1

Multipoles and Coherent Gluon RadiationPlenary session

Lanny Ray, Univ. of Texas at Austin

STAR Collaboration Meeting LBNL 10/17/2013

Higher-order harmonics ?

BFKL Pomeron diagrams and v2

On to the LHC

Summary and Conclusions

2

Event 1

Event 2

ρsibling(p1,p2)

ρreference(p1,p2)

Correlation measure

:where

"" Gaussian) 2D side Same(

)2cos(2)cos(

, 1),(

),(

2

0

Model Fitting

n

QD

mix

sibch

ref

v

AAA

dd

dN

Fill 2D histograms

(1-2,1-2), (pt1,pt2)

Number of correlated pairs

per final-state particle

21

21

2

22

vd

dNA ch

Q

Relation between the

quadrupole amplitude and v2

3

What about higher harmonics, vn?Example: 200 GeV Au+Au 5-9%

No additional

model elements

required

Introduce a sextupole 2AScos(3); maintain away-side fit:

QD SQD QDSQD

net

sextupole

contribution

Same-side 2D peak = 1D ridge + reduced 2D Gaussian = Non-Gaussian 2D peak

Issue is description of the same-side peak. (LR, Prindle, Trainor, arXiv:1308.4367)

4

Non-Gaussian models of same-side 2D peak200 GeV Au+Au 28-38%

scale

x16

sextupole SS 1DG ridge NG exponents

polynomial poly+NG quartic

4

2

4

2

2D

2

4

4

2

2

2D

22

2D

2/

SSG

2

1exp

:Quartic

2

1exp1

:exponent NG or without with polynomial

2

1exp

:exponentsGaussian -Non

:ridgeGaussian 1D Side-Same22

A

A

A

eAevenk

k s

modelpeak 2D SS

Gaussian-Non

modelfit

Standard

scale

x16

Non-Gaussian models

Slight leptokurtic shape at 2-3 significance.

(LR, Prindle, Trainor, arXiv:1308.4367, accepted Phys. Rev. C)

5

Sextupole (v3) – one example of a NG peak

Reduction in

c2/DoF using

sextupole

The net effect of the sextupole (v3) is to allow a

small non-Gaussian shape for the same-side 2D

peak. It is not unique in that regard; other NG

models work as well or better. The only issue

here is the small NG shape of the SS 2D peak.

absolute c2/DoF

and using the

other NG models

(LR, Prindle, Trainor, arXiv:1308.4367, accepted Phys. Rev. C)

6

ATLAS Pb+Pb 2.76 TeV 0 – 1%, pt = 2 – 3 GeV/c; (ATLAS, PRC 86, 014907 (2012))

These data do not require a sextupole! v3>0 fits can be forced but give poor c2.

Std. Fits with NG exponents, AQ < 0

ASG<0, no quad AQ ,AS<0 ASG, AS<0

Data Fit

(LR, Prindle, Trainor, arXiv:1308.4367, accepted Phys. Rev. C)

7

BFKL Pomerons - gluon interference

E. Levin and A. H. Rezaeian, Phys. Rev. D 84, 034031 (2011)

Two-BFKL Pomeron

Exchange with two-gluon

emission & interference

N

N

Multiple gluon emission from 2 or more

Pomerons interfere producing azimuth

anisotropy wrt momentum transfer

Resulting correlation:

Random emission results in uniform

dependence.

This mechanism was proposed to explain the

same-side ridge. However, it is a pQCD

prediction for a quadrupole correlation, or v2.

TQ

)2cos(

(Balitsky, Fadin, Kuraev, Lipatov)

8

BFKL Pomerons & color-dipoles

Color Dipole Model: Kopeliovich et al.

Phys. Rev D78, 114009 (2008).

BFKL-saturation (glasma) model:

Dusling and Venugopalan,

arXiv:1210.3890

back-to-back

di-gluons

Quadrupole (v2)

(from Raju)

2v

9

May 2013 – http://indico.cern.ch/conferenceDisplay.py?confId=223909

MIT p+Pb Workshop – in honor of Wit Busza

Many, very interesting talks:

Miklos Gyulassy – “The Revenge of Wit : Will the Biblical Pillars

of AA 2003 be left Standing after the pA of 2013?”

