Global Hyperon Polarization in Heavy-Ion
Collisions at RHIC-STAR
Isaac Upsal
SDU/BNL
09/05/18

Deconfined color charges
Quark-gluon plasma
Color confined inside
net-color-neutral hadrons(e.g. proton)
Isaac Upsal – September 2018

Thermodynamic degeneracy

QCD: Early universe

QCDTransition
2

The Early Universe, Kolb & Turner

2

QCD: Heavy-ion physics

Lattice QCD calculation:••

T<150 MeV : interacting hadrons
T>150 MeV : deconfined quarks

Color confined inside
net-color-neutral hadrons(e.g. proton)
Isaac Upsal – September 2018

F. Karsch, arXiv:0711.0656[hep-lat]

Deconfined color charges
Quark-gluon plasma~ Thermodynamic degeneracy* (150 MeV = 2x1012 K ~ 105 T)33

Nuclear matter phase diagram
Deconfined color charges
Quark-gluon plasma

The QGP is very nearlya perfect fluid

4

Isaac Upsal – September 20184

Isaac Upsal – September 20185

At mid-rapidity:

⃗⊗B

⊗ ⃗L

(net + charge)++ + ++++++++++ + +(net + charge)• |L| ~ 103 ħ in non-central collisions• How much is transferred to particles at mid-rapidity?
• Does angular momentum get distributed thermally?
• How does that affect fluid/transport?
1⃗⃗ ≡ ∇×⃗v• Vorticity: ω2• How would it manifest itself in data?
Isaac Upsal – September 20186

Vortices
1 ⃗Classical Vorticity: ω⃗ ≡ ∇ ×⃗v
2
Rigid-body-like
VortexIrrotationalvortexv ∝rv ∝1/r

Like the moon, always
the same side toward Earth
Isaac Upsal – September 2018

Notice the rotation, or lack thereof, in the fluid elements
7

HIC Vorticity
formation

In collisionc.m. frame

Local fluidcell frame

Localized vortex generation via baryon stopping
Viscosity dissipates vorticity to fluid at larger scale
Vorticity – fundamental sub-femtoscopic structureof the “perfect fluid” and its generation

Isaac Upsal – September 20188

Hydrodynamic evolution

From a (lumpy) initial state, solve hydro equations:dmT mn =0um dm P =-movies by Bjorn Schenke

T m ,n =eum un - ( p+ P) D mn + p mn
ö1
1 zT æ t( P + zq ) - P dl ç P ul ÷tP
2 tP è zT ø& many more terms...
Isaac Upsal – September 20189

Final state particles from hydroemitted hadron(color confined)

System cools & expands →Hadronization & “Freezeout”• emitted particles reflect propertiesof parent fluid cell (Cooper-Frye)• chemical potentials, thermal &collective velocities

movies by Bjorn Schenke

fluid cell at
freeze-out

QGP fluid:colored quarks deconfined
Isaac Upsal – September 201810

Theory Background

Local OAM (vorticity) transferred tospin degree of freedom of final-state hadrons(Such transfer is rare – discussed below)

Isaac Upsal – September 201811

Theory work – broad and incomplete
overview• Voloshin, arxiv:nucl-th/0410089• Liang and Wang, PRL94 102301 (2005) [errat-ibid 96 (2006)
039901• Liang and Wang PLB629 (2005) 20 (2005)• Betz, Gyulassy, Torrieri PRC76 044901 (2007)• Gao et al, PRC77 044902 (2008)• Gao et al, PRL 109 232301 (2012)• Becattini et al., PRC88 034905 (2013)• Becattini et al., JPhys 509 012055-5 (2014) (SQM2013)• Csernai et al., JPhys 012054-5 (2014) (SQM2013)• Grossi JPhys 527 012015-5 (2014) (XIV Conf. Th. Physics)• Becattini et al. arxiv:1501.04468• Jiang, Lin, and Liao, arxiv:1602.06580• many others .......

