structure functions and extraction of pdfs...
TRANSCRIPT
N. Raicevic
Moriond QCD 2006
1
Structure Functions and Extraction of PDFs
at HERA
NatašaRaičevië
University of Montenegro
On behalf of the H1 and ZEUS Collaborations
XLIstRecontresde Moriond, QCD and HadronicInteractions
La thuile, March 18th–25th, 2006
Outline:
�HERA accelerator and luminosity
�DIS physics
�Main input from HERA-I data for PDF extraction
�Highlights from HERA-II
�Results from QCD fits -PDFsand αs
�Combined QCD and electro-weak fit from HERA-I
�Improvements of PDFsexpected from HERA-II
�Summary and outlook
N. Raicevic
Moriond QCD 2006
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In 2000-2002 HERA-I upgraded to HERA-II
•Increased luminosity
•Polarisedleptons -new feature of HERA
HERA will run until summer 2007
> 40
≈100
e+p
> 150
≈15
e-p
HERA-II
luminosity
(pb-1)
HERA-I
Luminosity
(pb-1)
HERA
beams
HERA
Luminosity per experiment, roughly
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Moriond QCD 2006
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Charged Current (CC) ZEUS CC event display
Neutral Current (NC) H1 NC event display
qpQ
x•
=2
2
kp
qp
y••
=
22
2)'
(k
kq
Q−
−=
−=
Virtualityof exchanged
boson:
Fraction of proton
momentum carried
by struck quark
Fraction of energy
transferred from
incoming lepton at
proton rest frame
Inclusive Deep Inelastic Scattering (DIS)
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Moriond QCD 2006
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Cross Sections and Structure Functions
2Z
Z2e2
e22γZ
Ze
22
FK)
a(v
FK)
(vF
F~+
+−
=
3ZZ2
ee
3γZ
Ze
3F
xK
a2v
Fx
Ka
F~x
+−
=
FL= (Q2/4πα)σ
L
-dominant contribution
-importantonly at high Q
2
-sizable contribution for high y
∑+
+=
)q
xq
x(]a
v,v
2e
,[e
]F
,F
,F[
q2q2
q22Z
2γZ
2
∑−
=)
qx
qx
](a
v,a
[e2
]Fx
,Fx [
3Z3γZ
),
(~
2
Qx
NC
σ-NC reduced cross-section
γ-exchange
γZ-interference
Z-exchange
W2
W2
2 Z
22
2
Z
θcos
θsin
4
1
)M
Q(
QK
+=
Generalised
Structure
Functions
(SF)
Neutral current cross section
y)
(11
Y2
−±
=±
][
F~x
YYF~
YyF~
YQx2
Qdxd
)p
e(d
3L
2
242
2NC
2
+−
++
±
−απ
=σ
m
In the Quark PartomModel (QPM):
FL= 0
SFs
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Moriond QCD 2006
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Charged current cross section (LO)
)](
)1(
)(
[)
(2
2
22
2
42
2
2
sd
xy
cu
xM
Qx
MG
dxdQ
d
W
WF
pe CC
+−
++
+=
+
π
σ
)](
)1(
)(
[)
(2
2
22
2
42
2
2
sd
xy
cu
xM
Qx
MG
dxdQ
d
W
WF
pe CC
+−
++
+=
−
π
σ
),
(~
2
Qx
CC
σ-CC reduced cross-section
Sensitivity to the
flavor of the valence
distributions at high x
u vat high x
dvat high x
�Quark PDFs-from NC (F2) and CC DIS
�Gluon –from scaling violation -dF2/dlnQ2
�SF can also constrain PDFsand quark couplings to the Z boson (v q, a q)
FL~ αs ·xg(x,Q
2)
In pQCD:
))
)2
22
,(
,,
(,
,(
Qx
xgx
qx
xxq
-Parton
Density Functions -PDFs
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Moriond QCD 2006
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Main Inputs from HERA-I Data for the PDF Extraction
F2em(x,Q
2) ~ Σ
q e q2(q + q)
δF2/F
2 ~ 30%
Q2 / GeV
2
δF2/F
2 ~ 2-3%
_
12
0.51
0.2
5
0.5
0.7
51
10
-21
0-1
10
-21
0-1
10
-21
0-1
HE
RA
Ch
arg
ed
Cu
rren
t
Q2 =
280 G
eV
2
σ
∼
H1 e
- p
ZE
US
e- p
98-9
9
H1 e
+p
94-0
0
ZE
US
e+p
99-0
0
SM
e- p
(C
TE
Q6D
)
SM
e+p
(C
TE
Q6D
)
Q2 =
530 G
eV
2Q
2 =
950 G
eV
2
Q2 =
1700 G
eV
2Q
2 =
3000 G
eV
2Q
2 =
5300 G
eV
2
Q2 =
9500 G
eV
2Q
2 =
17000 G
eV
2Q
2 =
30000 G
eV
2
x · u
(1-y
)2x · d
x
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Moriond QCD 2006
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Measurements of CC Cross Sectionsfrom HERA-IIwith
Longitudinally PolarisedBeams
SM:
Linear dependence of CC cross
section on Pe
σ σσσ±(Pe) = (1±P e)σ σσσ±(Pe=0)
�ZEUS andH1 measurements
in agreementwithSM
�no right handed charged currents
LH
RH
LH
RH
eN
N
NN
P+−
=
Textbook measurements
H1 Collaboration , Phys. Lett. B 634 (2006), ZEUS Collaboration , DESY-06-015 (February 2006) -submitted to Physics Letters B
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Moriond QCD 2006
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Measurements of NC Cross Sectionswith HERA-II
with Longitudinally PolarisedBeams
•For NC, em. contribution which
dominates at low Q
2does not
depend on polarisation
•Polarisationdependence occures
via interference between γand Z
boson exchanges
Measurements well described
