Fragmentation Functions and Fragmentation Processes

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Fragmentation Functions and Fragmentation
Processes
Fragmentation Functions

• Stefan Kretzer
• Brookhaven National Laboratory RIKEN-BNL

XXXIV International Symposium on Multiparticle
DynamicsJuly 26 - August 1, 2004Sonoma State
University, Sonoma County, California, USA
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http//www.pv.infn.it/radici/FFdatabase/maintain
ed by M. Radici (Pavia) and R. Jakob (Wuppertal)
To be updated
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• Outline
• Status / overview of global analysis of
  (unpolarized) fragmentation functions (incl. a
  brief conceptual introduction)
• Fragmentation processes 2 examples of
  hadroproduction at (not-so) high pT
• The double spin asymmetry
• Rho mass shift in
  at high pT

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Factorization and universality
p
p
p
p
a
a
c
c
b
b
p
p
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Global analysisofFragmentation
Functions (largely avoiding advertisement plots)
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The Field Feynman picture of cascade
fragmentation
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Bilocal operator
hadron
P z k
D(z)
k
quark/gluon
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Collinear factorization
ee- annihilation (1h inclusive)
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Fragmentation (or Decay) Functions
Scale dependence from renormalization or mass
factorization DGLAP
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?2 Analysis of ee-?hX Data
Alternative model approaches Indumathi et
al. Bourrely Soffer
Kniehl Kramer Pötter
Kretzer
Bourhis Fontannaz Guillet Werlen
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How well are Fragmentation Functions determined
from ee-?
u,d,s flavours and gluons
Sum over all flavours (singlet combination)
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Semi-Inclusive Deep Inelastic Scattering
Flavour Separation
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E. Christova, SK, E. Leader
valencefavouredrank 1
seaunfavouredrank 2
favoured gt unfavouredfavoured unfavoured
strangerank 2
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Comparison with previous leading particle guess
As seen in the HERMES pion multiplicities
Leading particle ansatz works well.
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Fractional contributions from initial/final state
partons
Hadroproduction pp?? X at 200 GeV cms
Central Rapidity
Forward Rapidity
gq
qggq
qq
initial
gg
qq
gg
qg
Dq
Dq
final
Dg
Dg
E? GeV
P? GeV
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Average Scaling Variables
Central Rapidity

• Symmetric / asymmetric kinematics for central /
  forward rapidity
• Large z fragmentation is probed.

P?? GeV
Forward Rapidity
E? GeV
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Factorized NLO pQCD and RHIC pp data
STAR forward rapidity
PHENIX central rapidity
Gluon FF and large-z constraints from
hadroproduction.
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The gluon fragmentation function has been
measured. Hasnt it?
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d s(3 jet) fragmentation tagging-function
Laenen Keller
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LO
NLO
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Onset of pQCD in hadronic collisions
soft
T. Hirano _at_ QM04
hard
(1/pT)(dN/dpT)
pT
??? GeV
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The double-spin asymmetry
for .
can be shown to be (basically) positive definite
in the few GeV range (at leading power accuracy).
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Taking Moments, e.g.turns the non-local (xa ?
xb) convolution into a local (in N) product
The minimum by variation d(?s)/d(?g)0 is at
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Inverted (from N to x)bounds ?s from below
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ALL? is (perturbatively) bounded by
Jäger, SK, Stratmann, Vogelsang (PRL 2004)

