22nd Winter Workshop on Nuclear Dynamics

“Can STAR p+p data help constrain fragmentation functions for strange hadrons”

Mark Heinz (for the STAR collaboration)

Yale University

mark.heinz@yale.edu WW San Diego, March 20062

Outline

Perturbative QCD Methods Factorization Fragmentation functions

Next-to-Leading order calculations (NLO) Calculations by KKP, Kretzer, AKK,

Vogelsang Leading order MC (Pythia)

PT-spectra <pT> systematics Gluon vs Quark jets

mark.heinz@yale.edu WW San Diego, March 20063

Factorization Ansatz

c

chbbaa

abcdba

T

hpp

z

Dcdab

td

dQxfQxfdxdxK

pdyd

d

0

/222

)(ˆ

),(),(

LO parton processes

NLO parton processes

Fragmentation Function (non-pert.)

BKK, Phys Rev D (1995)

Pions

Parton Distribution Function(non-pert.)

RHIC

K-Factor

mark.heinz@yale.edu WW San Diego, March 20064

Universality of Fragmentation func.

Suggested by Paper by Kniehl,Kramer & Poetter (2001)

Experimental data from different collisions systems have been fit with the same fragmentation function

KKP, Nucl.Phys.B597(2001)

Fragmentation function for inclusive hadrons

KKP, Nucl.Phys.B582(2000)

s=91.2 GeVOPAL,ALEPH

uds-quark

c-quark

b-quark

all

mark.heinz@yale.edu WW San Diego, March 20065

The gluon FF

Collider data available from 3-jet events from ALEPH and OPAL

Statistics still very limited

Dotted: DelphiDashed: BKKFull: KKP (new)Mf=52 + 80 GeV

AKK, Nucl.Phys.B725(2005)

Curves scaled by 1/100

mark.heinz@yale.edu WW San Diego, March 20066

NLO for non-strange particles Inclusive charged hadrons have been well described for the last 10 years by Fragmentation functions

(FF) from Kretzer, KKP and others. Baryons have been notoriously difficult to fit, due to limited knowledge of FF. Albino, Kramer and Kniehl (AKK) use latest OPAL data to calculate light flavor (u,d,s) separated

fragmentation functions for the first time.

Van Leeuwen, nucl-ex/0412023 STAR Preliminary

STAR 200 GeV p+p data for identified non-strange mesons and baryons agrees well with NLO calculation by AKK.

mark.heinz@yale.edu WW San Diego, March 20067

NLO for strange particles First NLO predictions for RHIC energies K0s and Lambda were obtained by

W.Vogelsang (RIKEN) In 2005 calculations at NLO by Albino, Kniehl & Kramer (AKK) for K0s and Lambda

produced better agreement. Shape of GluonLambda FF was constrained by Gluon Proton FF Magnitude was constrained by STAR data

mark.heinz@yale.edu WW San Diego, March 20068

Consistency with data at 630 GeV

How well does the constrained fragmentation function extrapolate to other energies?

K0s

NLO Lines are for μ=2*pT, pT, pT/2

UA1 (630GeV)

STAR (200GeV)

UA1 (630GeV)

STAR (200GeV)

Albino,Kniehl,Kramer et al. ,hep-ph/0510173

mark.heinz@yale.edu WW San Diego, March 20069

Leading order pQCD (PYTHIA)

Parton showers based on Lund String Model JETSET was used to successfully describe e+e- collisions Flavor dependence introduced by strange quark suppression

factor Baryon production governed mainly by di-quark probabilities K-Factor accounts for NLO perturbative processes

“Lund Symmetric fragmentation function”

z = fractional momentum of parton/hadron a, b = tunable parameter

mark.heinz@yale.edu WW San Diego, March 200610

pT-spectra for strange particles

PYTHIA Version 6.3 used (January 2005) Incorporates parameter tunes from CDF New multiple scattering and shower algorithms

Necessary tune: K-Factor, which accounts for NLO processes in hard cross-section

mark.heinz@yale.edu WW San Diego, March 200611

What about non-strange particles ?

Comparison to published STAR data Good agreement for pions with K=1 and proton with K>1 However only lower pT region measured

mark.heinz@yale.edu WW San Diego, March 200612

What about strange resonances ?

