Transcript Parton Densities and strong coupling

Structure function measurements and
what they tell us about PDFs and the
strong coupling constant
Tomáš Laštovička (H1 collaboration)
DESY Zeuthen, Charles University Prague
at LLWI2003, Lake Louise, Canada
H1 and ZEUS
Structure functions
at HERA
αs and PDFs
Summary/Outlook
H1 and ZEUS at HERA
HERA at DESY, Hamburg
ep accelerator ring, 27.5 x 920 GeV
circumference: 6.3km
ZEUS
4 experiment halls
H1
Tomas Lastovicka, LLWI 2003
2/22
H1 and ZEUS experiments
nearly 4 aparatus
delivering data since
early 90ies
2
recently both
experiments upgraded
Tomas Lastovicka, LLWI 2003
3/22
Deep Inelastic Scattering
Four-momentum transfer squared:
L
Bjorken scaling variable:
W 
Inelasticity scaling variable:
Centre of mass energy squared:
Tomas Lastovicka, LLWI 2003
4/22
Cross-sections and Structure Functions
NC Cross Section:
~ NC ( x, Q
NC Reduced cross section: 
2
)
2

2
d  NC (e p) 2 
~  y ~  Y ~ ]

[
xF 3
FL
2
4 Y F2
dxd Q
xQ
Y
Y
2
2

1

(
1

y
)
Y
Dominant contribution
Sizeable only at high y (y>~0.6)
CC Cross Section:
Contribution only important at high Q2
2

2
4
1
1
d  CC (e p) G F M W
2

[

y
W L  Y  xW 3]
Y
W 2
2
2
2
2x (Q  M W2 ) 2
dxd Q
2
~
(
x
,
)
Q
CC Reduced cross section:  CC
Tomas Lastovicka, LLWI 2003
5/22
DIS slang reminder
low Q2 - transition domain from non-perturbative
domain to deep inelastic domain
strong coupling is large, limits of pQCD
 S (Q2 )
high Q2 - strong coupling is relatively small
pQCD calculations reliable
xF3 and CC enter the game at large Q2
low x (high y) - driven by gluons
sea (confinement) region
longitudinal str. function FL
unique acceptance by H1
high x (low y) - driven by quarks
valence quark region
fixed target experiments
Tomas Lastovicka, LLWI 2003
6/22
Kinematic plane coverage

covered almost to the
limits of phase space

compared to fixed target
experiments,
measurements extend to
high Q2 and high y by
more than 2 orders of
magnitude
Tomas Lastovicka, LLWI 2003
7/22
The Structure Function F2
 F2 is not calculable from the first principles
 Various theoretical predictions a decade ago
 during its running HERA made an impressive progress

F2 
2
e
 i x(qi  qi ) - directly related to quark densities
quarks
Tomas Lastovicka, LLWI 2003
1993
2000
8/22
The Structure Function F2
Tomas Lastovicka, LLWI 2003
9/22
Scaling violations of F2
at low x driven by gluons
described by QCD:
DGLAP evolution equations
 many open questions:
 does F2 saturate?
when gluon density is
large -> gluon fusion
 low Q2 region


 QCD analysis digests
quarks and gluon densities
from fits to F2
(parametrised at an initial scale,
then DGLAP evolution takes over)

2
e.g.
g
(
x
,

F )  F ( g , qi )
2
 ln  F
Tomas Lastovicka, LLWI 2003
10/22
CC and NC measurements
Tomas Lastovicka, LLWI 2003

Standard model describes
both NC and CC very well
over a large range of Q2

Electroweak unification at
about MZ2 scale

e+ and e- cross sections
different due to different
quark contribution and
helicity structure of EW
interactions
11/22
xF3 and FL measurements
xF3 errors dominated by
stat. errors, higher
luminosity needed
FL not measured directly,
runs at different beam
energies needed
Tomas Lastovicka, LLWI 2003
12/22
PDF fits and the strong coupling
QCD analyses require many choices to be made
Should be reflected in PDF uncertainty:










