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Multi-particle production in small systems from CGC Prithwish Tribedy 7th International Workshop on Multiple Partonic Interactions at the LHC The Abdus Salam International Centre for Theoretical Physics (ICTP), Trieste, Italy 1 outline

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SLIDE 1

Multi-particle production in small systems from CGC

Prithwish Tribedy

1

7th International Workshop on Multiple Partonic Interactions at the LHC

The Abdus Salam International Centre for Theoretical Physics (ICTP), Trieste, Italy

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SLIDE 2
  • utline
  • Introduction
  • Framework of color glass condensate
  • Phenomenology of high multiplicity events
  • Combining CGC with PYTHIA

2

Based on the work done in collaboration with :

  • K. Dusling, L. McLerran, B. Schenke, S. Schlichting & R. Venugopalan
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SLIDE 3

Multi-particle production at high energies

Goal : Study correlated production of particles We need :

  • An ab-initio framework of particle production
  • Full treatment of different sources of fluctuations
  • State-of-the art treatment of fragmentation

* dN dy1 d2p⊥1 . . . dyq d2p⊥q + ( ) ⌧ dN dy1 d2p⊥1

  • . . .

* dN dyq d2p⊥q +

3

Focus : Collisions of small systems p+p and p+Pb are interesting as final state effects are minimal

slide-4
SLIDE 4

Phenomena we want to describe

Origin of high multiplicity events

4 arXiv: 1011.5531

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SLIDE 5

Phenomena we want to describe

Origin of high multiplicity events Systematics of Δη-Δφ correlations Energy dependence of ridge in p+p Similar underlying dynamics must drive these phenomenon

5

p+p p+A

arXiv: 1011.5531 arXiv: 1509.04776, 1210.5482

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SLIDE 6

Particle production at high energies

6

Multi-particle production at high energies in Regge Gribov limit (x→0)

Colliding hadrons/nuclei :

  • Saturation : Non-linear process strops growth of gluons, semi-

hard saturation scale Qs(x) > ΛQCD

  • Gluon dominated wave function, peaked at Qs(x~x0e
  • Y)

arXiv: 1212.1701

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SLIDE 7

Particle production at high energies

7

Multi-particle production at high energies in Regge Gribov limit (x→0)

Colliding hadrons/nuclei :

  • Saturation : Non-linear process strops growth of gluons,

semi-hard saturation scale Qs(x) > ΛQCD

  • Gluon dominated wave function, peaked at Qs(x~x0e
  • Y)

0.2 0.4 0.6 0.8 1 1.2 0.1 1 10 Q0

2=0.168 GeV2

Y=0 Y=4 Y=8 Y=12

Qs

N

  • n

r e g i m e

  • f QCD

linear

un-integrated gluon distribution arXiv: 1212.1701 Dusling, Li, Schenke 1509.07939 parton transverse momentum (kT) GeV

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SLIDE 8

Particle production at high energies

8

Multi-particle production at high energies in Regge Gribov limit (x→0)

Particle production :

  • t-channel exchange of ladder

like emissions of gluons,

  • Strong color fields, weak

coupling, high occupation of gluonic states f(k) ~ A2~1/g2

Initial configuration JIMWLK evolution dN/d p 3

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SLIDE 9

Particle production at high energies

Color Glass condensate effective field theory → ab-inito framework to this problem

9

Multi-particle production at high energies in Regge Gribov limit (x→0)

Particle production :

  • t-channel exchange of ladder

like emissions of gluons,

  • Strong color fields, weak

coupling, high occupancy of gluonic states ~1/g2

(classical approximation)

Initial configuration JIMWLK evolution Single gluon emission A (classical field)

McLerran, Venugopalan hep-ph/9309289

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SLIDE 10

Details of CGC the framework

  • Fundamental objects are Color

Charge density matrices ρa(x⊥,Y) Local Gaussian distribution W[ρ] (MV-Model)

  • Color field before collisions : solving

Yang Mills equations [Dμ,Fμν] = Jν for each configuration of source

ρ(x⊥)

10

Domains of chromo-electric field

⌦ ρa(x⊥)ρb(y⊥) ↵ = δabδ2(x⊥−y⊥)g 2µ2(x⊥)

Glasma flux tubes —> free streaming gluons

before collisions (τ<0)

hρρi

A

h i hρρi

B

hV †V i

A

hV †V i

B

classical color charge classical color field

D F = J D F = J D F = J

B

A

after collisions (τ>0)

D F = 0 hep-ph/9809433, hep-ph/0303076, arXiv: 1206.6805 arXiv: 1202.6646

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SLIDE 11

Details of the CGC framework

Input is constrained by dipole-cross sections in e+p/A collisions Perturbative approach