10

11

12

13

14

15

But these questions have already been raised.

ST

Angular correlations –

jets, dijets (away-side)

not dissipated

Glauber superposition of

minijets (transparency);

large quadrupole (v2)

Constituent v2 – transverse rapidity

boost, non-hydro (Romatschke)

Quadrupole log(s)Nbin

scaling – initial-state only;

final-state effects ?

gluon-interference ?

All of this and much more

were known before p+Pb,

BES, LHC.

16

BFKL Pomeron Application to 200 GeV p+p(work in progress)

4

2

242

23,

2

2

3242t

tT

t

tT

tt

tqQp

t q

pQ

q

pQ

qp

qd

pdyd

dtTt

2cos12

14

22

t

Tt

q

Qp azimuthal

anisotropy

2

IPhN

Two-gluon density for

2-Pomeron exchange:

is the prob. for

two parton showers in a

N-N collision.

Construct correlations;

estimate momentum

integrals using the saturation

limit (QS):

15/

saturated-semi

~~ :saturation

for

llisionshowers/coPomeron No.

44 mQ

QqQ

Qp

n

T

StT

St

(Levin, Rezaeian PRD 84, 034031 (2011))

17

Fit 200 GeV p+p frequency distribution

assuming 1, 2, … parton showers with

probabilities P1, P2, …

Mean Nch per parton shower equals the

minbias mean

Each shower produces a Poisson distribution.

P1 = 0.91, P2 = 0.09, P3 = P4 ~ 0

/5.2chN

Data (NBD)

1Pom

1Pom + hard

1&2Pom + hard (fit)

Poisson

P1 P2

BFKL Pomeron Application to 200 GeV p+pEstimate Pomeron probabilities:

ch

chh

chs

h

hsch

n

nn

nn

n

nnn

1

unit per 005.0 ,

hard soft ,

2(STAR, PRD 74,032006)

18

Prindle (STAR) ISMD-2013

STAR

Preliminary

Probability weighted

sum over 1 & 2

Pomeron diagrams;

pt-integral correlation;

Levin & Rezaeian QS2.

222222

84

42

4

4

2

4

42

22

1

21

2

ref

GeV 6.18.0,GeV 6.0 ,(GeV/c) 188.0 ,5.2/

sat-semi , 15/

saturated , /11

2cos22cos1

4

4

2|

mQpN

Qm

Q

qQ

Aq

QpPP

PN

Stch

S

S

T

QTtch

Quad

AQ = 0.0003 – 0.003; [semi-sat – saturated]

From D. Prindle (STAR) ISMD-2013 poster:

AQ = 0.002 for 200 GeV p-p NSD minbias; v2 = 0.072

Predicted Minimum-bias

quadrupole amplitude:

BFKL Pomeron Application to 200 GeV p+pEstimate p+p minbias quadrupole, v2:

2

22

vd

dNA ch

Q

19

Nch dependent quadrupole:

2cos15

1)(

2

pairs # total

pairs 2Pom correl. #

2

2

8

42

22

12

ref

ch

S

tchchch

ch

ch

n

Q

mpnnnP

n

n

QS2=0.6 GeV2

QS2=0.8 GeV2

Prindle (STAR) ISMD-2013

STAR

Preliminary

BFKL Pomeron Application to 200 GeV p-p

20

Saturation limit

Semi-saturated, m2=1.6 GeV2

Semi-saturated, m2=0.8 GeV2

BFKL Pomeron Application to 200 GeV p-pNch dependent quadrupole:

Or, find QS for the three saturation assumptions in L & R:

Fit Data:

Solve for QS

2

000064.00007.0)(

s

chQ

s

ch nnA

n

n

Prindle (STAR) ISMD-2013

STAR

Preliminary

21

7 TeV p+p from CMS

CMS Collaboration,

JHEP 1009,091(2010).

TeV 7at 28at 008.0

:/ toconvertingafter obtain 034020] 84, D Rev. [Phys. Fits

1.0,110,

d

dNA ch

pNQ

ref

t

Quadrupole

22

Fit the CMS p+p NSD 7 TeV minbias

multiplicity frequency distribution data;

Mean nch/ = 6.0; assume ~ 0.02;

minbias average probabilities:

P1-4 = {0.67, 0.27, 0.06, 0.0}

P1

P2

P3

Data, || < 0.5

Fit with 1,2,3 P + nh

1, 1&2, 1,2&3 Pomerons,

no hard scattering

Pomeron Probabilities

BFKL Pomerons for 7 TeV p+p

Illustrative only!

