fragmentation and correlation of hadrons in ep collisions

1. Motivation2. DIS kinematic variables 3. and particle production4. Bose-Einstein correlations between and5. Charged particle momentum distributions6. Azimuthal asymmetry of particle production

through the energy flow7. Summary

Fragmentation and correlation of hadrons in ep collisions

Artur Ukleja (Warsaw University)

on behalf of H1 and ZEUS Collaborations

XXXVI International Symposium on Multiparticle Dynamics

September 02–08, 2006, Paraty, Rio de Janeiro, Brazil

, 0SK KKKK SS 00

2Artur Ukleja, Warsaw University (on behalf of H1 and ZEUS Collaborations)

XXXVI International Symposium on Multiparticle Dynamics, 02–08.09.2006, Paraty, Brazil

Motivation

HA

DR

ON

ISA

TIO

N

1. Produce partons (Matrix Element)

2. Fragmentation (Parton Shower)

3. Hadronisation

Measuring hadrons would contain information on:

• Fragmentation properties ( production, BEC, charged particle momentum)

• Matrix Element (charged particle momentum, azimuthal asymmetry)

, , 0SK



DIS kinematic variables

)(ke

)(Pp

)'(' ke

xP

222 'kkqQ

ehXep

h

X

The photon virtuality Q2 and Bjorken variables are defined as:

2QqP

Qx

2

2

kP

qPy

collisions at HERA give information about soft and hard processes

ehXepHERA:

The CMS energy squared of the ep system:

2Pks

GeV 318300 s1994-97

1998-06



and particle production , 0SK

0.950.02 GeV 255

95.002.0 GeV 2522

22

yQ

yQ

DIS

PHP

0.950.2 GeV 1 22 yQ

particle fragmentation



OBS

2

:PHP

:DIS

xp

Qxp

T

T

resolved 75.0

direct 75.0

2

OBS

OBS

jets

jets

OBS

jets

x

x

yE

eE

xe

T

direct resolved

• Baryon-antibaryon asymmetry

• Baryon to meson ratio

)()(

)()(

NN

NNA

)(

)()(0SKN

NNR



Baryon-antibaryon asymmetry

PHPin % 0.10.6 predictionPYTHIA % 6.007.0

lowat % 0.21.0 prediction ARIADNE % 6.12.1

high at % 0.20.4 prediction ARIADNE % 3.13.0

0.10.1

27.01.2

25.08.0

A

QA

QA

• No evidence of baryon numbers propagated to central rapidity

• Baryon and antibaryon are produced according to the same mechanism

ARIADNE: with a strangeness factor of S=0.3 and 0.22

Q2>25 GeV2

0.02<y<0.95



Baryon to meson ratio

• ARIADNE (S=0.3) follows the shape of the data

• Baryon to meson ratio increases at low xOBS up to 0.7, not

predicted by PYTHIA (is flat at about 0.4)

• For high xOBS same baryon to meson ratio as in DIS and e+e-



Baryon to meson ratio (R) in PHP

• R is bigger, most significantly at high pT

LAB for the fireball enriched

• PYTHIA predicts almost the same R for both sample

• PYTHIA prediction approximately follows the measured values of R for the fireball depleted

Fireball depleted

Fireball enrichedJet of the highest ET

contributed at most 30% to the total hadronic ET



BEC have been observed in DIS at HERA.

(gives information about hadronisation process)

The two-particle correlation

function is studied as:

M – invariant mass of the pair

BE correlations between and KKKK SS 00

2bosons

222112 4)( mMppQ

Two bosons with momenta p1 , p2 produced at points r1 and r2

1 2 – bosons

BEC as the method of determination of the size of the particle emission source



Bose-Einstein correlation function

)(

)()(

12ref

1212 QP

QPQR

Standard parametrisation of R(Q12)

is Goldhaber-like parametrisation

) 1)(1()( 1212

2212 QeQR rQ

r – radius of the particle emission source – coherence strength factor

=0 since linear behavior in the high Q12 region

P(Q12) – the two-particle distribution for identical kaon pairs

Pref(Q12) – the reference distribution in the absence of BEC



BEC function for 00SSKK

22112 )( ppQ

231B583(2004)Phys.Lett. (ZEUS)

0.0220.036-

00

fm syst)()0.009(stat0.666r

similar to is for r value

SSKK

fm syst)(0.08(stat)0.61r 0.070.08-



BEC function for KK

22112 )( ppQ

(ZEUS) 00

0.070.08-

231B583(2004)Phys.Lett. (ZEUS)

0.0220.036-

00

fm syst)(0.08(stat)0.61r


and


SKSK

SSKK

KK

fm syst)(0.09(stat)0.57r 0.150.06-



BEC comparison with LEP

A good agreement with LEP for radius

ZEUS r=0.57±0.09(stat) fm

ZEUS r=0.61±0.08(stat) fm



Charged particle momentum distributions

Qp

phx 2

Scaled momentum distribution is defined in the Breit Frame as:

ph – momentum of charged track in the current region of Breit FrameQ – virtuality of the exchange boson

Parton splitting in pQCD causes scaling violations in structure functions. Also seen in fragmentation functions. Test pQCD.



