p-p Correlations at √s = 200 GeV

Jeff Porter

MIT Workshop

April, 2005

Porter 2

Agenda

• Minimum-bias p-p correlations on (yt,yt) and (η∆,φ∆)

• Conventional single-particle fragmentation functions

• Two-particle p-p fragment distributions on rapidity

• Low-Q2 jet angular morphology

• Jet angular correlations at low Q2

• jt and kt at low Q2 – η,φ asymmetry of jt

low-Q2 partons in p-p collisions

before we try to understand QCD in A-A collisionswe should understand it in elementary collisions

Porter 3

pt (GeV/c)

1/n s 1

/pt d

N/d

p t

yt

1/n s 1

/yt d

N/d

y t10

-710

-510

-310

-11010 310 510 710 9

10 1110 1310 15

0 2 4 610

-610

-410

-21

10 210 410 610 8

10 1010 1210 14

1 2 3 4yt

1/n s 1

/yt d

N/d

y t − S

0(yt)

yt

H(n

ch,y

t)

S0(yt)

H(nch,yt)

H0(yt)

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

2 2.5 3 3.5

10-3

10-2

10-1

1

1 2 3 4

yt

∆ρ /

√ρre

f

y t

1

2

3

4

51

23

45

00.010.020.030.040.050.060.07

away

1

1.5

2

2.5

3

3.5

4

4.5

1 2 3 4

CI

1

1.5

2

2.5

3

3.5

4

4.5

1 2 3 4

p-p Minijet Correlations on (yt1,yt2) and (η∆,φ∆)

subtract soft reference

minijetfragments

∆ρ/

∆ρ/

∆ρ/

∆ρ/

�ρρ ρρ ref

�

∆ρ∆ρ∆ρ∆ρ

• Minijet correlations down to hadron pt ~ 0.35 GeV/c: probe A-A medium

-2-1.5

-1-0.5

00.5

11.5

2

-10

12

34

0

0.005

0.01

0.015

ρρ∆

∆φ ∆η

same side

1D 2Dp-p200 GeV

nch=1

nch=10

pt → yt

0.15 61pt (GeV/c)

• p-p minijet correlations on transverse rapidity yt like string correlations on yz

stringfragments

STAR preliminary

φ∆

∆ρ /

√ρre

f

η ∆

2

02

4

-2

-1

0

1

2

-0.010

0.010.020.030.040.050.06

away side hadron pt ~ 0.5 GeV/c

~yz∆∆∆∆ yt1

yt2 yt2

∆ρ/∆ρ/∆ρ/∆ρ/

�

ρρρρref

nch

Porter 4

p-p Correlations on (yt1,yt2)

yt

∆ρ /

√ρre

f

y t

1

2

3

4

51

23

45

00.010.020.030.040.050.060.070.08

yt

∆ρ /

√ρre

f

y t

1

2

3

4

51

23

45

00.010.020.030.040.050.060.07

yt

∆ρ /

√ρre

f

y t

1

2

3

4

51

23

45

-0.05-0.04-0.03-0.02-0.0100.010.020.03

yt

∆ρ /

√ρre

f

y t

1

2

3

4

51

23

45

00.010.020.030.040.050.060.07

yt

∆ρ /

√ρre

f

y t

1

2

3

4

51

23

45

00.010.020.030.040.050.060.07

yt

∆ρ /

√ρre

f

y t

1

2

3

4

51

23

45

00.010.020.030.040.050.060.070.08

yt

∆ρ /

√ρre

f

y t

1

2

3

4

51

23

45

-0.03-0.02-0.0100.010.020.030.040.050.06

yt

∆ρ /

√ρre

f

y t

1

2

3

4

51

23

45

00.010.020.030.040.050.060.070.08

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

φ∆

η ∆

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

0 2 4

ASSS

SS - same side AS - away sideLS US LS US

CD CI CI

string and parton fragmentation: two-particle fragment distributions

STAR preliminaryCD

0.151.0

10.0

pt (GeV/c)

{ }0 0ln ( ) / /t t t t ty m p m p m γ β≡ + ≡

Porter 5

p-p Correlations on (η∆,φ∆)

