Classical fields in heavy-ion collisions · Classical field in heavy-ion collisions Non-equilibrium...

Classical fields in heavy-ion collisions

Vladimir Skokov

Brain workshop

[email protected] Classical fields Brain workshop 1 / 20

Outline

Raju Venugopalan this morning: Glasma andthermalization

Electromagnetic fields acting on in- andout-of-equilibrium plasmaColor fields in-equilibrium: non-trivial holonomy A0

Chiral condensate and manifestation of its dynamics:chiral crossover, chiral critical point, quarkyonic phase


Outline

Raju Venugopalan this morning: Glasma andthermalizationElectromagnetic fields acting on in- andout-of-equilibrium plasma

Color fields in-equilibrium: non-trivial holonomy A0



Outline

Raju Venugopalan this morning: Glasma andthermalizationElectromagnetic fields acting on in- andout-of-equilibrium plasmaColor fields in-equilibrium: non-trivial holonomy A0



Classical field in heavy-ion collisions

Non-equilibrium Equilibrium Freeze-out

Color glass condensate GlasmaEa & Ba

High EM fieldsE & Ba

Classical color A0

(Inhomogeneous) chiral condensate

Almost on every stage of heavy-ion collisions, classical fields play significant role.


(Electro)-magnetic field in HIC

HICs create not only strong colorbut also extremely strong (electro)-magnetic fields.

Strong ≡ of the hadronic scales, eB ∼ m2π.

b = 12 fmb = 8 fmb = 4 fm

!(fm)

eB(M

eV2)

32.521.510.50

105

104

103

102

101

100

D. Kharzeev, L. McLerran and H. WarringaNucl.Phys. A803 (2008) 227-253

0 0.1 0.2 0.3 0.4 0.5t, fm/c

0

0.5

1

1.5

2

2.5

eBy/m

π

2

sNN

1/2=130 GeV

sNN

1/2=200 GeV

b = 4 fm

V. S., Y. Illarionov and V. ToneevarXiv:0907.1396


Origin of (electro)-magnetic field in HIC

In the 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.


Fluctuations of (electro)-magnetic field

A. Bzdak and V.S.Phys.Lett. B710 (2012) 171

0 2 4 6 8 10 12 14b fm

0

2

4

6

8

10

12

e·Field/m

2 �

AuAu, �

s =200 GeV

�|Bx|�

�|By|�

�

By

�

Fluctuations of participant and reactionplanes( J. Bloczynski et al, Phys.Lett. B718 (2013) 1529)

Non-zero electric field can induceseparation of charges;j = σEmeasurements of electric conductivity(talk by Y. Hirono)

Lifetime of (electro)-magnetic field?!


Lifetime of magnetic field

External magnetic field might live longer because of conductivity effects:

j = σOhm · E + σχ · Bwhere σOhm is electric conductivity and σχ is chiral-magnetic conductivity

(D. Kharzeev et al).

Electric conductivity:quenched lattice QCD calculations σLQCD

Ohm = (5.8 ± 2.9) TTc

MeV.

Chiral magnetic conductivity:σχ =

(e2

2π2 Nc∑

f q2f

)µ5, let µ5 ∼ 1 GeV, then σχ ∼ 15 MeV.


Lifetime of magnetic field

σ=0σLQCD102 σLQCD103 σLQCD

eB /

m2 π

10−6

10−4

10−2

1

t / RAu

−1 0 1 2

S. Lin, L. McLerran and V.S.

Even for σOhm = 102σLQCDOhm magnetic

field falls quite fast.σOhm ∼ σ

LQCDOhm is an optimistic

estimate, since in early stage thereare no charge carriersMagnetic field acts on very early(non-equilibrium) nuclear matter


Observable effects: QCD phase diagram

Modification of QCD phase diagram in high magnetic field.

Probably (unless system is in local equilibrium at times less then 0.1 fm/c),not relevant for HIC phenomenology owing to short lifetime of magnetic field.

