m going to review the recent correlation measurements from RHIC
!3
Initial geometry (+fluctuations), shear viscosity !Local parity violation, chiral magnetic effect
Source size, geometrical anisotropy at freeze-out
Susceptibility, QCD critical point
/20H. Masui, KPS, Nov/1/2013
PHENIX
• Fast triggers ‣ Hard probes by electrons &
photons
• TOF + EMC + Aerogel ‣ hadrons
• Forward beam counters (BBC, MPC, RXN)
‣ support measurements of azimuthal anisotropy
‣ large pseudorapidity gap reduces ‘non-flow’ effects
• VTX, FVTX ‣ heavy flavors
!4
/20H. Masui, KPS, Nov/1/2013
STAR
• Large acceptance - Time Projection Chamber (TPC)
• PID capabilities have been (will be) significantly improved ‣ TOF (2009-) - charged hadrons ‣ MTD (2013-) - muons ‣ HFT (from 2014) - heavy flavors
!5
Heavy Flavor Tracker
Muon Telescope Detector
Time Of Flight
Time Projection Chamber
/20H. Masui, KPS, Nov/1/2013
Azimuthal anisotropy
!6
React
ion
plan
e ΨRP
XZ
Y Px
Py
Pz
coordinate space momentum space
/20H. Masui, KPS, Nov/1/2013
12
Central-forward (d-going side)
When correlated with d-going side, there is no local maximum in
correlations at ∆φ ~0
The correlation is dominate by c
1
contribution
13
Central-backward (Au-going side) When correlated with
Au-going side, there is significant correlations
at ∆φ ~0
The nearside correlation decreases when moving to peripheral d+Au collisions
c1 and c
2 are comparable
in central d+Au collisions
12
Central-forward (d-going side)
When correlated with d-going side, there is no local maximum in
correlations at ∆φ ~0
The correlation is dominate by c
1
contribution
12
Central-forward (d-going side)
When correlated with d-going side, there is no local maximum in
correlations at ∆φ ~0
The correlation is dominate by c
1
contribution
5
FIG. 2: (color online) Sample comparison of Y (∆φ) and∆Y (∆φ) for same and oppositely charged pairs for 1.25 <paT < 1.5 GeV/c and 0.48 < |∆η| < 0.7. The symbols, curve,and shaded band are as described in the Fig. 1 caption.
peak. To assess the systematic influence of any residualunmodified jet correlations, we analyzed charge-selectedcorrelations. Charge-ordering is a known feature of jetfragmentation which leads to enhancement of the jet cor-relation in opposite-sign pairs, and suppression in like-sign pairs, in the near side peak (e.g. Ref. [24]). A rep-resentative pT selection of Y (∆φ) and ∆Y (∆φ) distribu-tions are shown in Fig. 2, where all charge combinationsexhibit a significant cos 2∆φmodulation. The magnitudeof the modulation is larger in the opposite-sign case, indi-cating some residual unmodified jet correlation contribu-tion. We also varied the |∆η| window which changes theresidual jet contribution. Both of these cross-checks areused to estimate the systematic uncertainty, as discussedlater.In order to quantify the relative amplitude of the az-
imuthal modulation we define cn ≡ an/ (bcZYAM + a0)where bcZYAM is bZYAM in central events. This quantity isshown as a function of associated pT in Fig. 3 for central(0–5%) collisions.The centrality dependence will be analyzed in further
detail in a forthcoming publication, though we note thatwe have observed a signal of similar magnitude for the0–20% most central collisions. The ATLAS c2 results [9]have a qualitatively similar paT dependence, but with asignificantly smaller magnitude. However, it must benoted that the c2 values from PHENIX and ATLAS arenot directly comparable since c2 is a function of the pTof both particles and the trigger particle pT range is notidentical in the two analyses. ATLAS has also used amuch larger ∆η separation between the particles.The c3 values, shown in Fig. 3, are small relative to c2.
Fitting the c3 data to a constant yields (6±4)×10−4 witha χ2/dof of 8.4/7 (statistical uncertainties only). Thecurrent precision is inadequate to reveal the existence ofa significant c3 signal.In p+Pb collisions the signal is seen in long range ∆η
FIG. 3: (color online) The nth-order pair anisotropy, cn, ofthe central collision excess as a function of associated par-ticle paT . PHENIX (filled [red] circles) c2 and (open [black]circles) c3 are for 0.5 < ptT < 0.75 GeV/c, 0.48 < |∆η| < 0.7and ATLAS (filled [green] squares) c2 [9] are for 0.5 < ptT <4.0 GeV/c, 2 < |∆η| < 5.
FIG. 4: (color online) Charged hadron second-orderanisotropy, v2, as a function transverse momentum for (filled[blue] circles) PHENIX and (open [black] circles) ATLAS [9].Also shown are a hydrodynamic calculation [14, 25] for (up-per [blue] curve) d+Au collisions at
√sNN
= 200 GeVand (lower [black] curve) 0–4% central p+Pb collisions at√sNN
= 4.4 TeV.
correlations. Here, signal is measured at midrapidity,but it is natural to ask if previous PHENIX rapidity sep-arated correlation measurements [18] would have beensensitive to a signal of this magnitude, if it is present.The maximum c2 observed here is approximately a 1%modulation about the background level. Overlaying amodulation of this size on the conditional yields shown inFig. 1 of Ref. [18] shows that the modulation on the near
Flow in d+Au ?
• Large v2 in 0-5% d+Au collisions at √sNN = 200 GeV
• Near side correlation in 0-5% on Au-going side ‣ No near side peak on d-going side ‣ Need to understand away side jet contributions to extract vn
• Interesting to see the centrality dependence ‣ (Two-particle) non-flow scales like 1/N
!7
|Δη|=0.48-0.7 Δη>3PHENIX, arXiv:1303.1794v1 [nucl-ex]
12
Central-forward (d-going side)
When correlated with d-going side, there is no local maximum in
correlations at ∆φ ~0
The correlation is dominate by c
1
contribution
12
Central-forward (d-going side)
When correlated with d-going side, there is no local maximum in
correlations at ∆φ ~0
The correlation is dominate by c
1
contribution
PHENIX, IS2013
/20H. Masui, KPS, Nov/1/2013
Geometry control
• Test the relation between initial geometry and final momentum anisotropy
‣ Achieve higher density in deformed collisions with the same energy ‣ Path length dependence ‣ Finite odd harmonics from geometry overlap ‣ Control magnetic field (test chiral magnetic effect)
!8
Collisions with deformed nuclei; U+ U Asymmetric collisions; Cu + Au
body-body collision
tip-tip collision* Average deformation of Uranium ~ 28% Cu ~ 16%, Au ~ -13%
/20H. Masui, KPS, Nov/1/2013
0.0 0.5 1.0 1.5 2.0 2.5 3.0
0.0
0.1
0.2
0.3
0.4(a)30-40%
)1,SMDΨ (1v
0.5 1.0 1.5 2.0 2.5 3.0
0.0
0.1
0.2
0.3
0.4
0.0
0.1
0.2
0.3
0.4(b)40-50%
0.0
0.1
0.2
0.3
0.4
0.0 0.5 1.0 1.5 2.0 2.5 3.0
(c)50-60%
0.0
0.1
0.2
0.3
0.4
0.5 1.0 1.5 2.0 2.5 3.00.0
0.1
0.2
0.3
0.4(d)30-60%
= 200 GeVNNsCu+Au
(GeV/c)T
p (GeV/c)T
p
x 1
01v
x 1
01v
Use of normalized multiplicity cancels out multiplicity independent efficiency
Can!we!see!a!difference!between!Au+Au!and!U+U?!
