Structure Functions at HERA

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Structure Functions at HERA

• Antonio Pellegrino
• NIKHEF, Amsterdam

On behalf of the H1 ZEUS Collaborations
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Outline

• Introduction
• HERA and DIS
• QCD-improved parton model and Parton Density
  Functions (PDF)
• F2 measurements
• Low x behavior, QCD fits and gluon density
• (LHC interlude)
• The transition to low Q2
• High Q2 inclusive measurements
• Neutral and Charged Current Cross Sections
• Valence quark densities
• Outlook

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HERA at DESY Hamburg
H1
e 27.5GeV
ZEUS
P 920GeV
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HERA Kinematics
Neutral current Scattered e in main detector e
balances hadronic pT
Charged current Scattered ? invisible pT
imbalance hadronic system only
2 independent variables Q2 ? sxy
Q2 ? -q2 -t (k-k)2 negative 4-momentum
squared
x ? Q2/(2qp) -t/(us) (0x1) parton
momentum fraction (x Bjorken)
y ? (qp)/(kp) (us)/s (0y1) fract.
energy transfer in p-rest frame
W2 ? (Pq)2 Q2(1-x)/x stu photon-proton
CM energy
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The H1 detector
HERA-I compl. Sep/00 HERA-II start 2002
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The ZEUS detector
HERA-I compl. Sep/00 HERA-II start 2002
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NC event from H1 02-03
Scattered e in main detector, e balances hadronic
pT
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CC event from ZEUS 02-03
Scattered ? invisible, pT imbalance, hadronic
system only
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Where do we measure?
High x probing parton (quarks)
High Q2 EW Unification and new Physics
Low Q2 Transition to non-perturbative
Low x high gluon-density and saturation
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What PDF from what data?
q(x) reasonably constrained by fixed-target DIS
and Drell-Yan data
g(x) more uncertain

• x 10-3 essentially HERA
• x 10-2 momentum sum rule
• 0.05 lt x lt 0.2 jet production at the Tevatron
• high x ? 0.1 photon data most sensitive, but
  only on paper

Data used in CTEQ5 Fit
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Nucleon Structure in eP Scattering
e(k)
e(k)
g,Z
W
q
q
Factorization
xP
universal parton density
p(P)
p remnant
partonic cross-section
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From F2 to Multi-jet Final States
PDF ? jets
F2 fit ? PDF
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Neutral Current DIS
If we had pure lepton-quark scattering (Born
terms)
sPARTONIC ?
F2 structure function
Parity-violating gZ interference piece
Where Af and Bf contain Electro-Weak Couplings,
e.g.
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QCD-improved Parton Model
Large-momentum scale ? write cross section as a
convolution
fa ? PDF, long-distance proton structure
sa ? partonic c.s. calculable in powers of aS
(asymptotic freedom)
dWp ? p final-state partons phase space
M(n),p ? n-th order matrix element to produce
p partons
OJp ? functional defining measured observable
(d(p-p0), jet algorithm, etc.)
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Inclusive DIS in Perturbative QCD
Partonic-cross-section Matrix Elements
Perturbative description (DGLAP) of PDF
factorization-scale dependence
Probability of emitting a parton with momentum
fraction z/y for Q2?Q2dQ2
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F2 at Low x

• statistical precision and systematic accuracy
  2 in most of measured region!
• overlap with fixed-target at high x
• fit based on QCD-improved parton model describes
  data over decades in x and Q2
• low-x rise, observed down to low Q2, getting
  steeper with increasing Q2
• associated to low-x rise of gluon and sea density

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Gluon Density at Low x

• gluon density enters only as O(aS1) in F2 and
  thus gluon density fit parameters strongly
  correlated with aS

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Gluon Density at Low x (contd)

• gluon density steep at low x
• gluon density well determined for 0.001ltxlt0.1,
  error gets bigger at higher x

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Sea Density at Low x

• Writing explicitly down flavor symmetry
• gluon g(x) and flavor singlet qSI(x) coupled in
  DGLAP evolution. Flavor singlet at low x
  dominated by sea xS(x) sea rises at low x
• uncertainty 10, gets bigger at higher x and
  smaller at high Q2

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HERA Added Value

• Excluding HERA data from QCD Fit shows
• low-x rise steeper than could have extrapolated
  from fixed-target data
• huge error band in g and xS at low-x
• gluon and sea at low x come from HERA!

