First Measurements of CC Cross Sections with HERA with Longitudinally Polarised Positrons H1 Collabo

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Structure Functions and Extraction of PDFs at
HERANataa RaicevicUniversity of
MontenegroOn behalf of the H1 and ZEUS
Collaborations

• Outline
• HERA accelerator and luminosity
• DIS physics
• Main input from HERA-I data for PDF extraction
• Highlights from HERA-II
• Results from QCD fits - PDFs and as
• Combined QCD and electro-weak fit from HERA-I
• Improvements of PDFs expected from HERA-II
• Summary and outlook

XLIst Recontres de Moriond, QCD and Hadronic
Interactions La thuile, March 18th 25th, 2006

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HERA
Luminosity per experiment, roughly
In 2000-2002 HERA-I upgraded to HERA-II

• Increased luminosity
• Polarised leptons - new feature of HERA
• HERA will run until summer 2007

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Inclusive Deep Inelastic Scattering (DIS)
Neutral Current (NC) H1 NC event display
Virtuality of exchanged boson
Fraction of proton momentum carried by struck
quark
Charged Current (CC) ZEUS CC event display
Fraction of energy transferred from incoming
lepton at proton rest frame
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Cross Sections and Structure Functions
Neutral current cross section

• NC reduced cross-section
  

Z-exchange
?-exchange
?Z-interference

• dominant contribution

Generalised Structure Functions (SF)
- important only at high Q2
FL (Q2/4pa)sL

• sizable contribution for high y

FL 0
In the Quark Partom Model (QPM)
SFs
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FL as xg(x,Q2)
In pQCD
- Parton Density Functions - PDFs
dv at high x
Charged current cross section (LO)
Sensitivity to the flavor of the valence
distributions at high x
- CC reduced cross-section
uv at high x

• Quark PDFs - from NC (F2) and CC DIS
• Gluon from scaling violation - dF2/dlnQ2
• SF can also constrain PDFs and quark couplings
  to the Z boson (vq, aq)

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Main Inputs from HERA-I Data for the PDF
Extraction
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F2em(x,Q2) Sq eq2(q q)
dF2/F2 2-3
Q2 / GeV2
dF2/F2 30
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Measurements of CC Cross Sections from HERA-II
with Longitudinally Polarised Beams
H1 Collaboration , Phys. Lett. B 634 (2006), ZEUS
Collaboration , DESY-06-015 (February 2006) -
submitted to Physics Letters B

• SM
• Linear dependence of CC cross section on Pe
• s(Pe) (1Pe)s(Pe0)
• ZEUS and H1 measurements
• in agreement with SM
• ? no right handed charged currents

Textbook measurements
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Measurements of NC Cross Sections with HERA-II
with Longitudinally Polarised Beams
ZEUS Collaboration , DESY-06-015 (February 2006)
- submitted to Physics Letters B

• For NC, em. contribution which
• dominates at low Q2 does not
• depend on polarisation
• Polarisation dependence occures
• via interference between ? and Z
• boson exchanges

Measurements well described by the SM
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HERA PDFs for the LHC

• Proton structure described by precise
• PDFs needed for making accurate
• predictions for any process involving
• protons

• DGLAP QCD evolution provides Q2
• dependence of the PDFs ? x
• dependence must come from data

HERA covers the most important region for the
LHC
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Additional Constrains on Gluon Density from JETS
Events with distinct jets in the final state
Sensitive to as and quark/gluon density

• Break the strong correlation between as and the
  gluon PDF from DGLAP
• as can be free parameter simultaneously with all
  the PDFs (ZEUS-JETS fit)

• Jet data constrain g(x) at medium and high-x
  (0.01-0.4)

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QCD Fits from HERA-I

• In global fits main contributions from HERA
  data from low-x sea and gluon

• Advantage of using data from one experiment
• Systematic uncertainties understood
• Pure proton target ? no uncertainties of heavy
  target corrections
• ? no need for
  strong isospin assumptions

QCD analysis requires many choices to be made
Q02 starting scale for parameterization, cuts
for perturbative phase space (Q2min) , choice of
PDFs to parameterize, treatment of heavy quarks,
allowed functional form of parameterization,
treatment of exp. uncertainties, renormalisation
/ factorisation scales . Should be reflected in
PDF uncertainty
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Extracted PDFs

• Still large uncertainties on gluon
• density and on d density at large x

• Results broadly consistent within
• uncertainties (also consistent with
• global fitters)

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Strong Coupling Constant - as

• Inclusion of jet data significantly improves
  as
• ?as(th.) 0.005 mainly due to the
  uncertainty of the renormalisation scale
• ? NNLO QCD
  analysis
• NNLO calculations available (hep-ph/0403192,
  0404111)

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H1 Combined QCD and EW fit
H1 Collaboration, Phys. Lett. B632 (2006) 35-42