  • Employ kT-factorization (pT>Qs), dilute-dilute/dense

systems Non-perturbative approach

  • Full solutions of CYM on 2+1D lattice : IP-Glasma

Monte-Carlo model of initial conditions

11

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SLIDE 12

Multi-particle productions

  • n

D

dN dypd2p⊥

E ⇠ ⌦ |M|2↵ ⇠ hρ∗

1ρ1ρ∗ 2ρ2i

M ⇠ ρ1(k⊥) k⊥2 ρ2(p⊥ k⊥) (p⊥ k⊥)2 Lγ(p, k⊥)

Color Averaging

12

Single-Inclusive

p q

C2(p, q) ≡ ⌧ dN2 dypd2p⊥dyqd2q⊥

  • −

⌧ dN dypd2p⊥ ⌧ dN dyqd2q⊥

  • ↓

↓ connected disconnected

⊥ ⊥ ⊥ ⊥

⌦ |M|2↵ ! hρ∗

1ρ∗ 1ρ1ρ1ρ∗ 2ρ∗ 2ρ2ρ2i )

⌦ ↵

Double-Inclusive

p q

8 topologies 1 topology It can be shown Dumitru, Gelis, McLerran, Venugopalan 0804.3858

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SLIDE 13

n-particle correlations

p

1

p

2 ...

p

q

p

q ...

p

2

p

1

p

1 ...

p

q

p

q ...

p

1

Naturally generates Negative Binomial distribution probability distribution

13

CGC framework is extendable to n-particle correlations

High-multiplicity events —> originate from correlated production of n-particles —> Highly non-perturbative

P

NB

n

= Γ(k + n) Γ(k)Γ(n + 1) ¯ nnkk (¯ n + k)n+k

k = κ(Nc

2 − 1)Qs 2S⊥

2π

2n(n-1)! topologies

Gelis, Lappi, McLerran 0905.3234

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SLIDE 14

Description of Multiplicity distribution/ high multiplicity events

  • 1. Collision geometry

and impact parameter

  • 2. Color charge
  • 3. Rare Fock-Space

configurations

14

IP-Glasma model : combines CGC framework & different sources of initial state fluctuations

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SLIDE 15

(I) Fluctuation of collision geometry

Making Nucleus out of proton scattering

SA

dip(r⊥, x, b⊥) = A

Y

i=0

Sp

dip(r⊥, x, b⊥)

Si

p

)

  • Collision geometry is not calculable from first principle

Tp(s⊥) = 1 2πBG exp ✓s⊥2 2BG ◆ Z Tpp(b) = Z d2s⊥ T A

p (s⊥) T B p (s⊥ b⊥).

dP d2b(b) = 1 e−σggN2

gTpp(b)

R d2b ⇣ 1 e−σggN2

g Tpp(b)⌘,

Overlap function Impact parameter distribution

  • Eikonal model with thickness profile from HERA data

15

color charge distribution in nucleus

Proton profile

Q2

sA ⇠ A1/3Q2 sp

Nuclear saturation scale :

Schenke, Tribedy, Venugopalan 1311.3636

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SLIDE 16

(II) Fluctuation of color charge

Entries

/dy

g

dN

5 10 15 20

Entries

10

2

10

3

10

Entries

0<b<0.5 fm 0.5<b<1.0 fm 1.0<b<1.5 fm 1.5<b<2.0 fm

= 0.48 fm τ p+p 7 TeV,

IP-Glasma

For a given geometry fluctuations of color charge —> Negative Binomial distribution at each impact parameter

16

However the distribution is not wide enough to describe data Some sources of fluctuation missing

10-4 10-3 10-2 10-1 100 101 2 4 6 8 10

P(Nch/〈 Nch 〉)

Nch/〈 Nch 〉

IP-Glasma

p+p 7 TeV CMS

Convolution of many NBDs

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SLIDE 17

Input to CGC framework —> dipole cross section e+p/A

(III) Intrinsic fluctuations of saturation scale

r q q z 1-z

* γ

s

With evolution of rapidity each dipole split with probability ~ αs dY —> dipole splitting is however stochastic Color dipole picture : distribution of partons —> dist. of color dipoles Stochastic dipole splitting —> not present in BK/JIMWLK —>beyond CGC

17

2

log(r /r )

2

α

2

α

2

r

i 2

log(r /r )

2

T dipoles T

saturation

r

i

1

2

log(r /r )

2

α

2

α

2

r

i 2

log(r /r )

2

T dipoles T

saturation

r

i

1

2

log(r /r )

2

α

2

α

2

r

i 2

log(r /r )

