monique werlen (lapth)
DESCRIPTION
Quark and gluon fragmentation functions into hadrons and photons. Main sources of uncertainty. Monique Werlen (LAPTH). Thanks to. Patrick Aurenche, Zouina Belghobsi, Thomas Binoth, Luc Bourhis, Pierre Chiappetta, Michel Fontannaz, Mario Greco, Jean-Philippe Guillet, - PowerPoint PPT PresentationTRANSCRIPT
Monique Werlen, Feb.25,2008 Parton fragmentation workshop, ECT2
Thanks to
Patrick Aurenche, Zouina Belghobsi,Thomas Binoth, Luc Bourhis, Pierre
Chiappetta, Michel Fontannaz, Mario Greco,
Jean-Philippe Guillet, Gudrun Heinrich, Bernd Kniehl,
Eric Pilon, Simona Rolli, …
And of course, all mistakes, due to a poor experimentalist’s interpretation
even after years of collaboration, are mine!
Monique Werlen, Feb.25,2008 Parton fragmentation workshop, ECT3
Outline
• Terminology• Major sources of uncertainties in inclusive
hadron cross sections • NLO Fragmentation functions fits on e+e-
and pp data: methodology (CGGRW, BFGW) • Theoretical and experimental sources of
uncertainty in FF
• Inclusive photon cross sections• Photon FF
The PHOX Family
Monique Werlen, Feb.25,2008 Parton fragmentation workshop, ECT4
Fragmentation functions
Dhi (z, t) gives the distribution
of momentum fraction z for hadrons of type h in a jet initiated by a parton of type
i, produced in a hard process at scale t.
Like for parton distributions in a hadron, Fhi (x, t), these are
factorizable quantities, in which infrared divergences of PT can be factorized out and replaced by experimentally measured factor that contains all long-distance effects.
Monique Werlen, Feb.25,2008 Parton fragmentation workshop, ECT5
a b
dc
BA
PDF or structure function: density of parton a(b) in hadron A(B) with fraction xa(xb) of A(B) momentum
Hard sub-process
X
Hadro-production of pionsAB→π X
xaxb
FAa(xa,M2) FB
b (xb,M2)
π
Dπc
Fragmentation function Dπc(z,M2
F):density of π in parton c with fraction z of c momentum
z
Monique Werlen, Feb.25,2008 Parton fragmentation workshop, ECT6
Origin of fragmentation scale M2F
This scale separates • short distance (calculated perturbatively)from• long distance (experimental
measurement)
similar to factorization scale M2 for structure function
Monique Werlen, Feb.25,2008 Parton fragmentation workshop, ECT7
Theoretical and experimental sources of uncertainties
• data:– statistical error, – systematic, – normalization– z and Q2 range, sensitivity to quark, gluon FF
• theory:– choice of functional form, z range of
assumptions– choice of scales– order of theory (leading, NLO, resum)– further parameters (Structure Function, αs )
Monique Werlen, Feb.25,2008 Parton fragmentation workshop, ECT8
PDF uncertainties: an old debate
See Joel Feltesse introduction to the technical session on PDF uncertainties at PDF4LHC meeting (Feb.22-23, 2008)
Many issues are similar (in particular the treatment of experimental systematic errors) but not yet so much debated for FF uncertainties
Monique Werlen, Feb.25,2008 Parton fragmentation workshop, ECT9
Importance of uncertainties on inclusive hadron cross sections
• Do we care about the uncertainty in fragmentation function?
• How does it compare to other uncertainties?
Monique Werlen, Feb.25,2008 Parton fragmentation workshop, ECT10
hep-ph/0311131 prepared forCERN YR-2004-009Hard probes in heavy-ion collisions at LHC
γ/π0
BFG: photon FF KKP: pion FF
Monique Werlen, Feb.25,2008 Parton fragmentation workshop, ECT11
Eur. Phys. J. C4,7 Binoth, Guillet,Pilon, M.W.
