Particle Correlations

Fuqiang Wang

Purdue University

Outline

• Why particle correlations? – Few-body (jet-like) correlations – Many-body (flow) correlations – Analysis techniques

• Particle correlations in heavy-ion collisions – Near-side ridge correlation – Away-side double-peak correlation – Triangular flow background

• Particle correlations in small systems – Revisit two-particle acceptance correction

• Flow correlations – Some new idea: initial state anisotropy, quantum mechanics

2

Artist’s view of heavy-ion collisions

3

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LHC

5

BRAHMS

PHOBOS

PHENIX

CMS STAR

ALICE

6

PHENIX

Why particle correlations?

• Single particles can only measure production rates and kinematic distributions

• High-energy collisions are complex—need particle correlations to measure the complex structure of the collision system

• Particle correlations measure jet-like correlations, flow, etc.

• Majority of measurements in heavy-ion collisions are done by particle correlations

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Two categories of correlations

• Few-body, e.g. – Jets

– Resonance decays

• Many-body, event-wise – Collective flow

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Analysis techniques

9

hadrons

q

q

hadrons

leading particle

leading particle

well calibrated: can be

calculated by pQCD.

q

q

Associated particles

Associated particles

,assoc trig assoc trig

𝑺(∆𝜼, 𝜟𝝓)=𝟏

𝑵𝒕𝒓𝒊𝒈 𝒅𝟐𝑵𝒔𝒂𝒎𝒆

𝒅𝜟𝜼𝜟𝝓

• Tracking efficiency is corrected for associated particles. • Trigger particles are often uncorrected, because correlations are normalized per trigger.

Better to have trigger particle correction as well. • Two-particle acceptance often corrected by mixed-events: 𝑩(∆𝜼, 𝜟𝝓)/ 𝑩(𝟎, 𝜟𝝓).

𝑩(∆𝜼, 𝜟𝝓)=𝟏

𝑵𝒕𝒓𝒊𝒈 𝒅𝟐𝑵𝒎𝒊𝒙

𝒅𝜟𝜼𝜟𝝓

max max

1 2 2 1

max

/ const. ( )

/ const const ( )

| |1

2

dN d

dN d d d

dN/

2max 2max

Particle correlations in heavy-ion collisions

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Jet correlations

• Hard-scattering between

partons in pp.

• Calculable by pQCD

• Fragmentation of partons produces back-to-back jets of hadrons.

• Jets are clustered in angle and rich in high-pT particles.

• Jets produced in AA traverse and interact with the medium, lose energy and thus carry information of the medium.

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hadrons

q

q

hadrons

leading particle

leading particle

well calibrated: can be

calculated by pQCD.

q

q

hadrons Au+Au

AA

ove

r b

ina

ry-s

ca

led

pp

pTtrig>4 GeV/c, 2<pT

assoc<4 GeV/c

away-side particles

suppressed at high pT

pTtrig=4-6 GeV/c, pT

assoc=0.15-4 GeV/c

STAR PRL95 (2005) 152301

Particle correlations: focus on away side

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STAR PRL91

(2003) 072304

STAR PRL91

(2003) 072304

The near-side is also interesting

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Au+Au ridge

STAR, PRL 95 (2005); PRC82 (2010)

Away-side

trigger jet

0 p 1 -1

pTtrig=4-6 GeV/c

pTassoc=0.15-4 GeV/c

pTtrig=2.5-4 GeV/c

pTassoc=1-2 GeV/c

pTtrig > 4 GeV/c

pTassoc > 2 GeV/c

STAR, PRC 80 (2009)

pT > 0.7 GeV/c

Triangular flow in heavy-ions

• Double-peak away-side correlations

• Long-range near-side ridge

• Triangular flow, v3

• Other odd harmonics

Au+Au ridge

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vn are measured by two-particle correlations

• Vn from two-particle correlation

• Subtract vn from two-particle correlation

• Almost a tautology

• Comparison to hydro gives us confidence that vn are mostly from flow

• Quantitatively how much is flow and how much is nonflow— still an open question.