• The!U+U!v2!shows!a!stronger!mulBplicity!dependence.!• A linear fit for v2, the slope parameter!• The!differences!in!the!slope!parameters!between!Au+Au!
and!U+U!increase!in!more!central!collisions!• Compare!with!eccentricity!calculated!from!glauber!
simulaBons(!scaled!down!0.2!for!UU!and!0.25!for!AuAu!!!!!!!to!match!the!experimental!v2!)!
STAR!Preliminary!
STAR!Preliminary!
zdc (%)-110 1
Slop
e
-0.06
-0.04
-0.02
0
U+U dataAu+Au data
U+U glauberAu+Au glauber
Slope parameter
13!Zero!Degree!Calorimeter!(ZDC)were!used!to!trigger!on!spectator!neutrons!
Multiplicity/<Multiplicity>0.9 1 1.1 1.2
0.01
0.02
0.03
0.04
v2
O2.76eO02!+/O!5.34eO04!
Multiplicity/<Multiplicity>0.9 1 1.1 1.2
0.01
0.02
0.03
0.04
v2 O2.25eO02!+/O!9.76eO04!
U+U!
Au+Au!
STAR!Preliminary!
1%!ZDC!Centrality!
Results
• v2 slope shows clear difference between Au+Au and U+U ‣ super central U+U could enhance tip-tip collisions
• Large v1 @ mid-rapidity in Cu+Au (not observed in Au+Au) ‣ also for pions. Need more statistics for protons
!9
Slope of v2 for multiplicity dependence
Centrality percentile by ZDC0.1% most central
√sNN = 193 GeV
STAR Preliminary
STAR, APS2013
PHENIX, RHIC&AGS users meeting
/20H. Masui, KPS, Nov/1/2013
Break down of NCQ scaling
• Number of Constituent Quark scaling of v2 ‣ Indication of deconfinement at early stage of heavy ion collisions
• Meson-baryon splitting at 62.4 GeV - NCQ scaling of v2 ‣ No difference between particles and anti-particles
• Meson-baryon splitting is gone at 11.5 GeV
• NCQ scaling is broken between particles and anti-particles
!10
While in Auþ Au collisions atffiffiffiffiffiffiffiffisNN
p ¼ 200 GeV asingle NCQ scaling can be observed for particles andantiparticles, the observed difference in v2 at lower beamenergies demonstrates that this common NCQ scaling ofparticles and antiparticles splits. Such a breaking of theNCQ scaling could indicate increased contributions fromhadronic interactions in the system evolution with decreas-ing beam energy. The energy dependence of v2ðXÞ %v2ð !XÞ could also be accounted for by considering anincrease in nuclear stopping power with decreasing
ffiffiffiffiffiffiffiffisNN
pif the v2 of transported quarks (quarks coming from theincident nucleons) is larger than the v2 of produced quarks[25,26]. Theoretical calculations [27] suggest that thedifference between particles and antiparticles could beaccounted for by mean field potentials where the K% and!p feel an attractive force while the Kþ and p feel arepulsive force.
Most of the published theoretical calculations can repro-duce the basic pattern but fail to quantitatively reproducethe measured v2 difference [25–28]. So far, none of thetheory calculations describes the observed ordering ofthe particles. Therefore, more accurate calculations fromtheory are needed to distinguish between the differentpossibilities. Other possible reasons for the observationthat the !% v2ðpTÞ is larger than the !þ v2ðpTÞ is theCoulomb repulsion of !þ by the midrapidity net protons(only at low pT) and the chiral magnetic effect in finitebaryon-density matter [29]. Simulations have to be carriedout to quantify if those effects can explain ourobservations.In Ref. [21], the study of the centrality dependence of
"v2 for protons and antiprotons is extended to investigateif different production rates for protons and antiprotons asa function of centrality could cause the observed differ-ences. It was observed that the differences, "v2, aresignificant at all centralities.The v2ðmT %m0Þ and possible NCQ scaling was also
investigated for particles and antiparticles separately.Figure 3 shows v2 as a function of the reduced transversemass, (mT %m0), for various particles and antiparticles atffiffiffiffiffiffiffiffisNN
p ¼ 11:5 and 62.4 GeV. The baryons and mesons areclearly separated for
ffiffiffiffiffiffiffiffisNN
p ¼ 62:4 GeV at ðmT %m0Þ>1 GeV=c2. While the effect is present for particles atffiffiffiffiffiffiffiffisNN
p ¼ 11:5 GeV, no such separation is observed forthe antiparticles at this energy in the measured (mt %m0)range up to 2 GeV=c2. The lower panels of Fig. 3 depictthe difference of the baryon v2 relative to a fit to the mesonv2 data with the pions excluded from the fit. The antipar-ticles at
ffiffiffiffiffiffiffiffisNN
p ¼ 11:5 GeV show a smaller differencecompared to the particles. At
ffiffiffiffiffiffiffiffisNN
p ¼ 11:5 GeV thedifference becomes negative for the antiparticles at(mT %m0)<1 GeV=c2 but the overall trend is still similarto the one of the particles and to
ffiffiffiffiffiffiffiffisNN
p ¼ 62:4 GeV.
0
0.1
0.211.5 GeV (a)
pΛ
-Ξ-Ω
+π+K
s0K
φ
0 1 2 3-0.05
0
0.05
62.4 GeV (b)
Au+Au, 0%-80%
0 1 2 3
0-mTm
11.5 GeV (c)
pΛ
+Ξ
+Ω
-π-
K
s0K
φ
0 1 2 3)2
62.4 GeV (d)
-sub EPη
0 1 2 3
2v(B
)-fit
2v
(GeV/c
FIG. 3 (color online). The upper panels depict the elliptic flow v2 as a function of reduced transverse mass (mT %m0) for particles,(a) and (b), and antiparticles, (c) and (d), in 0%–80% central Auþ Au collisions at
ffiffiffiffiffiffiffiffisNN
p ¼ 11:5 and 62.4 GeV. Simultaneous fits tothe mesons except the pions are shown as the dashed lines. The difference of the baryon v2 and the meson fits are shown in the lowerpanels.
(GeV)NNs0 20 40 60
)X( 2
(X)-
v2v
0
0.02
0.04
0.06 Au+Au, 0%-80%-sub EPη
+Ξ--Ξ
pp-Λ-Λ
--K+K-π-+π
FIG. 2 (color online). The difference in v2 between particles(X) and their corresponding antiparticles ( !X) (see legend) as afunction of
ffiffiffiffiffiffiffiffisNN
pfor 0%–80% central Auþ Au collisions. The
dashed lines in the plot are fits with a power-law function. Theerror bars depict the combined statistical and systematic errors.