φ∆

∆ρ /

√ρre

f

η ∆

02

4

-2

-1

0

1

2

-0.2-0.1

00.10.20.30.40.50.60.70.8

φ∆

∆ρ /

√ρre

f

η ∆

02

4

-2

-1

0

1

2

-0.2-0.1

00.10.20.30.40.50.60.70.8

φ∆

∆ρ /

√ρre

f

η ∆

02

4

-2

-1

0

1

2

-0.3-0.2-0.1

00.10.20.30.40.50.60.7

φ∆

∆ρ /

√ρre

f

η ∆

02

4

-2

-1

0

1

2

-0.4-0.2

00.20.40.60.8

1

φ∆

∆ρ /

√ρre

f

η ∆

02

4

-2

-1

0

1

2

-0.050

0.050.1

0.150.2

0.250.3

0.350.4

φ∆

∆ρ /

√ρre

f

η ∆0

24

-2

-1

0

1

2

-0.050

0.050.1

0.150.2

0.250.3

0.350.4

φ∆

∆ρ /

√ρre

f

η ∆

02

4

-2

-1

0

1

2

-0.2-0.1

00.10.20.3

φ∆

∆ρ /

√ρre

f

η ∆

02

4

-2

-1

0

1

2

-0.10

0.10.20.30.40.50.60.7

longitudinal string fragments: �pt� transverse parton fragments: � jt �, �kt�

a study in local charge and momentum conservation

LS US LS US

CD CI CD CISTAR preliminary

yt1

y t2

1

1.5

2

2.5

3

3.5

4

4.5

1 2 3 4

PF

SF

SF PF

Porter 6

Parton Ejection and Fragmentation

e

e

pγ, Z0

xQ2

e−

e+

Z0

s

HERALEP

RHIC

q

q

p

p

Q2x1x2

fragmentation – three issues:

how distributed on pt

how distributed on angle(s)

e-p

e-e

p-p

s, Q2

parton → hadron jet(x,Q2) Σ(pt,φ,η)i

?what recoil

Porter 7

pt (GeV/c)

1/n s 1

/pt d

N/d

p t

S0

total

H0 /10

10-6

10-5

10-4

10-3

10-2

10-1

1

10

0 2 4 6

Fragmentation: Linear vs Logarithmic

H1, e-p ξ ξ ξ ξ � ln(1/x)≅≅≅≅ ∆∆∆∆yt

STAR p-p

D(pt) =exp(−−−−pt/����pt����)

log-linear

linear-log yt

1/n s 1

/yt d

N/d

y t − S

0(yt)

H(nch,yt)nhns

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

2 2.5 3 3.5

STAR p-p

H1, e-p

STAR preliminary

Porter 8

Conventional Fragmentation Functions

e++++e− CCOR

√√√√s = 63 GeV

( )1( ) exp - / ; 1/ 6 - 7hadron

trigger

dND x x x x

N dx= ∝ �

, , , ,

, ,

/ ; /

/ ;

t hadron t part trig t trig t part

E t assoc t trig E trig

z p p z p p

x p p z x z

= =

= ≈

jet reconstruction leading particle

xE

( )exp - /x x∝?

A.L.S. Angelis et al., NPB 209 (1982)x

per Jia, Rak

symmetrize:trigger, associated→→→→ particles 1,2

Republican economy

trigger vs associated

collinear approximation

fragmentation function

Porter 9

-2-1.5

-1-0.5

00.5

11.5

2

-10

12

34

0

0.005

0.01

0.015

ρρ∆

∆φ ∆η

Symmetrized Fragment Distributions

US

yt

y t

1

1.5

2

2.5

3

3.5

4

4.5

1 2 3 4

US - SS

on logarithmic variables

yt

y t

yt

y t

yt

y t

yt

y t

1

1.5

2

2.5

3

3.5

4

4.5

1 2 3 4 1

2

3

4

12

34

00.20.40.60.8

11.2

1

1.5

2

2.5

3

3.5

4

4.5

1 2 3 4 1

1.5

2

2.5

3

3.5

4

4.5

1 2 3 4

Q/2~[1.7,4.5] GeV/c

Q/2 > 5 GeV/c

H1, e-p

( ){ }2( )xF( , ) exp / / 2

2ch

p

n Qx Q ξ

ξ

ξ ξ σσ π

� �= − −� �

−−−−ξξξξp

�ln(xp)

Q/2

yt,peak

STAR preliminary

Porter 10

Q/2 (GeV)

n ch

Q/2 (GeV)

ξ peak

Q/2 (GeV)