Scaling violations

• Number of hadrons:

increase at small xp with ↗Q

100<Q2<20000 GeV2

0.05<y<0.6



Charged particle momentum distributionsCompared with e+e- experiments

100<Q2<20000 GeV2 0.05<y<0.6

• Number of hadrons:

increase at small xp with ↗Q

decrease at large xp with ↗Q

The cause of the scaling violations is the same as for the scaling violations observed for the deep inelastic structure functions.

• e+e- data show the same behavior as ep data



Charged particle momentum distributionsCompared with LO MC predictions

100<Q2<20000 GeV2 0.05<y<0.6

• CDM and PS models provide general reasonable description of the data

• At high xp HERWIG predictions even fail to show scaling behavior producing a flat spectrum



2sinsin2coscos)(

EDCBAd

d hXeep

Azimuthal asymmetry

2

2sin 2

sin

2

cos2 2

cos

A

E

A

DA

C

A

B

Azimuthal asymmetry comes from:• two-body processes (BGF and QCDC)• photon polarisation• longitudinally polarized electron beam• final hadron polarisation• intrinsic parton momentum in the proton

2cos BGF

cos QCDC

qqg

qgq



2sinsin2coscos)(

EDCBAd

d hXeep

Azimuthal asymmetry

In the Born approximation

for purely electromagnetic interactions

with unpolarised initial electron beam

the terms containing sin and sin2 vanish

as a consequence of a time-reversal invariance

X X

The coefficients D and E arise

from parity violating weak interactions

or polarisation of the initial electron beam



Energy flow method

Each particle is weighted with its energy

Multiplicity methodPhys.Lett.B481(2000)199-212

Jet analysisPhys.Lett.B551(2003)226-240

i i

i i

E

EHCM

,T

HCMHCM,THCM

coscos



Asymmetry as a function of HCMNC DIS: 100<Q2<8000 GeV2 0.01<x<0.1 0.2<y<0.8

tsignifican is cos HCM

Energy flow method



Cut ET>2 GeV is sufficient to removed non perturbative effectsProposed by Chay et al. Phys.Lett.B269(1991)175-182

Asymmetry as a function of HCMminT,E

spredictionby described good is 2cos

sprediction above cos 01at

sprediction below cos 5.25at

HCM

HCMHCM

HCMHCM



Summary and conclusionsMeasurements: and production BEC charge particle momentum

• have been made at HERA• ep data show the similar behavior as e+e- data

Detailes, for example:• The baryon to meson ratio increases at low x

OBS up to 0.7, not predicted by PYTHIA (is flat at about 0.4)

Azimuthal asymmetry is investigated for cos , cos2 , sin , sin2as a function of and ET,min

• cos and cos2 is significant• sin and sin2 consistent with null• NLO better describe ZEUS data then LO MC predictions

, 0SK



BACK UP



Fireball enriched and fireball depleted

Line represents the cut used to separate fireball enriched and fireball depleted

Fraction of the total ET carried by two jets of highest transverse energy

Fireball depleted events are dominated by dijet events carrying most of the total ET

Fireball enriched and fireball depleted has about the same number of events



• good agreement with LEP for radius

• higher value then for ALEPH, DELPHI

• the f0 (980) resonance is expected in the same low Q12 region where BEC are measured

• small contribution of f0 (980) in data can significantly change value

• the estimation of f0 (980) in data is 10 %

• the ALEPH, DELPHI removed f0 resonance

BE correlations between 00SSKK

231B583(2004)Phys.Lett.

(ZEUS) 0.022

0.036-

0.0110.003-

00


syst)(stat)(007.0475.0


SSKK



BE correlations between KK

• good agreement with LEP for radius

• smaller value then for e+e-

• different fragmentation processes in e±p and e+e-

• proton influence is expected – ZEUS data populate mostly proton fragmentation region

• K+K- can be production from 0 (1020) resonance dacay – strong signal of 0 (1020) in ZEUS data

(ZEUS) 00

0.070.08-

0.280.08-

231B583(2004)Phys.Lett.

(ZEUS) 0.022

0.036-

0.0110.003-

00

fm syst)(0.08(stat)0.61r

syst)(stat)(29.016.1


syst)(stat)(007.0475.0

and similar to is for r value

SKSK

SSKKKK



Charge particle momentum distributionsCompared with NLO QCD predictions

100<Q2<20000 GeV2 0.05<y<0.6

The data show a clear sensitivity to the fragmentation function used in the NLO QCD predictions



Summary and conclusions• Measurements of and production have been made at HERA

• No evidence of baryon numbers propagated to central rapidity• The baryon to meson ratio increases at low x

OBS up to 0.7, not predicted by PYTHIA (is flat at about 0.4)

• BEC have been measured in DIS at HERA• The radius value for KS

0KS0 is consistent with K±K± and with ±±

• The radius value is compatible with LEP results

• Scaled charge particle momentum is investigated at high Q2

• e+e- data show the same behavior as ep data• MC tuned from LEP data can successfully described ep data over

large region of Q

Azimuthal asymmetry is investigated for cos , cos2 , sin , sin2as a function of and ET,min

• cos and cos2 is significant• sin and sin2 consistent with null• NLO better describe ZEUS data then LO MC predictions

, 0SK

fragmentation and correlation of hadrons in ep collisions

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