PRL 110, 142301 (2013) P HY S I CA L R EV I EW LE T T E R Sweek ending5 APRIL 2013
142301-5
STAR PRL110, 143201 (2013), PRC88, 014902 (2013)
/20H. Masui, KPS, Nov/1/2013
Femtoscopy!11
A charge-coupled device camera images thegas from a direction perpendicular to the axialdirection (z) of the trap and parallel to theapplied magnetic field direction (y). The smallrepulsive potential induced by the high-fieldmagnet is along the camera observation axisand does not affect the images. The remainingattractive potential has cylindrical symmetryand corresponds to a harmonic potential with anoscillation frequency for 6Li of 20 Hz at 910 G.Resonant absorption imaging is performed on acycling transition at a fixed high magnetic fieldby using a weak (I/Isat ! 0.05), 20-"s probelaser pulse that is #– polarized with respect tothe y axis. Any residual #$ component is re-jected by an analyzer. At 910 G, the transitionsoriginating from the two occupied spin statesare split by 70 MHz and are well resolvedrelative to the half-linewidth of 3 MHz, permit-ting precise determination of the column den-sity and hence the number of atoms per state.The magnification is found to be 4.9 % 0.15 bymoving the axial position of the trap through0.5 mm with a micrometer. The net systematicerror in the number measurement is estimatedto be –6%
$10% (26). The spatial resolution is esti-mated to be &4 "m by quadratically combiningthe effective pixel size, 13.0 "m/4.9, with theaperture-limited spatial resolution of &3 "m.
Figure 1 shows images of the anisotropicexpansion of the degenerate gas at varioustimes t after release from full trap depth. Thegas rapidly expands in the transverse direction(Fig. 2A) while remaining nearly stationary inthe axial direction (Fig. 2B) over a time periodof 2.0 ms. In contrast to ballistic expansion,where the column density is ' 1/t2, the columndensity decreases only as 1/t for anisotropicexpansion. Consequently, the signals are quitelarge even for long expansion times.
One possible explanation of the observedanisotropy is provided by a recent theory ofcollisionless superfluid hydrodynamics (18).After release from the trap, the gas expandshydrodynamically as a result of the force froman effective potential Ueff ( εF $ UMF, whereεF(x) is the local Fermi energy and UMF(x) isthe mean field contribution. In general, UMF 'aeff n, where n is the spatial density and aeff isan effective scattering length. However, thistheory is not rigorously applicable to our exper-iment, as it was derived for the dilute limitassuming a momentum-independent scatteringlength aeff ( aS. This assumption is only validwhen kFaS ) 1, where kF is the Fermi wavevector. By contrast, our experiments are per-formed in the intermediate density regime (7),where kFaS ** 1, and the interactions areunitarity-limited. We have therefore attemptedto extend the theory in the context of a simplemodel. We make the assumption that unitaritylimits aeff to &1/kF. As n ' kF
3 and εF(x) (+2kF
2/(2M), where + is Planck’s constant divid-ed by 2,, we obtain UMF ( -εF(x), where - isa constant. This simple assumption is further
justified by more detailed calculations (7)showing that - is an important universal many-body parameter. With this assumption,Ueff(x) ( (1 $ -)εF(x). Because εF ' n2/3, itthen follows that Ueff ' n2/3.
For release from a harmonic trap and Ueff
' n., the hydrodynamic equations admit anexact solution (18, 27),
n (x, t) ( [n0(x/bx, y/by, z/bz)]/bxbybz (1)
where n0(x) is the initial spatial distributionin the trap, and bi(t) are time-dependent scal-ing parameters that satisfy simple coupleddifferential equations with the initial condi-tions bi(0) ( 1, bi(0) ( 0, where i ( x, y, z.Because the shape of the initial distribution(even with the mean field included) is deter-mined by the trap potential, n0 is a functiononly of r/ where 02r/2 ( 0!
2 (x2 $ y2) $ 0z2z2
and 0 ( (0!2 0z)
1/3. Hence, the initial radii ofthe density distribution n0 are in the propor-tion #x(0)/#z(0) ( 1 2 0z/0!. For our trap,1 ( 0.035. Then, during hydrodynamic ex-pansion, the radii of the density distributionevolve according to
#x(t) ( #x(0)bx(t)
#z(t) ( #z(0)bz(t) (2)
We determine bx(t) ( by(t) and bz(t) from theirevolution equations (18). For . ( 2/3, bx (0!
2 bx37/3bz
32/3 and bz ( 0z2bx
34/3bz35/3.
From the expansion data, the widths #x(t)and #z(t) are determined by fitting one-dimen-sional distributions (28) with normalized, zero-temperature Thomas-Fermi (T-F) distributions,n(x)/N ( [16/(5,#x)](1 – x2/#x
2)5/2. As shownin Fig. 2A, the zero-temperature T-F fits to thetransverse spatial profiles are quite good. Thisshape is not unreasonable despite a potentiallylarge mean field interaction. As noted above,UMF(x) ' εF(x). Hence, the mean field simplyrescales the Fermi energy in the equation ofstate (18). In this case, it is easy to show that theinitial shape of the cloud is expected to be thatof a T-F distribution. This shape is then main-tained by the hydrodynamic scaling of Eq. 2.
Figure 3A shows the measured values of#x(t) and #z(t) as a function of time t afterrelease. To compare these results with the pre-dictions of Eq. 2, we take the initial dimensionsof the cloud, #x(0) and #z(0), to be the zero-temperature Fermi radii. For our measurednumber N ( 7.5–0.5
$0.8 4 104 atoms per state, and0 ( 2, 4 (2160 % 65 Hz), the Fermi temper-ature is TF ( +0(6N)1/3/kB ( 7.9–0.2
$0.3 "K at fulltrap depth. One then obtains #x(0) ( (2kBTF/M0x
2)1/2 ( 3.6 % 0.1 "m in the transversedirection, and #z(0) ( 103 % 3 "m in the axialdirection. For these initial dimensions, we ob-tain very good agreement with our measure-ments using no free parameters, as shown bythe solid curves in Fig. 3A.
Figure 3B shows the measured aspect ratios#x(t)/#z(t) and the theoretical predictions based
on hydrodynamic, ballistic, and attractive (- (–0.4) or repulsive (- ( 0.4) collisionless meanfield scaling (18). The observed expansion ap-pears to be nearly hydrodynamic. For compar-ison, we also show the measured aspect ratiosobtained for release at 530 G, where the scat-tering length has been measured to be nearlyzero (19, 21). In this case, there is excellent
Fig. 1. False-color absorption images of astrongly interacting, degenerate Fermi gas as afunction of time t after release from full trapdepth for t ( 0.1 to 2.0 ms, top to bottom. Theaxial width of the gas remains nearly stationaryas the transverse width expands rapidly.
R E P O R T S
13 DECEMBER 2002 VOL 298 SCIENCE www.sciencemag.org2180
16
FIG. 13 The homogeneity lengths can be measured in three independentdirections. By convention and convenience, these are chosen along thebeam axis (“long”), along the transverse motion of the pions (“out”)and perpendicular to these two directions (“side”). See text for details.