• Hydro has some tension to simultaneously describe v2 and v3

• Important to reduce/eliminate nonflow contributions to flow; do as best a job as we can.

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ALICE, Phys. Rev. Lett. 107 (2011) 032301

EP-dep. correlation with vn subtraciton

Strategy:

• Measure vn by two-particle correlation with one particle at as low pT as feasible, to maximally reduce nonflow contaminations.

• Subtract vn measurements from two-particle correlations at high and intermediate pT.

Open questions:

• Effect of jets on event plane reconstruction?

• Are any remaining correlations still coming from hydro flow, i.e. jets are completely gone?

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Particle correlations in small systems

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usual p-p collision high multiplicity p-p collision

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Ridge in small systems

CMS, JHEP 1009 (2010) 091

• Why wasn’t it discovered long ago by HEP?

• Two types of discoveries: – Theoretically predicted, and experimentally verified

– Surprises

• HEP moved on to more exclusive processes

• There may be still important physics that were missed in last half century

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p-p collision (high Mult.) p-Pb collision (high Mult.)

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Physical origin unclear

CMS, PLB718 (2013) 795

CMS, JHEP 1009 (2010) 091

CGC/Glasma

Dusling & Venugopalan 1211.3701

Dusling and Venugopalan, arXiv:1302.7018

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Another explanation: Hydro flow

• In heavy-ions, subtract v2 non-zero finite correlation: near-side large ridge, away-side double peak v3

• In pp, pA (and possibly dA) systems, subtract uniform pedestal non-zero finite correlation: large ridge v2 (and v3)

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Acceptance correction revisited

• Two-particle acceptance correction by mixed-events is, in principle, wrong.

• Should just be corrected by single particle efficiencies:

• How much error it makes?

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dN/d

max max 21

trig assoc

trig

d N

N d d

2 21 1same mix

trig trig

d N d N

N d d N d d trig

k = ¼ -2 < < 2

L.Xu,C.H.Chen,FW, PRC88 (2013) 064907

Dihadron per trigger pair density

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p-going trigger Pb-going trigger Low

multiplicity

High multiplicity

Shape reflects single particle dN/d

L. Xu (CMS) QM 2014

Ridge yield vs assoc

• Near-side ridge yield: different dependences for p-going and Pb-going triggers

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Near-side ridge after jet subtraction

L. Xu (CMS) QM 2014

-dependence of v2()/v2(0)

• v2 shape is dependent in p+Pb!

• v2 asymmetric about mid-rapidity

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L. Xu (CMS) QM 2014

Flow correlations

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coordinate-space-anisotropy momentum-space-anisotropy

Anisotropy Parameter v2

y2 x2

y2 x2v2 cos2 , tan1(

py

px)

Initial/final conditions, EoS, degrees of freedom

y

x

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Collectivity, Deconfinement at RHIC

• Low pT (≤ 2 GeV/c): hydrodynamic mass ordering

• High pT (> 2 GeV/c): number of constituent quarks scaling

Quark degrees of freedom, deconfinement, Partonic Collectivity,

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Comparison with Hydrodynamics

Small value of viscosity to entropy density ratio η/s Model uncertainty dominated by initial eccentricity ε

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Model: Song et al. arXiv:1011.2783

Low η/s for QCD Matter at RHIC

• η/s ≥ 1/4π • η/s(QCD matter) < η/s(QED matter)

RHIC results

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Viscosity quantum limit

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v

~ 4 Bs nk

/ / 4 Bs k p

F v

A y

F A

y

/ 1/ 4s p

Kovtun, Son, Starinets, PRL 94 (2005) 111601 Schafer, arXiv:0912.4236

Does it have to be all pressure-driven hydro flow?