Isaac Upsal – September 201812

Barnett effect• Nice parallel in Barnett effect• BE: uncharged object rotating withangular velocity ω magnetizes

Spins align with vorticity → B field

M =χ ω/ γ• γ = gyromagnetic ratio, χ = magnetic
susceptibility.
• Inverse of Einstein-de Haas effect,
Science 15 42 (1915); Phys. Rev. 6, 239–270 (1915)

B field →rotation• Einstein-de Haas effect, (onlypublished experiment of Einstein!)• EdHE:Magnetic field induces
rotation
Physical Review (Series I), Vol. 26, Issue 3, pp. 248–253 (1908)
Isaac Upsal – September 201813

Vorticity → Global Polarization

LL• Vortical or QCD spin-orbit:
aligned with L

Isaac Upsal – September 2018

Lambda and Anti-Lambda spins

14Magnetic field → Global Polarization

LL
Bothmay
contribute• Vortical or QCD spin-orbit:
aligned with L

Lambda and Anti-Lambda spins• (electro)magnetic coupling:
Lambdas aligned

Lambdas anti-aligned, and Anti-

Isaac Upsal – September 201815

How to quantify the effect (I)●Lambdas are “selfanalyzing”●Reveal polarization bypreferentially emitting
daughter proton in spindirection⃗S *Lq*⃗p *pIsaac Upsal – September 2018

⃗p *p

BBCs

Spinning
LambdasBBCs

spectators⃗ follow the distribution:
L s with Polarization PdN
11**
⃗
^
()
=1+αP
⋅
p=1+αP
cosq()
p*4pdΩ 4pα=0.642±0.013 [measured]*p^ p is the daughter proton momentum direction inthe L frame (note that this is opposite for L )*⃗ 3^
0<|⃗
P|<1 : P=pα p16

How to quantify the effect (II)BBCsSpinning
LambdasBBCsspectators^
Symmetry: |η|<1 , 0<ϕ<2 p →|| L⃗ L dN ⃗^Statistics-limited experiment: we report acceptance-integrated polarization, Pave ≡∫ d β
P (⃗βL )⋅L⃗d βL*8 ⟨sin (ϕb^ −ϕ p )⟩P AVE = p α** where the average is performed over events and Ls
(1)
R EP
R(1)
EP is the first-order event plane resolution and ϕ b^ is the impact parameter angle** if v 1⋅y>0 in BBCs ϕb^ =Ψ EP , if v 1⋅y<0 in BBCs ϕb^ =Ψ EP +p
Isaac Upsal – September 201817

Ingredients: Using STAR
Protons and pions reconstructed in STAR
TPC and TOF for |η|<1
TPC: Tracking + PID
TOF: PID

Event planes found using(forward/backward) BBCs
3.4 < |η| < 5
Isaac Upsal – September 201818

Ingredients: Using STAR (PID)

ppp
Protons and pions reconstructed in STAR
TPC and TOF for |η|<1
TPC: Tracking + PID
TOF: PID

Isaac Upsal – September 2018p19

Ingredients: Using STAR (tracking)Protons and pions reconstructed in STAR
TPC and TOF for |η|<1
TPC: Tracking + PID
TOF: PID
Lambdas are found topologically using
identified protons and pions
Isaac Upsal – September 201820

Ingredients: Using STAR (Event Plane)⃗bΨ 1, West

Event planes found using(forward/backward) BBCs
3.4 < |η| < 5

Ψ 1, East
Isaac Upsal – September 201821

Global polarization measure• Measured Lambda and AntiLambda polarization• Includes results fromprevious STAR null result(2007)

arXiv: 1805.04400
arXiv: 1805.04400• P H (L) and P H ( L̄)>0
implies positive vorticity• P H ( L̄)> P H (L) would
imply magnetic couplingSTAR, Nature 548, 62–65 (2017)
STAR, arXiv: 1805.04400
Isaac Upsal – September 201822

Global polarization measure• Measured Lambda and AntiWe can study
more
Lambdapolarization
fundamental propertiesof the system
results from• Includes
previous STAR null result(2007)

arXiv: 1805.04400
arXiv: 1805.04400• P H (L) and P H ( L̄)>0
implies positive vorticity• P H ( L̄)> P H (L) would
imply magnetic couplingSTAR, Nature 548, 62–65 (2017)
STAR, arXiv: 1805.04400Isaac Upsal – September 201823

