Legacy of HERA
A M Cooper-Sarkar
INT 10-3
October 18 2010
Combination of ZEUS and H1 data and PDF fits to these data:
1. Inclusive cross-sections HERA-1 (1992-2000):arxiv:0911.0884 -improved constraints
at low-x
2. F2(charm) data (preliminary)- constraints on the charm mass parameter, mc(model)
3. Low energy runs – FL- 2007- (preliminary) –tension with low x, Q2 data?
4. Inclusive cross-sections HERA-II (2003-2007)- (preliminary) -improved constraints at
high-x
Predictions for LHC cross-sections
Predictions for Tevatron cross-sections
Still to come
F2(beauty)
Jets and αS(MZ), perhaps forward jets
NOT COVERED: dffractive physics
Why combine ZEUS and H1 data?
At the LHC we collide protons Protons are
full of partons. Our knowledge of partons
comes from Deep Inelastic Scattering
data. HERA dominates these data and is
most relevant for the kinematic region of
early LHC data
We think we know how to extrapolate in Q2
using (N)NLO QCD (using the DGLAP
equations) but we don’t a priori know the
shapes of the parton distributions in x. The
HERA data is our best guide
DGLAP eqns
AT this meeting I am also allowed to say that having the highest precison
measurements in the low-x region is interesing in its own right!
A substantial part of the uncertainty on parton distributions comes from the need to use
many different input data sets with large systematic errors and questionable levels of
consistency- i ncreased χ2 tolerances are used to account for this
Averaging H1 and ZEUS data provides a model independent tool to study
consistency of the data and to reduce systematic uncertainties:

Experiments cross calibrate each other JHEP 1001.109 arxiv:0911.0884

The combination method includes accounting for full systematic error correlations.
The resulting combination is much more accurate than expected from the
increased statistics of combining two experiments. It’s like having had the best

features of both detectors
The post-averaging systematic errors are smaller than the statistical across a large
part of the kinematic plane

Data Sets
2009 average based on the complete HERA-I inclusive NC and CC DIS data:
 Ep=820 (s=300) and Ep=920 (s=320) GeV
200 pb-1 of e+p , 30 pb-1 of e-p
• CC e- p data: H1 98, ZEUS 98 (250 ≤ Q2 ≤ 15000 GeV2)
• CC e+p data: H1 94-97, H1 99-00, ZEUS 94-97, ZEUS 99-00 (250 ≤ Q2 ≤ 15000 GeV2)
• NC e- p data: H1 98, ZEUS 98 (200 ≤ Q2 ≤ 30000 GeV2
• NC e+p data: ZEUS 96-97, ZEUS 99-00, H1 99-00 “high Q2”,H1 96-00 “bulk”, H1 95-00
“low-Q2”, ZEUSBPC/BPT, SVX95 “low-Q2” (0.045 < Q2 < 30,000 GeV2)
The NCe+p data sets cover 5 decades of the kinematic plane in Q2 and x. The
scaling violations of these data give us our best handle on the low-x gluon
which is very important for Standard Model LHC physics at the W/Z scale but is
also interesting in its own right
The new combination supercedes all these data sets
This gives 110 correlated systematic error sources
But they are all small !
3 “procedural uncertainties” related to the averaging procedure
1402 data points are averaged to 741 combined data points
χ2/ndf =637/656
Combining the experiments
accounting for the systematic
uncertainties is like having had
a much better detector
ZEUS γp background
uncertainty is reduced by a
factor of 3
H1 LAr hadron calorimeter
energy scale uncertainty is
halved
Resulting total uncertainties are <2% over a
large part of the kinematic plane AND the
contribution of correlated systematics to this
errors is now < statistical error
This page shows NC e+
combined data but NCe- and
CCe+ and e- are also combined
Results of the combination
compared to the separate
data setsillustration just for a few of
the NCe+ data
These data are used for extracting parton distributions:
HERAPDF1.0
Some of the debates about the best way of estimating PDF uncertainties concern the
use of many different data sets with varying levels of consistency.
The combination of the HERA data yields a very accurate and consistent data set for 4
different processes: e+p and e-p Neutral and Charged Current reactions.