by the SM
ZEUS Collaboration , DESY-06-015 (February 2006) -submitted to Physics Letters B
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Moriond QCD 2006
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HERA PDFsfor the LHC
•Proton structure described by precise
PDFsneeded for making accurate
predictionsfor any process involving
protons
•DGLAP QCD evolution provides Q2
dependence of the PDFs�x
dependence must come from data:
HERAcovers the most important
region for the LHC
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Moriond QCD 2006
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Additional Constrains on Gluon Density from JETS
Sensitive to αs and quark/gluondensity
�Break the strong correlation between αsand the gluon PDF from DGLAP
�αs can be free parameter simultaneously with all the PDFs(ZEUS-JETS fit)
Events with distinct
jets in the final state
�Jet data constrain g(x) at medium and high-x (0.01-0.4)
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Moriond QCD 2006
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epvalence and
sea terms
Fitted
distributions
----
BCDMS,NMC,E665,
CCFR (µp, µd, νFe)
----
BCDMS (µp)
Data from
other exp
ZEUS-JETS
Eur. Phys. J C42 (2005)
ZEUS-S
Phys. Rev. D67 (2003)
H1 PDF 2000
Eur. Phys. J C30 (2003)
H1 PDF 1997
Eur. Phys. J C21 (2001)
Fits from
HERA-I
cu,s
d
s,d
c,u
g,
++
++
ud
S,
,d,
ug,
vv
−
Advantage of using data from one experiment:
�Systematic uncertainties understood
�Pure proton target �no uncertainties of heavy target corrections
�no need for strong isospinassumptions
Q02starting scale for parameterization, cuts for perturbativephase space (Q
2min) , choice of PDFsto
parameterize, treatment of heavy quarks, allowed functional form
of parameterization, treatment of exp.
uncertainties, renormalisation/ factorisationscales …. Should be reflected in PDF uncertainty
QCD analysis requires many choices to be made:
QCD Fits from HERA-I
�In global fitsmain contributions from HERAdata from low-x sea and gluon
pdfs,α
spdfs, αs
pdfs
αs, g(x)
Purpose
ud
S,
,d,
ug,
vv
−
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Moriond QCD 2006
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•Results broadly consistent within
uncertainties (also consistent with
global fitters)
Extracted PDFs
•Still large uncertainties on gluon
density and on d density at large x
)(
cux
+=
)(s
dx
+=
)(
cu
x+
=
)(
sdx
+=
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Moriond QCD 2006
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Strong Coupling Constant -α s
�Inclusion of jet data significantly improves αs
�∆α s(th.) = ±0.005 mainly due to the uncertainty of the renormalisationscale
�NNLO QCD analysis
�NNLO calculations available (hep-ph/0403192, 0404111)
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Moriond QCD 2006
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H1 Combined QCD and EW fit
�Determination of light quark axial (au, ad) and vector (vu, vd) couplings
to Z-bosonfor the first time at HERA (all HERA-I data)
�Combined fit of a u, v u, a d, v dand PDFs(H1 PDF 2000 scheme)
�HERA-II will bring improvement with statistics and polarisation
�H1 measurement determine sign of precise measurements from LEP
Standard Model:
aq= I q3
au = +1/2, ad= -1/2
Vq= I q3–2e qsin2θWH1 Collaboration, Phys. Lett. B632 (2006) 35-42
∑−
=)
qx
qx(
ae
2Fx
3γZ More sensitivity to au
then to v u
_
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Moriond QCD 2006
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Improvements on PDFsexpected
with HERA-II shouldcome from
:
�Higher precision measurements
of F2and CC cross section
�Precise measurement of xF3
�Direct measurement of FL
�Jet data–new results are still
coming from HERA-I (see talk
of C. W
issing)
�Higher precision of heavy flavor
contribution–new results are still
coming from HERA-I (see talk of
B. List)
SF –xF3
When enough statistics �possible
consistency check of valence
contribution
_
xF3~ σ- N
C –σ+
NC
xF3= -aeK
zxF3γZ+ Z-exchange
xF3γZ~ 2x Σ
qeqaq( q –q ) ~ qv
~ ~
x
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Moriond QCD 2006
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�Gluon distributions obtained in global NLO
analysis
Direct measurement of FLrequire
runs with lower protonbeam energy:
�For the same (Q
2,x) σ rto be measured
from different beam energies (i.e. y)