Published STAR data for , K* Preliminary STAR data for * (baryon resonance) K-factor = 3 fits all resonances very nicely

STAR Preliminary

PYTHIA 6.3 PYTHIA 6.3PYTHIA 6.3PYTHIA 6.3,K=3 PYTHIA 6.3,K=3PYTHIA 6.3,K=3

mark.heinz@yale.edu WW San Diego, March 200613

K-factor in LO pQCD

How is the K-factor defined? 2 Definitions:

Kobs= exp / LO

Kth= NLO / LO Flavor dependence of K-

factor, ie. NLO contributions ?

For h- it decreases for collision energy, ie. contribution of NLO processes is smaller at higher energies

STAR

Eskola et al Nucl. Phys A 713 (2003)

mark.heinz@yale.edu WW San Diego, March 200614

<pT> systematics in p+p

Perturbative QCD models are ideal to look at Mini-jet phenomenology High multiplicity p+p events more mini-jets Higher pT final states higher

<pT> of hadrons

XN.Wang et al (Phys Rev D45, 1992)

Nch

Njet=2

dNch/d

<p

T>

mark.heinz@yale.edu WW San Diego, March 200615

Charged multiplicity distribution

Pythia + Simulated Trigger and detector acceptance. Probability of high multiplicity events is very sensitive to NLO corrections

STAR Preliminary

STAR data

PYTHIA 6.3PYTHIA 6.3, K=3

STAR data

mark.heinz@yale.edu WW San Diego, March 200616

PYTHIA <pT> vs Nch

More sensitive observable to implementation of multiple scattering algorithm This phenomenology has also been previously attributed to mini-jets

Higher K-factor, more NLO contributions, are required to account for increase of <pT> with charged multiplicity

mark.heinz@yale.edu WW San Diego, March 200617

Gluon vs Quark jets

Extensive studies of jet properties have been done in e+e- data

Gluon jets produce higher particle multiplicity

Quark jets fragment produce a harder pT-spectrum

The ratio of anti-particle to particle production should be sensitive to quark-vs-gluon jet

mark.heinz@yale.edu WW San Diego, March 200618

Ratios vs pT (gluon vs quark jet)

Gluons have equal probability of fragmenting into particles or antiparticles, Quarks fragment predominantly into particles

At higher pT (higher z) we are probing the quark-jet dominated region.

STAR (Phys Lett. B submitted)

p+pSTAR preliminary

d+Au

mark.heinz@yale.edu WW San Diego, March 200619

mT - scaling

mT-scaling first studied with ISR data.

In the Color Glass Condensate (CGC) picture mT-scaling would be indicative of evidence of gluon saturation.

No absolute scaling. Species are scaled with arbitrary prefactors to overlap in low pt region

STAR data reveals an interesting feature of baryon vs meson splitting above 2 GeV in mT

STAR preliminary

mark.heinz@yale.edu WW San Diego, March 200620

mT scaling in PYTHIA

Gluon jets produce meson vs baryon “splitting”, Quark jets produce mass splitting in mT. This confirms that our p+p events are gluon jet dominated.

PYTHIA Preliminary DATA

Arbitrarily scaled mT-spectra data and PYTHIA simulation agree well

Gluon jet Quark jet

mark.heinz@yale.edu WW San Diego, March 200621

Baryon-meson “anomalies” Baryon production at intermediate pT is interesting since fragmentation by itself

cannot describe data Strange baryon/meson ratio is under-predicted by PYTHIA at 200 and 630 GeV Magnitude of UA1 ratio is similar to central Au+Au in STAR.

PYTHIA 6.3

mark.heinz@yale.edu WW San Diego, March 200622

Summary

Most recent NLO calculations by AKK using constrained fragmentation functions reproduce STAR and UA1 strangeness data nicely

Latest version of the PYTHIA model (6.3) describes strange particle and resonance data well if a LO K-factor=3 is used

Increase of <pT> of strange hadrons with Nch due to mini-jets & multiple scattering is successfully modeled in PYTHIA 6.3 with K-factor 3

In p+p collisions the anti-baryon/baryon ratio vs pT does not yet show any clear quark vs gluon jet signature due to limited statistics. In d+Au however a significant drop of the ratio is observed.

Perturbative QCD models are unable to reproduce the large baryon/meson ratio at intermediate pT

mT scaling of identified particles may be a useful tool for investigating quark vs gluon jets phenomena