σ ξ

Q/2 (GeV)

y t0

1

2

3

4

5

6

7

1 101

1.2

1.4

1.6

1.8

2

2.2

2.4

2.6

2.8

3

1 10

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

1 101

1.5

2

2.5

3

3.5

4

4.5

1 10

H1- Hera e-p

STARnch = 2

34

6

1

Q/2

−−−−ξξξξp

�ln(xp)

Q/2Q/2

parton jet nucleon

Breit

NPB 445, 3 (1995)

QCD: ( )

12exp ln

6 2

chn Q

Q

b

�

� � � � �� �� �

1QCD: ( ) ln

2 2p

QQ �ξ

�Λ� �

341

QCD: ( ) ln2 2

QQ �ξσ � �

� � �� �� �

Λ~0.23 GeV

QCD=MLLA

DIS

Q/2 (GeV)

y t

1

1.5

2

2.5

3

3.5

4

4.5

1 10yt

y t

1

1.5

2

2.5

3

3.5

4

4.5

1 2 3 4

ypeak

Q/2 2 3 4

1

yt

y t1

1.5

2

2.5

3

3.5

4

4.5

1 2 3 41

1.5

2

2.5

3

3.5

4

4.5

1 2 3 4

yt∆∆∆∆

∆∆∆∆yt~ξξξξ

−−−−ξξξξp

�ln(xp)

Porter 11

Fragmentation on yt

yt

1/σ

dσ/d

y t

yt

1/σ

dσ/d

y t

yt

1/σ

1/(y

t − 0

.75)

dσ/

dyt

yt

1/σ

dσ/d

y t

0

1

2

3

4

5

6

7

8

0 2 4 6 80

1

2

3

4

5

6

7

8

0 2 4 6 8

00.5

11.5

22.5

33.5

44.5

5

0 2 4 6 80

1

2

3

4

5

6

7

8

0 2 4 6 8

CDF 350 GeV

different cone angles

ln(1/x)

OPAL – 91 GeV

TASSO – 14 GeV

LEPe-e

CDFp-p

STAR

LEPe-e

LEPe-e

ln(1/x)

ln(p)

biggest

MLLA

CDF jets: 105, 225, 350, 625 GeV LEP jets: 14, 44, 91 GeV

big

smallcone angle

yt

ln{2Ejet/mππππ}

θθθθ

for densityon radius

350 GeV

yt = ln{(mt+pt)/mππππ}

p-p

ymax(√s/2;m)

<nch

>

e-e

0

5

10

15

20

25

30

2 4 6 8

Porter 12

Jet Morphology Relative to Thrust

z

φ

pt1

pt2 jtηjtφ

xη

jet thrust axis (parton momentum)p-p collision axis

jt – transverse momentumrelative to jet thrust axis

φ∆

∆ρ

/ √ρ re

f

η ∆

2

02

4

-2

-1

0

1

2

-0.010

0.010.020.030.040.050.06 jtηηηη

jtφφφφ

y

the most probable parton Q/2 for the distribution at right is 1-2 GeV/c, comparable to the intrinsic parton kt

parton kt

hadron momenta

STAR preliminary

Porter 13

Symmetrized Angular Kinematics

pout

pt1,2, φ1,2 independent random variables

| | |sin |yp p ��ˆy ��

pt,2

pΣΣΣΣ /2/2/2/2

we now remove the trigger/associated asymmetry

pt,part

φ1φ2

jt scaling (not generally valid)

pt,1

( )2 2 2 2 2 2 2 2, , , , ,sin 1 2 /out t assoc ta ty assoc at ty trig ty assoc t assocSS SS SS SS SS

p p j x j j pφ= = + −

2 2 2 2,2 ,1 ,1 22 2 2 2 2

,1 ,2 12 ,1 22 2 2 2,1 ,2 ,1 ,2

sin 2t t t t

t t t tSSt t t t

p p j jp p j j

p p p p

φ φφ φφ = + −

asymmetric:

symmetric:

2 2 2,1 1 ,1

2 2 2,2 2 ,2

sin

sin

t ty

t ty

p j

p j

φ

φ

≡

≡kinematic limit

ˆy ��

,1tyj

,2tyj

symmetrize:trigger, associated→→→→ particles 1, 2

per Rak, Jia

Porter 14

CI

1

1.5

2

2.5

3

3.5

4

4.5

1 2 3 4

Symmetrize �| jtφ |� on yt⊗yt and (η∆,φ∆)

