Magnetic field in HIC in Au-Au, Cu-Cu and isobar...

Magnetic field in HIC in Au-Au, Cu-Cu and isobarcollisions

Vladimir Skokov

March 2, 2016

[email protected] B in HIC QCD Workshop 1 / 23

Outline

Introduction

Magnetic field at early stage and evolution

Magnetic field of isobars

Outlook and Conclusions


Introduction

Magnetic field of hadronic scale, eB ∼ m2π, may be responsible for

number of observablesBesides CME/CMW: photon azimuthal anisotropy. Signal isproportional to B2 cos 2(ΨB − ΨPP)

Synchrotron radiationK. Tuchin Phys.Rev. C87 (2013) 2, 024912

Conformal AnomalyG. Bazar, D. Kharzeev and V.S. Phys.Rev.Lett. 109 (2012) 202303

Chiral anomalyK. Fukushima and K. Mameda Phys.Rev. D86 (2012) 071501

Ho-Ung Yee, Phys.Rev. D88 (2013) 2, 026001

Extension on Conformal Anomaly: dilepton productionG. Basar, D. Kharzeev, E. Shuryak Phys.Rev. C90 (2014) 1, 014905

Isobars may be crucial to test effect of magnetic fieldSystematical studies are neededMost of this talk: magnetic field at t = 0.


Origin of (electro)-magnetic field in HIC

In first approximation, colliding nuclei are two positive charges moving with ultrarelativistic velocities in opposite directions.

Two currents in opposite direction.Magnetic fields of the two sources add up,

while electric fields nearly cancel each other.Out-of-plane direction of magnetic field:

〈eBy〉 ∼ m2π, 〈eBx〉 ∼ 〈eBz〉 ∼ 0

〈eEx〉 ∼ 〈eEy〉 ∼ 〈eEz〉 ∼ 0

Charge distribution in nuclei is not uniform.Lumpy distribution of electric charge in

colliding nuclei results in nonzero randomlyoriented magnetic field even in central

collisions.


Time dependence

Formation of conducting mediummay increase magnetic field lifetimeFull 3+1D anomalous hydro +

Maxwell equationsFor now modification of Maxwellequations: j = σOhmE + σχB andswitching σ’s at t = 0Little information about σ’s at veryearly stage, approximated by σLQCD

Numerical solution of Maxwellequations with external currentdefined by participants. Conductivityis switched on at t = 0 in finitevolume.

σ=0σLQCD102 σLQCD103 σLQCD

eB /

m2 π

10−710−610−5

0.00010.0010.010.1

110

t / RAu

−1 0 1 2

L. McLerran, V. S. Nucl.Phys. A929 (2014) 184-190

Conductivity does increase lifetime, butfield magnitude is small.

Talk by K. Tuchin


Time dependence II

Similar result for Milne coordinates(τ, x⊥, η) and expanding fireballThis is not final conclusion!Formation of knots of magnetic fluxAssuming non-trivial linking,conservation of helicity results inconservation of total magnetic energyPower law decay of B: t−1/2 insteadof t−2

Talk by Y. Hirono

0 1 210-6

10-5

10-4

10-3

10-2

10-1

100

101

102

B y [fm

-2]

t [fm]

Au+Au, s1/2=200 GeVb=6 fm, x=y=z=0

Participants

B.G. Zakharov Phys.Lett. B737 (2014) 262-266

L. McLerran, V. S. Nucl.Phys. A929 (2014) [email protected] B in HIC QCD Workshop 6 / 23

Properties of B at initial state

Magnetic field life time is uncertainNonetheless we still can answer some important questions:

How homogeneous is B?Direction of B vs direction of reaction plane?Does naive Z scaling holds for system of different sizes?Does nucleus deformation change B?


Definitions

Average magnetic field in y direction 〈By〉

Average magnitude squared 〈B2〉

Observable related average O = 〈B2 cos[2(ΨB − ΨPP)]〉For all of above

∫d2x⊥ over R = 0.25 fm

Centrality instead of impact parameter


Importance of centrality

0.0 0.5 1.0 1.5 2.0 2.5 3.00.00

0.01

0.02

0.03

0.04

0.05

Au+Au, b=0

B- 2

0.5 1.0 1.5 2.0 2.5 3.00.00

0.02

0.04

0.06

0.08

B- 2

Au+Au, b=5 fm

0.5 1.0 1.5 2.0 2.5 3.00.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

B- 2

Au+Au, b=10 fm

Talk by J. LiaoJ. Bloczynski, Xu-Guang Huang, X. Zhang, J. Liao Phys.Lett. B718 (2013) 1529-1535