�Perform straight line fit of σrvsf(y)
to extract F2and FL
Longitudinal SF -FL
Longitudinal SF -FL
�FrompQCD
�Much more precise input for low-x gluon
distribution is necessary �via precise
measurement of FL
xg(x) ~FL (at very low x)
x
σ r
f(y)
01
F2
F2-FL
σr= F2(x,Q
2) –f(y) •FL(x,Q
2)
�High precision measurement of FLcan be
only achieved by measuring it directly
··
·
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Moriond QCD 2006
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Summary and Outlook
�HERA has provided crucial input for understanding proton structure
�PDFshave been extracted using HERA data only with the high precision
�First results from HERA-II about CC and NC cross section from polarised
beams published �
H1 and ZEUS measurements in agreement with
Standard Model expectations
�Combined QCD+EW fit from HERA-I data �a first measurement at
HERA of the light quark weak couplings to the Z-boson
�Still, results from HERA-I are coming and can be used as inputs for the
PDFsextraction (see also talks of C. W
issingand B. List)
�HERA-II is running and additional data are coming with significantly
improved statistics �improvement of PDF uncertainties
N. Raicevic
Moriond QCD 2006
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extras
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Moriond QCD 2006
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General Fitting Procedure for PDF extraction
�Parametrisationof PDFsat starting scale Q02
Some parameters constrained by the
number and momentum sum rules
�Evolve in Q
2using DGLAP pQCDevolution in NLO
�Convolute PDFswith coefficient functions to give structure functions and cross
sections
�Make fit to data iteratively changing starting parameters until best fit is found
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Moriond QCD 2006
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H1 QCD Analysis
�Data: 8·10-5 < x < 0.65, 1.5 < Q
2< 30000 GeV
2
�Q20 = 4 GeV
2, Q2min= 3.5 GeV
2
�Parameterisationof: xU, xD, xU, xD, xg
xU= x(u+ c)
xD= x(d+ s)
xU= x(u+ c)
xD= x(d+ s)
�Parameterisationof each PDF by searching χ2saturation
�Fit performed in ZERO MASS scheme (appropriate for high Q
2)
�Use H1+BCDMS p and D data as a cross check
__
_Bellow bottom threshold
__
_
Χ2/ndf = 0.88
__
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Moriond QCD 2006
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Performed dedicated QCD analysis to determine gluon density and αs:
�Use precise H1 and BCDMS-p F2 data to constrain valence region
(proton target only �no nuclear corrections required)
�Parametrisationof: xg, xV, xA
xV= 9/4u v + 3/2dv
xA= u + ¼(uv + 2 dv)
F2= 1/3xV + 11/9xA
�Use massive 3-flavour number scheme
H1 QCD Analysis, g(x) and αs
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Moriond QCD 2006
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ZEUS Only QCD Analysis
�Data: 6.3·10-5< x < 0.65, 2.7 < Q
2< 30000 GeV
2, W
2> 20 GeV
2
(W2> 20 GeV
2 –removes higher twists)
�Q20= 7 GeV
2, Q2min= 2.5 GeV
2
�Parameterisationof: xu v, xdv, xg, Sea, x∆= x(d–u)
-fix A
∆consistent with Gottfried sum rule (no sensit. from HERA)
�Experimental systematic uncertainties are propagated onto finalPDF
uncertainty
�Use Thorne/Roberts Variable FlavourNumber scheme
�Compared to global fits, information lost on high-x sea and gluon:
�Use ZEUS global fit to constrain high-x sea and gluon (c sand cg)
__
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Moriond QCD 2006
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ZEUS-JETS QCD Analysis
A complete NLO calculation for jet cross sections for each iteration of the χ2
minimisationis extremely slow.
Method:
1.Use NLO QCD program initially to produce grid of weights (x,µF2), giving
perturbativelycalculable part of cross section
2. Convolute with PDFsto produce fast prediction for cross section:
Grid cross section reproduce real NLO predictions to better than0.5%
DIS jets:125 < Q2 < 30000 GeV2, EBT,jet> 8 GeV, -2 < ηBjet< 1.8
γp dijets:ETjet1,(2)> 14 (11) GeV, -1 < ηjet1,2< 2.4, xγobs> 0.75,
134 < W
2γp< 277 GeV
2
Now, direct information on gluon available �
gluon parameters free
Χ2/ndf = 0.81
Direct-process
enriched region
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Moriond QCD 2006
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Extracted PDFs