Whereas the data set does not give information on every possible PDF flavour it does:
•Give information on the low-x Sea (NCe+ data)
•Give information on the low-x Gluon via scaling violations (NCe+ data)
•Give information on high-x u (NCe+/e- and CCe-) and d ( CCe+ data) valence PDFs
•Give information on u and d-valence shapes down to x~3 10-2 (from the difference
between NCe+ and NCe-)
We can set the experimental uncertainties on our PDFs at 68% CL by the conventional
χ2 tolerance Δχ2 = 1, because we have a consistent data set
NOTE the use of a pure proton target means d-valence is extracted without need for
heavy target/deuterium corrections or strong iso-spin assumptions these are the only
PDFs for which this is true
Furthermore, the kinematic coverage at low-x ensures that these are the most crucial
data when extrapolating predictions from W, Z and Higgs cross-sections to the LHC
Where does the information on parton distributions come from?
CC e-p
CC e+p
d2(e-p) = GF2 M4W [x (u+c) + (1-y)2x (d+s)]
dxdy
2x(Q2+M2W)2
d2(e+p) = GF2 M4W [x (u+c) + (1-y)2x (d+s)]
dxdy
2x(Q2+M2W)2
•We can use the reduced cross-sections to learn about high-x valence PDFs
For NC e+ and ed2(e±N)
dxdy
2
2

s Y+ [ F (x,Q2) - y2 F (x,Q2) ± Y_xF (x,Q2)], Y± = 1 ± (1-y)2
=
2
L
3
4
Q
Y+
Y+
F2 = F2γ –ve PZ F2γZ + (ve2+ae2)PZ2 F2Z
xF3 =
- ae PZ xF3γZ + 2veae PZ2 xF3Z
Where PZ2 = Q2/(Q2 + M2Z) 1/sin2θW , and at LO
[F2 ,,F2γZ, F2Z] = i [ei2,2eivi,vi2+ai2][xqi(x,Q2) + xqi(x,Q2)]
[xF3γZ, xF3Z ] = i [eiai,viai]
[xqi(x,Q2) - xqi(x,Q2)]
So that xF3γZ = 2x[euauuv + edaddv] = x/3 (2uv+dv)
Where xF3γZ is the dominant term in xF3
The difference between NC e+
and e- cross-sections gives the
valence structure function xF3 due
to γ/Z interference and Z
exchange
Note this is obtained on a pure
proton target so
•No heavy target corrections
•No assumptions on strong isospin
(Unlike xF3 determined from neutrino
scattering on heavy isocalar targets)
RESULTS for HERAPDF1.0 –arxiv:0911.0884
And here is a summary plot of the
PDF results. We estimate model and
parametrisation uncertainties as well
as experimental uncertainties
To appreciate how much better this is
than uncombined HERA data compare
the red experimental errors to this plot
which shows the experimental errors
for a smilar PDf fit to uncombined data
Consequences for W and Z production at the LHC
Look at predictions for W/Z rapidity distributions: Pre- and Post-HERA
Note difference
in scale for
fractional errors
Just fixed target
DIS data ~15%
uncertainty
Why such an
improvement
?
These illustrations at 14 TeV
Separate HERA
data sets~5%
uncertainty
Combined HERA
data set~1.5%
uncertainty
It’s due to the improvement in the low-x sea
and gluon At the LHC the q-qbar which
make the boson are mostly sea-sea partons
And at Q2~MZ2 the sea is driven by the
gluon
Model errors are the most
signficant in the central region:
mc, mb, fs, Q2min
mc =1.35 – 1.65 GeV is the
dominant contribution… but this
can be improved if F2(charm)
data are used…..
However PDF fitting should
also include consideration of
model errors and
parametrisation errors
HERAPDF1.0
experimental plus
model errors plus
parametrisation
Recently the PDF4LHC group has
been considering the role that the
uncertainty in the value of αS(MZ)
plays in the overall uncertainty of
predictions- PDFs are provided at
a fixed αS(MZ) .
This is not a large effect for W/Z
production
Plot from G.Watt -MSTW
Comparisons of W+ cross-section
as a function of αS(MZ)
MSTW08
CTEQ66
HERAPDF1.0
NNPDF2.0
ABKM09
GJR08
The PDF4LHC group has been
considering all these PDFs at NLO
But the value of mc AND the
scheme used to account for heavy
quark production are..
NOTE many of the PDFs (NNPDF,
CTEQ, MSTW,HERAPDF) are now
provided for a range of αS(MZ) values
H1 and ZEUS have also
combined charm data recently
And the HERAPDF1.0 gives a good description
of these data –within its error bandThe error band spans mc=1.35 (high) to mc=1.65
(low) GeV
The data show some preference for higher charm
mass than the standard choice mc=1.4 GeV
If we input the charm data to the PDF fit it does not change the PDFs significantly BUT
Before charm is input the χ2
profile vs the charm mass
parameter is shallow..
