Lambda polarization* and femtoscopy** at RHIC …Iurii Karpenko, Femtoscopy and Lambda polarization...
Transcript of Lambda polarization* and femtoscopy** at RHIC …Iurii Karpenko, Femtoscopy and Lambda polarization...
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Lambda polarization∗ and femtoscopy∗∗
at RHIC BES energies
Iurii KARPENKO
*with Francesco Becattini
**with P.Batyuk, R.Lednicky, L.Malinina, K.Mikhailov, O.Rogachevsky,D.Wielanek
Istituto Nazionale di Fisica Nucleare - sezione Firenze,Universitá di Firenze
Iurii Karpenko, Femtoscopy and Lambda polarization at RHIC BES energies 1/26
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Highlight: recent Λ polarization measurementPreliminary results from STAR, talk of M. Lisa at QCD Chirality Workshop 2016
CorrectedRPres&combinatoricbkgrnd&feed-down
M.A.Lisa-QCDChiralityWorkshop-UCLA-February2016 22
• Subtrac+ngresidualeffectfromcombinatoricbackgroundbelowmasspeak• Correc+ngforfeed-downfromSigma0
• previousSTARresults(correctedforsign)con+nuesystema+cs
Σ0
12+!→Λ
12+! + γ
1−!
p-wave decay( )• Asignificantfrac+on(~30%)ofourLambdasareactuallyfeed-downfromSigma0• ThedaughterLambdatendstohavespindirec+onoppositethatoftheparentSigma
sta+s+calerrorsonly.
This measurement can be realized because of “self-analyzing” nature of Λ decay, which preferentially emits
daugter proton in the direction of Λ spin: dWdΩ∗ = 1
4π(1 + αP cosθ ∗)
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Theory side: polarization of fermions in fluidF. Becattini, V. Chandra, L. Del Zanna, E. Grossi, Ann. Phys. 338 (2013) 32(also Ren-hong Fang, Long-gang Pang, Qun Wang, Xin-nian Wang, ICTS-USTC-16-05, arXiv:1604.04036)
For the spin 12 particles produced at the particlization surface:
Sµ (p) =1
8m
∫dΣλ pλ f (x ,p) · (1− f (x ,p))εµνρσ pσ ∂ν βσ∫
dΣλ pλ f (x ,p)
where βµ =uµ
T is inverse four-temperature field.
The polarization depends on the the thermal vorticity ωµν =−12 (∂µ βν −∂ν βµ ).
polarization is close or equal for particles and antiparticlescaused not only by velocity, but also temperature gradients
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Existing polarization calculations from hydro models (1)F. Becattini, L.P. Csernai, D.J. Wang, and Y.L. Xie,Phys. Rev. C 88, 034905 (2013)√
sNN = 200 GeV, midrapidity Λ
Initial state from Yang-Mills dynamics + 3D ideal hydroexpansion
X
Z
Y
J
Λ Λ
Λ
Py on the order of few % even at px = py = 0 and up to 8% (with oppositesign) for high px !
