Soft physics at RHIC · 2018-02-23 · STAR, APS2013 PHENIX, RHIC&AGS users meeting. H. Masui, KPS, Nov/1/2013 /20 Break down of NCQ scaling

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



!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


STAR only

Test run

• Variety of collision systems (d to U), wide range (5-200 GeV) of collision energies



!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


STAR only

Test run


• QGP properties at top RHIC energy



!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


STAR only

Test run



• Search for QCD critical point & phase boundary by Beam Energy Scan (BES) program phase-I



!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


STAR only

Test run



• Search for QCD critical point & phase boundary by Beam Energy Scan (BES) program phase-I

Study structure of QCD phase diagram


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


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


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


Azimuthal anisotropy

!6

React

ion

plan

e ΨRP

XZ

Y Px

Py

Pz

coordinate space momentum space


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





1

contribution

12





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





1

contribution

12





1

contribution

PHENIX, IS2013


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%


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


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


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


p ¼ 11:5 GeV show a smaller differencecompared to the particles. At


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


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


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


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)


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

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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


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]


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


Fluctuations!14


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)


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


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


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!predicòns!for!all!the!energies!

Sσ !• !decreases!with!increasing!colliding!energy!• !At!higher!energies!Comparable!with!the!model!predicòns!• !At!lower!energies!experimental!values!are!!!!lower!than!HRG!predicòns.!

κσ2 '•  No!energy!dependence!observed!in!data!!also!!!!!!!!!!supported!by!HRG!predicòns!!• !!HRG!predicòns!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


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


Back up

!20


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


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


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


p ¼ 11:5 GeV show a smaller differencecompared to the particles. At


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


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


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


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)


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

Documents

Soft physics at RHIC · 2018-02-23 · STAR, APS2013 PHENIX, RHIC&AGS users meeting. H. Masui, KPS, Nov/1/2013 /20 Break down of NCQ scaling