After charm is input the χ2
profile vs the charm mass
parameter gives
mc = 1.57 ± 0.02 GeV
But the HERAPDF uses the Thorne General
Mass Variable Flavour Number Scheme for
heavy quarks as used by MSTW08
This is not the only GMVFN
CTEQ use ACOT- χ
NNPDF2.0 use ZMVFN
These all have different preferred charm mass
parameters, and all fit the data well when used
with their own best fit charm mass
We have re-analysed the HERAPDF+F2c data using
several different heavy quark schemes
Model and param.
Errors included
We then use each of these schemes to
predict W and Z cross-sections at the LHC
(at 7 TeV) as a function of charm mass
parameter
If a fixed value of mc is used then the
spread is considerable (~7%)- but if each
prediction is taken at its own optimal mass
value the spread is dramatically reduced
(~2%) even when a Zero-Mass (ZMVFN)
approximation has been used
The PDFs MSTW08, CTEQ6.6,
NNPDF2.0 do NOT use charm mass
parameters at the optimal values- and this
may explain their differing predictions.
H1 and ZEUS have also combined the e+p NC inclusive data from the lower proton
beam energy runs (PP = 460 and 575) and produced a common FL measurement
When the low energy
data are input to the
HERAPDF fit it
becomes evident that
the low Q2/low-x data
are not so well fit –
Imposing a harder Q2
cut Q2 > 5 improves
the situation
The resulting PDFs
have a somewhat
different shape- less
valence-like gluon at
low Q2… steeper
gluon at higher Q2
This is also true if you
make an x cut
x > 5 10-4
or a combined cut
Q2 > 0.5 x-0.3
Our Regge prejudices led us to think
that the sea and gluon would have soft
slopes at low x ~ x -0.08 at the starting
scale and THEN evolution would make
them steeper. However at Q2~2
the sea has a steeper slope x -0.15
and the gluon is valence-like x +0.2
If however we distrust the formalism for
low x and Q2 and we fit only data for
Q2 > 5
the sea has a softer slope x -0.11
But the gluon is less valence-like x +0.08
i.e. they are both closer to the Regge
soft Pomeron value of -0.08
So NLO DGLAP maybe showing signs failure at low-x, Q2
But how about NNLO DGLAP?...
HERAPDF1.0 is also available at NNLO for two values of αS(MZ)
since many analyses indicate that alphas seems to be smaller at NNLO than at NLO and our
own data prefer a lower value
NNLO fits to HERA-I data give:
First fit αS(MZ) for NLO → 0.1166 ± 0.0044(exp) χ2= 574.8 /592
Then fit αS(MZ) at NNLO→0.1145 ± 0.0042(exp) χ2= 623.5 /592
NNLO is important for precision studies of cross-section uncertainties.
There are far fewer NNLO PDFS: MSTW08, ABKM
NOTE: NNLO has worse χ2 than NLO and
does not fit low-x Q2 data better. The χ2 is
also improved if low x, Q2 cuts are imposed.
In fact it is the 920 data which are worst fit
at NNLO. Tension between the low and
high-energy data shows up at low-x,Q2 and
is not solved by moving to NNLO.
NNLO using
αs(MZ)=0.1145
NLO using
αs(MZ)=0.1176
NNLO
Χ2/ndf 873.7/806
X/N CCEP =
1.04 34
X/N CCEM =
0.57 34
X/N NCEP=
1.24 379
X/N NCEM=
0.75 145
X/N NCEP 460/575
= 1.07 224
NLO
χ2 818.5/806
X/N CCEP =
0.86 34
X/N CCEM =
0.59 34
X/N NCEP=
1.13 379
X/N NCEM=
0.74 145
X/N NCEP 460/575
= 1.04 224
NNLO
Q2 > 5
Χ2/ndf 762.4/771
X/N CCEP =
0.93 34
X/N CCEM =
0.56 34
X/N NCEP=
1.10 353
X/N NCEM=
0.76 145
X/N NCEP 460/575
= 0.85 215
NLO
Q2 > 5
Χ2/ndf 698.3/771
X/N CCEP =
0.85 34
X/N CCEM =
0.58 34
X/N NCEP=
1.03 353
X/N NCEM=
0.75 145
X/N NCEP 460/575
= 0.82 215
What about changes in the heavy quark scheme?