FIG. 14 Hydrodynamic predictions (4) of theratio of homogeneity lengths Rout/Rside as afunction of energy. Thick lines are for tran-sition into QGP during the collision, whilethin lines are for no transition. The variouslinestyles and the two panels represent variousassumptions within the model.
about collective dynamics of the system.Looking further at the Figure, we also notice that the homogeneity region has a distinct “tilt”– the long axis of its
ellipse makes an angle with respect to the reaction plane. By measuring these “tilts,” we gain geometrical informationabout the overall shape of the source when it begins to emit particles. The relevance of this shape information tounderstanding the collision evolution was discussed in Section IV.C.2.
Finally, we know that collective dynamical effects (“flow”) represent a crucial feature which we’d like to study. Asdiscussed in Section IV.C.2, we can do this by measuring homogeneity lengths as a function of particle momentum. Infact, by measuring the ways in which the size and shape of the homogeneity region vary with momentum, we extractdetails on the magnitude and microscopic nature of the collective flow which dominates the collision evolution.
Here, I have simply sketched out how our technique of measuring geometry can be extended to obtain this moredetailed information, without going through all the math to prove it to you. For those who want more details, pleasesee (12).
VI. GEOMETRICAL OBSERVATIONS AT RHIC
Now that we have discussed the ways in which we measure geometry and some of the physics information we canextract from it, I will only very briefly discuss a few of the geometrical results we have obtained at RHIC.
A. Elliptic flow
As discussed in Section IV.C, this is an important diagnostic tool to determine (a) whether we have indeed createda system in the collision, and (b) the magnitude of the pressure generated in this system (this gives insight into theEquation of State discussed in Section IV.A).
Thus, when one of the very first analyses of RHIC data showed clear evidence of very strong elliptic flow (13),it generated huge community interest. Elliptic flow at RHIC continues to be studied in ever-increasing detail, both
16
FIG
.13
The
hom
ogen
eity
lengt
hsca
nbe
mea
sure
din
thre
ein
dep
enden
tdirec
tion
s.B
yco
nve
ntion
and
conve
nie
nce
,th
ese
are
chos
enal
ong
the
bea
max
is(“
long”
),al
ong
the
tran
sver
sem
otio
nof
the
pio
ns
(“ou
t”)
and
per
pen
dic
ula
rto
thes
etw
odirec
tion
s(“
side”
).See
text
for
det
ails.
FIG
.14
Hydro
dynam
icpre
dic
tion
s(4
)of
the
ratio
ofhom
ogen
eity
lengt
hs
Rou
t/R
sid
eas
afu
nct
ion
ofen
ergy
.T
hic
klines
are
for
tran
-sition
into
QG
Pduring
the
collisio
n,
while
thin
lines
are
for
no
tran
sition
.T
he
variou
slines
tyle
san
dth
etw
opan
els
repre
sent
variou
sas
sum
ption
sw
ithin
the
model
.
abou
tco
llec
tive
dyn
amic
sof
the
syst
em.
Loo
king
furt
her
atth
eFig
ure
,w
eal
sonot
ice
that
the
hom
ogen
eity
regi
onhas
adis
tinct
“tilt”
–th
elo
ng
axis
ofits
ellipse
mak
esan
angl
ew
ith
resp
ectto
the
reac
tion
pla
ne.
By
mea
suri
ng
thes
e“t
ilts
,”w
ega
inge
omet
rica
lin
form
atio
nab
out
the
ove
rall
shape
ofth
eso
urc
ew
hen
itbeg
ins
toem
itpar
ticl
es.
The
rele
vance
ofth
issh
ape
info
rmat
ion
tounder
stan
din
gth
eco
llis
ion
evol
ution
was
dis
cuss
edin
Sec
tion
IV.C
.2.
Fin
ally
,w
ekn
owth
atco
llec
tive
dyn
amic
aleff
ects
(“flow
”)re
pre
sent
acr
uci
alfe
ature
whic
hw
e’d
like
tost
udy.
As
dis
cuss
edin
Sec
tion
IV.C
.2,w
eca
ndo
this
bym
easu
ring
hom
ogen
eity
lengt
hs
asa
funct
ion
ofpar
ticl
em
omen
tum
.In
fact
,by
mea
suri
ng
the
way
sin
whic
hth
esi
zeand
shape
ofth
ehom
ogen
eity
regi
onva
ryw
ith
mom
entu
m,w
eex
trac
tdet
ails
onth
em
agnitude
and
mic
rosc
opic
nat
ure
ofth
eco
llec
tive
flow
whic
hdom
inat
esth
eco
llis
ion
evol
ution
.H
ere,
Ihav
esi
mply
sket
ched
out
how
our
tech
niq
ue
ofm
easu
ring
geom
etry
can
be
exte
nded
toob
tain
this
mor
edet
aile
din
form
atio
n,w
ithou
tgo
ing
thro
ugh
allth
em
ath
topro
veit
toyo
u.
For
thos
ew
ho
wan
tm
ore
det
ails
,ple
ase
see
(12)
.
VI.
GEO
MET
RIC
AL
OB
SERVAT
ION
SAT
RH
IC
Now
that
we
hav
edis
cuss
edth
ew
ays
inw
hic
hw
em
easu
rege
omet
ryan
dso
me
ofth
ephy
sics
info
rmat
ion
we
can
extr
act
from
it,I
willon
lyve
rybri
efly
dis
cuss
afe
wof
the
geom
etri
calre
sults
we
hav
eob
tain
edat
RH
IC.
A.
Ellip
tic
flow
As
dis
cuss
edin
Sec
tion
IV.C
,th
isis
anim
por
tant
dia
gnos
tic
tool
todet
erm
ine
(a)
whet
her
we
hav
ein
dee
dcr
eate
da
syst
emin
the
collis
ion,an
d(b
)th
em
agnitude
ofth
epre
ssure
gener
ated
inth
issy
stem
(this
give
sin
sigh
tin
toth
eE
quat
ion
ofSta
tedis
cuss
edin
Sec
tion
IV.A
).T
hus,
when
one
ofth
eve
ryfirs
tan
alys
esof
RH
ICdat
ash
owed
clea
rev
iden
ceof
very
stro
ng
elliptic
flow
(13)
,it
gener
ated
huge
com
munity
inte
rest
.E
llip
tic
flow
atR
HIC
cont
inues
tobe
studie
din
ever
-incr
easi
ng
det
ail,
bot
h
Figure 1.3: The evolution of energy density in the transverse plane from a simulated event, at time as indicated. Red indicates high and grey indicates low energy density. The QGP is assumedto convert to hadrons at e
hadron
= 0.508GeV/fm3 (indicated by the thin purple line at the edge ofthe grey region).
The VISH2+1 code simulates the evolution of the energy density distribution, and outputsinformation like flow velocity, energy density, etc. along a constant temperature (isothermal)freeze-out surface, whose functionality depends on the type of simulations:
1. In a purely hydrodynamic simulation, both the quark-gluon plasma and the re-scattering ofthe emitted hadrons are simulated using hydrodynamics. In such an approach, the freeze-out surface is defined as the surface outside which hadrons cease to interact and reach thedetectors by streaming freely.
2. In a hybrid hydrodynamic simulation, only the quark-gluon plasma is simulated hydrody-namically, and the scattering of the hadrons, after they materialize from the quark-gluonplasma, is simulated using a hadron re-scattering simulator based on a transport approach.In such an approach, the freeze-out surface (or better “switching surface”) is the surfacethat separates the quark-gluon plasma phase from the hadronic phase.