Reducible π π and γπ vs irreducible γ γ backgrounds to
H→γ γ search
Explore with DIPHOX the strong isolation cuts, uncertainties due to large z pion FF
Monique Werlen, Feb.25,2008 Parton fragmentation workshop, ECT12
EPJ C13,347
Monique Werlen, Feb.25,2008 Parton fragmentation workshop, ECT13
u(KKP)/u(BKK )
Gluon(KKP)/Gluon(BKK)
Better fit with fragmentation functions KKP than BKK
<z> 0.75-0.9Binoth,Guillet,Pilon,M.W. EPJC24,245
M=MF=μ=pT/3
MF=3 GeV
Production of π0, E706 data vs NLO theory
Monique Werlen, Feb.25,2008 Parton fragmentation workshop, ECT14
Typical SF uncertainties in π0 production?
Monique Werlen, Feb.25,2008 Parton fragmentation workshop, ECT15
Uncertainties at RHIC energy due tofragmentation, factorization and renormalization scales
Improved with ln(1-z) resummation of soft gluons ?
Monique Werlen, Feb.25,2008 Parton fragmentation workshop, ECT16
Uncertainties at LHC energy due to fragmentation, factorization and renormalization scales
Rem. scales frozen below M0=2GeV, Mf0=sqrt(2) GeV
Monique Werlen, Feb.25,2008 Parton fragmentation workshop, ECT18
Typical fragmentation function and scale uncertaintiesin charged hadron production at RHIC energy
uncertainties from scale > uncertainties from FF
Monique Werlen, Feb.25,2008 Parton fragmentation workshop, ECT20
Importance of uncertainties on inclusive hadron cross sections
At RHIC energy, uncertainties from:• scales are important: +-50% at pt= 8 GeV/c as well as from • different FF sets
(Kretzer set reduces sizably the cross section compared to KKP and BFGW sets)
At LHC energy, uncertainties from • scales are of order of: +-20% for pt> 10 GeV/c while • differences from FF sets are dominant
• Do we care about the uncertainty in hadron fragmentation function?
• How does it compare to other uncertainties?
Monique Werlen, Feb.25,2008 Parton fragmentation workshop, ECT21
Vogelsang + de FlorianPR D71 (2005) 114004
much reduced scale dependencewith threshold resummmation (NLL)
( rem: NLO with small scale pt/3 to pt/2 rough approximation)
Production of π0, E706 data vs NLO and NLL theory
Monique Werlen, Feb.25,2008 Parton fragmentation workshop, ECT22
Fragmentation functions: methodology
•Parametrize FF z dependence at a given scale (MF=2GeV)
•Fit inclusive cross section data (pp and/or e+e-) with NLO theory
•Further uncertainties from:• structure functions, • factorization scale M (evol. SF)• fragmentation scale MF (evol. FF)• renormalization scale μ (evol. αs )• running coupling constant αs
Complementarities pp and e+e-:• pp data more sensitive to gluon FF• e+e- data more sensitive to quark FF• z range : LEP most statistics z<0.7
Neutral pions:Chiappetta, Greco, Guillet,Rolli, M.W. Nucl. Phys. B412,3 (1994)
(first attempt to get NLL πo FF)
Charged hadrons:Bourhis, Fontannaz,Guillet, M.W. Eur. Phys. C19,89 (2001)
Monique Werlen, Feb.25,2008 Parton fragmentation workshop, ECT23
NLO QCD fits for fragmentation Get the parton i to hadron h fragmentation function Di(z,MF2) by fitting the inclusive
cross section data in e+e- →h X and pp →h X with NLO QCD theory
,,, 111111
iiiiii NN get
2
22 )(
data
datai
fiti
data
DT
minimize
Calculate NLL cross section at scale MF2 for all data points: ,...),( 2MFzT fit
DGLAP: qggqqqMF
MFqPDPD
d
zdD
)log(
),(2
2evolution from MF2
0 to MF2data
aiiii zzNMFzD )1(),( 2
0 assume shape at MF2=MF2
0
get parameters witherrors and correlation(covariance matrix)
Monique Werlen, Feb.25,2008 Parton fragmentation workshop, ECT24
NLO QCD fits for fragmentation “theoretical” systematic uncertainties from
,,, 111111
iiiiii NN get
2
22 )(
data
datai
fiti
data
DT
minimize