Changes in the Thorne GMVFN make little difference
But a change to ACOT does – this has one less power of αS in the definition of FL
RT VFN
χ2 818.5/806
X/N CCEP =
0.86 34
X/N CCEM =
0.58 34
X/N NCEP=
1.13 379
X/N NCEM=
0.74 145
X/N NCEP 460/575
= 1.04 224
ACOT VFN
ACOT-χ VFN
χ2 788.6/806
χ2 793.2/806
X/N CCEP =
0.89 34
X/N CCEP =
0.88 34
X/N CCEM =
0.59 34 X/N CCEM =
0.58 34
X/N NCEP=
1.09 379 X/N NCEP=
1.13 379
X/N NCEM=
0.74 145 X/N NCEM=
0.75 145
X/N NCEP 460/575
X/N NCEP 460/575
= 0.98 224
= 0.92 224
And so does the use of a Fixed
Flavour Number sheme
FFN
χ2 724.7/738
X/N CCEP =
X/N CCEM =
X/N NCEP=
1.08 379
X/N NCEM=
0.76 145
X/N NCEP 460/575
= 0.92 224
But all of these are improved further by x
or Q2 cuts
NOTE there is no improvement from cutting high y.
Applying x,Q2 cuts does NOT have a big effect on the description of FL.
Changes of heavy quark scheme to ACOT, FFN
or a change from NLO to NNLO have a bigger effect on FL
Describing the integrated FL vs Q2 plot and describing the full differential
cross-section data for three different proton energies are not achieved in
identical ways. A precision measurement of FL(x,Q2) would have been nice.
Returning to NLO fits: How hard do we need to cut such that DGLAP fits of just
Ep=920 data and fits including lower energy data are once more in good agreement?
Q2 > 1.0 x-0.3
575
This implies that the ‘true’ gluon could be a little bit steeper than the
HERAPDF1.0 gluon- or indeed CTEQ6.6 or MSTW08 gluons
However this effect only starts to become important for x < 10-3 so W/Z cross-sections
at the LHC are only marginally affected- 1-1.5% up at 7 TeV
HERA- I combination only ~250 pb-1 of data
HERA-II gives 4 times as much data in total
The triggers were such that most of this is at higher
x and Q2
We have made a preliminary HERA-II combinationnot all of the separate ZEUS and H1 inclusive data
which go into this combination are yet published.
H1 and ZEUS have also combined preliminary high Q2 HERA-II data along with the
HERA-I data and HERAPDF1.0 has recently been updated to HERAPDF1.5 by
including these data
The data on the left has been updated to the data on the right
The HERAPDF1.0 fit on the left has been updated to the HERAPDF1.5 fit on the right
The data on the left has been updated to the data on the right
The HERAPDF1.0 fit on the left has been updated to the HERAPDF1.5 fit on the right.
The CCe- data is improved because at HERA-1 there were only 30 pb-1 of e- data, at
HERA-II there are ~350pb-1
The data on the left has been updated to the data on the right
The HERAPDF1.0 fit on the left has been updated to the HERAPDF1.5 fit on the right
In this case ~200pb-1 of HERA-I data has been supplemented by ~300pb-1 of HERAII data. Extra CCe+ helps to determine the d quark at high-x
The PDF uncertainties have been reduced at high-x
These plots show total uncertainties (model and parametrization included)
Improved determination of the
d/u ratio at high-x.
The only PDF which
measures d in a proton rather
than an isoscalar target
This reduced high-x error results in a reduced error at high rapidity for W/Z
production at the LHC
How about Tevatron results?
We don’t include Tevatron data in the fits but we can
describe it – we CAN describe Tevatron jet data
despite having a relatively soft gluon (we have
harder quarks) AND we have a reasonable
description of the D0 electron asymmetry data which
is troublesome for some of the PDFs
Note some of the trouble comes from tension with NMC
and BCDMS fixed target deuteron data- deuterium
corrections are one possible explanation- the HERAPDF
uses only proton data and is not subject to this uncertainty
Things still to come:
Inclusion of F2b- more information on gluon/heavy quark schemes
Inclusion of HERA jets data-- decrease in gluon uncertainty using fixed αS(MZ)
-- decrease in gluon uncertainty using free αS(MZ)
and determination of alphas and PDF simultaneously within the fit
--decrease in the uncertainty of αS(MZ)
Jet illustrations use
ZEUS combined
HERA not yet ready
NOTE the HERA-jet data already give very competitive
αS(MZ) determinations (not covered here)
What about Forward Jets?- combined data are still to come
Comparison to conventional LO
and NLO calculations- NLO below
data, especially at small xBj
Look at the hadron final states..lack of pt
ordering has its consequences. Forward jets
with xj » x and ktj 2 ~ Q2 are suppressed for
DGLAP evolution but not for kt disordered BFKL
evolution
But there are some things that HERA did not do
(apart from fail to fully exploit the low-x region!):
flavour separation in the sea
Strangeness has been assigned
a large model error at Q20=2
sbar = (0.45± 0.15) dbar
Could HERA measure strangeness?
