Transcript ZEUS PDF fits

PDF studies at ATLAS
HERA-LHC workshop 2007
A M Cooper-Sarkar, Oxford
At the LHC high precision (SM and BSM) cross
section predictions require precision Parton
Distribution Functions (PDFs)
How do PDF uncertainties affect BSM physics?
high ET jets..contact interactions/extra dimensions
How do PDF Uncertainties affect SM physics
What measurements can we make at ATLAS to
improve the PDF uncertainty?
HERA and the LHC- transporting PDFs to hadron-hadron cross-sections
QCD factorization theorem for shortdistance inclusive processes
where X=W, Z, D-Y, H, high-ET jets,
^prompt-γ
and  is known
• to some fixed order in pQCD and EW
• in some leading logarithm
approximation (LL, NLL, …) to all orders
via resummation
pA
fa
x1
ˆ
pB
x2
fb
X
Knowledge of the PDFs is vital
What has HERA data ever done for us?
W+
Lepton+
W-
Lepton-
Z
Pre-HERA W+/W-/Z and
W+/- → lepton+/- rapidity spectra
~ ± 15% uncertainties !
Why? Because the central rapidity range
AT LHC is at low-x (5 10-4 to 5 10-2)
NO WAY to use these crosssections as a good luminosity
monitor
W+
Lepton+
W-
Lepton-
Z
Post-HERA W+/W-/Z and
W+/- → lepton+/- rapidity
spectra
~ ± 5% uncertainties !
Why? Because there has been a
tremendous improvement in our
knowledge of the low-x glue and thus
of the low-x sea
Pre-HERA sea and glue distributions
Post HERA sea and glue distributions
How to constrain gluon-PDFs at LHC
single Z and W± Production
W+- diff. cross section
5
MRST2002-NLO
LHC
dW/dyW . Bl
(nb)
4
x1 = 0.006
x2 = 0.006
x1 = 0.12
x2 = 0.0003
x1 = 0.0003
x2 = 0.12
3
2
W±
Symmetric
1
MRST PDF
0
-6
-4
-2
0
2
4
6
yW
PDF Set
NNLO corrections small ~ few%
NNLO residual scale dependence < 1%
W  BW l W  BW l  Z  BZ ll

(nb)