Calculate NLL cross section at scale MF2 for all data points: ,...),( 2MFzT fit
DGLAP: qggqqqMF
MFqPDPD
d
zdD
)log(
),(2
2
aiiii zzNMFzD )1(),( 2
0 functional shape at MF2=MF2
0
choice of scales inSF evolution (pp) and αs
choice of scales, running coupling αs
in evolution from MF2
0 to MF2data
Monique Werlen, Feb.25,2008 Parton fragmentation workshop, ECT25
Inclusive π0 production in NLO approximation
AB = pp or e+e-
Monique Werlen, Feb.25,2008 Parton fragmentation workshop, ECT26
Fragmentation function: evolution
density ofinside the parton i carrying a fraction z of the parton impulsionat fragmentation scale Mf
Petronzio, Furmansky Phys. Lett. B97,437 (1980)code from P.NASON
gqgqqqMF
MFqPDPD
d
zdD
)log(
),(2
2
gggqgqMF
MFgPDPD
d
zdD
)log(
),(2
2
Monique Werlen, Feb.25,2008 Parton fragmentation workshop, ECT27
Fragmentation function: parameterization
9 parameters
For valence quark, sea quark , and gluon fragmentation
Dv(z)=Nv(1-z)βvzαv
Ds(z)=Ns(1-z)βszαs
Dg(z)=Ng(1-z)βgzαg
set I fix av=as=ag=0
Monique Werlen, Feb.25,2008 Parton fragmentation workshop, ECT28
NLO fits to e+e- dataquark fragmentation
NLO theoryAltarelli, Ellis, Martinelli, PiNucl. Phys. B160,301 (1979)
Monique Werlen, Feb.25,2008 Parton fragmentation workshop, ECT29
NLO fits to pp data gluon fragmentation
NLO theory
Ellis, Sexton: matrix elementsNucl. Phys. B269,445 (1986)
Aversa,Chiappetta,Greco,GuilletNucl. Phys. B327,105 (1989)
Order αs2
Order αs3
Monique Werlen, Feb.25,2008 Parton fragmentation workshop, ECT30
NLO fits to pp data gluon fragmentation
Data at √s=23,31,63,540,630 GeV
• WA70 Z.Phys. C38,371 (1988)• E706 Phys. Rev.D45,3899 (1992)• R806 Z.Phys. C5,104 (1980) • UA2 Z. Phys C27,329 (1985)
Phys. Lett. B176,239 (1986)
pp->u+d
pp->g
Monique Werlen, Feb.25,2008 Parton fragmentation workshop, ECT31
Correlation Nglue-Nsea
ISR pp data very sensitive to Ng… but have a scale dependence
Complementarities of e+e- and pp
data for the Ng and Ns
determination
illustrative only
Monique Werlen, Feb.25,2008 Parton fragmentation workshop, ECT32
Theoretical and experimental sources of uncertainties
• data:– statistical error, – systematic, – normalization– z and Q2 range, sensitivity to quark, gluon FF
• matching theory and data (binning, cuts, defs,..) • theory:
– choice of functional form, z range of assumptions
– choice of scales– order of theory (leading, NLO,…)– further parameters (Structure Function, αs )
Monique Werlen, Feb.25,2008 Parton fragmentation workshop, ECT33
Systematic uncertainties from data Normalization
free parameter allowed to vary within 3σ ofnormalization uncertainty quoted by expt
.
Fitted normalization
exp
1 12
2
2n
i
n
jdataji
theorj
dataji
data
DN
TDN
Point to point independent systematicssometime added in quadrature to statistical
uncertainties
Monique Werlen, Feb.25,2008 Parton fragmentation workshop, ECT34
Typical z range of LEP data sets (for BFGW fits)
Monique Werlen, Feb.25,2008 Parton fragmentation workshop, ECT35
z range of pp→πoX at 31 GeV (E706, ISR)
Monique Werlen, Feb.25,2008 Parton fragmentation workshop, ECT39
ln (1-z) resummation of soft gluons in FF
• Resummation reduces dependence on renormalization and fragmentation scale for e+e-
• “optimized scales” in BFGW fit to e+e- (μ/Q≈ 0.2 at large x) was a rough approximation (for a new approach, see AKK, arXiv 0711.1086)
ResummationCacciari Catani NPB617,253(2001)
Monique Werlen, Feb.25,2008 Parton fragmentation workshop, ECT40
Uncertainties on gluon fragmentation BFGW low and high Ng/BFGW
Monique Werlen, Feb.25,2008 Parton fragmentation workshop, ECT41
Fragmentation to charged hadron
#param data used χ2 / #points rem.