Choice of data sets used
Treatment of experimental systematic uncertainties
Q02 starting scale
Q2min of data included in fit
Renormalisation / factorisation scales
Choice of densities to parameterise
Allowed functional form of PDF parameterisation
Cuts to limit analysis to perturbative phase space
Treatment of heavy quarks
etc...
Tomas Lastovicka, LLWI 2003
13/22
Results on the strong coupling constant
• H1
• ZEUS
0.1150 +-0.0017(exp) +0.0009 -0.0007(model)
H1 + BCDMS precise data
if: systematíc errors are not fitted: +0.0005
NMC replaces BCDMS 0.116+-0.003 (exp)
4 light flavours: +0.0003
BCDMS deuteron data added: 0.1158 +- 0.0016 (exp)
EPJ C21(01)33
0.1166 +-0.0008(unc) +-0.0032(corr) +-0.0036(norm) +-0.0018(model)
p:BCDMS,NMC,E665 d:NMC,E665 d/p: NMC xF3: CCFR
systematíc errors are not allowed to vary in chi2 minimisation
Q2>2.5 GeV2, W2>20GeV2, RT-VFNS, b(uv)=1/2, b(dv)=1/2
fit alphas, xg, uv, dv, sea, dbar-ubar (MRST)
Phys.Rev. D67(03)
if fixed flavour scheme is used: +0.0010
large chi2 variations if Q2  (¼ .. 4) Q2 renormalisation scale:+-0.005 (H1)
 (½ .. 2) : +- 0.004 (ZEUS) not included in error
Tomas Lastovicka, LLWI 2003
14/22
Parton distribution functions from NLO QCD fits (ZEUS)
dv
uv
Sea, g
 xg and Sea distributions determined by
low x / Q2 HERA F2 data
 xuv determined from high x NC data
 xdv determined from high x CC e+ data
Tomas Lastovicka, LLWI 2003
15/22
Parton distribution functions from NLO QCD fits (H1)
CC and NC cross sections
are sensitive only to
U, antiU, D,antiD
(F2N has c-s admixture)
H1+BCDMS
H1 only
uv, dv, sea are replaced by the
observables
! possible to determine
PDFs with H1 data alone
(with assumption on sea
symmetry)
Tomas Lastovicka, LLWI 2003
H1 ICHEP02
16/22
Parton distribution functions from NLO QCD fits
H1 vs ZEUS
~3%
comparison of PDFs
independent fits,
different approaches
~10%
Tomas Lastovicka, LLWI 2003
only experimental errors!
(matter of choice)
17/22
NLO gluon momentum density
fixed flavour number scheme
Laenen, Riemersma, Smith, vanNeerven
needs precision data at low Q2, all x!
needs precision FL measurement!
H1 EPJ C21(01)33
Tomas Lastovicka, LLWI 2003
18/22
New low Q2
measurements
low Q2 1999
dedicated run
low Q2 x-section and F2
determination at low x
shifted vertex
2000 run
Transition region
between perturbative
and non-perturbative
kinematic range
Tomas Lastovicka, LLWI 2003
19/22
New measurements at low Q2, small x
Extended phase space:
Data fill the gap in precision measurements
around Q2~1GeV2
and extend phase space
to higher y at all Q2
(till 12 GeV2)
r changes behavior
at high y (small x)
g FL signature
(even at very low Q2)
Data with Q2 g 0:
Valuable for studying
underlying dynamics
of DIS → γp
Tomas Lastovicka, LLWI 2003
20/22
Rise of F2 towards low x
 H1 / ZEUS / NMC data
used to fit Q2 dependencies
for x<0.01 :
F2  c(Q ).x
2
 (Q2 )
 Behaviour is changing at
around 1 GeV2
 Theory expects λ to reach
value of ~0.08 for Q2 → 0
 No sign of saturation at
small x observed (yet)
Tomas Lastovicka, LLWI 2003
21/22
Summary (concluding remarks)
First phase of HERA running delivered many interesting results
Precision of ~2−3 % achieved for F2
The inclusive DIS data at HERA are confronted with NLO QCD
analyses
QCD (the DGLAP equations) is able to describe
all the cross section data: e+p, e-p, NC, CC
in a wide kinematical range: both Q2 & x covering 5 orders
of magnitude
 S extracted from DIS data is competetive with the world
average
Fits allow HERA data to constrain PDFs
HERA 2 (after luminosity upgrade): high precision xF3
direct measurement of FL
The next important step: e-d runs (dv/uv at high x), HERA
Tomas Lastovicka, LLWI 2003
3
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22/22