The QCD Workshop on Chirality, Vorticity and Magnetic Field in Heavy Ion Collisions, Feb.23-26, 2016, UCLA Guo-Liang Ma/(SINAP)

AMPT simulations of isobaric collisions

Guo-Liang Ma

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⎯ 9640Zirconium vs 9644Ruthenium

This work is in collaboration with Xu-Guang Huang (FDU) and Wei-Tian Deng (HUST).

Shanghai Institute of Applied Physics, Chinese Academy of Sciences

Guo-Liang Ma/(SINAP)The QCD Workshop on Chirality, Vorticity and Magnetic Field in Heavy Ion Collisions, Feb.23-26, 2016, UCLA

• Motivation

• The AMPT model (CME)

• Ru+Ru vs Zr+Zr

• Summary

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Outline

Guo-Liang Ma/(SINAP)The QCD Workshop on Chirality, Vorticity and Magnetic Field in Heavy Ion Collisions, Feb.23-26, 2016, UCLA

Chiral Magnetic Effect=> charge separation

•The RHIC data are consistent with the CME expectation (dipole charge separation).

PRL 103, 251601 (2009)

dipole

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Guo-Liang Ma/(SINAP)The QCD Workshop on Chirality, Vorticity and Magnetic Field in Heavy Ion Collisions, Feb.23-26, 2016, UCLA

dipole charge separation

(1) Introduction

•We include initial dipole charge separation mechanism into AMPT model.We switch the py values of a percentage f% of the downward moving u quarks with those of the upward moving u-bar quarks, and likewise for d-bar and d quarks.

•We focus on final state effects on the charge separation, including parton cascade, hadronization, resonance decays.

•We do not include magnetic and electric fields, because we assume B and E vanish quickly.

G.-L. Ma, B. Zhang, PLB 700 (2011) 39

dipole

The AMPT model with CME charge separation

⇀ ⇀

u u u u

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f%=(N+upward-N+downward)/(N+upward+N+downward)

Guo-Liang Ma/(SINAP)The QCD Workshop on Chirality, Vorticity and Magnetic Field in Heavy Ion Collisions, Feb.23-26, 2016, UCLA

•The normal AMPT model underestimates the STAR data.•A constant initial charge separation ~10% can describe same-charge data in the presence of final state interactions.•From a percentage of charge separation of 10% in the beginning →1-2% percentage in the end.

G.-L. Ma, B. Zhang, PLB 700 (2011) 39

AMPT results on <cos(ϕa+ϕβ)>

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Guo-Liang Ma/(SINAP)The QCD Workshop on Chirality, Vorticity and Magnetic Field in Heavy Ion Collisions, Feb.23-26, 2016, UCLA

• We use Lienard-Wiechert potential to calculate the impact parameter b dependence of averaged <By> , perpendicular to the reaction plane.

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W.T. Deng and X.G. Huang, PRC 85, 044907 (2012)

b-dependent Magnetic field

<By>(0,0, t=0)

Guo-Liang Ma/(SINAP)The QCD Workshop on Chirality, Vorticity and Magnetic Field in Heavy Ion Collisions, Feb.23-26, 2016, UCLA

f%=(1146.1*A-4/3)*By(b)

• By fitting Au+Au and Cu+Cu data, we get the initial charge separation percentage f%=1146.1A-4/3By.

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b-dependent initial charge sep. percent

open: AMPT (10 mb)solid: Exp. data

blue: opp chargered: same charge

diamond: Au+Autriangle: Cu+Cu

f%=(N+upward-N+downward)/(N+upward+N+downward)~JπR2/Nmult~ A-4/3By

f%=1146.1A-4/3By(b)

Guo-Liang Ma/(SINAP)The QCD Workshop on Chirality, Vorticity and Magnetic Field in Heavy Ion Collisions, Feb.23-26, 2016, UCLA

⎯ 9640Zirconium vs 9644Ruthenium

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Zr+Zr and Ru+Ru 200 GeV

Guo-Liang Ma/(SINAP)The QCD Workshop on Chirality, Vorticity and Magnetic Field in Heavy Ion Collisions, Feb.23-26, 2016, UCLA

Glauber parameters for Zr96 and Ru 96

setting 2 R0 a(d) β2 β4

Ru96 5.0845 0.567 0.053 0.009

Zr96 5.0212 0.574 0.217 0.01

• Two opposite settings of Glauber parameters for Ru96 and Zr96 (http://nrv.jinr.ru/nrv/webnrv/map/).