Vortical and Magnetic Contributions• Magneto-hydro equilibrium interpretation**⃗ /T)P∼exp(−E /T +m B B /T + ω⃗⋅⃗S /T + m⃗⋅B
arXiv: 1805.04400
arXiv: 1805.04400• for small polarization:
1 ω mL B–P L≈+2TT

1 ω mL B
P L≈+2TT• vorticity from addition:
ω =P +PLLT• B from the difference:
STAR, Nature 548, 62–65 (2017)
STAR, arXiv: 1805.04400

B
1=(P L −P L )T 2m L** ℏ=k B =1

But, even with topological cuts, significant feed-down from Σ0 , Ξ 0/- , Σ* ±/ 0… which themselves will be polarized...

Becattini,
Lisa,Upsal, Voloshin Phys. Rev. C 95, 054902 (2017)
Isaac UpsalKarpenko,– September
2018

24

Vortical and Magnetic Contributions
L(1450), L(1520)... ® L
Σ* ® Σ 0 ® LΞ® L
Σ* ® LΣ0 ® L

But, even with topological cuts, significant feed-down from Σ0 , Ξ 0/- , Σ* ±/ 0… which themselves will be polarized...

Becattini,
Lisa,Upsal, Voloshin Phys. Rev. C 95, 054902 (2017)
Isaac UpsalKarpenko,– September
2018

25

Accounting for polarized feeddown

Becattini,Lisa,Upsal, Voloshin Phys. Rev. C 95, 054902 (2017)
Isaac UpsalKarpenko,– September
2018

26

Accounting for polarized feeddown

Becattini,Lisa,Upsal, Voloshin Phys. Rev. C 95, 054902 (2017)
Isaac UpsalKarpenko,– September
2018

27

Accounting for polarized feeddown

Becattini,Lisa,Upsal, Voloshin Phys. Rev. C 95, 054902 (2017)
Isaac UpsalKarpenko,– September
2018

28

Accounting for polarized feed-down
21
ωf
C−f Σ R C Σ R S R ( S R +1 )∑LR L RR
33T=B
21f
C−f CS ( S +1 )∑T
3 R LR L R 3 Σ R Σ R R R( )[((0000))

21f
C−f C∑( S +1 ) m R
3 R LR LR 3 Σ R Σ R R
21f
C−f C
∑
( S +1 ) m R
3 R LR LR 3 Σ R Σ R R((− f L R = fraction of L s that originate from parent R→ L− C L R = coefficient of spin transfer from parent R to daughter L− S R= parent particle spin
− m R is the magnetic moment of particle R0000))−1−1**]( )PmeasLP measL

From a statistical
hadronization modelwith STARmeasurements asparameter inputs(THERMUS)− overlines denote antiparticles** ℏ=k B =1
Becattini,
Lisa,
Upsal, Voloshin Phys. Rev. C 95, 054902 (2017)
Isaac UpsalKarpenko,– September
2018

29

Extracted Physical Parameters• Significant vorticity signal– Falling with energy, despite
increasing Jsys
– 6σ average for 7.7-39 GeV– P L = ω ∼5σ average  %2Tprimary• Magnetic fieldeℏ– mN≡, where m p is the2 mp
proton mass
– positive value, 1.5σ average σ averagefor 7.7-39 GeV
Isaac Upsal – September 201830

Vorticity ~ theory expectation• Thermal vorticity:ω ≈ 2−10 %Tω≈0.02−0.09 fm−1 (T assumed =160 MeV)

• Magnitude, √s-dep. in range oftransport & 3D viscous hydrocalculations with rotation
Jiang et al,PRC94 044910 (2016)
Csernai et al, PRC90 021904(R) (2014)

Isaac Upsal – September 201831

Polarization ~ theory expectation (I)●3+1D viscous hydrodynamics●Not very sensitive to shearviscosity●●

Very sensitive to initial conditions

arXiv: 1805.04400
arXiv: 1805.04400

Expectation: falling with √sSTAR, Nature 548, 62–65 (2017)

Compare “feed-down corrected” curve indashed magenta line
Iu. Karpenko and F. Becattini Eur. Phys. J. C (2017) 77: 213
Isaac Upsal – September 201832

