correlations in heavy ion collisions and the cosmic ... · jose l. munoz~ (cpan days 2016)...

Correlations in Heavy Ion Collisions and the CosmicMicrowave Background

Jose Luis Munoz Martınez

Universidad Complutense de Madrid(Depto. Fısica Teorica I)

29th November 2016

Contents

1 Introduction

2 Angular spectrum for a RHIC event

3 Some Examples at the LHC

4 Conclusions

Jose L. Munoz (CPAN Days 2016) Correlations in RHIC and the CMB 29th November 2016 1 / 34

1 Introduction



4 Conclusions

Introduction

From http://pla.esac.esa.int/pla/#home.


Introduction

Multipolar expansion

∆T

T(θ, φ) =

∞∑l=1

+l∑m=−l

almYlm(θ, φ)

S. Dodelson, “Modern Cosmology”,Academic Press, Amsterdam (2003)

Angular spectrum: 〈alma∗l ′m′〉 = δll ′δmm′Cl⟨∣∣∣∣∆T

T(θ, φ)

∣∣∣∣2⟩

=1

4π

∑l

(2l + 1)Cl

〈. . . 〉 over ensemble... but just one universe!

−→ Cl =1

2l + 1

∑m

|alm|2 =⇒⟨Cl

⟩= Cl

⇒Cosmic variance: σl ≡√⟨

(Cl−Cl)2⟩

C2l

=√

22l+1


Introduction

http://pla.esac.esa.int/pla/#home.

DTTl ≡ l(l + 1)Cl/(2π)


Introduction

RHIC (Relativistic Heavy Ion Collisions)

CERN Courier 53N4, 31, May 2013

High-energy nuclei colliding⇒ Hot nuclear matter system in the centerof collision (“fireball”)

http://www.star.bnl.gov/ gorbunov/main/node5.html.

Freeze out ⇔ Last Scattering SurfaceJose L. Munoz (CPAN Days 2016) Correlations in RHIC and the CMB 29th November 2016 5 / 34

1 Introduction



4 Conclusions

Angular spectrum for a RHIC event

Acoustic peaks ⇐⇒ 1st order QCD phasetransition??

First-order phase transition −→ Hadronic bubbles −→Surface tension γ −→ Restore force against pressure=⇒ Acoustic oscillations

http://www.quantumdiaries.org/2010/04/26/the-quark-gluon-plasma/ Nature 443, 637-638 (2006)



Staig & Shuryak, Phys. Rev. C 84, 044912 (2011): Damping of aperturbation

δTµν = δTµν(0) ekz(x−tcs)e−k2/k2

v

“Viscous horizon scale”:

k−1v = Rv =

√2τf3T

η

s

Perturbations with λ/(2π) = k−1 < Rv damped by viscosity

Sound horizon scale:

Hs =

∫ τf

τi

cs(τ)dτ ∼ 0,3± 0,1 fm

Recent lattice calculations indicate Rv ∼ 0,6 fm −→ Rv ∼ Hs

=⇒ If there were any oscillations, the acoustic peaks will besuppressed (overdamped oscillator)



The transverse momentum pt reflects the temperature

dNi

dypEtdEt∼√

TEte−Et/T

Where E 2t = m2 − p2

t

https://indico.cern.ch/event/353906/contributions/2274036/attachments/1330492/1999385/conf12 stachel 2.pdf.



Multipolar expansion

∆ptpt

(θ, φ) =∞∑l=0

+l∑m=−l

aplmYlm(θ, φ)

Angular spectrum: ⟨aplma

p∗l ′m′⟩

= δll ′δmm′Cpl

(Average 〈. . . 〉 over events −→ no more cosmic variance)

For one event:

aplm =

∫dΩ Y ∗lm(θ, φ)

∆ptpt

(θ, φ) −→ Cpl =

1

2l + 1

∑m

|aplm|2

For an infinitely large ensemble of events:⟨Cpl

⟩= Cp

l



Generalize to any distribution function f (θ, φ),

aflm =

∫ π

0dθ sin θ

∫ 2π

0dφ f (θ, φ)Y ∗lm(θ, φ)

⇒ We compute it numerically using SHTOOLS (Fortran, Python)

For a given lmax , SHGLQ prepare a grid (Nφmax ,Nxmax ) to divide thesphere in latitude (x ≡ cos θ) and longitude, and calculates the aflm bythe Gauss-Legendre Quadrature numerical integration method.

SHPowerSpectrum calculates (2l + 1)C fl from aflm.