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Existing polarization calculations from hydro models (2)
F. Becattini, G. Inghirami et al., Euro Phys. J. C 75:406(2015)√
sNN = 200 GeV, b = 11.6 fm, midrapidity Λ
X
Z
Y
J
Λ Λ
Λ
Obtained with optical Glauber IC + parametrized rapidity dependence a-láP. Bozek and I. Wyskiel, Phys. Rev. C 81 (2010) 054902
Π0x
-4 -3 -2 -1 0 1 2 3 4
px [GeV]
-4
-3
-2
-1
0
1
2
3
4
py [G
eV
]
-2.0 10-3
-1.5 10-3
-1.0 10-3
-5.0 10-4
0.0 100
5.0 10-4
1.0 10-3
1.5 10-3
2.0 10-3
Π0y
-4 -3 -2 -1 0 1 2 3 4
px [GeV]
-4
-3
-2
-1
0
1
2
3
4
py [G
eV
]
-2.0 10-3
-1.5 10-3
-1.0 10-3
-5.0 10-4
0.0 100
5.0 10-4
1.0 10-3
1.5 10-3
Momentum integrated Px and Pz average out to zero, and Py ≈−0.4%.Iurii Karpenko, Femtoscopy and Lambda polarization at RHIC BES energies 5/26
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Existing polarization calculations from hydro models (3)Long-Gang Pang, Hannah Petersen, Qun Wang, Xin-Nian Wang,arXiv:1605.04024
Initial state from AMPT + 3D viscous hydro
2
0
2
4
P(
1)P
(2)
|Y| [0, 1]
|Y| [2, 3]
|Y| [4, 5]
×10 6
(a) v/s = 0. 08v/s = 0. 0
0 /4 /2 3 /4= | 1 2|
5
0
5
10
P(
1)P(
2) Y [0, 1]Y [2, 3]Y [4, 5]
×10 6
(b)
0
0. 5
1
1. 5
2
P(
1)P(
2)
×10 5 (a) |Y| [2, 3], v/s = 0. 08
0 /4 /2 3 /4= | 1 2|
5
0
5
10
P(
1)P(
2)
Au + Au 62. 4 GeVAu + Au 200 GeVPb + Pb 2. 76 TeV
×10 6 (b) |Y| [0, 1], v/s = 0. 08
20 30% 0 5%20 30% 0 5%20 30% 0 5%20 30% 0 5%
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Tool for investigation: cascade+hydro(+cascade) model for BES
Hybrid model: initial state + hydrodynamic phase + hadronic cascade thermalization particlization Initial state: thick pancakes
I boost ivariance is not a good approximation→ need for 3 dimensional evolution
I CGC picture does not work well either
Baryon and electric chargesI obtained from the initial stateI included in hydro phaseI taken into account at particlization
Event-by-event hydrodynamical treatment
Pictures taken from: https://www.jyu.fi/fysiikka/tutkimus/suurenergia/urhic
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The model: UrQMD + vHLLE + UrQMDPre-thermal evolution: UrQMD cascade until τ = τ0 = const , τ0 = 2R
γvzFluctuating initial state, event-by-event hydrodynamics
Hydrodynamic phase:
∂;νT µν = 0, ∂;νNν = 0 < uγ∂;γ π
µν >=−πµν −π
µν
NSτπ
− 43
πµν
∂;γuγ
* Bulk viscosity ζ = 0, charge diffusion=0vHLLE code: free and open source. Comput. Phys. Commun. 185 (2014), 3016https://github.com/yukarpenko/vhlle
Fluid→particle transition and hadronic phaseCooper-Frye prescription at ε = εsw:
p0 d3nid3p
= ∑ f (x ,p)pµ ∆σµ
f (x ,p) = feq ·(
1 + (1∓ feq)pµ pν πµν
2T 2(ε + p)
)∆σi using Corneliussubroutine∗
Hadron gas phase: back toUrQMD cascade
∗Huovinen and Petersen, Eur.Phys.J. A 48 (2012), 171
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Validating the model for bulk hadronic observables
y-4 -3 -2 -1 0 1 2 3 4
dN/d
y
0
20
40
60
80
100
120/s=0.2η
-πNA49, NA49, K+NA49, K-
=40 A GeVlabE0-5% central
(c)
-m [GeV]Tm0 0.2 0.4 0.6 0.8 1 1.2
dy)
T d
mT
N/(
m2 d
-110
1
10
210
310
/s=0.2η-πNA49,
NA49, K-NA49, K+NA49, p
=40 A GeV, 0-5% centrallabE
(c)
η-5 -4 -3 -2 -1 0 1 2 3 4 5
η/d
chdN
0
100
200
300
400
500
600
700
=200 GeVs=62.4 GeVs=39 GeVs=19.6 GeVs
0-6% PHOBOS
η/dch
dN
[GeV]NNs10 210
nv
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.1EP2STAR vEP3STAR v
)s) and R(s/s(η, 2v)s) and R(s/s(η, 3v
, 20-30% centralEPnv
2v
3v
IK, Huovinen, Petersen, Bleicher, Phys.Rev. C91 (2015) no.6, 064901Iurii Karpenko, Femtoscopy and Lambda polarization at RHIC BES energies 9/26
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Λ polarization signal from the model
geometry sketch:
X
Z
Y
J
Λ Λ
Λ
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pT differential polarization of Λ,√
sNN = 19.6 GeV, 40-50% Au-Au
4 3 2 1 0 1 2 3 4px [GeV]
432101234
py [G
eV]
Pb , rest frame
0.01000.00750.00500.0025
0.00000.00250.00500.00750.0100
4 3 2 1 0 1 2 3 4px [GeV]
432101234
py [G
eV]
PJ , rest frame
0.0120.0090.0060.003
0.0000.0030.0060.0090.012
4 3 2 1 0 1 2 3 4px [GeV]
432101234
py [G
eV]
P||
0.040.030.020.01
0.000.010.020.030.04
only Λ produced at particlization
P|| is the largest component atlarge px and py
Pb and P|| average out to zero
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The quadrupole polarization patternsare induced by complex vorticitypatterns at the particlization surface:
Pb ∝ ωtzpy
PJ ∝ ωxzp0
ωµν =−12 (∂µ βν −∂ν βµ )
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Collision energy dependence
7.7 19.6 39.0 62.4 200√sNN [GeV]
0.000
0.002
0.004
0.006
0.008
0.010
0.012
0.014
0.016
0.018
P∗
Au-Au, 20-50% central
P ∗J
P ∗b
Is it a manifestation of larger fireball angular momentum at lower√
sNN?Iurii Karpenko, Femtoscopy and Lambda polarization at RHIC BES energies 12/26
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Not really: Jy actually increases with increase of√
sNN.