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Parton densities at LHC
Of crucial importance

• valid theoretical framework (uncertainties at
  low x could prove fatal!) and well determined QCD
  parameters
• well determined PDFs
• correct errors and correct error propagation

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Parton densities at LHC (contd)
The typical value of x is near the tt threshold.
Setting x1x2x
0.18 Tevatron 0.0025 LHC
Gluon dominates at LHC
qq-gttt gg-gttt
Tevatron 90 10
LHC 10 90
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Parton densities at LHC (contd)
Any experimental info is vital. ZEUS attempts to
measure FL using ISR
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Measurements of FL from ISR
Measure dFL from ISR as a function of y at high y
to determine FL

• first direct FL measurement at HERA
• large errors, but agreement with pQCD prediction
• Nothing crazy going on

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Scaling and Scaling Violations
Leading Order
Next-to-Leading Order
Virtual Corrections
QCD Compton
BGF

• scaling observed at high x probing the
  partons (quarks) in the proton
• scaling violations, increasing as x decreases
  QCD dynamics and high gluon density
• NLO QCD (DGLAP) gives a consistent description
  of the data over many decades in x and Q2

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Are QCD Fits Almighty?
How low in Q2 can we go, neglecting

• aS is large and perturbation theory may break
  down
• low Q2 at HERA is coupled to low x and thus
• ln(1/x) resummation may become important
• high-density effects may play a role

Extrapolate QCD fit backward to low Q2 into the
region of the precise ZEUS BPT data
QCD fit starts exceeding data at Q20.8 GeV2 and
clearly fails for Q20.6 GeV2
unable to accommodate the rapid transition to a
flatter F2 behavior at Q2lt1 GeV2
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Transition to Soft Energy-Dependence
Low-x behavior of F2 directly related to high-W
behavior of total gP cross section
BPT data show around Q21GeV2 a smooth transition
between

• steep energy-dependence (W2)0.2-0.4
• soft energy-dependence (W2)0.08

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Transition to low Q2
F2 must go like Q2 for Q2?0
EM-current conservation qmWmn 0 ? Wmn
singularities for Q2?0 cannot be real, scaling
cannot hold at low Q2
However, the scale for this transition is
neither theoretically nor experimentally specified
ZEUS BPT data show that the total gP cross
section starts flattening off for Q2 1 GeV2
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EW Unification
Q2 gtgt MZ, MW
Electro-Weak Unification
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High Q2 NC Data

• Only NC ep data used in the fit
• effect of xF3 clearly visible at high Q2

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xF3 at high Q2
xF3 determined

• show presence of Z exchange in space-like Q2
  region
• extend measured x range down to x0.05
• good agreement with Standard Model predictions
  using standard PDFs
• Provide access to valence quark densities at
  high Q2

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High Q2 CC Data
Leading Order
Helicity structure
Provide access to valence quark densities at
high Q2
no CC data used in the fit
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Valence Quarks

• Valence quarks xuV and xdV at high x constrained
  by fixed target data
• u-valence better determined (1 at x0.01) than
  d-valence (2)

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HERA Valence Quarks
Valence quarks from ZEUS data only

• xuV well determined (factor 2 less precise than
  with fixed-target)
• xdV much more poorly determined, BUT
• ZEUS high Q2 CC ep data do not suffer from the
  deuteron-binding correction uncertainty present
  in the fixed-target deuterium data
• The next high-precision high Q2 CC ep data will
  allow a greatly improved valence quark
  determination

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New High Q2 CC Data

• high Q2 CC e-p data give access to high x
  u-valence density
• high Q2 CC ep data give access to high x
  d-valence density

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Summary and Outlook

• Hera I analysis almost completed, waiting for
  large HERA II data sets
• F2 measurements
• Low x behavior
• QCD fits and gluon density
• The transition to low Q2
• High Q2 inclusive measurements
• Neutral and Charged Current Cross Sections
• Valence quark densities