Polarization ~ theory expectation (II)Phys. Rev. C 96, 024906(2017)

arXiv:1704.01507

AMPT

arXiv:1703.03770

Isaac Upsal – September 2018

Hydro

arXiv:1704.02142

33

B-Field ~ theory expectation
Magnetic field:• Expected signB∼10 14 TeslaeB∼1 m2p∼0.5σ average  fm−2
• Magnitude at high end of theory
expectation (expectations vary byorders of magnitude)• But... consistent with zero
– A definitive statement requires
improved statistics/EP
determination

effect of QGP
electricalconductivity

L. McLerran, V. Skokov Nucl.Phys. A929 (2014) 184-190
Isaac Upsal – September 201834

Comparison of QGP superlatives
Supercell
tornadoOcean
flow

Jupiter’s
spotSTAR

Soap
bubbles

QGP!!

Superfluid
nanodroplets

Explosivecharges

Pulsars

EarthSunspotsFridgemagnets

Nat’l High
MagneticField Lab

QGP??

Magnetars
Isaac Upsal – September 201835

Connection: CVEBBBBB• Polarization not inherentlychiral• Large uncertainty term, μ5σ average ,in the delta correlator(related to Chern–Simons)

BBBBB• For neutral baryons(Lambdas) correlator
predicts separation of B#
along vorticity, ωJ E=N c m5σ average 3p2STAR PRC8154908 (2010)

mB ωLiwen Wen

Isaac Upsal – September 201836

Connection: CME• Large theoreticaluncertainly on B (orders ofmagnitude + √sNN)• Large uncertainty term, μ5σ average ,in the delta correlator(related to Chern–Simons)-----+++++• For charged particles CME
predicts separation of +/along B

J E=N c m5σ average 
3p2

BIsaac Upsal – September 2018

STAR PRC8154908 (2010)37

Summary I• Non-central heavy-ion collisions create QGP with highvorticity– generated by early shear viscosity (closely related to initial conditions),
persists through low viscosity– fundamental feature of any fluid, unmeasured until now in heavy-ioncollisions• relevance for other hydro-based conclusions?

• Huge and rapidly-changing B-field in non-central collisions– not directly measured– theoretical predictions vary by orders of magnitude– sensitive to electrical conductivity, early dynamics• Both of these extreme conditions must be established &understood to put recent claims of chiral effects on firm ground
Isaac Upsal – September 201838

Summary II• Global hyperon polarization: unique probe of vorticity & Bfield– non-exotic, non-chiral– quantitative input to calibrate chiral phenomena• Interpretation in magnetic-vortical model:– clear vortical component of right sign
– magnetic component of right sign, magnitude hinted at in BES, butconsistent with zero at each √sNN

• Azimuthal dependence may offer more insight into modeling–hint of BES signal, but clearer 200 GeV signal–results for Lambda and Anti-Lambda are consistent for 200GeV

Isaac Upsal – September 201839

BES-II: 2019-2020

BES-II ~ 2019-2020• Collider (e-cooling) & detector upgrades• Finer-grained measurements•

what drives energy dependence of P?

• Increase statistics by order of magnitude•stat. errorbars reduced by ~3• Improve avg 1st-order RP resolution by2x
Isaac Upsal – September 2018•stat. errorbars reduced by another ~240

END
Isaac Upsal – September 2018

41

Azimuthal dependence (I)• Naively collision starts with strongest
vorticity gradient in plane• A model predicts the opposite
dependence• The dependence of P H on ϕ L−Ψ1tests spin local thermal equilibrium
and model initial conditions
Karpenko & Becattini EPJC (2017)77:213Isaac Upsal – September 2018

42

Azimuthal dependence (II)• In opposition to themodel prediction
STAR sees a larger
polarization in in-plane
than in out-of-plane• Represents animportant tension inthe measurement
Biao Tu, poster @ QM18

Isaac Upsal – September 2018

43

Centrality

STAR, arXiv: 1805σ average .04400●Jiang et al, PRC90 021904(R) (2014)