Nonetheless, as we learned from talk by Y. Hidaka, QCD calculations with magneticfield showed that existing low-energy effective models does not capture essentialchiral and deconfinement properties of QCD.

0 5 10 15 20 250.98

1

1.02

1.04

1.06

1.08

1.1

1.12

1.14MFFRG

eB/m𝜋2

T pc (B

)/ T pc

V.S. Phys.Rev. D85 (2012) 034026 G. S. Bali et al JHEP02 (2012) 044

FRG: functional renormalization group will be discussed in talk by Y. Tanizaki


Observable effects

Chiral Magenetic Effect and Chiral Magnetic Wave: j ∼ σχB.Photon production in strong magnetic fieldConformal anomaly: G. Bazar, D. Kharzeev and V.S. Phys.Rev.Lett. 109 (2012) 202303

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

Ho-Ung Yee, arXiv:1303.3571

Photon azimuthal anisotropy (quantified by v2) is approximately the same as for chargeparticles. In contradiction to expectations: photon production ∼ T4,

however, momentum azimuthal anisotropy is small.Hydrodynamic calculations underestimate photon v2 by factor of 5.


Photon production

eB

Usually photon production from two gluons issuppressed by αEM compared to

quark-antiquark annihilation or Comptonscattering

If magnetic field of hadronic scaleseB ∼ m2

π, two gluon produce one photonwith rate similar to quark-antiquark

annihilation and Compton scattering.

0 0.5 1 1.5 2 2.50

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

p⊥, GeV

v 2

PHENIX direct photons

Calculations withmagnetic field

Au-Au min bias√s=200 GeV

Experimental data was underpredicted bya factor of 5 in hydro calculations.


Photon production details

Resummed contribution from gluons in color singlet state.In vacuum, dilaton is an effective description of Yang-Mills theory.Assumption: single scalar meson saturates conformal anomaly.Dilatation current acting color singlet states〈0|Dµ|σ〉 = iqµfσ; 〈0|∂µDµ|σ〉 = m2

σ fσFrom decay of lowest glueball state to two photons decay to twophotons coupling gσγγ of following effective Lagrangian is obtainedLσγγ = gσγγ σ FµνFµν withσ ∼ θ

µµ = ∂µDµ = θ

µµ =

β(g)2g GµνaGµνa +

∑q mq(1 + γm(g))qq,

Photon production rateq0

d3Γdq3 ∝

[(B2

y − B2x)q2

x + Bx2q2⊥

]ρθ(q0),

where ρθ(q0) is spectral function for trace of energy momentumtensor, in hydrodynamical limit ρθ(q0) ≈ 9

πq0ζ


Non-trivial holonomy A0 at finite T

In equilibrium, color background field A0 is expected

Characterized by Polyakov loop L = Tr P exp(ig

∫ 1/T0 A0dτ

), which also play a

role of order parameter for deconfinement in Yang Mills theory

R. Pisarski

Effective theory to study properties of YM sectorHigh T: effective potential obtainedperturbativelyVpert = 2π2

3 T4(− 4

15 (N2c − 1) +

∑Ncij=1 q2

ij(1 − qij)2),

qij = |qi − qj|

Anzatz Aij0 = 2πT

g qiδij,

∑i qi = 0

(Gross-Pisarski-Yaffe/Weiss potential)Non-trivial solution for qi demandsnon-perturbative potential which is assumed to beVnon−pert = T2T2

d

[C1

∑Ncij=1 q2

ij(1 − qij)2

+C2∑Nc

ij=1 qij(1 − qij) + C3

]Further discussion in talk by K. Kashiwa


Comparison to lattice

A. Dumitru et al Phys.Rev. D86 (2012) 105017

Good description of YM thermodynamics, interface tension for SU(2) and SU(3).


