Fragmentation in e+-e Collisions

Dave KettlerCorrelations and Fluctuations

Firenze

July 7-9, 2006

phadron

e

e+

, Z0

LEPPETRA

q

q color dipole

s = Q2

Dave Kettler 2

QCD Issues for Nuclear Collisions

• How do partons scatter at low Q2 (invariant mass squared)

• How do low-Q2 partons fragment to hadrons• What happens to low-Q2 partons in heavy ion collisions

to understand the second point we examine the systematics of parton fragmentation in p-p and especially e-e collisions

we observe that a large fraction of RHIC C/F are due to minijets = low-Q2 parton fragments

Dave Kettler 3

Two-component p-p Spectrum Model

‘hard’ component: parton scattering and fragmentation

pt and yt spectra

S0

hard component vs nch

H0

200 GeV p-p

minijets are isolated in single-particle spectra

subtract S0

replot

Dave Kettler 4

Parton Scattering and Fragmentation

e

e´

, Z0

xQ2

e

e+

Z0

s

HERALEP

RHIC

q

q

pproton

pproton

Q2x1x2

fragmentation – two issues:

how distributed on momentum p

how distributed on angle(s)

e-pe-e

p-p

s, Q2

parton hadron jet(x,Q2) i(pt,)i

pproton

Dave Kettler 5

phadron

Parton Fragmentation in e+- e

e

e+

, Z0

LEPPETRA

q

q color dipole

how are parton fragments (hadrons) distributed on momentum

s = Q2

LEP, PETRA fragmentation data: 1985-2000

color dipole radiation:

ln(phadron)

LEPPETRA

e-e

ln(pparton)

gluon coherence: a QCD triumph

s, Q2

?

an equilibration process

Dave Kettler 6

Conventional Fragmentation Studies

ee CCOR

s = 63 GeV

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

trigger

dND x x x x

N dx

, , , , / ; /

/ , /

t assoc t trig trig t trig t part

E hadron parton p hadron parton

x p p z p p

x E E x p p

jet reconstruction leading particle

xE

exp - /x x?

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

trigger vs associated

fragmentation function

‘leading-particle’ strategy

jet is not reconstructed, estimate parton with high-pt leading particle

Dave Kettler 7

ln(p) rapidity y

Fragment Distributions on Momentum

p = ln(1/xp)

fragmentation functions on logarithmic variables

alternative:fragmentation functions on rapidity y

ln ( ) /y E p m

s

conventional:fragment momentumrelative toparton momentum

D(

p,s

)D

(y,y

max

)

D(l

n(p

),s)

D(x

,s)

xp = phadron/pparton fragmentation function

D(x,s) D(y, ymax)

LEPPETRA

e-e

non-pQCD physics!

scaling violationspQCD

Dave Kettler 8

Precision Analysis of Fragmentation

1 1max( , ) ( ; , ) (1 ) / ( , )p qg u y u p q u u B p q

max max max( , ) 2 ( ) ( , )D y y n y g u y

fragmentation functions well described by simple model function

g

(u,y

max

) =

beta distribution on normalized rapidity u precisely models fragmentation functions

( ) ( )( , )

( )

p qB p q

p q

min

max min

y yu

y y

(normalized)

ymin

normalized rapidity

redundant

7

46 GeV = Q/222

a form of equilibration

p-pp-p - FNALe-e - LEP

STAR

D(y

,ym

ax)

dijet multiplicity

( ; , )u p q

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Why a Beta Distribution?Maximum Entropy Distributions

Gaussian Exponential

BetaDistribution

Maximize Shannon Entropy )]([ln)( xpxpdxSwithconstraints

2,x x x

)1(ln,ln xx

• Bounded interval• Constraints reflect parton splitting and gluon coherence

Dave Kettler 10

Identified Hadrons and Partons

identified hadron fragments identified partons

the flavor/color chemistry of fragmentation

pions kaons

increasing meson mass

bottom quark is anomalous

quark and gluon shapes are different

heavier fragments stay close to parent parton

udsc

gluon

b

Dave Kettler 11

ymax ~ ln( Q/ )

Fragmentation Energy Systematics

fits to quark and gluon jet multiplicities (p,q)

fits to fragmentation functions with beta distribution (p,q)

fragmentation functions represented over a broad energy range to few %!

parton rapidity

frag

men

t ra

pid

ity

400 GeV

fit parameters

extrapolation to non-perturbative regime

energy systematics

( ; , )u p q

(p,q)

(p,q)

non-pQCD

g - g

q - qpQCD

fit (p,q)

2n(y

max

)

g(u,ymax)

ln( / )s m

-q q

-g g

energy sum rule

Dave Kettler 12

Scaling Violations – Conventional

Q/2 (GeV)G. Abbiendi et al. (OPAL Collab.), Eur. Phys. J. C 37, 25 (2004)

excellent agreementwith recent measurements

data at right

g-g

q - q

Dave Kettler 13

Scaling Violations – Logarithmic

near uniformity to right of dotted line

CA/CF=2.25

ratio 2.25

ln ( , ) / ln 32.25

ln ( , ) / ln 4 / 3g E A

q E F

d D x s d s C

d D x s d s C

P. Abreu et al. (DELPHI Collab.), Eur. Phys. J. C 13, 573 (2000)

related to anomalousdimensions of QCD

for xE 1 and s large

ratio 2.25

Dave Kettler 14

Comparisons with pQCD

conventionalFF description

formfactoron u

MLLA gaussians

q - q

g - g

peak modes

8%

10 GeV

Dave Kettler 15

Summary• Low-Q2 partons play a dominant role in HI collisions

• Little was known about low-Q2 parton scattering and fragmentation prior to this work

• We have described all measured e-e fragmentation functions with a precise (few %) model function

• The model function (beta distribution) allows us to extrapolate fragmentation trends to low Q2

• That system can then be used to describe low-Q2 parton fragmentation in p-p and HI collisions

‘theoretical’ basis for minijet correlations in nuclear collisions