KKP
(2000)
3*5*3 e+e- →π,k, p
TPC,LEP,SLD
0.2< χ2 /DF
<1.28
no error for parameters
Kretzer
(2000)
30 e+e- → π,k SLD
e+e- → h ALEPH
not given
not given
flavor tag
sum rule
BFGW
(2001)
13 e+e- → h
LEP, PETRA
pp→ h UA1
201/217
~ok
error analysis
Nason code
PMS scales
AKK
(2005)
3*6*3 e+e- →π,k, p
pp RHIC
χ2 /DF=1.15
ok
DSS
(2007)
5*8(p)
5*5
e+e-, pp, SIDIS
res. h
171.9/159
1227/661
flexible shape
π k DSS1
Monique Werlen, Feb.25,2008 Parton fragmentation workshop, ECT42
Parton to hadron fragmentation
pt balance between hadron and jet at RHIC energy using JETPHOX
direct access to fragmentation function
may help discriminate setsat large z
with Belghobsi, Fontannaz, Guillet, Heinrich, Pilonpreliminary
at LO
CTEQ6M, M=Mf=μ=pt(h)/2pt(h)>25GeV pt(jet)>30GeV
Monique Werlen, Feb.25,2008 Parton fragmentation workshop, ECT44
O(ααs)
O(ααs2)
O(αs2α(1/αs+g))
Important at high √s and low pt
(NLO ACFGP NPB399,34)
Monique Werlen, Feb.25,2008 Parton fragmentation workshop, ECT45
“Direct” γ
Fragmentation
Direct photon production
Only the sum σ(D) + σ(F) is a physical observable
O(ααs)
O(ααs2)
Monique Werlen, Feb.25,2008 Parton fragmentation workshop, ECT46
Direct photon production
Guillet, DIS04
Monique Werlen, Feb.25,2008 Parton fragmentation workshop, ECT47
The PHOX Family
http://www.lapp.in2p3.fr/lapth/PHOX_FAMILY/main.html
P.Aurenche, T.Binot, M.Fontannaz, J.Ph.Guillet, G.Heindrich, E.Pilon, M.W.
NLO event generators (parton level) for large pt PHOton (hadron or jet) X-sections
DIPHOX:h1 h2 →γ γ+Xh1 h2 →γ h3+Xh1 h2→h3 h4 +X
Monique Werlen, Feb.25,2008 Parton fragmentation workshop, ECT48
Aurenche, Fontannaz, Guillet, Pilon, M.W. Phys. Rev. D73, 094007 (2006)
23 GeV≤√s≤1.96TeVData vs NLO QCD
Monique Werlen, Feb.25,2008 Parton fragmentation workshop, ECT49
Aurenche, Fontannaz, Guillet, Pilon, M.W. Phys. Rev. D73, 094007 (2006)
23 GeV≤√s≤1.96TeVData vs NLO QCD
Phenix and D0 data clarify the data/theory puzzle
Monique Werlen, Feb.25,2008 Parton fragmentation workshop, ECT50
Importance of uncertainties on inclusive photon cross sections
• Do we care about the uncertainty in photon fragmentation function?
• Most of collider data obtained with isolation cuts
• How does it compare to other uncertainties?
Monique Werlen, Feb.25,2008 Parton fragmentation workshop, ECT51
Parton to Photon fragmentation
Bourhis, Fontannaz, Guillet
Eur. Phys. C2,529 (1998)
BFG set I and II gluon fragmentation
set II
set I
Monique Werlen, Feb.25,2008 Parton fragmentation workshop, ECT52
Scales uncertainty Fragmentation BFGI/BFGII
Theoretical uncertainties at RHIC energy
Uncertainties from scales > from fragmentation
Monique Werlen, Feb.25,2008 Parton fragmentation workshop, ECT53
Scales uncertainty Fragmentation BFGI/BFGII
Theoretical uncertainties at LHC energy
Uncertainties from gluon fragmentationinto photon dominates at low pt
Monique Werlen, Feb.25,2008 Parton fragmentation workshop, ECT54
Theory with 40 CTEQ6 sets/ theory with CTEQ6M
Theoretical uncertainties from structure functions
Less than +-10%
Monique Werlen, Feb.25,2008 Parton fragmentation workshop, ECT55
Importance of uncertainties on inclusive photon cross sections
At RHIC energy, small effect
At LHC, the gluon fragmentation uncertainty is dominant for low pt photon production
BFG I reduces cross section by up to 2.5 at pt=3 GeV/c compared to BFGII
• Do we care about the uncertainty in photon fragmentation function?