W+ +s → c
Charm production in CCe+..
There is still some work going on, but
statistics will be poor
There is also some HERMES data
which suggests that strange is not the
same shape as dbar….
Then there is dbar-ubar
We know this is not zero at high-x from E866 Drell-Yan measurements
The HERAPDFs are NOT in
disagreement with this but could
do better!
Along with most other PDFs it
assumed that dbar=ubar at
small-x
What if we relax this assumption…
This Toy PDF is called the
HERAPDF1.u ‘unconstrained’ or
‘dissident’ PDF
It comes in two varieties:
1. dbar≠ubar at small x
2. dbar≠ubar at small x plus
strangeness fixed to the
HERMES shape
The dissident fit has dbar very much smaller than ubar at small-x (although slightly
larger at high-x so not in disagreement with Drell-Yan data).
Strangeness evolves to become
almost the same size as dbar, ubar
and the difference in the Standard
and the HERMES strangeness is not
significant
As Q2 increases the difference between dbar and ubar remains constant but the size
of ubar and dbar increase rapidly at low-x so that by Q2~MW,Z 2 this difference is not
very significant. However for the LHC it is still visible….
For the Tevatron x values are higher and
W,Z are q-q dominated so such a
‘dissident’ PDF is not excluded
For the LHC there should be obvious
differences – we may even be able to
exclude this with data taken this year
SUMMARY
Combination of ZEUS and H1 data and PDF fits to these data:
1. Inclusive cross-sections HERA-1 (1992-2000):arxiv:0911.0884 -improved constraints
at low-x
2. F2(charm) data (preliminary)- constraints on the charm mass parameter, mc(model)
3. Low energy runs – FL- 2007- (preliminary) –extends the kinematic reach in the same
direction as EIC-- tension with low x, Q2 data?
4. Inclusive cross-sections HERA-II (2003-2007)- (preliminary) -improved constraints at
high-x ----using only proton target
Still to come:
1. F2(beauty)
2. HERA jet data
What HERA could not do: u,d,s flavour separation in the Sea
What HERA did not do: fully exploit the low-x region, precision measurement of FL
extras
LHeC
PDF improvement
100 GeV e on 7 TeV
LHeC
Low-x
Expansion of the kinematic regime
so that low-x, x~10-4 now has Q2 up
to 100 rather than 10
Can measure F2 and FL and hope to
distinguish models with/without
saturation etc
Averaging procedure
•
•
•
Swim all points to a common x-Q2 grid
Moved 820 GeV data to 920 GeV p-beam energy
Calculate average values and uncertainties
This is done by making a χ2 fit to the data points of both experiments which
simply assumes that for each process (NC or CC, e+ or e-) and each x, Q2
point (i) there is only one ‘true’ value of the cross-section- these are the
predictions mi – whereas there can be several measurements of this value,
from ZEUS and H1 and from different years of running- these are the
measurements µi
•
•
The chisq accounts for the correlated systematics of the data points- each
data point can have several such uncertainties Γ, hence sum over j for each
data point i, but these uncertainties are common to all data points for large
sub-sets of data. The fit determines the value of the cross-sections mi and
the systematic shift parameters bj
Evaluate further uncertainties due to choices in combination procedure,e.g.
Correlations between ZEUS and H1
1402 data points are averaged to 741 combined data points
χ2/ndf =637/656
Systematic shift parameters b,
shift most systematics < 1 std
deviation
But the fit also determines
uncertainties on the shift
parameters Δb, some of these
are much reduced e.g
ZEUS γp background
uncertainty is reduced by a
factor of 3
H1 LAr hadron calorimeter
energy scale uncertainty is
halved
Resulting total uncertainties are <2% over a
large part of the kinematic plane AND the
contribution of correlated systematics to this
errors is now < statistical error
Correlated systematic uncertainties, χ2 and Δχ2
The data combination results in a data set which not only has improved statistical
uncertainty, but also improved systematic uncertainty.