In both types of simulation, the temperature of the freeze-out surface is a tunable parameter,although for the hybrid simulations people choose it according to the results from lattice QCDcalculations [16, 17].
The next stage of the simulation is to generate the momentum distributions of particles fromthe freeze-out surface. The Cooper-Frye formula (see Sec. 7.3 for details) is used to calculate themomentum distribution of the emitted particles from the surface.
For purely hydrodynamic simulations, knowing these distributions as continuous functionsenables one to calculate many observables. However, in real experiments, each collision only emitsa limited number of particles and calculations done using the continuous distribution functiondo not allow one to study the fluctuations caused by finite statistics. To study finite-statisticsfluctuations, one can also simulate a finite number of particles emitted from the freeze-out surfaceby Monte-Carlo sampling the continuous Cooper-Frye distribution.
For hybrid simulations one must in any case simulate the emission of finite numbers of particles,which is required by the hadron re-scattering simulator.
There is one more subtlety: even for purely hydrodynamic simulations, although the emittedparticles are assumed to stop interacting, unstable particles continue to decay into lighter onesbefore they reach the detectors, and this process changes the momentum distributions of the lightparticles. This process is called resonance decay and it needs to be additionally computed. Forhybrid simulations, the decay of unstable particles is usually included in the hadronic re-scatteringsimulator and it does not need to be computed separately.
Our group uses the iS code to calculate the continuous distributions of emitted particles andtheir resonance decays, and the iSS code to simulate the emission of a finite discrete number ofparticles. The methodology used for sampling in the iSS code will be explained in chapter Chap. 7.
For purely hydrodynamic simulations, this is the end of the simulation process. All of mypublications are based on purely hydrodynamic simulations, but since part of the work I havecontributed is a package for hybrid calculations, I will explain it briefly.
Once the emissions of hadrons has been successfully simulated, they can then be passed to thehadronic re-scattering simulator, from which the final-state momenta of the particles are produced,which can be analyzed to generate simulated observables. Our group uses the UrQMD code [18]
5
?
At the beginning of the RHIC Now
/20H. Masui, KPS, Nov/1/2013
partN0 100 200 300
-0.1
0
0.1
s,02 / Rs,3
22R
partN0 100 200 300
-0.1
0
0.1
o,02 / Ro,3
2-2R
partN0 100 200 300
-0.1
0
0.1
l,02 / Rl,3
2-2R
partN0 100 200 300
-0.1
0
0.1
s,02 / Ro,3
2-2R
partN0 100 200 300
-0.1
0
0.1
s,02 / Ros,3
22R
-π-π++π+π
Au+Au 200GeV
PHENIX Preliminary
partN0 100 200 300
-0.1
0
0.1
s,02 / Rs,3
22R
partN0 100 200 300
-0.1
0
0.1
o,02 / Ro,3
2-2R
partN0 100 200 300
-0.1
0
0.1
l,02 / Rl,3
2-2R
partN0 100 200 300
-0.1
0
0.1
s,02 / Ro,3
2-2R
partN0 100 200 300
-0.1
0
0.1
s,02 / Ros,3
22R
-π-π++π+π
Au+Au 200GeV
PHENIX Preliminary
Centrality dependence of relative amplitudes
Rµ2
φpair- Ψ3
0 π/3 2π/3
Rµ,32
Rµ,02
! Oscillation of Rs shows is almost zero within systematic error
" Slightly negative value in peripheral ? ! Ro has finite oscillation except peripheral event
HBT radii w.r.t 3rd-order event plane
! Rout clearly shows a finite oscillation w.r.t Ψ3 in most central event
" Strength w.r.t Ψ3 is comparable to w.r.t Ψ2 ! What make this Ro oscillation?
" Triangular spatial shape? " Triangular flow?
# v3 is comparable to v2 in most central " Emission duration?
[rad]nΨ - φ-3 -2 -1 0 1 2 3
]2 [f
m2 s
R
0
5
10
[rad]nΨ - φ-3 -2 -1 0 1 2 3
]2 [f
m2 o
R
0
5
10
-π-π++π+π Au+Au 200GeV 0-10%
2Ψw.r.t
3Ψw.r.t
Average of radii is set to “10” or “5”for w.r.t Ψ2 and w.r.t Ψ3
PRL.107.252301
8
data. (iv) For both R2s and R2
o, the oscillations for the ge-ometrically deformed source and for the source with onlya deformed flow profile are out of phase by π/3. Only forthe flow-anisotropy-dominated case (thick red lines) dothe HBT radii oscillate in phase with the experimentalobservations.Fig. 4 illustrates that, in a coordinate system whose
x axis points along the triangular flow vector such thatΨ3 =0, the sources for these two scenarios appear ro-tated by 60 relative to each other. The left sketch showsthe 50% contour of the emission function for pions withK⊥=0 for the source with ϵ3 =0.25, v3 =0 while thesource corresponding to the right sketch has ϵ=0 andv3 =0.25.
!3
!a"
!3
!b"
FIG. 4: Half-maximum contour plots for the emission func-tions for K⊥ =0 pions, for two sources with ϵ=0.25, v3 =0(“geometry dominated”, left) and with ϵ=0, v3 =0.25 (“flowanisotropy dominated”, right). In both cases the sources areoriented such that the triangular flow angle Ψ3 points in xdirection.
Of course, in general the source will exhibit flow andgeometric anisotropies concurrently. Figure 5 showsthe triangular oscillations of R2
o,s for a sequence ofsources that all have the same triangular flow anisotropyv3 =0.25 but feature varying degrees of spatial triangu-larity ϵ3. The oscillation amplitudes, as well as the meanvalues, of both R2
s and R2o increase monotonically with
triangularity ϵ3. As Fig. 1 shows, just after ϵ3 reaches thevalue 0.26, the flow angle Ψ3 flips from 0 to π/3. Thisis reflected in Fig. 5 by a sudden 60 phase shift rela-tive to Ψ3 of both R2
s and R2o oscillations. For the given
flow anisotropy v3 =0.25, as long as ϵ3 < 0.26, R2o has a
minimum for emission along the triangular flow plane,as observed in experiment; only for spatial deformationϵ3 > 0.26 the outward radius becomes maximal for emis-sion in Ψ3 direction. The observed phase of the sidewardand outward HBT thus tells us only that the measuredHBT oscillations correspond to a source in which triangu-lar flow anisotropies dominate over geometric triangulardeformation effects that are boosted by superimposed ra-dial flow. Thus, while a direct measurement of ϵ3 is notpossible, the observed oscillation phase can perhaps beused to put limits on the ratio ϵ3/v3 in theoretical mod-els. It is, however, likely that such limits depend on thedetails of the model emission function.
Ε3#0
Ε3#0.1
Ε3#0.25
Ε3#0.3
K!#0.5 GeV
v 3#0.25 GeV
!a"5
10
15
20
25
Rs2 !fm
2 "
!b"
$Π $2Π#3 $Π#3 0 Π#3 2Π#3 Π
10
15
20
25
&$!3
Ro2 !fm
2 "
FIG. 5: (Color online) Triangular oscillations of R2s (a) and
R2o (b) for pion pairs with momentum K⊥ =0.5GeV, as a
function of emission angle Φ relative to the triangular flowdirection Ψ3. Shown are results for a source with fixed tri-angular flow anisotropy v3 =0.25, for a range of triangularspatial deformations ϵ3. One sees that the phase of the HBToscillations relative to the flow angle Ψ3 flips by π/3 betweenϵ3 = 0.25 and 0.3, as a result Ψ3 itself flipping by π/3 (seeFig. 1).