Soft-hard decomposition

remains to do.

(CM

S,

JHE

P0

1,

07

9 (

20

11))

23

BFKL Pomerons for 7 TeV p+p

222222

84

42

4

4

2

4

42

22

1

GeV 6.18.0,GeV 6.0 ,(GeV/c) 2.0 ,0.6/

sat-semi , 15/

saturated , /11

included showersPomeron 3 and 2 , 1

)1(2

mQpN

Qm

Q

qQ

qQpnnP

NA

Stch

S

S

T

Tt

n

nch

Q

Predicted range for AQ for 7 TeV p+p minbias: 0.006 to 0.05

Compared to 200 GeV minbias p+p: 0.0003 to 0.003

The increase is due to the larger pre-factor dNch/d, larger 2-Pomeron

probability, and the appearance of 3-Pomeron shower events.

Illustrative only!

Soft-hard decomposition

remains to do; as well as

QS estimates.

24

5.02 TeV p+Pb at the LHC

ATLAS, PRL 110, 182302 (2013)

LHCat ]20,2[

.similar at (0.008) quadrupole

pp TeV 7 n thelarger tha4x -3

30 ,5 at 0.03-0.02 0,

:quadrupoleFit with

part

N

N

d

dNA

ch

chQ

Monotonic increase in same-side

-extension, ~ inc. quadrupole amplitude

In the BFKL-Pomeron model

typical high multiplicity p+Pb

collisions will have a couple of

multi-Pomeron events producing

quadrupoles.

Those quad. correlations add;

they do not cancel with random

orientation of each N-N scattering

plane: binN

QuadQuad NpAp )()(

25

NN Superposition for 200 GeV p+Au

In Kopeliovich et al’s color dipole model v2 in p+A is computed from the singles anisotropy wrt

the p+A reaction plane. Random N-N orientation suppresses the net anisotropy and v2.

However, RP and EP are irrelevant for inclusive v2 measurements which equal the correlations

on relative azimuth.

In a Glauber superposition model quadrupoles

from N+N add linearly in p+A and A+A. Naively

we expect AQ(p+A) ~ AQ(NN,minbias) and

AQ(A+A) ~ (Nbin/Npart)AQ(NN,minbias).

p+Au Monte Carlo Glauber

Sample b, find Nbin

Sample p+p NBD and get nch(NN)

Use AQ(nch) to calculate (NN)

Sum to get (p+Au), Nch(p+Au)

and AQ(p+Au)

AQ(p+Au) increases with multiplicity

AQ,p+p(nch) ~ parabolic

~ linear

= constant

Predicted

Nch frequency

distribution

26

6

10

20

NN Superposition for 200 GeV p+Au

The naïve expectation AQ(p+A) ~ AQ(NN,minbias) ~ 0.002 was not realized. Why?

To illustrate this I applied the MCG superposition model for larger numbers of N-N collisions.

Eventually, we recover the naïve expectation, however large quadrupoles persist at higher Nch.

The p+A quadrupole increases at

the upper end of the frequency

distribution because those events

are biased toward higher nch N+N

collisions, with larger AQ.

minbias),(NNAQ

27

Summary & Conclusions

Higher-order harmonic (sextupole - v3) descriptions of 2D angular correlations are

actually describing small, non-Gaussian structure in the same-side 2D (minijet) peak.

The detailed structure of this peak is the real issue. Claims that these higher-order vn

have been “discovered” in the data are questionable.

Given the properties of angular correlations and the quadrupole in particular we may

ask if there is a pQCD explanation for v2.

The BFKL-Pomeron model of Levin and Rezaeian was applied to 200 GeV and 7 TeV

p+p frequency distributions and quadrupole correlations. Although there are large

uncertainties due to saturation scale estimates (QS), the quadrupole predictions are

consistent with recent data.

Further study and application of pQCD (BFKL Pomerons, color-dipole) to the

quadrupole correlations now observed in p+p, p+A and A+A at RHIC and LHC is

warranted.