Lambda polarization* and femtoscopy** at RHIC …Iurii Karpenko, Femtoscopy and Lambda polarization...

30
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

Transcript of Lambda polarization* and femtoscopy** at RHIC …Iurii Karpenko, Femtoscopy and Lambda polarization...

Page 1: Lambda polarization* and femtoscopy** at RHIC …Iurii Karpenko, Femtoscopy and Lambda polarization at RHIC BES energies2/26 Theory side: polarization of fermions in fluid F. Becattini,

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

Page 2: Lambda polarization* and femtoscopy** at RHIC …Iurii Karpenko, Femtoscopy and Lambda polarization at RHIC BES energies2/26 Theory side: polarization of fermions in fluid F. Becattini,

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 ∗)

Iurii Karpenko, Femtoscopy and Lambda polarization at RHIC BES energies 2/26

Page 3: Lambda polarization* and femtoscopy** at RHIC …Iurii Karpenko, Femtoscopy and Lambda polarization at RHIC BES energies2/26 Theory side: polarization of fermions in fluid F. Becattini,

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

Iurii Karpenko, Femtoscopy and Lambda polarization at RHIC BES energies 3/26

Page 4: Lambda polarization* and femtoscopy** at RHIC …Iurii Karpenko, Femtoscopy and Lambda polarization at RHIC BES energies2/26 Theory side: polarization of fermions in fluid F. Becattini,

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 !

Iurii Karpenko, Femtoscopy and Lambda polarization at RHIC BES energies 4/26

Page 5: Lambda polarization* and femtoscopy** at RHIC …Iurii Karpenko, Femtoscopy and Lambda polarization at RHIC BES energies2/26 Theory side: polarization of fermions in fluid F. Becattini,

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

Page 6: Lambda polarization* and femtoscopy** at RHIC …Iurii Karpenko, Femtoscopy and Lambda polarization at RHIC BES energies2/26 Theory side: polarization of fermions in fluid F. Becattini,

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%

Iurii Karpenko, Femtoscopy and Lambda polarization at RHIC BES energies 6/26

Page 7: Lambda polarization* and femtoscopy** at RHIC …Iurii Karpenko, Femtoscopy and Lambda polarization at RHIC BES energies2/26 Theory side: polarization of fermions in fluid F. Becattini,

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

Iurii Karpenko, Femtoscopy and Lambda polarization at RHIC BES energies 7/26

Page 8: Lambda polarization* and femtoscopy** at RHIC …Iurii Karpenko, Femtoscopy and Lambda polarization at RHIC BES energies2/26 Theory side: polarization of fermions in fluid F. Becattini,

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

Iurii Karpenko, Femtoscopy and Lambda polarization at RHIC BES energies 8/26

Page 9: Lambda polarization* and femtoscopy** at RHIC …Iurii Karpenko, Femtoscopy and Lambda polarization at RHIC BES energies2/26 Theory side: polarization of fermions in fluid F. Becattini,

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

Page 10: Lambda polarization* and femtoscopy** at RHIC …Iurii Karpenko, Femtoscopy and Lambda polarization at RHIC BES energies2/26 Theory side: polarization of fermions in fluid F. Becattini,

Λ polarization signal from the model

geometry sketch:

X

Z

Y

J

Λ Λ

Λ

Iurii Karpenko, Femtoscopy and Lambda polarization at RHIC BES energies 9/26

Page 11: Lambda polarization* and femtoscopy** at RHIC …Iurii Karpenko, Femtoscopy and Lambda polarization at RHIC BES energies2/26 Theory side: polarization of fermions in fluid F. Becattini,

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

Iurii Karpenko, Femtoscopy and Lambda polarization at RHIC BES energies 10/26

Page 12: Lambda polarization* and femtoscopy** at RHIC …Iurii Karpenko, Femtoscopy and Lambda polarization at RHIC BES energies2/26 Theory side: polarization of fermions in fluid F. Becattini,

The quadrupole polarization patternsare induced by complex vorticitypatterns at the particlization surface:

Pb ∝ ωtzpy

PJ ∝ ωxzp0

ωµν =−12 (∂µ βν −∂ν βµ )

Iurii Karpenko, Femtoscopy and Lambda polarization at RHIC BES energies 11/26

Page 13: Lambda polarization* and femtoscopy** at RHIC …Iurii Karpenko, Femtoscopy and Lambda polarization at RHIC BES energies2/26 Theory side: polarization of fermions in fluid F. Becattini,

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

Page 14: Lambda polarization* and femtoscopy** at RHIC …Iurii Karpenko, Femtoscopy and Lambda polarization at RHIC BES energies2/26 Theory side: polarization of fermions in fluid F. Becattini,

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.