• Determination of light quark axial (au, ad) and
  vector (vu, vd) couplings
• to Z-boson for the first time at HERA (all
  HERA-I data)

• Combined fit of au, vu, ad, vd and PDFs (H1 PDF
  2000 scheme)

Standard Model aq Iq3 au 1/2, ad
-1/2 Vq Iq3 2eqsin2?W
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More sensitivity to au then to vu
? H1 measurement determine sign of precise
measurements from LEP
? HERA-II will bring improvement with statistics
and polarisation
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SF xF3
Improvements on PDFs expected with HERA-II
should come from

xF3 s-NC sNC xF3 -aeKzxF3?Z
Z-exchange xF3?Z 2x Sqeqaq( q q ) qv

• Higher precision measurements
• of F2 and 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. Wissing)
• Higher precision of heavy flavor
• contribution new results are still
• coming from HERA-I (see talk of
• B. List)

_
x
When enough statistics ? possible consistency
check of valence contribution
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Longitudinal SF - FL
? Gluon distributions obtained in global NLO
analysis

• Much more precise input for low-x gluon
• distribution is necessary ? via precise
• measurement of FL

xg(x) FL (at very low x)

• From pQCD

• High precision measurement of FL can be
• only achieved by measuring it directly

x
sr F2(x,Q2) f(y) FL(x,Q2)

• Direct measurement of FL require
• runs with lower proton beam energy
• For the same (Q2,x) sr to be measured
• from different beam energies (i.e. y)
• Perform straight line fit of sr vs f(y)
• to extract F2 and FL

sr



F2
F2-FL
f(y)
0
1
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Summary and Outlook

• HERA has provided crucial input for
  understanding proton structure
• PDFs have 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 QCDEW 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
• PDFs extraction (see also talks of C.
  Wissing and B. List)
• HERA-II is running and additional data are
  coming with significantly
• improved statistics ? improvement of PDF
  uncertainties

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extras
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General Fitting Procedure for PDF extraction

• Parametrisation of PDFs at starting scale Q02

Some parameters constrained by the
number and momentum sum rules

• Evolve in Q2 using DGLAP pQCD evolution in NLO

• Convolute PDFs with 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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H1 QCD Analysis

• Data 810-5 lt x lt 0.65, 1.5 lt Q2 lt 30000 GeV2
• Q20 4 GeV2, Q2min 3.5 GeV2
• Parameterisation of xU, xD, xU, xD, xg
• xU x(u c)
• xD x(d s)
• xU x(u c)
• xD x(d s)
• Parameterisation of each PDF by searching ?2
  saturation
• Fit performed in ZERO MASS scheme (appropriate
  for high Q2)
• Use H1BCDMS p and D data as a cross check

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Bellow bottom threshold
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?2/ndf 0.88
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H1 QCD Analysis, g(x) and as

• Performed dedicated QCD analysis to determine
  gluon density and as
• Use precise H1 and BCDMS-p F2 data to constrain
  valence region
• (proton target only ? no nuclear corrections
  required)
• Parametrisation of xg, xV, xA
• xV 9/4uv 3/2dv
• xA u ¼(uv 2 dv)
• F2 1/3xV 11/9xA
• Use massive 3-flavour number scheme

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ZEUS Only QCD Analysis

• Data 6.310-5 lt x lt 0.65, 2.7 lt Q2 lt 30000
  GeV2, W2 gt 20 GeV2
• (W2 gt 20 GeV2 removes higher twists)
• Q20 7 GeV2, Q2min 2.5 GeV2
• Parameterisation of xuv, xdv, xg, Sea, x? x(d
  u)
• - fix A? consistent with Gottfried sum rule
  (no sensit. from HERA)
• Experimental systematic uncertainties are
  propagated onto final PDF
• uncertainty
• Use Thorne/Roberts Variable Flavour Number
  scheme

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• Compared to global fits, information lost on
  high-x sea and gluon
• ? Use ZEUS global fit to constrain high-x sea
  and gluon (cs and cg)

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ZEUS-JETS QCD Analysis
DIS jets 125 lt Q2 lt 30000 GeV2, EBT,jet gt 8
GeV, -2 lt ?Bjet lt 1.8 ?p dijets ETjet1,(2) gt
14 (11) GeV, -1 lt ?jet1,2 lt 2.4, x?obs gt 0.75,
134 lt W2?p lt 277 GeV2
Direct-process enriched region

• A complete NLO calculation for jet cross sections
  for each iteration of the ?2
• minimisation is extremely slow.
• Method
• Use NLO QCD program initially to produce grid of
  weights (x,µF2), giving
• perturbatively calculable part of cross
  section
• 2. Convolute with PDFs to produce fast prediction
  for cross section

?2/ndf 0.81
Grid cross section reproduce real NLO predictions
to better than 0.5
Now, direct information on gluon available ?
gluon parameters free
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Extracted PDFs