We can generate f (θ, φ) on the grid.


1 Introduction



4 Conclusions

Some Examples at the LHC

ALICE (A Large Ion Collider Experiment)

186 ALICE events together in Mollweide projection. Data fromhttp://opendata.cern.ch/collection/ALICE-Reconstructed-Data



TPC (Time Projection Chamber)η coverage: |η| < 0,9φ coverage: 360o , except for 2o dead angle each 20o (bars)

=⇒ Acceptance function A(θ, φ)

A(θ, φ) =

0 if θ /∈ [44,25o, 135,7o] or φ ∈ n × 20o ± 1o1 otherwise

J. Alme et al. [ALICE Collaboration],Nuclear Instruments and Methods inPhysics Research Section A 622, I1,316-367 (2010).



Acceptance function effect in angular spectrum


Correlations in RHIC

Ridge structure approximated1 by f (φ) = 0,033 + 0,001 cos(2φ)

1L. Milano [ALICE Collaboration], Nucl. Phys. A 931, 1017 (2014).Jose L. Munoz (CPAN Days 2016) Correlations in RHIC and the CMB 29th November 2016 14 / 34


pt-fluctuations angular spectrum

Just a few thousand particles per event (best cases), we have to

Tile the sphere: divide φ, θ coordinates in Nφmax ,Nxmax (x ≡ cos θ)

Count particles per box and average pt in each one

pit =1

Ni

Ni∑n=1

pnt (θ, φ) , (θ, φ) ∈ i-box

Normalize the pt in each box to the average over the entire sphere

∆ptpt

(θ, φ) =pit − pt

pt, pt =

1

4π

∫dΩ pt(θ, φ)



Combining 186 events (87623 particles)

D. A. Teaney, arXiv:0905.2433 [nucl-th]

LAB. SYSTEM: Can not average

Need to orient them to someintrinsic axis (Reaction plane)

=⇒ Choose to align quadrupole

(Qx ,Qy ) =

N in event∑particles j=1

pjt cos (2φj) ,N∑j=1

pjt sin (2φj)

−→ ΨR = arctan

(Qy

Qx

)For each particle:

φj = φj −ΨR



(cos θ, φ) subdivisions: (20, 36)



Angular spectrum of 186 ALICE events


1 Introduction



4 Conclusions

Conclusions

A CMB-like map for a RHIC event can be drawn for pt-fluctuations.

CMB anisotropies analysis method adapted for RHIC using pt as aproxy for T . Through a numerical-calculation method withSHTOOLS, we calculate the angular spectrum Cl of:

ALICE TPC acceptance (simplified).The ridge structure.Some actual ALICE events.

No acoustic peaks observed (compatible with a crossoverQGP−→hadron gas).

Not understanded depression in l = 6.

Very important effect of the detector’s acceptance.

With publically available ALICE statistics we are not able to extractphysics information of the angular spectrum calculated.ALICE-collaboration could calculate it with more precision.


Correlations in Heavy Ion Collisions and the CosmicMicrowave Background

Jose Luis Munoz Martınez

Universidad Complutense de Madrid(Depto. Fısica Teorica I)

29th November 2016

Mollweide Projection

x =2√

2

πRλ cosβ

y =√

2R sinβ

2β + sin 2β = π sinψ

M. Lapaine, KoG 15 N15 p7-16 (2011).

ψ, λ - Latitude, longitude

R - Sphere radius


A closer look at the angular spectrum of the acceptance

η cut



One bar



All bars


ITS η-acceptance (|η| < 1,9)


Introduction

Nature 443, 637-638 (2006)

At T = Tc : nucleation of hadronic bubbles

F γr − F p

r = −4πr2(pQGP − pH)− 8πrγ

Critical radius of the bubble

req(T ) =−2γ(T )

(pQGP − pH)(T )=−2γ

∆P

Introduce a perturbation: r = req + rpert

[(ρ+ p)QGP

] d2rpertdt2

= −8π (γ + ∆Preq) rpert

=⇒ The surface oscillates:

ω =

√−8πγ

(ρ+ p)QGP


Subtracting Cm=0l (P. Naselski et al., Phys. Rev. C 82, 035203)


In previous works...

U.W. Heinz, J. Phys. Conf. Ser. 455, 012044 (2013).


In previous works...

A. Mocsy & P. Sorensen, arXiv:1008.3381 [hep-ph].


correlations in heavy ion collisions and the cosmic ... · jose l. munoz~ (cpan days 2016)...

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