7.7 19.6 39.0 62.4 200√sNN [GeV]
0
20000
40000
60000
80000
100000
120000
140000
160000
J [
]
J vs √sNN
20-50% central
7.7 19.6 39.0 62.4 200√sNN [GeV]
0
1
2
3
4
5
J/E
[fm
]
J/E vs √sNN
20-50% central
Total angular momentum increases with increasing energy of the fireball.Jy/E shows weak dependence on
√sNN.
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Centrality dependence
Simulation of√
sNN = 39 GeV Au-Au, 0-50% central events:
0 50 100 150 200 250 300 350 400Npart
0
50000
100000
150000
200000
J [
]
√sNN =39 GeV Au-Au
J vs Npart
0 50 100 150 200 250 300 350 400Npart
0.005
0.000
0.005
0.010
0.015
0.020
0.025
PJ
√sNN =39 GeV
PJ vs Npart
Total angular momentum has a peak at a certain Npart, whereas thepolarization steadily increases towards low Npart.
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Sensitivity to parameters of the model
7.7 19.6 39.0 62.4 200√sNN [GeV]
0.000
0.005
0.010
0.015
0.020
P∗ J
20-50% central
P ∗J vs
√sNN
η/s ± 100%R ± 40%Rη ± 40%εsw ± 40%
Collision energy dependence is robust with respect to variation of theparameters of the model.
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Why does PJ increase at lower BES energies?
1) Different initial vorticity distribution:
baryon stopping at lower√
sNN⇓
shear flow in beam directiontransparency at higher
√sNN
β field
1.5 1.0 0.5 0.0 0.5 1.0 1.5η
6
4
2
0
2
4
6
x [fm
]
√sNN =7.7 GeV, 20-50% central Au-Au, averaged IC
0.0
0.4
0.8
1.2
1.6
2.0
2.4
2.8
3.2
β field
4 3 2 1 0 1 2 3 4η
8
6
4
2
0
2
4
6
8
x [fm
]
√sNN =62.4 GeV, 20-50% central Au-Au, averaged IC
0
2
4
6
8
10
12
14
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Why does PJ increase at lower BES energies?2) Longer hydrodynamic evolution at higher
√sNN further dilutes the vorticity
1 2 3 4 5 6τ [fm/c]
0.05
0.00
0.05
0.10
0.15
0.20
xz
xz, √sNN =7.7 GeV, 20-50% central
1 2 3 4 5 6τ [fm/c]
0.05
0.00
0.05
0.10
0.15
0.20
xz
xz, √sNN =62.4 GeV, 20-50% central
Figs: Distribution of xz component of thermal vroticity (responsible for PJ at px = py = 0) overparticlization hypersurface.