−0.5 0.0 0.5 1.0 1.5

(ΨB − Ψ2)/π

0.0

0.5

1.0

1.5

2.0

2.5

Au 0-5%

Cu 0-5%

−0.5 0.0 0.5 1.0 1.5

(ΨB − Ψ2)/π

0.0

0.5

1.0

1.5

2.0

2.5

Au 30-40%

Cu 30-40%

−0.5 0.0 0.5 1.0 1.5

(ΨB − Ψ2)/π

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

Au 70-80%

Cu 70-80%

V.S. 2016


Centrality dependence in Au-Au

Calculated at geometrical center ofparticipantsReminder:

〈O〉 = 〈B2 cos(2(ΨB − ΨPP))〉

Expected linear dependence of By oncentrality and quadratic dependenceof 〈O〉 and B2

0-5%: significant contribution of Bx

to magnitude of B0-5%: non-zero 〈O〉

020406080100

Centrality

−3.5

−3.0

−2.5

−2.0

−1.5

−1.0

−0.5

0.0

Normalized

by〈B

y〉a

t0-5%

〈O〉−〈By〉−〈 ~B2/2〉


Homogeneity of B: x direction

How homogeneous B in HIC?Consider

O(r) = [eB(r)]2 cos[2(ΨB(r) − ΨPP)]

Correlation function

C(r) = N−1〈δO(r)δO(0)〉

Center is defined by participantsCorrelation length in x-direction isabout 2.5 fm. Almost independent ofcentrality.


Homogeneity of B: y direction

Correlation length in y-direction isextremely large.What does this mean and why is itimportant?


Sphaleron transitions and directions of B

Assume two regions separated by 2-3fm contributing to observableSame conditions (i.e. windingnumber)Magnetic field, its directions relativeto participant plane is stronglycorrelatedSignal is double of individualcontribution

B

B


Sphaleron transitions and directions of B

Decorrelation is significant if thedistance larger than 2.5 fmSignal is half of individual

B B


Observables in Au and Cu

Naive expectations for observablesrelated to

〈O〉 ∝ Z2

Z2Au/Z

2Cu = 7.4

Experimental signal for CMEobservables has different trend:γCu > γAu :

020406080100

Centrality

−3.0

−2.5

−2.0

−1.5

−1.0

−0.5

0.0

〈O〉

Au-Au

Cu-Cu


Observables in Au and Cu: beyond Z2 scaling

Charge ratio Z2Au/Z

2Cu = 7.4

Significant deviation due to differencein nuclei geometryNon-monotonous behavior asfunction of centrality

020406080100

Centrality

0

2

4

6

8

10

〈O〉 A

u/〈O〉 C

u


Observables in Au and Cu: dilution effect

If signal is extracted from twoparticle correlation function (say γ’s):dilution effect is inevitableAssuming that number of correlatedpairs is proportional to total numberof particles, dilution brings factorκ/Nch

020406080100

Centrality

−0.08

−0.07

−0.06

−0.05

−0.04

−0.03

−0.02

−0.01

0.00

〈O〉/〈N

ch〉

Au-Au

Cu-Cu


Isobrars: charge dependence

Non-trivial charge dependence inCu-Cu and Au-Au collisions. Shouldwe worry about isobars?Consider A = 96 and vary Z for fixedcentralityIsobars of interest Z = 40 and 44.Ratio squared 1.21.MC for 〈O〉 approximately followsnaive scaling!

〈O〉(

Z,%

) / 〈O

〉(Z=

35,%

)


Isobars: deformation

Isobars Zr and Ru are expected to be deformedElectron scattering

β2(Zr) = 0.08 β2(Ru) = 0.158

Model calculationβ2(Zr) = 0.217 β2(Ru) = 0.053

Contradicting results.


Isobars: deformation

Is of any significance for B?Centrality classes do not change fordifferent β (unless very central eventsare considered)B does not vary as well!

Z=40

〈O〉(β,

%) /

〈O〉(β=

0,0-

5%)


Isobrars: observable for isobars and effect of dilution

020406080100

Centrality

−4.5

−4.0

−3.5

−3.0

−2.5

−2.0

−1.5

−1.0

−0.5

〈O〉

Z=40

Z=44

020406080100

Centrality

−0.25

−0.20

−0.15

−0.10

−0.05

0.00

〈O〉/〈N

ch〉

Z=40

Z=44

Normalized by B2y of Z = 40 at 0 − 5%


Isobrars: comparison to Au and Cu

020406080100

Centrality

−0.25

−0.20

−0.15

−0.10

−0.05

0.00〈O〉/〈N

ch〉

Cu

Zr

Ru

Au


Conclusions

At given centrality, naive scaling of magnetic field on Z breaks down for systemswith vastly different geometriesDilution effect is significantFor systems with same A: B2 cos 2(ΨB −ΨPR) is proportional to Z2. This supports20% difference in magnetic field related observables for isobars Zr and RuIn wide range of centralities, magnetic field is independent on nucleardeformation.9642Mo ?!


Magnetic field in HIC in Au-Au, Cu-Cu and isobar...

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