• which is more ellipsoidal? Ru96 or Zr96?

setting 1 R0 a(d) β2 β4

Ru96 5.0845 0.567 0.1579 0.00

Zr96 5.0212 0.574 0.08 0.00

El.-Magn. properties

Radius[4,5,6] (fm) & Deformation[3]

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Guo-Liang Ma/(SINAP)The QCD Workshop on Chirality, Vorticity and Magnetic Field in Heavy Ion Collisions, Feb.23-26, 2016, UCLA

Impact parameter dependence of elliptic flow

• v2 in Zr+Zr ≉v2 in Ru+Ru at small b due to ellipsoidal deformation. • v2 in Zr+Zr ≈v2 in Ru+Ru at large b, where B field differs largely. We

expect to see little v2 effect on CME signal difference.• We choose the setting 2 in the following CME study.

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Guo-Liang Ma/(SINAP)The QCD Workshop on Chirality, Vorticity and Magnetic Field in Heavy Ion Collisions, Feb.23-26, 2016, UCLA 11

• We calculate the b dependence of averaged <By> for Ru+Ru and Zr+Zr.

• <By>(Ru+Ru) is larger than <By>(Zr+Zr) by 10% at large b.

b-dependent Magnetic field

Guo-Liang Ma/(SINAP)The QCD Workshop on Chirality, Vorticity and Magnetic Field in Heavy Ion Collisions, Feb.23-26, 2016, UCLA

• We apply f%=1146.1A-4/3By(b) to introduce the initial charge separation into Ru+Ru and Zr+Zr.

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b-dependent initial charge sep. percent

Centrality bmin (fm) bmax (fm)

0-10% 0 3.9

10-20% 3.9 5.5

20-30% 5.5 6.8

30-40% 6.8 7.8

40-50% 7.8 8.8

50-60% 8.8 9.6

60-70% 9.6 10.3

Centrality cuts for Ru+Ru and Zr+Zr

f%=1146.1A-4/3By(b)

Guo-Liang Ma/(SINAP)The QCD Workshop on Chirality, Vorticity and Magnetic Field in Heavy Ion Collisions, Feb.23-26, 2016, UCLA

• We see a reasonable magnitude ordering that Au+Au < Ru+Ru, Zr+Zr < Cu+Cu.

diamond: Au+Au (STAR data)circle: Ru+Ru (AMPT CME)square: Zr+Zr (AMPT CME)triangle: Cu+Cu (STAR data)

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AMPT (CME) results on <cos(ϕa+ϕβ-2ѱ2)>

opp-charge

same-charge

Guo-Liang Ma/(SINAP)The QCD Workshop on Chirality, Vorticity and Magnetic Field in Heavy Ion Collisions, Feb.23-26, 2016, UCLA

initial state final state

• After final state interactions, the <cos(ϕa+ϕβ-2ѱ2)> difference between Ru+Ru and Zr+Zr tends to disappear.

circle: Ru+Rusquare: Zr+Zrblue:opp-chargered: same-charge

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<cos(ϕa+ϕβ-2ѱ2)> in Ru+Ru and Zr+Zr

(parton cascade, hadronization, resonance decays)

Guo-Liang Ma/(SINAP)The QCD Workshop on Chirality, Vorticity and Magnetic Field in Heavy Ion Collisions, Feb.23-26, 2016, UCLA

• The CME effect increases the magnitude of <cos(ϕa+ϕβ-2ѱ2)> for both same- and opposite-charge correlations in Ru+Ru and Zr+Zr.

Ru+Ru Zr+Zr

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<cos(ϕa+ϕβ-2ѱ2)> with and without CME

open: AMPT (normal)solid: AMPT (CME)

opp-charge

same-chargeopen: AMPT (normal)solid: AMPT (CME) same-charge

opp-charge

Guo-Liang Ma/(SINAP)The QCD Workshop on Chirality, Vorticity and Magnetic Field in Heavy Ion Collisions, Feb.23-26, 2016, UCLA

• If Ɣ=<cos(ϕa+ϕβ-2ѱ2)>, We define the CME contribution H by H=Ɣ(AMPT CME)-Ɣ(AMPT normal).