Large Nc limit

Potential in explicit form

V/(N2c − 1) ≡ Veff(q) = − d1(T) V1(q) + d2(T) V2(q) ,

Vn(q) = 1/(N2c − 1)

Nc∑i,j=1

|qi − qj|n(1 − |qi − qj|)n

It is useful to introduce eigenvalue densityρ(q) = 1

Nc∑

i δ(q − qi)→∫ 1

0 dxδ(q − q(x)) = dx/dqThen

1/Nc

∑i

f (qi)→∫ 1

0dxf (qx) =

∫dq

dxdq

f (q) =

∫dqρ(q)f (q)

Terms in the potential

Vn(q) =

∫dq

∫dq′ ρ(q) ρ(q′)|q − q′|n(1 − |q − q′|)n .

non-local field theory


Solution in large Nc limit

Solution for eigenvalue density(d = 12d2/d1)

ρ(q) = 1+b cos(d q) , q : −q0 → q0

q0 and b are given by

cot(d q0) =d3

(12− q0

)−

1d (1/2 − q0)

,

b2 =d4

9

(12− q0

)4

+d2

3

(12− q0

)2

+1

0.3 0.2 0.1 0.0 0.1 0.2 0.30

2

4

6

8

10T/Tc =1.2

T/Tc =1.1

T/Tc =1.05

T/Tc =1.03

R. Pisarski and V.S.Phys.Rev. D86 (2012) 081701


Gross-Witten-Wadia phase transition

What is order of deconfinement phase transition in large Nc limit?

Effective matrix model: critical first order phase transition (PT): aspects of both first order andsecond order PTs.

Discontinuity as in first order PT. Approaching Td+ Polyakov loop jumps from 0.5 to 0.Divergence of order parameter susceptibility as in second order PT.

Critical exponents obtained analytically:

l ∼ (T/Td − 1)β, β = 2/5

cV ∼ (T/Td − 1)−α, α = 3/5

l − 1/2 ∼ h1/δ, δ = 5/2

Griffith’s scaling relation 2 − α = β(1 + δ) is satisfied.

GWW PT was also obtained in SU(∞) on femtosphere. This suggests that in infinitevolume, the Gross-Witten-Wadia transition may be an infrared stable fixed point of a

SU(∞) gauge [email protected] Classical fields Brain workshop 17 / 20

Scattering processes and non-trivial holonomy

A0 modifies not only thermodynamicsScattering processes are also modified compared toperturbative/HTL results, e.g.

shear viscosity η ∼ l2

heavy-quark energy loss dE/dx ∼ lhard photon production q0dΓ/dq3 ∼ l (another step to solve photon v2 puzzle)dilepton production q0dΓ/dq3 ∼ (1 − l)work in progress Y. Hidaka, S. Lin, R. Pisarski and V. S.


Outlook

I had no time to talk about:Quark production in Glasma: F. Gelis, K. Kajantie and T. Lappiperturbative results not reproduced at large k⊥Quark production in Glasma in presence of strong (electro)magnetic fieldwork in progress R. Venugopalan and V.S.Chiral condensate and its manifestation in HIC (talk by K. Morita):

signals of criticality on crossover phasetransition line

0.5 1 1.5Τ/T

pc

-0.04

-0.02

0

0.02

χB 6

µq/T=0

PQM

signals critical point

0.0 0.5 1.0 1.5 2.0µ/Tpc

0.2

0.4

0.6

0.8

1.0

T/T

pc

1052

02510

Kurtosis of baryon number fluctuationssignals of quarkyonic phasebackground contribution (baryon number conservation, volume fluctuations and etc)


Conclusions

(Electro)magnetic field in HIC is of hadronic scales. Short lifetime.It gives significant contribution to photon azimuthal anisotropy atRHIC energies. Motivated to study QCD at finite magnetic field.Non-trivial classical A0 field: effective description of Yang-Millsthermodynamics. Modification of scattering processes.In large Nc

limit, deconfinement phase transition in SU(∞) theory is ofGross-Witten-Wadia type?! This is suggested both by an effectivemodel and SU(∞) on femtosphere.


Classical fields in heavy-ion collisions · Classical field in heavy-ion collisions Non-equilibrium...

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