Signal increasing with decreasing centrality falls well in line with theory

Isaac Upsal – September 201844

Polarization along the beam direction
Takafumi Niida, talk @ QM18

beam direction●2nd-order
event plane• Local velocity gradients dueto elliptic flow may produce
vorticity along beam
direction• This is a brand new area tolook!
• Look for sinusoidal
polarization structure
projected onto the beam
direction
S. Voloshin, EPJ Web Conf. 17(2018)
Isaac Upsal10700– September 2018

●F. Becattini and I. Karpenko,
PRL.120.012302 (2018)

Clear signal at
200 GeV
Signalqualitatively
disagrees withhydro model45

Phi Meson Polarization (I)Region of recombinationof polarized quarks

Polarized quark
fragmentation region

Chensheng Zhou (CPOD 2017)
Isaac Upsal – September 201846

Phi Meson Polarization (II)●●Polarization
measure is madeWRT both thefirst and second
order event planes
Significant
deviation from
1/3 is seen forhigher energies
Chensheng Zhou (CPOD 2017)

Isaac Upsal – September 2018

47

ALICE Results●●●At 2.76TeV ALICEsees a null result
Strongly supports
vorticity falling withbeam energy
No hint of LambdaAntiLambda
difference

M. Konyushikhin QM 2017 (poster)
Isaac Upsal – September 201848

B field BES II Projection●●

Using statistics fromChi Yang's QM
2017 talk for BES IIand 1B events for
27GeV in 2018
Assuming presentcenterpoints 9.6
sigma result

Isaac Upsal – September 2018

49

EPD BBC comparison

Isaac Upsal – September 2018

50
50

Production Plane – NOT Global Polarization
Known effect in p+p collisions[e.g. Bunce et al, PRL 36 1113 (1976)]• Lambda polarization at forward rapidity relative toproduction planeLpp

L
L

Bothmay
contribute• Vortical or QCD spin-orbit:
Lambda and Anti-Lambda spinsaligned with L• (electro)magnetic coupling:
Lambdas anti-aligned, and AntiLambdas aligned• Polarization w/ production plane:• No integrated effect at midrapidity for Lambda• No (known) effect at all for AntiLambdas

Isaac Upsal – September 201851

Topological dependent efficiency (I)In Lambda frame, proton & pion have equal-magnitude momentum, but not in STAR framepion emitted backward in Lambda c.m., → tight curl, large DCA (distance to collision vertex)→ much-reduced efficiency→ higher efficiency to find negative-helicity Lambdas

ppp
proton emitted
backward in Λ frame
Isaac Upsal – September 2018

pproton emittedforward in Λ frame
52

Topological dependent efficiency (II)• Same effect seen in embedding/GEANT simulations• pT-dependent• not correlated with RP• explicitly cancels when summing regions separated
by 180 degrees

effect does not affect PHHIJING events through simulated STAR detector & tracking

input
outputp̂proton ×p̂L
Isaac Upsal – September 2018

53

Azimuthal dependence (BES)2• Measure Lambda azimuthal
dependence by fitting (likev2) a second-order azimuthal

2

χ=

∑

∑

Centrality, i ϕ bins, j( P H + R i P 2 cos(2 x j )−Pi , j )2σi , jdependent polarization P2STAR preliminary• To properly perform
resolution correction
2χminimize
where x isϕ L−Ψ 1 (second order)• Uncertainties for AntiLambda results larger thanplot range
Isaac Upsal – September 2018

54

Azimuthal dependence (BES)• Measure Lambda azimuthal
dependence by fitting (likev2) a second-order azimuthal
dependent polarization P 2

χ2=

∑

∑

Centrality, i ϕ bins, j( P H + R i P 2 cos (2 x j )−P i , j )2σ 2i , jSTAR preliminary• To properly perform
resolution correction
2minimize χ where x is
ϕ L −Ψ 1 (second order)• Errors for Anti-Lambda
results are too large todisplay
Isaac Upsal – September 201855

27GeV (2018) Magnetic Search ( P L−P L )27GeV (basedon BES I errorbars)●Assuming
REPD = 2RBBC●Z axis depicts
the significanceof the gap in
between theLambda andAntiLambda
Polarizations

Significance of Lambda-AntiLambda●

Isaac Upsal – September 2018

BUR

56

EPD BBC comparison (I)Isaac Upsal – September 201857