2

T dipoles T

saturation

r

i

1

2

log(r /r )

2

α

2

α

2

r

i 2

log(r /r )

2

T dipoles T

saturation

r

i

1

dipole-probe target

Iancu, Mueller, Munier (hep-ph/0410018) Golec-Biernat, Wusthoff hep-ph/9807513

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SLIDE 18

Intrinsic fluctuations of saturation momentum of a proton/nuclei

10-4 10-3 10-2 10-1 100 101 0.5 1 1.5 2 2.5 3 P(QS/〈 QS 〉) QS/〈 QS 〉 σ=0.4 σ=0.5

P(ln(Q2

S/hQ2 Si)) =

1 p 2πσ exp ✓ ln2(Q2

S(s⊥)/hQ2 S(s⊥)i)

2σ2 ◆

σ2(Y ) = σ2

0(Y0) + σ2 1(Y Y0),

0.2 0.4 0.6 0.8 1 0.1 1 10 T(r,Y) log(r0

2/r2)

Y=8 Y=0

Dipole amplitude Saturation scale Stochastic splitting of dipole leads to a distribution of Qs

18

Marquet, Soyez, Xiao hep-ph/0606233

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SLIDE 19

Distribution of multiplicity

19

10-4 10-3 10-2 10-1 100 101 2 4 6 8 10

P(Nch/〈 Nch 〉)

Nch/〈 Nch 〉

IP-Glasma σ=0.4 p+p 200 GeV UA5

10-4 10-3 10-2 10-1 100 101 2 4 6 8 10

P(Nch/〈 Nch 〉)

Nch/〈 Nch 〉

IP-Glasma σ=0 IP-Glasma σ=0.5

p+p 7 TeV CMS

pp@LHC pp@RHIC

Origin of High multiplicity events (Tail of distributions)

High multiplicity events —> rare configuration of high color charge density (1/g2)

McLerran, Tribedy 1508.03292

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SLIDE 20

Azimuthal Correlations in CGC

∼ Q−1

s ~ E

20

  • Intrinsic momentum space

correlation from initial state

  • Originate probe scattering
  • ff a color domain
  • Suppressed by number of

color sources/domains Very distinct from Hydrodynamic flow (driven by geometry )

Kovner, Lublinsky 1012.3398 Lappi, Schenke, Schlichting, Venugopalan 1509.03499 Dumitru, Giannini 1406.5781 Dumitru, Dusling, Gelis, Jalilian-Marian, . Lappi, Venugopalan 1009.5295 Dusling, Venugopalan 1201.2658 Kovchegov, Wertepny 1212.1195

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SLIDE 21

Two particle correlation in CGC

Δφ = π trigger

back-to-back in 0 & π

π/2 π

Jet Graph

Y(Δφ)

21

Δφ

Kinematically constrained (back-to-back)

Δφ = π trigger

Symmetric around π/2 Glasma Graph Not kinematically constrained

Dusling, Venugopalan 1201.2658, 1210.3890

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SLIDE 22

Two particle correlation in CGC

Di-Jet Graph

22

π/2 π

Y(Δφ) Δφ

Jet + BFKL emissions

gluon emissions between two triggered hadrons—> broadening of the away side (de-correlation)

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SLIDE 23

Origin of ridge-like correlations

η ∆

  • 4
  • 2

2 4 φ ∆ 2 4

φ ∆ d η ∆ d

pair

N

2

d

trg

N 1

1.30 1.35 1.40

CMS Preliminary 110 ≥ = 7 TeV, N s pp <3 GeV/c

trig T

2<p <2 GeV/c

assoc T

1<p

  • 4
  • 2

φ ∆ 2 4

1.30 1.35 1.40

1 NTrig d2N d∆η d∆φ

∆φ π

1 NTrig d2N d∆φ

q p

Glasma Graph

q p

Jet Graph

23

But why ridge appears in high multiplicity events ?

In CGC, high occupancy ~1/g2 —> effective coupling 1/g2 x g = 1/g

Dusling, Li, Schenke 1509.07939

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SLIDE 24

Picture in high multiplicity events

24

1/g2 g2 g g2 g g2 g2 1/g2 g2 1/g 1/g low density (min-bias events) high density (high multiplicity events) g2 strong color field in CGC g—> ρg~1/g2 g~1/g