• Hopp and Hsame looks similar between Ru+Ru and Zr+Zr.

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different CME between Ru+Ru and Zr+Zr ?

3.8M eventsopp-charge

same-charge

Guo-Liang Ma/(SINAP)The QCD Workshop on Chirality, Vorticity and Magnetic Field in Heavy Ion Collisions, Feb.23-26, 2016, UCLA

• The difference between two systems’ (Hopp-Hsame) could be seen in very peripheral collisions (50-70%). (It needs more event statistics.)

3.8M events

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different CME between Ru+Ru and Zr+Zr ?

Guo-Liang Ma/(SINAP)The QCD Workshop on Chirality, Vorticity and Magnetic Field in Heavy Ion Collisions, Feb.23-26, 2016, UCLA

initial state

final state

• After final state interactions (parton cascade, hadronization, resonance decays), the charge separation percentage decreases.

• But the ratio of f%(Ru+Ru) to f%(Zr+Zr) seems to keep, which is equal to <By>(Ru+Ru) /<By>(Zr+Zr).

red: Ru+Rublue: Zr+Zr

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Discussion I: final interaction effect on charge separation

f%(Ru+Ru)f%(Zr+Zr)

initial state final state

(parton cascade, hadronization, resonance decays)

Guo-Liang Ma/(SINAP)The QCD Workshop on Chirality, Vorticity and Magnetic Field in Heavy Ion Collisions, Feb.23-26, 2016, UCLA

• If f%~A-4/3By2 , the relative f% ratio of Ru+Ru to Zr+Zr will be changed from <By>(Ru+Ru) /<By>(Zr+Zr) into <By>2(Ru+Ru) /<By>2(Zr+Zr). => The final CME signal difference between Ru+Ru and Zr+Zr can be enhanced.

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Discussion II: By dependence of initial charge sep. percentage

f%~A-4/3By

f%~A-4/3By2

initial state final state

f%=(N+up-N+down)/(N+up+N+down) ~ A-4/3By or A-4/3By2?

f%(Ru+Ru)f%(Zr+Zr)

Guo-Liang Ma/(SINAP)The QCD Workshop on Chirality, Vorticity and Magnetic Field in Heavy Ion Collisions, Feb.23-26, 2016, UCLA

Summary

• Two major features found in AMPT simulations of isobaric collisions at 200GeV:

• v2 difference between central Ru+Ru and central Zr+Zr collisions⇒deformation shape of Ru and Zr.

• CME observable difference between peripheral Ru+Ru and peripheral Zr+Zr collisions (needs more statistics)⇒ CME difference due to different B fields.

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Guo-Liang Ma/(SINAP)The QCD Workshop on Chirality, Vorticity and Magnetic Field in Heavy Ion Collisions, Feb.23-26, 2016, UCLA

Backup

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Guo-Liang Ma/(SINAP)The QCD Workshop on Chirality, Vorticity and Magnetic Field in Heavy Ion Collisions, Feb.23-26, 2016, UCLA

open: AMPTsolid: Exp. data

Normal AMPT results on <cos(ϕa+ϕβ-2ѱ2)>

blue: opp chargered: same charge

diamond: Au+Autriangle: Cu+Cu

• The normal AMPT model underestimate the STAR data for Au+Au 200 GeV and Cu+Cu 200 GeV.

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Guo-Liang Ma/(SINAP)The QCD Workshop on Chirality, Vorticity and Magnetic Field in Heavy Ion Collisions, Feb.23-26, 2016, UCLA

• I check the case of Zr+Zr with same Glauber parameters as Ru+Ru.=> The effect of deformation on CME signal is small.

<cos

(ϕa+ϕβ

-2ѱ2

)>

centrality bin

open circle: RuRusolid square: ZrZropen square: ZrZr(same shape as RuRu)

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Shape effect on <cos(ϕa+ϕβ-2ѱ2)>