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Uncertainty principle

/ 2x p

y

x

x yp p

2 22 2

22 2 2 2cos2

x y

x y

p py xv

y x p p

D. Molnar, FW, and C.H. Greene, arXiv:1404.4119 34

Infinite square well

22

cos

2

sin

odd

even

nx

aE

nmx

a

p

p

22 2 2 2

2

2 2 22 2 2

Take even mode for example:

2 ; ;

4

2 2 > / 24 4

oddx

x odd

a np k x k

k a

k ap x n

p

p

2 2 2 2

2 2 22 2 for all .

x y

x y

p p b av n

b ap p

a

b

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Harmonic oscillator

22 2 21 1

; 2 2 2

m x E E nm

22 2

2 2

1 1 1

2 2 2 2 2

1

2

x

x

p Em x n

m

p x n

2 2

2 2 2

2 2

2 2

2 for each and all

x y x y

x yx y

x y

x y

p pv

p p

y x

y x

v n

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Bose-Einstein Condensate

Single ground state in anisotropic trap large momentum anisotropy

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D. S. Jin and C. A. Regal

Thermal probability

then it’s independent of potential. It’s isotropic at all temperature because K=(px

2+py2)/2m is isotropic.

Because This is classical physics limit.

x, y at same Fermi energy, so different number of filled energy levels.

At high temperature, classical limit, sum is approximated by integral:

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Is QGP hot?

Size r ~ 1 fm Intrinsic momentum/energy scale ~ 1/r ~ 200 MeV

QGP temperature T ~ 300 MeV

Typical momentum/energy ~ T ~ 300 MeV

QGP is not hot at all. Quantum effect must be present.

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Thermal probability weight

40

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Initial v2 from QM

D. Molnar, FW, and C.H. Greene, arXiv:1404.4119

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D. Molnar, FW, and C.H. Greene, arXiv:1404.4119

Typical Au+Au collisions

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D. Molnar, FW, and C.H. Greene, arXiv:1404.4119

Transverse profile from SHO

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This may not correspond exactly to heavy-ion collision energy density profile, but close.

Cold atoms Strong elliptic anisotropy

K. M. O’Hara et al., Science 298, 2179 (2002).

Lithium atoms M ~ 6000 MeV Temperature T ~ 1 mK ~ 10-16 MeV Trap size x ~ 20 mm, y ~ 100 mm Typical momentum (TM)1/2 ~ 10-6 MeV Intrinsic momentum quantum ~ 1/r ~ 10-8 MeV, negligible. Typical energy ~ T ~ 10-16 MeV Intrinsic energy quantum 1/(mr2) ~ 10-20 MeV, negligible. Cold Lithium atoms are actually “hotter” than the hot QGP.

~ 10-5

The observed large v2 is indeed due to strong interactions. 45

Is quantum v2 real?

• It should be… but need experiment to verify

• Would be neat to verify QM and uncertainty principle

• Need trap size x100 smaller • Or need nano-Kelvin temperature

Cold atom experiment

Proposing a cold atom quantum simulator for high-energy nuclear physics

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Control the interaction

• Hydrodynamics is only an assumption

• Is initial QM v2 important after hydro evolution?

• When does hydro sets in and takes over?

• Will the initial QM v2 be washed out by hydro?

• Current hydro implementation is classical

• Need to incorporate QM into hydro: quantum hydrodynamics

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Shooting fast atoms through trap

• jet-quenching partonic energy loss mechanisms are far from clear. A very active and extensive field

• Can we gain insights from cold atoms?

• Shoot fast atoms through cold atom system

• External hard probes under full control

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Summary

• Particle correlations are a powerful tool to study pp, pA, AA collisions

• Unambiguous signal of strongly interacting QGP from high-pT jet-quenching data.

• Low pT anisotropic flow data indicate hydrodynamic behavior of sQGP. Extracting transport properties (such as /s) from measured data still need extra effort. Initial anisotropy may not be neglected.

• There should be indispensable information at intermediate pT from jet-medium interactions (not discussed in this lecture). Need creative mind and novel approaches.

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