To explore this last question a bit further, wereturn to the completely “geometry dominated”(ϵ=0.25, v3 =0) and completely “flow anisotropy dom-inated” (ϵ=0, v3 =0.25) sources studied in Figs. 3 and4. In Fig. 6 we show for these extreme models the K⊥-dependence of their third-order oscillation amplitudesR2
s,3 and R2o,3. At low K⊥, the opposite signs of the os-
Ro,32
Rs,32
!a"
0.0 0.2 0.4 0.6 0.8 1.0
$4
$2
0
2
4
0.0 0.2 0.4 0.6 0.8 1.0
KT !GeV"
R s,32,R
o,32!fm
2 "
Ro,32
Rs,32
!b"
0.0 0.2 0.4 0.6 0.8 1.0
0.0 0.2 0.4 0.6 0.8 1.0
KT !GeV"
FIG. 6: (Color online) K⊥-dependence of the third-order os-cillation amplitudes of R2
s and R2o, for the “geometry domi-
nated” (a) and “flow anisotropy dominated” (b) sources stud-ied in Figures 3 and 4.
Triangular oscillation
• Rout shows clear oscillation with respect to Ψ3
• Finite Rout, zero Rside ‣ could suggest triangular flow is dominated at freeze-out
- whereas triangular source shape is very small at freeze-out
‣ Important to study kT dependence of asHBT
!12
PHENIX, QM2012
C. J. Plumberg, C. Shen, U. Heinz, arXiv:1306.1485 [nucl-th]
/20H. Masui, KPS, Nov/1/2013
NN
s1 10
2103
10
Fε
0
0.1
0.2
0.3
0.4 = 0.15-0.6 GeV/ctK
*Model centralitiescorrespond to data
STAR preliminary
E895 - PLB 496, 2004 (7.4-29.7%)
CERES - PRC 78, 2008 (10-25%)
STAR (-0.5<y<0.5, 10-30%)
STAR (-1<y<-0.5, 10-30%)
STAR (0.5<y<1, 10-30%)
URQMDHybrid[BM]+UrQMD
Hybrid[HG]+UrQMD
2D hydro EoS-Q
2D hydro EoS-H
2D hydro EoS-I
FεExcitation function for freeze-out eccentricity,
Figure 3: Freeze out eccentricity, " f , as a function ofp
sNN for data and models [9] (color online).
4. Summary60
To summarize, - correlation function is presented. Fits to data with di↵erent potential61
models suggest that - interaction is attractive. A negative scattering length gives indication62
towards non-existence of bound H-dibaryon. A clear source asymmetry signal is observed in63
pion-kaon correlation function and the o↵set is roughly half of the source size. The azimuthal64
HBT measurement shows a monotonic decrease for freeze out eccentricity as a function of beam65
energy.66
67
References68
[1] R. Ja↵e, Phys. Rev. Lett. 38 (1977) 195.69
[2] T. Inoue et al. [HAL QCD collaboration], Phys. Rev. Lett. 106 (2011) 162002 and S. Beane et al.70
[NPLQCD Collaboration], Phys. Rev. Lett. 106 (2011) 162001 .71
[3] C. Dover, P. Koch and M. May, Phys. Rev. C 40 (1989) 115 and L-W. Chen (Private communication).72
[4] M.A. Lisa, S. Pratt, R. Soltz, and U. Wiedemann, Ann. Rev. Nucl. Part. Sci. 55 (2005) 31173
[5] F. Retiere and M. Lisa,Phys. Rev. C 70 (2004) 044907.74
[6] A. Ohnishi, HHI workshop proceedings 2012.75
[7] Z. Chajecki and M. Lisa, Phys. Rev. C 78 (2008) 064903, D. Brown et al., Phys.Rev. C72 (2005)76
054902 and D. Brown and A. Kisiel, Phys. Rev. C80 (2009) 064911.77
[8] STAR Collaboration, J. Adams et al., Phys. Rev. Lett. 91 (2003) 262302.78
[9] M. Lisa, E. Frodermann, G. Graef, M. Mitrovski, E. Mount, H. Petersen and M. Bleicher, New J.79
Phys. 13 (2011) 06500680
4
Freeze-out eccentricity @ BES
• Spatial anisotropy is sensitive to equation of state ‣ might be signal for 1st order phase transition
• Pion freeze-out eccentricity smoothly decreases as a function of beam energy ‣ STAR data don’t show non-monotonic energy dependence
!13
16
FIG. 13 The homogeneity lengths can be measured in three independentdirections. By convention and convenience, these are chosen along thebeam axis (“long”), along the transverse motion of the pions (“out”)and perpendicular to these two directions (“side”). See text for details.
FIG. 14 Hydrodynamic predictions (4) of theratio of homogeneity lengths Rout/Rside as afunction of energy. Thick lines are for tran-sition into QGP during the collision, whilethin lines are for no transition. The variouslinestyles and the two panels represent variousassumptions within the model.
about collective dynamics of the system.Looking further at the Figure, we also notice that the homogeneity region has a distinct “tilt”– the long axis of its
ellipse makes an angle with respect to the reaction plane. By measuring these “tilts,” we gain geometrical informationabout the overall shape of the source when it begins to emit particles. The relevance of this shape information tounderstanding the collision evolution was discussed in Section IV.C.2.
Finally, we know that collective dynamical effects (“flow”) represent a crucial feature which we’d like to study. Asdiscussed in Section IV.C.2, we can do this by measuring homogeneity lengths as a function of particle momentum. Infact, by measuring the ways in which the size and shape of the homogeneity region vary with momentum, we extractdetails on the magnitude and microscopic nature of the collective flow which dominates the collision evolution.
Here, I have simply sketched out how our technique of measuring geometry can be extended to obtain this moredetailed information, without going through all the math to prove it to you. For those who want more details, pleasesee (12).
VI. GEOMETRICAL OBSERVATIONS AT RHIC
Now that we have discussed the ways in which we measure geometry and some of the physics information we canextract from it, I will only very briefly discuss a few of the geometrical results we have obtained at RHIC.
A. Elliptic flow
As discussed in Section IV.C, this is an important diagnostic tool to determine (a) whether we have indeed createda system in the collision, and (b) the magnitude of the pressure generated in this system (this gives insight into theEquation of State discussed in Section IV.A).
Thus, when one of the very first analyses of RHIC data showed clear evidence of very strong elliptic flow (13),it generated huge community interest. Elliptic flow at RHIC continues to be studied in ever-increasing detail, both
16
FIG
.13
The
hom
ogen
eity
lengt
hsca
nbe
mea
sure
din
thre
ein
dep
enden
tdirec
tion
s.B
yco
nve
ntion
and
conve
nie
nce
,th
ese
are
chos
enal
ong
the
bea
max
is(“
long”
),al
ong
the
tran
sver
sem
otio
nof
the
pio
ns
(“ou
t”)
and
per
pen
dic
ula
rto
thes
etw
odirec
tion
s(“
side”
).See
text
for
det
ails.