Even though there are 113 sources of correlated systematic uncertainty on the data
points these uncertainties are small. The total systematic uncertainty is significantly
smaller than the statistical uncertainty across the the kinematic region used in the
QCD fits
This means that the method of treatment of correlated systematic uncertainties in
our PDF fits is not crucial. We obtain similar results treating all systematic errors as
correlated or as uncorrelated.
For our PDF fits we combine 110 sources of systematic uncertainty from the separate
experiments in quadrature and OFFSET the 3 procedural systematics which derive from the
method of data combination.
We set the experimental uncertainties on our PDFs at 68% CL by the conventional
χ2 tolerance
Δχ2 = 1
Theoretical framework
Fits are made at NLO in the DGLAP formalism -using QCDNUM 17.00
The Thorne-Roberts massive variable flavour number scheme is used (2008 version) and
compared with ACOT
The staring scale Q20 (= 1.9 GeV2) is below the charm mass2 (mc=1.4 GeV) and charm and
beauty (mb=4.75) are generated dynamically
A minimum Q2 cut Q2 > 3.5 GeV2 is applied to stay within the supposed region of validity
of leading twist pQCD (no data are at low W2 )
Parametrisation and model assumptions
We chose to fit the PDFs for:
gluon, u-valence, d-valence and the Sea u and d-type flavours:
Ubar = ubar, Dbar = dbar+sbar (below the charm threshold)
To the functional form
The normalisations of the gluon and valence PDFs are fixed by the momentum and
number sum-rules resp. Further constraints are:
B(d-valence) = B(u-valence), B(Dbar) = B(Ubar), low-x shape of Sea same for u-type+d-type
A(Ubar) = A(Dbar) (1-fs), where sbar = fs Dbar, so that ubar → dbar as x→ 0 (fs=0.31)
Uncertainties due to model assumptions are evaluated by varying input values
Variation of heavy quark masses:
Mc=1.35 to1.65 GeV (the pole-mass)
Mb= 4.3 to 5.0 GeV
Variaion of the sea fraction
Fs=s/(d+s) = 0.23 to 0.38
Variation of the minimum Q2 cut on data entering the fit
Q2 min= 2.5 to5.0 GeV2
We also vary the value of the starting scale Q20 from1.5 to 2.5 GeV2:
this is considered as a parametrisation uncertainty rather than a model
uncertainty…
Parametrisation uncertainties- indicative, not exhaustive
The central fit is chosen as follows: start with a 9 parameter fit with all D and E
parameters = 0 and then add D and E parameters one at a time noting the χ2
improvement. Chose the fit with the lowest χ2. This has E(u-valence) ≠ 0 and
χ2/ndf = 574/582.
This is the central fit
We then start with this 10 parameter fit and add all the other D and E parameters one
at a time noting the χ2 improvement. It turns out that there is no significant further
improvement in χ2 for 11 parameter fits.
An envelope of the shapes of these 11 parameter fits is formed and used as a
parametrization error. This gives the parametrization uncertainty at high-x.
Low-x parametrisation uncertainty is accounted for by the following additional
variations:
1. Bdv free –this results in Bdv ≈ Buv
2. A negative gluon term: - A xB(1-x)C is added to the usual gluon term, when the
starting scale of the fit is lowered to Q20=1.5 GeV2 – this results in a small –ve gluon
term but the gluon itself does not become negative in the kinematic range of the data
Compared to various NLO DGLAP fits
And compared to alternative
theoretical predictions:
White and Thorne (WT) which
has NLL ln1/x resummation
included
So do we have a smoking gun?
Maybe not- but the circumstantial evidence
is building up….
Dipole Models which can
accommodate non-linear effects/
saturation eg IIM colour glass
condensate
The PDF4LHC group has been comparing PDFs at the level of parton-parton lumiosities
Plot from G.Watt -MSTW
HERAPDF1.0 has a rather high qqbar luminosity at high scale.
This is reduced in HERAPDF1.5
Let’s look at the modern PDFsets
MSTW08
CTEQ66
HERAPDF1.0
NNPDF2.0
ABKM09
GJR08
Overall disagreement ~8% in W, Z
cross-sections
The PDF4LHC recommendation is
to take the envelope of the
NNPDF, MSTW, CTEQ predictions
--even this may not be enough!
Plots from G.Watt -MSTW
Plots from G.Watt -MSTW
Plots from G.Watt -MSTW
Plots from G.Watt -MSTW
Spread in Higgs production crosssections is now > 15%
Dependence on alphas is also
increased