{ }2 2,2 ,12 2 2 2 2 2 2

,1 ,2 ,1 ,2 12 1 22 2,1 ,2

sin 2 sin sint t

t t t t SSt t

p pj j p p

p pφ φ φ φ φ+ = +

{ }2 2 2 2 2,1 ,2 1 22

12 2 2 2 2,2 ,1 ,1 ,2

sin 2 sin sint t SSt

t t t t

p pj

p p p pφ

φ φ φ∆ +≡

+

0.15 61pt (GeV/c)

yt2 yt∆∆∆∆ ytΣΣΣΣ

φ∆

∆ρ /

√ρre

f

η ∆

2

02

4

-2

-1

0

1

2

-0.010

0.010.020.030.040.050.06 φφφφ∆∆∆∆SS

( ) { }{ } ( ) ( ){ }

22

2 2/ 2 expsin / 2 2 sin / 2 2

2cosht

SSt

m y

yπ φ φΣ

∆ ∆∆

≈ +

this weighted average favors the jtφof the parton fragment with smaller pt

conditional (∆φ=φ12)

autocorrelation (φ∆=φ12)

φ

∆∆∆∆yt

yt1

( ),t ty yΣ ∆

( )2

12,t t tj y yη Σ ∆same for

(consistent with asymmetric special case)

( ) ( )2 2sin / 2 sin /φφ σ π∆∆ →

weighted average

weights

STAR preliminary

Porter 15

φ∆

∆ρ /

√ρre

f

η ∆

2

02

4

-2

-1

0

1

2

-0.010

0.010.020.030.040.050.06

Symmetrize �| ktφ |� on yt⊗yt and (η∆,φ∆)

0.15 61pt (GeV/c)

yt2 yt∆∆∆∆ ytΣΣΣΣ

φφφφ∆∆∆∆AS

∆∆∆∆yt

yt1

away

1

1.5

2

2.5

3

3.5

4

4.5

1 2 3 4

yt∆∆∆∆ ytΣΣΣΣ

( ),t ty yΣ ∆

2 2 2 2 2 2,1 ,2 1 ,1 1 ,22 ,

2 2 2 2, ,1 , ,2 ,1 ,2 , ,

sin ,ty ty ty ty t ipp i

t part t part t t t part i

k k z k z k pz

p p p p pφ ≈ + ≈ + ≡

{ }2 22 2,1 ,22 2

212 2 2 2 2,2 ,1 ,1 ,2

sin sin

1 2 sin

t t AS SSt

t t t t SS

p pz k

p p p pφ

φ φ

φ

∆ − ∆≡

− ∆+

( ) { }{ }

( ) ( ){ }( )

2 22

2

sin / 2 sin / 2/ 2 exp

2cosh 1 2 sin / 2

t AS SS

tSS

m y

yπ

φ φ

φ

∆ ∆Σ

∆ ∆

−≈

−

conditional (∆φ=φ12)

autocorrelation (φ∆=φ12)

(~ consistent with asymmetric special case)note

( ) ( )2 2sin / 2 sin /φφ σ π∆∆ →

STAR preliminary

Porter 16

Angular Correlation Measurements

yt1

y t2

1

1.5

2

2.5

3

3.5

4

4.5

1 2 3 4

exp{−ytΣ/2}

σ φ

data

exp{−ytΣ/2}

σ φ

Pythia

|φ∆| > π/2

0

0.2

0.4

0.6

0.8

1

1.2

0 0.05 0.1 0

0.2

0.4

0.6

0.8

1

1.2

0 0.05 0.1exp{−ytΣ/2}

σ η

Pythia

exp{−ytΣ/2}

σ φ

Pythia

|φ∆| < π/2

0

0.2

0.4

0.6

0.8

1

1.2

0 0.05 0.10

0.2

0.4

0.6

0.8

1

1.2

0 0.05 0.1

exp{−ytΣ/2}

σ η

CI

LSUS

data

6.6 2.2 1.3 0.95 0.74 0.6pt (GeV/c)

exp{−ytΣ/2}

σ φ

data

|φ∆| < π/2

0

0.2

0.4

0.6

0.8

1

1.2

0 0.05 0.10

0.2

0.4

0.6

0.8

1

1.2

0 0.05 0.1

ytΣΣΣΣ

SS - same side AS - away side

φ∆

∆ρ

/ √ρ re

f

η ∆

2

02

4

-2

-1

0

1

2

-0.010

0.010.020.030.040.050.06

SSAS

jt scaling

minimum-bias results

STAR preliminary

Porter 17

yt

y t

1

1.5

2

2.5

3

3.5

4

4.5

1 2 3 4

ytΣ/2

<|j tη

|> (

GeV

/c)

data

ytΣ/2

<|j tφ

|> (

GeV

/c)

data

ytΣ/2

<|j tη

|> (

GeV

/c)