• Positivity
• Underlying parton dynamics

The upper bound holds up to dependence on the
scale where positivity is saturated. The lower
bound is obtained under low p? approximations.
The order of magnitude must be correct in both
cases if the dynamics are
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Perturbative high pT pions are produced in parton
scattering and are decoupled (at leading twist)
from the remnant. A statistical ensemble can
realize J1 either through angular momentum of
spinless (Goldstone) bosons or through the spin
of massive baryons. This must be expected to be
disfavoured over J0, i.e. A nonperturbative
asymmetry of O(1), even smaller than 1, is
enough to produce a characteristic transition
from negative to positive asymmetry with
increasing pT into the perturbative regime around
1-2(?) GeV.
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PHENIX hep-ex/0404027
Frank Bauer _at_ DIS04
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Rho mass shift in pp extends to high pT
STAR data
Does the observation contradict
?
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Resonant (p-wave) contribution to the 2-pion
fragmentation function. (Bachetta Radici)
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P
(Sudakov)
k
q
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• Qualitative (dual) features
• Heavier (light) hadrons come with a harder FF.
  (The low scale evolution is cut-off.)
• Heavier hadrons are suppressed. (The virtual
  parton has to survive a multiple of its
  perturbative lifetime)
• Resonances will be shifted to lower mass.

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Quantitative (order of magnitude) estimate
And slowly approaching with increasing
.
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• Summary (with apologies for the omission of
  heavy quark fragmentation)
• Fragmentation functions are determined from,
  mostly, ee- annihilation data. Other processes,
  such as hadro/photo-production have provided
  tests of consistency and universality. Next
  steps
• Include new data processes in the fit
• Update ee- fits (large-z data from uds
  continuum at e.g. BELLE)
• Semi-inclusive DIS (flavour)
• Hadroproduction (gluons, large-z, RHIC pp norm
  predictions for AA and spin), enabled by NLO
  Mellin moment evaluation.
• Consistency checks with jet data.
• Error analysis and coupled analysis with parton
  densities (à la CTEQ)
• Two recent RHIC measurements resonance
  production and the double spin asymmetry for pion
  production - exemplify the rich phenomenology of
  identified particle production in hard QCD
  processes
• The perturbative spin asymmetry can be bounded to
  be (basically) positive gtO(-103) for pT lt 4
  GeV.
• Resonance mass shifts of the observed order are
  to be expected at large pT from parton
  fragmentation into the resonance decay products.

short term
not-so-short term
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Leftovers
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Brain(?)storm MotivationStatus of global fits
and issues for updateSIDISenergy sum rule
???Gluon Fragmentation / Jet FF measurement and
their interpretation / Tagging FunctionsRecombina
tion in twist expansion ???Parton model limit
g-gt0 ???Low pT exponentialALL positivity in
pQCD and cross-over from statistical
contributionrho-meson production and shifted rho
mass Collaborations with E. Christova, E.
Leader, W. Vogelsang, H. Yokoya, A. Dumitru, A.
Bachetta, M. Radici,
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Energy Conservation
?
kT orderingDGLAP
angular orderingMLLA
Not a practical constraint.
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Some Theory

• Parton Distributions
• Local operator product expansion in inclusive DIS
• Bilocal operator definition

• Fragmentation Functions
• No local OPE (no inclusive final state)
• Bilocal operator definition

Just as PDFs, FFs are well defined in terms of
Scale dependence enters through renormalization
DGLAP
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HERMES DIS ? multiplicities (unpolarized hydrogen
target)

• Curves
• LO
• NLO
• (NNLO)

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Factorized cross section pp?p(pT) X
Add polarization (double-spin asymmetry)
p
p
p
p
a
a
c
c
b
b
p
p
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2?2 channels

• Only (ii) has a negative asymmetry at parton
  level.
• (i) gtgt (ii) by about a factor 160!
• Does this mean that ALL? has to be positive?
• No Polarized parton densities may oscillate!

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Predictions for ALL? are all positive. Is this
accidental or is ALL? bounded from below?
The upper bound on ALL? depends on the scale at
which positivity ?g(x,µ) g(x,µ) is
saturated.
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Fragmentation Functions
Identified Particle Production in Hard QCD
Reactions
as in
2004 (selected issues)

• Stefan Kretzer
• Brookhaven National Laboratory RIKEN-BNL

XXXIV International Symposium on Multiparticle
DynamicsJuly 26 - August 1, 2004Sonoma State
University, Sonoma County, California, USA