• How does it compare to other uncertainties?
Monique Werlen, Feb.25,2008 Parton fragmentation workshop, ECT56
Parton to Photon fragmentation
Photon+jet correlation at RHIC energy
with non isolated photonpt(jet) fixed pt(photon) 3-16 GeV/cusing JETPHOX
May discriminate BFG sets I and II at low z
see however uncertainty from fragmentation scale
Belghobsi,Fontannaz, Guillet, Heinrich, Pilon, M.W.,preliminary
set II
set I
Monique Werlen, Feb.25,2008 Parton fragmentation workshop, ECT57
Summary I
Inclusive hadron Production
•In pp collisions, scale and fragmentation uncertainties are comparable at RHIC energy. Scales uncertainties are reduced by threshold resummation.
•The FF sets difference is dominated by the extrapolation to high z where e+e- statistics is poor
•The ln(1-z) soft gluon resummation reduces scale dependence.
•High z hadron fragmentation may be measured with hadron-jet correlations at RHIC energy
Monique Werlen, Feb.25,2008 Parton fragmentation workshop, ECT58
Direct photon production •PHENIX and D0 data favor the NLO QCD theory (like most of ISR and fixed target data)
•Photon fragmentation function at low z may be measured in photon-jet correlations at RHIC, a region not constrained by e+e- data
Summary II
Monique Werlen, Feb.25,2008 Parton fragmentation workshop, ECT59
extra slides:Charged hadrons at RHIC energies
Monique Werlen, Feb.25,2008 Parton fragmentation workshop, ECT60
PHENIX:PRL 91,072303
Fragmentation function BFGW
Monique Werlen, Feb.25,2008 Parton fragmentation workshop, ECT61
Typical scales uncertainties in charged hadron production
Monique Werlen, Feb.25,2008 Parton fragmentation workshop, ECT63
Why are direct photons interesting?
• Photons produced in the partonic interaction probe QCD dynamic without hadronic complications
• γ – quark: coupling precisely known (QED)
Two processes at lowest order:• QCD Compton : sensitive to gluon
distribution in the hadron and tag for quark fragmentation
• Annihilation: sensitive to the QCD running coupling constant αs and tag for gluon fragmentation
αs
αs αs
αs
α α
α
α
Monique Werlen, Feb.25,2008 Parton fragmentation workshop, ECT64
Aurenche, Fontannaz, Guillet, Kniehl, Pilon, M.W. Eur. Phys. JC9,107 (1999)
23 GeV ≤√s≤ 63 GeV
World Data vs NLO QCDINCNLO
Monique Werlen, Feb.25,2008 Parton fragmentation workshop, ECT65
Additional contributions to solve the Pb? NNLres
Monique Werlen, Feb.25,2008 Parton fragmentation workshop, ECT66
Presented by David Gross (S.Bethke, hep-ex/0407021)
UA6
UA
6
Monique Werlen, Feb.25,2008 Parton fragmentation workshop, ECT67
Aurenche, Fontannaz, Guillet, Pilon, M.W. Phys. Rev. D73, 094007 (2006)
23 GeV ≤√s ≤1.96TeV
Data vs NLO QCDINCNLO or JETPHOX
Phenix and D0 data clarify the data/theory puzzle
Monique Werlen, Feb.25,2008 Parton fragmentation workshop, ECT68
=0.5
Photon Isolation
Isolated/Non-isolatedJETPHOX NLOCTEQ6M BFG II M=MF=μ=pT
K.Odaka hep-ex/0501066
in a cone around photon with:
ET (parton) ≤ ET max =0.1Eγ
Isolated vs non-isolated: not much difference in data and in theory
R=