these two effects result in lower polarization at higher collision energies
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Interactions in the post-hydro stageSpin (polarization) transfer in two-body resonance decay: S∗
Λ,Σ0 = CX→Λ,Σ0 ·S∗X
S∗Λ =NΛS∗Λ,prim+∑
XNX S∗X[CX→ΛbX→Λ− 1
3 CX→Σ0 bX→Σ0 ]
NΛ+∑X
bX→ΛNX +∑X
bX→Σ0 NX
X JP SXSΛ,prim
CX→Λ,Σ0SΛ(X)
SΛ,prim
Σ0 (1/2)+ 1 −1/3 −1/3Σ(1385) (3/2)+ 5 1/3 5/3Λ(1405) (1/2)− 1 1 1Λ(1520) (3/2)− 5 −1/5 −1Λ(1600) (1/2)+ 1 −1/3 −1/3Σ(1660) (1/2)+ 1 −1/3 −1/3Σ(1670) (3/2)− 5 −1/5 −1
Dotted: primary+Σ0 + Σ(1385)
Dashed: primary+Σ0 + · · ·+ Σ(1670)
7.7 19.6 39.0 62.4 200√sNN [GeV]
0.000
0.002
0.004
0.006
0.008
0.010
0.012
0.014
0.016
0.018
P∗
Au-Au, 20-50% central
P ∗J
primary Λfeed-down corrected
P ∗b
What is not taken into account (yet):
Λ and Σ0 actively rescatter in hadronic phase
Elastic rescatterings are expected to randomize the spin orientation, thussuppressing the polarization signal.
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EoS dependence & femtoscopyfrom the model
Femtoscopy: P.Batyuk, R.Lednicky, L.Malinina, K.Mikhailov, O.Rogachevsky,IK, D.Wielanek
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EoS dependence: Chiral EoS vs ’EoS Q’
Take same parameters but change the EoS:
[fm/c]τ1 2 3 4 5 6 7 8 9 10
τdN
/d
0
100
200
300
400
500
600 Chiral EoSEoS Q
particlization
=200
GeV
s
39
19.6
7.7
[fm/c]τ2 4 6 8 10 12 14 16 18 20
τdN
/d
0
50
100
150
200
250
Chiral EoSEoS Q
last interactions
=200 GeV
s
39
19.6
7.7
EoS Q increases the average duration of hydro phase,especially at lower collision energies.
But the difference is smeared by the final stage hadronic cascade
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EoS dependence: Chiral EoS vs ’EoS Q’
Final multiplicities and rapidity distributions are unchanged.
[GeV]s10 210
> [
GeV
]T
<p
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
)s) and R(s/s(ηsame, EoS Q
> at midrapidity, 20-30% centralT
<p protons
kaons
pions
[GeV]s10 210
0
0.02
0.04
0.06
0.08
0.1EP2STAR vEP3STAR v
)s) and R(s/s(ηsame, with 1PT EoS
, 20-30% centralEP3 and vEP2v
2v
3v
EoS Q results in slightly less radial flow→ mean pT is decreased.The biggest effect is for the elliptic flow.
IK, P.Huovinen, H.Petersen, M.Bleicher, arXiv:1601.00800
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Femtoscopic radii from vHLLE+UrQMD
0-5% central Au-Au collisions: vHLLE+UrQMD using crossover EoS, 1PT EoS
0.2 0.4 0.6
[fm
]o
ut
R 4567
7.7 GeVNNs
0.2 0.4 0.6
4567
11.5 GeVNNs
0.2 0.4 0.6
4567
19.6 GeVNNs
0.2 0.4 0.6
4567
27 GeVNNs
0.2 0.4 0.6
4567
39 GeVNNs
0.2 0.4 0.6
4567
62.4 GeVNNs
0.2 0.4 0.6
[fm
]si
de
R
4
5
0.2 0.4 0.6
4
5
0.2 0.4 0.6
4
5
0.2 0.4 0.6
4
5
0.2 0.4 0.6
4
5
0.2 0.4 0.6
4
5
0.2 0.4 0.6
[fm
]lo
ng
R
4
6
8
0.2 0.4 0.6
4
6
8
0.2 0.4 0.6
4
6
8
0.2 0.4 0.6
4
6
8
0.2 0.4 0.6
4
6
8
0.2 0.4 0.6
4
6
8
0.2 0.4 0.6
sid
e/R
ou
tR
1.2
1.4
0.2 0.4 0.6
1.2
1.4
[GeV/c]Tm0.2 0.4 0.6
1.2
1.4
0.2 0.4 0.6
1.2
1.4
0.2 0.4 0.6
1.2
1.4
0.2 0.4 0.6
1.2
1.4
P.Batyuk, R.Lednicky, L.Malinina, K.Mikhailov, O.Rogachevsky, IK, D.Wielanek, in preparation
Iurii Karpenko, Femtoscopy and Lambda polarization at RHIC BES energies 21/26
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Rout/Rside and R2out−R2
side
0-5% central Au-Au collisions: vHLLE+UrQMD using crossover EoS, 1PT EoS
P.Batyuk, R.Lednicky, L.Malinina, K.Mikhailov, O.Rogachevsky, IK, D.Wielanek, in preparation
Iurii Karpenko, Femtoscopy and Lambda polarization at RHIC BES energies 22/26
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SummaryPolarization:
We observe a strong increase of mean Λ polarization towards lowest RHIC BESenergies.