FIG
.14
Hydro
dynam
icpre
dic
tion
s(4
)of
the
ratio
ofhom
ogen
eity
lengt
hs
Rou
t/R
sid
eas
afu
nct
ion
ofen
ergy
.T
hic
klines
are
for
tran
-sition
into
QG
Pduring
the
collisio
n,
while
thin
lines
are
for
no
tran
sition
.T
he
variou
slines
tyle
san
dth
etw
opan
els
repre
sent
variou
sas
sum
ption
sw
ithin
the
model
.
abou
tco
llec
tive
dyn
amic
sof
the
syst
em.
Loo
king
furt
her
atth
eFig
ure
,w
eal
sonot
ice
that
the
hom
ogen
eity
regi
onhas
adis
tinct
“tilt”
–th
elo
ng
axis
ofits
ellipse
mak
esan
angl
ew
ith
resp
ectto
the
reac
tion
pla
ne.
By
mea
suri
ng
thes
e“t
ilts
,”w
ega
inge
omet
rica
lin
form
atio
nab
out
the
ove
rall
shape
ofth
eso
urc
ew
hen
itbeg
ins
toem
itpar
ticl
es.
The
rele
vance
ofth
issh
ape
info
rmat
ion
tounder
stan
din
gth
eco
llis
ion
evol
ution
was
dis
cuss
edin
Sec
tion
IV.C
.2.
Fin
ally
,w
ekn
owth
atco
llec
tive
dyn
amic
aleff
ects
(“flow
”)re
pre
sent
acr
uci
alfe
ature
whic
hw
e’d
like
tost
udy.
As
dis
cuss
edin
Sec
tion
IV.C
.2,w
eca
ndo
this
bym
easu
ring
hom
ogen
eity
lengt
hs
asa
funct
ion
ofpar
ticl
em
omen
tum
.In
fact
,by
mea
suri
ng
the
way
sin
whic
hth
esi
zeand
shape
ofth
ehom
ogen
eity
regi
onva
ryw
ith
mom
entu
m,w
eex
trac
tdet
ails
onth
em
agnitude
and
mic
rosc
opic
nat
ure
ofth
eco
llec
tive
flow
whic
hdom
inat
esth
eco
llis
ion
evol
ution
.H
ere,
Ihav
esi
mply
sket
ched
out
how
our
tech
niq
ue
ofm
easu
ring
geom
etry
can
be
exte
nded
toob
tain
this
mor
edet
aile
din
form
atio
n,w
ithou
tgo
ing
thro
ugh
allth
em
ath
topro
veit
toyo
u.
For
thos
ew
ho
wan
tm
ore
det
ails
,ple
ase
see
(12)
.
VI.
GEO
MET
RIC
AL
OB
SERVAT
ION
SAT
RH
IC
Now
that
we
hav
edis
cuss
edth
ew
ays
inw
hic
hw
em
easu
rege
omet
ryan
dso
me
ofth
ephy
sics
info
rmat
ion
we
can
extr
act
from
it,I
willon
lyve
rybri
efly
dis
cuss
afe
wof
the
geom
etri
calre
sults
we
hav
eob
tain
edat
RH
IC.
A.
Ellip
tic
flow
As
dis
cuss
edin
Sec
tion
IV.C
,th
isis
anim
por
tant
dia
gnos
tic
tool
todet
erm
ine
(a)
whet
her
we
hav
ein
dee
dcr
eate
da
syst
emin
the
collis
ion,an
d(b
)th
em
agnitude
ofth
epre
ssure
gener
ated
inth
issy
stem
(this
give
sin
sigh
tin
toth
eE
quat
ion
ofSta
tedis
cuss
edin
Sec
tion
IV.A
).T
hus,
when
one
ofth
eve
ryfirs
tan
alys
esof
RH
ICdat
ash
owed
clea
rev
iden
ceof
very
stro
ng
elliptic
flow
(13)
,it
gener
ated
huge
com
munity
inte
rest
.E
llip
tic
flow
atR
HIC
cont
inues
tobe
studie
din
ever
-incr
easi
ng
det
ail,
bot
h
STAR, ISMD2012
/20H. Masui, KPS, Nov/1/2013
Fluctuations!14
/20H. Masui, KPS, Nov/1/2013
Higher (n>2) order moments
• At critical point (with infinite system) ‣ susceptibilities and correlation length diverge
- both quantities cannot be directly measured
• Experimental observables ‣ Moment (or cumulant) of conserved quantities: net-baryons, net-
charge, net-strangeness, ... ‣ Moment product (cumulant ratio) ↔ ratio of susceptibility !
!!
- directly related to the susceptibility ratios (Lattice QCD)
- higher moments (cumulants) have higher sensitivity to correlation length
• Signal = Non-monotonic behavior of moment products (cumulant ratios) vs beam energy
!15
2 =(N)2
↵ 2,3 =
(N)3
↵ 4.5,4 =
(N)4
↵ 3 h(N)i2 7
S =3
2 3
2, K2 =
4
2 4
2
M. A. Stephanov, PRL102, 032301 (2009)
/20H. Masui, KPS, Nov/1/2013
Non-gaussian fluctuations
• 3rd moment = Skewness S ‣ Asymmetry
• 4th moment = Kurtosis K ‣ Peakedness
• Both moments = 0 for gaussian distribution
• Critical point induces non-gaussian fluctuations
!16
From Wikipedia
/20H. Masui, KPS, Nov/1/2013
Moment Products: Energy Dependence !
! Deviations below Poisson !expectations are observed beyond statistical and systematic errors in 0-5% most central collisions for κσ2 and Sσ above 7.7 GeV. !! For peripheral collisions, the !deviations above Poission expectations are observed below 19.6 GeV.! !! UrQMD model show monotonic !behavior for the moment products, in! which non-CP physics, such as! baryon conservation, hadronic scattering effects, are implemented.!
Net-proton fluctuations
• Data ‣ efficiency uncorrected*
• Data compared to various expectations
‣ Poisson ‣ (Negative-) binomial*
!
• No significant excess compared to Poisson & UrQMD
‣ Need precision measurements at low energies
!* under investigation (not shown here)
!17
STAR, QM2012
/20H. Masui, KPS, Nov/1/2013
Comparison&of&moments:Data&vs.&model&
March&13,2013&8th&Interna1onal&Workshop&on&Cri1cal&Point&and&Onset&of&Deconfinement&
18&
σ2 /Μ '• !increase!with!increase!in!colliding!energies!• !Follows!the!HRG!predic`ons!for!all!the!energies!
Sσ !• !decreases!with!increasing!colliding!energy!• !At!higher!energies!Comparable!with!the!model!predic`ons!• !At!lower!energies!experimental!values!are!!!!lower!than!HRG!predic`ons.!
κσ2 '• No!energy!dependence!observed!in!data!!also!!!!!!!!!!supported!by!HRG!predic`ons!!• !!HRG!predic`ons!are!Consistently!higher!with!data!• !!Comparable!with!HIJING!and!URQMD!except!for!200!!!!!!!GeV!!
preliminary!
