Low-Q2 Partons in p-p and Au-Au Collisions

Tom Trainor

ISMD 2005 – Kroměříž, CR

August, 2005

Trainor 2

Agenda

• Survey of p-p correlations

• Fragment distributions on (yt,yt) in p-p

• Fragment distributions in Au-Au

• Angular correlations on () in p-p

• Angular correlations in Au-Au

• pt correlations in p-p and Au-Au

QCD from the bottom up

Trainor 3

Low-Q2 Partons in p-p Collisions

subtract soft reference

minijetfragments

√ r

ef

√

same side

1D 2Dp-p200 GeV

nch=1

nch=10

pt yt

0.15 61pt (GeV/c)

string fragments

away side hadron pt ~ 0.5 GeV/c

yt1

yt2 yt2

√ref

nch

parton fragments

0ln ( ) /t t ty m p m

minimum-bias: no trigger condition

Trainor 4

Analysis Method(yt1,yt2) correlations () correlations

√ r

ef

√ r

ef

( ) ( )/ | a b

ref ab

a b

n n n n

n n

modified Pearson’s coefficient:normalized covariance density

in each 2D bin:

– bin size

number of correlated pairs ‘per particle’

autocorrelations can be determined by pair countingor by inversion of fluctuation scale dependence

joint autocorrelation on two difference variables

,

( ) ( ) ( )

( )k a a k

k ref a a k a

A n n n n n

A n n n+

+

ì üD - -ï ïº í ýï ïî þ

average over aon kth diagonal

,

( ; ) ( )

( ; ) ( )x k

ref x x k ref

n k A n

n k A n

r e

r e eD

D D

D Dº

x1

x 2

k a+k

a

x x

k

(yt,)

/

/

ref

ref

Trainor 5

p-p Correlations on (yt1,yt2)

ASSS

SS – same side

AS – away side

LS – like sign US – unlike sign

string and parton fragmentation: first two-particle fragment distributions

0.151.0

10.0

p t (GeV/c)

√ r

ef

√ r

ef

√ r

ef

√ r

efHBT

stringaway-side partonfragmentation isindependent ofcharge combination

same-side partonfragmentationrestricted to US pairs

parton

parton parton

(except OPAL on )

string

Trainor 6

p-p Correlations on (,)local charge and momentum conservation

PF

SF

SF – string fragments

PF – parton fragments

LS – like sign US – unlike sign

√ r

ef

√ r

ef

√ r

ef

√ r

ef

away-side partonfragmentation isindependent ofcharge combination

string fragmentationreflects local measureconservation

HBT string

partonHBT

parton

joint autocorrelation on two difference variables

parton

Trainor 7

p-p jets: 105, 225, 350, 625 GeV e-e jets: 14, 44, 91 GeV

Single-particle Fragmentation – I

= ln(1/xp)

OPAL – 91 GeV

TASSO – 14 GeV

ln(pt)conventional

fragmentation functions on logarithmic variables

e-e fragmentation functions ontransverse rapidity yt –systematic variation described by single model function

transverse rapidity yt

xp =pt /Ejet

LEPPETRA

e-e

ln ( ) /t t ty m p m CDF PRD 68 (2003) 012003 OPAL PLB 247 (1990) 617 Biebel, Nason and Webber hep-ph/0109282 617

ssampling:

not full data!

LEP

Trainor 8

Single-particle Fragmentation – II

2 2,max 0 0 ,minln ( ) / 0.35t jet jet ty E m E m y

1 1( ; , ) (1 ) / ( , )p qu p q u u B p q

p = 2.9q = 3.55

14, 44, 91 GeV

e-e

2 2 2,max( , ) ( ln ) ( ln / ln )h

p tD x Q F y Q G u x Q

~ independent of yt,max

2

ch t,max t,minn = A y - y

nch and peak values from Bethke hep-ex/9812026

simple e-e systematics on transverse rapidity

unidentified hadrons from unidentified partons

A = 0.65

10.425

2peak

pu

p q

upeak

slope = 0.41

mode

t,max t,miny - y

u=

mode:

e-e

two-particle fragment distribution

fit: distribution

Trainor 9

Two-particle Fragment Distributions

US – same side

STAR preliminary

yt

yt~

yt,peak

Q/2 2 3 4

1

p≡ln(xp)

1 10

Q/2 (GeV)

an approach derived from fragmentation functions

construct a surfacerepresenting frag-mentation functions vs parton momentum Q/2

parton momentum

frag

men

t rap

idity

symmetrize the surface to representfragment-fragmentcorrelations

compare to data:general featuresagree; string fragments appear at small yt

nch

one can sketch a two-particle minimum-bias fragment distribution starting with a surface from which fragmentation functions are conditional slices

conditional: trigger particle data

Trainor 10

Number Correlations on ytyt

peripheral

centralSTAR preliminary

evolution of fragment distribution with Au-Au centrality

200 GeV p-p

√ r

ef

√ r

ef

√ r

ef

√ r

ef

√ r

ef

√ r

ef

200 GeV Au-Au

RAA

same-side - US

Trainor 11

Jet Morphology Relative to Thrust

z

pt1

pt2 jtjt

x

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

jt – transverse momentumrelative to jet thrust axis

jt

jt

y

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

parton kt

hadron momenta

√ r

ef

angular correlations

Trainor 12

Symmetrized Angular Kinematics

pout

pt1,2, independent random variables

ˆy f®

pt,2

p

remove the trigger/associated asymmetry

pt,part

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 p

asymmetric:

symmetric:

kinematic limit

ˆ ˆˆ ,y jf®

,1tyj

,2tyj

symmetrize:trigger, associated particles 1, 2

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 p

J. Rak, J. Jia

T. Trainor, J. Porter

remove trigger-associated asymmetry

Trainor 13

Symmetrize | jt| and | kt|

0.15 61pt (GeV/c)

yt2 yt yt

SS

22

2 2 2

12

/ 2 expsin / 2 2 sin / 2 2

2cosht

tSS

t

m yj

y

autocorrelation ()

yt

yt1 ,t ty y

2

12,t t tj y y same for 2 2sin / 2 sin /

STAR preliminary

2 22

2 2

12 2

sin / 2 sin / 2/ 2 exp

2cosh 1 2 sin / 2

t AS SSt

tSS

m yz k

y

0.15 61pt (GeV/c)

yt2 yt yt

yt

yt1

AS SS

AS

no small-angle approximation, similar fragment pt

Trainor 14

Angular Correlation Measurements yt

SS - same side AS - away side

SSAS

jt jt kt

large same-side ( asymmetry

STAR preliminaryjt scaling

Trainor 15

Fragment Asymmetry about Thrust

two-particle fragmentation

jt jt

previously unexplored region!

pQCD pQCD

STAR preliminary

evolution with Q2 of soft jet angular asymmetry

small Q2 larger Q2

200 GeV p-p

• Small-Q2 partons down to 1 GeV are detectable

• These softest jets are strongly elongated

in the azimuth direction in p-p collisions

no trigger particle t t t πy ln m + p /m

lo hi

hi

lo

yt cut space

pt combinations determine Q2 of parton interaction

softest jets ever! big non-perturbative effects

yt

1:1 aspect ratio

Trainor 16

Interpretation

contact plane

contactplane

water dropsvrel = 6 m/s

pt

low-Q2 fragmentation

broadened in contactplane (,pt), narrowedperpendicular to it ()

z

z

hydrodynamicsof parton collisions

Trainor 17

Minijet Deformation on () in Au-Au

p-p

HI

p-p HIperipheral

central

centrality

130 GeV Au-Au

widths

minbias p-p

low Q2

fragmentation asymmetry reverses – p-p Au-Au

130 GeV Au-Au mid-central

p-p

Au-Au

low Q2

low Q2

Trainor 18

The Other kt Broadening

azimuth broadening

pt,part,1 pt,part,2

kty,1+ kty,2

pt,part,1 pt,part,21 2||t tk klargest kt effects:

small q/2,

q/2-q/2

1tk

2tk

US

y t2

yt1

yt yt

STAR preliminary

interaction between intrinsic kt and momentum transfer q

||tk q

tk q

orientationtk vs q

pt broadening

the alignment between parton kts and q determines whether relative azimuth or relative pt of fragments will broaden

condition on (yt1,yt2) biasesaway-side azimuth broadening

SS - intrajet

AS - interjet

√ r

ef

Trainor 19

pt Fluctuations and pt Correlations

70-80%

20-30%

0-5%

full STAR acceptance

variance excess

fluctuation scaling

fluctuationinversion

subtractmultipoles

autocorrelation

STAR preliminary

centrality

pt fluctuations

partons and velocity correlations: how is pt distributed on ()?

• pt fluctuations invertible to pt autocorrelations

√ r

ef

√ r

ef

√ r

ef

√ r

ef

T. A. Trainor, R. J. Porter and D. J Prindle, J. Phys. G: Nucl. Part. Phys. 31 (2005) 809-824; hep-ph/0410182

Trainor 20

Compare with p-p pt Autocorrelations

Hijing Au-Au 200 GeV

p-p 200 GeV minbias

data Au-Au 200 GeV

p-p 200 GeV nch > 9

CI=LS+US

CD=LS–US

direct – from pair counting

from fluctuation inversion

70-80%

STAR preliminary

√ r

ef

√ r

ef

√ r

ef

√ r

ef

√ r

ef

net-charge correlations

Trainor 21

Model Fits

20-30%

data fit peakfit residuals

fitdatafit peak

red shifts and blue shifts

0-10%

0-10%

70-80%

quenchoff quench

on

Hijing

collision centrality

hijing

hijing

B1

B3

B2Hijing does not predict strong broadening or negative structure

peak amplitudes peak widths

negative structure is unanticipated –what is the origin?

Trainor 22

red shift

low-x partons

parton fragments

Au-Au pt autocorrelation

2q

1q

STAR preliminary

p-p pt autocorrelation

Au-Au200 GeV

bulk medium

• Response of medium to minimum-bias parton stopping

• Momentum transfer to medium

• Velocity structure of medium• Medium recoil observed via

same-side pt correlations

red shift: particle production may be from a recoiling sourceRecoil Response to Parton Stopping

20-30%

data model peak

recoil

fit residuals

fitdatamodel peak

STAR preliminary

80-90% ~ p-p

20-30% 0-5%

40-50%

Trainor 23

Energy Dependence: SPS RHIC

:t tp p n

CERES NPA 727 (2003) 97

2

dramatic increase of pt fluctuations with

increasing sNN

STAR preliminary

CERES

STAR

Hijing

full acceptance

centrality

STAR

ln /10 GeVNNsstring structure in Hijing does not appear in Au-Au data

!

Trainor 24

Summary• Precision survey of p-p correlation structure• Model-independent access to low-Q2 partons• Hydrodynamic aspects of parton scattering?

• The other kt broadening: pt asymmetry

• Low-Q2 partons as Brownian probes of A-A• Dissipation: p-p fragment distributions modified in A-A• Non-pQCD p-p angular correlations modified in A-A

• pt correlations: temperature/velocity structure of A-A

• Strong disagreement with pQCD Hijing Monte Carlo• Recoil response of A-A bulk medium: viscosity 0