The PJ is at least twice smaller than the (preliminary) experimental value.
The collision energy dependence is robust with respect to variation of modelparameters.
Feed-down from Σ0 and Σ(1385) counterplay and leave the polarization almostunchanged. As more resonances are included, the resulting Λ polarization goesdown by 15%.
Elastic rescatterings are expected to suppress the calculated polarization signal.
The polarization has a potential to rule out the initial state models, especially inthe BES energies. Differently prepared initial states can result in same flowobservables, but very different final Λ polarization.
Femtoscopy:
Femtoscopic observables seems to prefer chiral model EoS over Bag model EoS
R2out−R2
side shows monotonic increase in the model, and it essentially magnifiessmaller discrepancies for Rout and Rside between model/experiment.
Iurii Karpenko, Femtoscopy and Lambda polarization at RHIC BES energies 23/26
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Outlook:At lower end of the BES, pre-hydro stage in a “sandwich” approach is too long:
UrQMD 3.4, J. Auvinen, H. Petersen, Phys.Rev.C 88:064908,2013
Charged hadrons, b = 0 - 3.4 fm
Inte
grat
ed v
2
0
0.005
0.01
0.015
0.02
0.025
0.03
√sNN [GeV]10 100
Before hydroAfter hydroAfter hadronic rescattering
Event plane analysis
a) Charged hadrons, b = 8.2 - 9.4 fm
Inte
grat
ed v
20
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
√sNN [GeV]10 100
Before hydroAfter hydroAfter hadronic rescattering
Event plane analysis
b)
This can be overcome with multi-fluid dynamics (with cold nuclear matter IC),or with an IC model allowing for dynamical fluidization.
Iurii Karpenko, Femtoscopy and Lambda polarization at RHIC BES energies 24/26
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http://theory.gsi.de/~ivanov/mfd/
Iurii Karpenko, Femtoscopy and Lambda polarization at RHIC BES energies 25/26
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Some preparatory work: coupling old 3-fluid hydro to UrQMD
Iurii Karpenko, Femtoscopy and Lambda polarization at RHIC BES energies 26/26
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Backup slides
Iurii Karpenko, Femtoscopy and Lambda polarization at RHIC BES energies 26/26
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Parameter values used to approach the basic hadronicobservablesEoS: Chiral model, εsw = 0.5 GeV/fm3.√
s[GeV]
τ0[fm/c]
R⊥[fm]
Rz[fm]
η/s
7.7 3.2 1.4 0.5 0.28.8 2.83 1.4 0.5 0.211.5 2.1 1.4 0.5 0.217.3 1.42 1.4 0.5 0.1519.6 1.22 1.4 0.5 0.1527 1.0 1.2 0.5 0.1239 0.9* 1.0 0.7 0.0862.4 0.7* 1.0 0.7 0.08200 0.4* 1.0 1.0 0.08
*here we increase τ0 as compared toτ0 = 2R
γvz.
[GeV]NNs10 210
/sη0
0.05
0.1
0.15
0.2
0.25/s vs collision energyηeffective
Green band:same v2 and ±5% change in Teff.
! Actual error bar would require a proper χ2 fitting of the model parameters(and enormous amount of CPU time).
IK, Huovinen, Petersen, Bleicher, Phys.Rev. C91 (2015) no.6, 064901
Iurii Karpenko, Femtoscopy and Lambda polarization at RHIC BES energies 26/26