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SLIDE 25

Comparison to data

0.5 1 1.5 2 2.5 3

1.0 < pT

trig < 2.0 GeV; 1.0 < pT asc < 2.0 GeV

ATLAS Central ATLAS Peripheral

π π ∆φ

25

Consistent explanation in the CGC picture

Dusling, Venugopalan 1201.2658, 1210.3890, 1211.3701, 1302.7018

  • 0.02

0.02 0.04 0.06 0.08 0.1 0.12 0.5 1 1.5 2 2.5 3 d2N/d∆φ ∆φ p+p s1/2 = 7 TeV BFKL + glasma Q2

s0 = 1.008 GeV2

BFKL + glasma Q2

s0 = 0.840 GeV2

BFKL + glasma Q2

s0 = 0.672 GeV2

CMS: Ntrk>110, 1 GeV < pT

a,b < 2 GeV

p+p p+Pb

figure: Dusling, Li, Schenke 1509.07939

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SLIDE 26

0.01 0.02 0.03 0.04 0.05 20 40 60 80 100 120 140

Yint

Nch

rec

1< pasc,trg

T < 2 GeV

Glasma + BFKL

13 TeV (ATLAS acc.) 7 TeV (CMS acc. × 3.6) 13 TeV ATLAS Prelim. 7 TeV CMS × 3.6

Data

0.01 0.02 0.03 0.04 0.05 1 2 3 4 5

Yint

p

T

asc,trg [GeV]

Data: Nch

rec>110

13 TeV ATLAS 7 TeV CMS × 3.6

Glasma + BFKL

13 TeV (ATLAS acc.) 7 TeV (CMS acc. × 3.6) Nch

rec ~ 125

Nch

rec ~ 100

Energy independence of Ridge

26

  • Nrec

ch (√s) = Nrec ch (Qs2) , Yint(√s) = Yint(Qs2)

Energy dependence enters only though the saturation scale (only scale in problem) : Scaling of near side yield is natural in CGC approach

Dusling, Tribedy, Venugopalan 1509.04410

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SLIDE 27

Harmonics of azimuthal correlations

  • 0.02

0.02 0.04 0.06 0.08 0.1 1 2 3 4 5 6 7 8 v3 pT [GeV]

Gluons τ=0.4 fm/c ATLAS v3(2PC) 110 < Nch

rec < 140

CMS v3(2PC) 120 < Ntrk

  • ff < 150

Gluons τ=0.0 fm/c v3(EP/2PC) Gluons τ=0.2 fm/c v3(EP) v3(2PC) v3(EP)

0.05 0.1 0.15 0.2 1 2 3 4 5 6 7 8 v2 pT [GeV]

Gluons τ=0.2 fm/c ATLAS v2(2PC) 110 < Nch

rec < 140

CMS v2{4} 120 < Ntrk

  • ff < 150

Gluons τ=0.0 fm/c v2(2PC) v2(2PC) v2(EP)

27

…. + +

π/2 π Y(Δφ) Δφ π/2 π Y(Δφ) Δφ

even harmonics

  • dd harmonics

Schenke, Schlichting, Venugopalan 1502.01331

slide-28
SLIDE 28

Combining CGC and PYTHIA

  • Output distribution of Gluons from

CGC

  • Sample gluons in momentum space
  • Connect the gluons close in phase

space to color neutral strings

  • Input to PYTHIA and fragment into

final particles

28

rS

z t

1 QS

x x+

A = pure gauge 1

−

A = pure gauge 1 A = 0

T )

fragmentation

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SLIDE 29

Implementing PYTHIA Strings

gluons quarks anti-quarks strings

gluons quarks anti-quarks strings

px py px py y y

29

Work in progress

Connect the gluons close in phase space to color neutral strings

slide-30
SLIDE 30

30 10-4 10-3 10-2 10-1 100 101 1 2 3 4 5 6 7

P(N/〈 N 〉)

N/〈 N 〉

CMS Data Gluons Hadrons

IP-Glasma + PYTHIA 8.2 (p+p 7 TeV)

Preliminary results

  • Promising results on multiplicity distributions
  • Angular correlations, more observables are to be studied

Combining CGC and PYTHIA

slide-31
SLIDE 31

Outlook

  • Including diffractive process
  • Full 3+1D with JIMWLK rapidity evolutions
  • Implement color-reconnection in PYTHIA
  • Comparison to more data from LHC

31

Summary

The ab-initio framework of CGC constrained by HERA DIS data provide successful description of the phenomena seen in high multiplicity events at LHC

slide-32
SLIDE 32

32

back-up

slide-33
SLIDE 33

33

p q

k k k k p − k p − k q − k q − k

Momentum flow in Glasma graph (origin of ridge-like correlation)

Dusling, Li, Schenke 1509.07939

slide-34
SLIDE 34

34

Qualitative picture of correlations in small systems

Correlation strength Multiplicity for fixed system size

mini jets glasma graphs hydrodynamics parton escape initial state
 correlations response to
 initial geometry

8 Soeren Schlichting Quark Matter 2015