Iurii Karpenko, Femtoscopy and Lambda polarization at RHIC BES energies 13/26

Page 15: Lambda polarization* and femtoscopy** at RHIC …Iurii Karpenko, Femtoscopy and Lambda polarization at RHIC BES energies2/26 Theory side: polarization of fermions in fluid F. Becattini,

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.

Iurii Karpenko, Femtoscopy and Lambda polarization at RHIC BES energies 14/26

Page 16: Lambda polarization* and femtoscopy** at RHIC …Iurii Karpenko, Femtoscopy and Lambda polarization at RHIC BES energies2/26 Theory side: polarization of fermions in fluid F. Becattini,

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.

Iurii Karpenko, Femtoscopy and Lambda polarization at RHIC BES energies 15/26

Page 17: Lambda polarization* and femtoscopy** at RHIC …Iurii Karpenko, Femtoscopy and Lambda polarization at RHIC BES energies2/26 Theory side: polarization of fermions in fluid F. Becattini,

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

Iurii Karpenko, Femtoscopy and Lambda polarization at RHIC BES energies 16/26

Page 18: Lambda polarization* and femtoscopy** at RHIC …Iurii Karpenko, Femtoscopy and Lambda polarization at RHIC BES energies2/26 Theory side: polarization of fermions in fluid F. Becattini,

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

Iurii Karpenko, Femtoscopy and Lambda polarization at RHIC BES energies 17/26

Page 19: Lambda polarization* and femtoscopy** at RHIC …Iurii Karpenko, Femtoscopy and Lambda polarization at RHIC BES energies2/26 Theory side: polarization of fermions in fluid F. Becattini,

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.

Iurii Karpenko, Femtoscopy and Lambda polarization at RHIC BES energies 18/26

Page 20: Lambda polarization* and femtoscopy** at RHIC …Iurii Karpenko, Femtoscopy and Lambda polarization at RHIC BES energies2/26 Theory side: polarization of fermions in fluid F. Becattini,

EoS dependence & femtoscopyfrom the model

Femtoscopy: P.Batyuk, R.Lednicky, L.Malinina, K.Mikhailov, O.Rogachevsky,IK, D.Wielanek

Iurii Karpenko, Femtoscopy and Lambda polarization at RHIC BES energies 18/26

Page 21: Lambda polarization* and femtoscopy** at RHIC …Iurii Karpenko, Femtoscopy and Lambda polarization at RHIC BES energies2/26 Theory side: polarization of fermions in fluid F. Becattini,

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

Iurii Karpenko, Femtoscopy and Lambda polarization at RHIC BES energies 19/26

Page 22: Lambda polarization* and femtoscopy** at RHIC …Iurii Karpenko, Femtoscopy and Lambda polarization at RHIC BES energies2/26 Theory side: polarization of fermions in fluid F. Becattini,

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

Iurii Karpenko, Femtoscopy and Lambda polarization at RHIC BES energies 20/26

Page 23: Lambda polarization* and femtoscopy** at RHIC …Iurii Karpenko, Femtoscopy and Lambda polarization at RHIC BES energies2/26 Theory side: polarization of fermions in fluid F. Becattini,

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

Page 24: Lambda polarization* and femtoscopy** at RHIC …Iurii Karpenko, Femtoscopy and Lambda polarization at RHIC BES energies2/26 Theory side: polarization of fermions in fluid F. Becattini,

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

Page 25: Lambda polarization* and femtoscopy** at RHIC …Iurii Karpenko, Femtoscopy and Lambda polarization at RHIC BES energies2/26 Theory side: polarization of fermions in fluid F. Becattini,

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

Page 26: Lambda polarization* and femtoscopy** at RHIC …Iurii Karpenko, Femtoscopy and Lambda polarization at RHIC BES energies2/26 Theory side: polarization of fermions in fluid F. Becattini,

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.

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Page 27: Lambda polarization* and femtoscopy** at RHIC …Iurii Karpenko, Femtoscopy and Lambda polarization at RHIC BES energies2/26 Theory side: polarization of fermions in fluid F. Becattini,

http://theory.gsi.de/~ivanov/mfd/

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Page 28: Lambda polarization* and femtoscopy** at RHIC …Iurii Karpenko, Femtoscopy and Lambda polarization at RHIC BES energies2/26 Theory side: polarization of fermions in fluid F. Becattini,

Some preparatory work: coupling old 3-fluid hydro to UrQMD

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Page 29: Lambda polarization* and femtoscopy** at RHIC …Iurii Karpenko, Femtoscopy and Lambda polarization at RHIC BES energies2/26 Theory side: polarization of fermions in fluid F. Becattini,

Backup slides

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Page 30: Lambda polarization* and femtoscopy** at RHIC …Iurii Karpenko, Femtoscopy and Lambda polarization at RHIC BES energies2/26 Theory side: polarization of fermions in fluid F. Becattini,

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

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