A.Rostovtsev
DIS Structure Functions at HERA
Institute f. Theor. and Exp. Physics in Moscow,
DESY at Hamburg
May 2004
DIS kinematics
Q 2 x 1 d 2
r 
2 2 Y dxdQ2
Schematic view of the H1 detector
Kinematic plane coverage
Coverage
5 decades in x and Q2
Sensitivity to
Z0 exchange
FL
Saturation
Q2  s
y 1
x0
QCD evolution – over the
bulk of the data
x
F2 measurements
Proton structure function data
accurate to 2 to 3% over bulk of
phase space
Extraction of NLO PDFs
Direct constraint on d at high x
n
CC
e+
p
W+
d
Typical
systematic errors
are ~6%
Direct constraint on u at high x
~ CC
n
CC
ep
W-
u
Both e-p and e+p
are important
x
F2cc and F2 bb at high Q2
• Studies of beauty and charm
production using H1 central
silicon tracker (CST).
• Flavour identification using
distance of closest approach of
track to vertex d.
d1
B
d2
B
• Determine significance
S = d/(d) for all CST tracks.
• Use 2 tracks with largest
significance, S1 and S2
• Example, S2 distribution:
• Determine ratios
f
cc

F2cc
F2
and f
bb

F2bb
F2
• fb ~ 2%, fc ~ 25%
• Resulting F2cc
(large
acceptance,
extrapolations
small).
• First F2
measurement,
in good
agreement with
expectations
from NLO calc.
using H1 PDFs.
bb
New cross-section measurements
•
•
Some regions of kinematic plane
remain to be studied, particularly
intermediate x at low Q2.
Radiative events, effective
reduction in Ee.
coll. g
e+
g
q
p
•
2
Access larger x = Q ys
for given Q2.
Cross-section at low Q2
•
Identify ISR events
without tagging g via:
   E  pz
eh
•
 2E e  2E g
Mean “Eeff” ~ 15 GeV,
c.f. nominal value
Ee = 27.6 GeV.
• Use shifted vertex data (low Q2).
• BST and SpaCal necessary for
measurement of scattered electron
and rejection of photoproduction
background.
• Cross-section from H1
ISR and QED
Compton data (final
results) in good
agreement.
• Measurements
consistent with other
data in regions of
overlap.
Behaviour of F2 at low x
•
Can parameterise structure
function as
F2  x, Q
•
•
•
•
2
  c Q  x
2
 
l Q2
.
Extract l(Q2) by fitting F2 as
function of x at constant Q2.
Behaviour of l(Q2) in “transition
region” (Q2 ~ 1 GeV2) intriguing.
Probing limits of perturbative QCD.
Further investigation not possible
at HERA II because of acceptance
limitations introduced by new
focussing magnets.
• Measurements of l(Q2):
FL determination (H1)
 r  F2  y 2 FL / Y
Sensitivity to FL at high y (low x)
Assumptions:
F2  C  x l
FL  const
..at small x
Very good description
r shape is defined
by a kinematical
factor y2/Y+
FL results
The new ( ) data allow H1 to distinguish between various models
Still need to improve accuracy of the data
Possible future FL measurements at HERA
Measure cross section
at fixed x and Q2 varying y
by changing Ep in a range
from 400 GeV upwards.
From 3 to 10 pb-1 is
necessary at lower Ep
Systematic errors included
PDF extraction
PDF analysis of the data coming from a single experiment reduces the
uncertainty involved in the combination of correlated systematic errors from
many different experiments with possible incompatibilities.
The uncertainties from the Global (ZEUS + Fix target data) fit:
This gets worse when using ZEUS data alone:
…mid and high x gluons especially problematic
“One experiment” PDF extraction is dominated by stat. errors.
Include Jet measurements in PDF analysis
T
E
Jet [GeV ]
Jets in DIS (Breit frame)
T
EJet
[GeV ]
Di-jets in photoproduction (xg >0.75)
Jets constrain
medium x gluon
distribution
Improved precision
on the gluon at
higher x
x
Good agreement with the
Global ZEUS fit
Agreement with H1 PDFs
except for a small difference
in gluon shape
MRST2001 underestimates
gluon density at low x
Fractal structure of the protons
Scaling, self-similarity and power-law behavior are F2 properties,
which also characterize fractal objects
Serpinsky carpet
z = 10
20
50
D = 1.5849
1 10 .
x = . ..
100
1000
Proton: 2 scales
1/x , (Q 2o + Q2 )/Q2o
Generalized expression for unintegrated structure function:
Limited applicability of perturbative QCD
ZEUS hep-ex/0208023
For x < 0.01 и 0.35 < Q < 120 GeV2 : c2 /ndf = 0.82 !!!
With only 4 free parameters
Summary
HERA provides
• rich inclusive data with a 5 decades coverage in x
and Q2 with a precision reaching up to 2%.
• PDFs can be extracted from the data collected by
a single experiment
• FL measurement made down to Q2 of 1 GeV2
• information about heavy quark content of DIS
• much more which was not covered in this report