X. Dong Aug. 19th, 2013 Future Trends Workshop, Beijing
Higher Moments of Net-charge
18
• Net-charge fluctuation – related to freeze-out parameters
Bazavov et al, PRL 109 (2012) 192302
• Data - efficiency uncorrected *
• Data compared to various expectations - Poisson - (Negative-)Binomial *
• Need precision measurements.
* Currently under investigation
Net-charge fluctuations
• No significant excess compared to Poisson, models ‣ STAR ≠ PHENIX → acceptance ? efficiency correction ?
!18
STAR, QM2012PHENIX, CPOD2013
/20H. Masui, KPS, Nov/1/2013
Summary
• Multi-particle correlations are powerful tool to understand the underlying collision dynamics in heavy ion collisions !
• Azimuthal anisotropy ‣ Flow in d+Au ? Need centrality dependence ‣ Possibility to enhance tip-tip collisions by using v2 ‣ Hint of turn-off signal by breakdown of NCQ scaling between particles
and anti-particles
• Femtoscopy ‣ Triangular flow is dominated at freeze-out ? ‣ Smooth energy dependence of final freeze-out eccentricity
• Fluctuations ‣ Need precision measurements for QCD critical point search
!19
/20H. Masui, KPS, Nov/1/2013
Back up
!20
/20H. Masui, KPS, Nov/1/2013
While in Auþ Au collisions atffiffiffiffiffiffiffiffisNN
p ¼ 200 GeV asingle NCQ scaling can be observed for particles andantiparticles, the observed difference in v2 at lower beamenergies demonstrates that this common NCQ scaling ofparticles and antiparticles splits. Such a breaking of theNCQ scaling could indicate increased contributions fromhadronic interactions in the system evolution with decreas-ing beam energy. The energy dependence of v2ðXÞ %v2ð !XÞ could also be accounted for by considering anincrease in nuclear stopping power with decreasing
ffiffiffiffiffiffiffiffisNN
pif the v2 of transported quarks (quarks coming from theincident nucleons) is larger than the v2 of produced quarks[25,26]. Theoretical calculations [27] suggest that thedifference between particles and antiparticles could beaccounted for by mean field potentials where the K% and!p feel an attractive force while the Kþ and p feel arepulsive force.
Most of the published theoretical calculations can repro-duce the basic pattern but fail to quantitatively reproducethe measured v2 difference [25–28]. So far, none of thetheory calculations describes the observed ordering ofthe particles. Therefore, more accurate calculations fromtheory are needed to distinguish between the differentpossibilities. Other possible reasons for the observationthat the !% v2ðpTÞ is larger than the !þ v2ðpTÞ is theCoulomb repulsion of !þ by the midrapidity net protons(only at low pT) and the chiral magnetic effect in finitebaryon-density matter [29]. Simulations have to be carriedout to quantify if those effects can explain ourobservations.In Ref. [21], the study of the centrality dependence of
"v2 for protons and antiprotons is extended to investigateif different production rates for protons and antiprotons asa function of centrality could cause the observed differ-ences. It was observed that the differences, "v2, aresignificant at all centralities.The v2ðmT %m0Þ and possible NCQ scaling was also
investigated for particles and antiparticles separately.Figure 3 shows v2 as a function of the reduced transversemass, (mT %m0), for various particles and antiparticles atffiffiffiffiffiffiffiffisNN
p ¼ 11:5 and 62.4 GeV. The baryons and mesons areclearly separated for
ffiffiffiffiffiffiffiffisNN
p ¼ 62:4 GeV at ðmT %m0Þ>1 GeV=c2. While the effect is present for particles atffiffiffiffiffiffiffiffisNN
p ¼ 11:5 GeV, no such separation is observed forthe antiparticles at this energy in the measured (mt %m0)range up to 2 GeV=c2. The lower panels of Fig. 3 depictthe difference of the baryon v2 relative to a fit to the mesonv2 data with the pions excluded from the fit. The antipar-ticles at
ffiffiffiffiffiffiffiffisNN
p ¼ 11:5 GeV show a smaller differencecompared to the particles. At
ffiffiffiffiffiffiffiffisNN
p ¼ 11:5 GeV thedifference becomes negative for the antiparticles at(mT %m0)<1 GeV=c2 but the overall trend is still similarto the one of the particles and to
ffiffiffiffiffiffiffiffisNN
p ¼ 62:4 GeV.
0
0.1
0.211.5 GeV (a)
pΛ
-Ξ-Ω
+π+K
s0K
φ
0 1 2 3-0.05
0
0.05
62.4 GeV (b)
Au+Au, 0%-80%
0 1 2 3
0-mTm
11.5 GeV (c)
pΛ
+Ξ
+Ω
-π-
K
s0K
φ
0 1 2 3)2
62.4 GeV (d)
-sub EPη
0 1 2 3
2v(B
)-fit
2v
(GeV/c
FIG. 3 (color online). The upper panels depict the elliptic flow v2 as a function of reduced transverse mass (mT %m0) for particles,(a) and (b), and antiparticles, (c) and (d), in 0%–80% central Auþ Au collisions at
ffiffiffiffiffiffiffiffisNN
p ¼ 11:5 and 62.4 GeV. Simultaneous fits tothe mesons except the pions are shown as the dashed lines. The difference of the baryon v2 and the meson fits are shown in the lowerpanels.
(GeV)NNs0 20 40 60
)X( 2
(X)-
v2v
0
0.02
0.04
0.06 Au+Au, 0%-80%-sub EPη
+Ξ--Ξ
pp-Λ-Λ
--K+K-π-+π
FIG. 2 (color online). The difference in v2 between particles(X) and their corresponding antiparticles ( !X) (see legend) as afunction of
ffiffiffiffiffiffiffiffisNN
pfor 0%–80% central Auþ Au collisions. The
dashed lines in the plot are fits with a power-law function. Theerror bars depict the combined statistical and systematic errors.
PRL 110, 142301 (2013) P HY S I CA L R EV I EW LE T T E R Sweek ending5 APRIL 2013
142301-5
Large v2 difference for baryons
• Difference of v2 between particles and anti-particles increase in low energies
• Baryons show larger difference than mesons
!21
STAR PRL110, 143201 (2013), PRC88, 014902 (2013)
/20H. Masui, KPS, Nov/1/2013
Disappearance of charge separation
• Charge separation (γos-γss) at 200 GeV ‣ chiral magnetic effect ?
• Separation decreases with decreasing beam energies, disappears at √sNN = 11.5 GeV or less
!22
% Most Central
) s
- 2
2q +
1q
cos
(
-0.001
-0.0005
0
0.0005
0.001
0.0015
0.002
01020304050607080
19.6 GeV Au+Au
% Most Central0102030405060700
11.5 GeV Au+Au
STAR preliminary
% Most Central0102030405060700
7.7 GeV Au+Au
) s
- 2
2q +
1q
cos
(
-0 001
-0.0005
0
0.0005
0.001
0.0015
0.002
2.76 TeV Pb+Pb200 GeV Au+Au
Opposite sign
Same sign
62.4 GeV Au+Au39 GeV Au+Au 27 GeV Au+Au
γos
γss
γ = 〈c
os(φ
1+φ 2
-2Ψ
)〉ALICE, arXiv:1207.0900