Pythia

ytΣ/2

<|j tφ

|> (

GeV

/c)

Pythia

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

2 2.5 3 3.5 4 4.5 0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

2 2.5 3 3.5 4 4.5

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

2 2.5 3 3.5 4 4.5 0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

2 2.5 3 3.5 4 4.5

�| jty |� and �|kty |� Inferences

yt1

y t2

1

1.5

2

2.5

3

3.5

4

4.5

1 2 3 4

ytΣΣΣΣ( ) { }

{ } ( ) ( ){ }2

22 2 2

12

/ 2 expsin / 2 2 sin / 2 2

2cosht

txSS

t

m yj x x

yπ Σ

∆ ∆∆

≡ +

( ) { }{ }

( ) ( ){ }( )

2 22

2 2

12 2

sin / 2 sin / 2/ 2 exp2

cosh 1 2 sin / 2

t AS SSt

tSS

m yz k

yπ

φ

φ φ

φ

∆ ∆Σ

∆ ∆

−≡

−

{ }/ 2 ln / 2ty Q�Σ Λ

( ),t ty yΣ ∆

,x η φ=

2 / 2 /xx σ π∆ ∆→

STAR preliminary

Porter 18

yt

∆ρ /

√ρre

f

y t

1

2

3

4

51

23

45

00.010.020.030.040.050.060.07

The p-p Reference System for A-A

t

yt

jtabab

a

a

a

b

b

yz

minijet

string

soft

hard

pt

η ∆

φ∆

-2-1

01

2

02

4

-0.8-0.6-0.4-0.2

00.20.40.6

soft hard

STAR preliminary

yt

1/n s 1

/yt d

N/d

y t − S

0(y t)

yt

H(n

ch,y

t)

S0(yt)

H(nch,yt)

H0(yt)

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

2 2.5 3 3.5

10-3

10-2

10-1

1

1 2 3 4

�

∆ρ

{

{ }0

0

ln ( ) /

/t t t

t t

y m p m

p m γ β≡ +

≡

recoil

φ∆

∆ρ /

√ρre

f

η ∆

02

4

-2

-1

0

1

2

-0.4-0.2

00.20.40.60.8

1

Brownian probe system for A-A collisions

φ∆

∆ρ /

√ρre

f

η ∆

02

4

-2

-1

0

1

2

-0.2-0.1

00.10.20.30.40.50.60.70.8

φ∆

∆ρ /

√ρre

f

η ∆

02

4

-2

-1

0

1

2

-0.3-0.2-0.1

00.10.20.30.40.50.60.7

(a)

η ∆

φ∆

(b)

η ∆

φ∆

(c)

η ∆

φ∆

(d)

η ∆

φ∆

-2-1

01

2

02

4

-4-3-2-10123456

-2-1

01

2

02

4

-4-3-2-10123456

-2-1

01

2

02

4

-4-3-2-10123456

-2-1

01

2

02

4

-4-3-2-10123456

(a)η∆

φ∆

(b)η∆

φ∆

(c)η∆

φ∆

(d)η∆

φ∆

-2 -1 0 1 2

-2

0

2

-5-4-3-2-101

-2 -1 0 1 2

-2

0

2

-5-4-3-2-101

-2 -1 0 1 2

-2

0

2

-5-4-3-2-101

-2 -1 0 1 2

-2

0

2

-5-4-3-2-101

η ∆

∆ρ /

√ρre

f (G

eV/c

)2

φ∆-2

-1

0

1

2

02

4

0.010.0120.0140.0160.018

0.02

η ∆

∆ρ /

√ρre

f (G

eV/c

)2

φ∆-2

-1

0

1

2

02

4

-0.00250

0.00250.005

0.00750.01

0.01250.015

Porter 19

Summary

• Low-Q2 parton fragmentation in p-p is precisely accessible down to hadron pt ≅ 0.35 GeV/c

• Jet morphology at low Q2 requires new treatment of fragment pt distributions, angular correlations

• Jet fragment distributions on rapidity are ‘ infrared safe’ and exhibit interesting systematic behavior

• Jet angular correlations show strong asymmetry at low Q2, possibly related to parton collision details