(nb)
(nb)
ZEUS-S
12.07  0.41 8.76  0.30
1.89  0.06
CTEQ6.1
11.66  0.56 8.58  0.43
1.92  0.08
MRST01
11.72  0.23 8.72  0.16
1.96  0.03
Theoretical uncertainties dominated by PDFs
note that central values differ by more than
the MRST estimate of the error
To improve the situation we NEED to be
more accurate than this:~3%
Statistics are no problem we are
dominated by systematic uncertainty
BUT different PDF sets give
somewhat different estimates
of both the central values and
the uncertainties of the W
spectra
From LHAPDF eigenvectors
At y=0 the total uncertainty is
~ ±6% from ZEUS
~ ±4% from MRST01E
~ ±8% from CTEQ6.1
ZEUS to MRST01 central value difference ~5%
To improve the situation we NEED to be more
accurate than this:~4%
The uncertainty on the W/Z rapidity distributions is
dominated by –- gluon PDF dominated eigenvectors
Both low-x and high-x gluon
It may at first sight be surprising that W/Z
distns are sensitive to gluon
parameters BUT our experience is
based on the Tevatron where Drell-Yan
processes can involve valence-valence
parton interactions.
At the LHC we will have dominantly
sea-sea parton interactions at low-x
And at Q2~MZ2 the sea is driven by
the gluon- which is far less precisely
determined for all x values
So finally- can we improve our knowledge of PDFs using ATLAS data
itself?
W/Z production have been considered as good standard candle processes insensitive to
PDF uncertainties……? This is true WITHIN a PDFset ( see Thorne’s talk)
generator level
But how about comparing PDFsets?
We actually measure the decay
lepton spectra
electron
positron
ATLFAST
electron
positron
Generate with HERWIG+k-factors
(checked against MC@NLO) using
CTEQ6.1M ZEUS_S MRST2001
PDFs with full uncertainties
from LHAPDF eigenvectors
At y=0 the total uncertainty is
~ ±6% from ZEUS
~ ±4% from MRST01E
~ ±8% from CTEQ6.1
ZEUS to MRST01 central value
difference ~5%
To improve the situation we NEED to be
more accurate than this:~4%
Study of the effect of including the LHC W Rapidity distributions in global PDF fits
by how much can we reduce the PDF errors with early LHC data?
Generate data with 4% error using CTEQ6.1 PDF, pass through ATLFAST detector
simulation and then include this pseudo-data in the global ZEUS PDF fit Central
value of prediction shifts and uncertainty is reduced
BEFORE including W data
Lepton+ rapidity spectrum
data generated with CTEQ6.1
PDF compared to predictions
from ZEUS PDF
AFTER including W data
AMCS, A. Tricoli
(Hep-ex/0509002)
Lepton+ rapidity spectrum
data generated with CTEQ6.1
PDF compared to predictions
from ZEUS PDF AFTER these
data are included in the fit
Specifically the low-x gluon shape parameter λ, xg(x) = x –λ , was
λ = -.199 ± .046 for the ZEUS PDF before including this pseudo-data
It becomes λ = -.181 ± .030 after including the pseudodata
The uncertainty on the W/Z rapidity distributions is dominated by –- gluon PDF
dominated eigenvectors and there is cancellation in the ratios
AW = (W+ - W-)/(W+ + W-)
ZW = Z/(W+ + W-)
Remaining uncertainty comes from valence PDF related eigenvectors Well Known?
Gold plated?
We will measure the lepton asymmetry
Within each PDF set uncertainty in the lepton
asymmetry IS LESS than in the lepton rapidity
spectra, e.g about 2% for the asymmetry at
y=0, as opposed to about 4% for the lepton
rapidity spectra themselves (using MRST2001
PDFS)
However the PDF sets differ from each
other more strikingly- MRST01and
CTEQ6.1 differ by about 13% at y=0!
But this is an opportunity to use ATLAS
measurements to increase knowledge of
the valence PDFs at x~0.005 - see AMCS
February06 SM session
generator level
ATLFAST
Because the uncertainties in W+,Wand Z spectra are all coming from
the gluon PDF there is cancellation
in the ratios
AW = (W+ - W-)/(W+ + W-)
ZW = Z/(W+ + W-)
Remaining uncertainty comes from
valence PDF related eigenvectors
Well Known? Gold plated?
We will actually measure the lepton asymmetry
Uncertainty in the lepton asymmetry IS LESS than in
the lepton rapidity spectra, e.g about 4% for the
asymmetry at y=0, as opposed to about 8% for the
lepton rapidity spectra themselves (using CTEQ6.1M
PDFS)
mrst02
cteq61
W
BUT Compare CTEQ and
MRST PDF predictions for
the W asymmetryAW = (W + - W -)/(W + + W -)
In the measurable rapidity
range
Look closely at y~0
MRST is 25% different from
CTEQ
lepton
This difference persists in the
lepton asymmetry,
Al = (l+ - l-)/(l+ + l-),
Though it is diluted to ~13%
-but surely we could see
that?
Not so gold-plated when you compare predictions from different PDF sets –
But this is an opportunity to use ATLAS measurements to increase knowledge
of the valence PDFs at x~0.005 - see AMCS February06 SM session
Where does this difference come from?
• Dominantly, at LO
•
Aw= (u d – d u)
(u d + d u)
• And u = d = q at small x ( I will return to this..it can be challenged)
• So Aw~ (u – d) =
(uv – dv)
•
(u + d)
(uv + dv + 2 q )
• Actually this pretty good even quantitatively – Make this simple LO
calculation using the CTEQ and the MRST PDFs at Q2=MW 2 and
x~0.006 (corresponding to zero rapidity) and you’ll find that it DOES
explain the Aw difference between MRST and CTEQ.
- let’s see the evidence
CTEQ6.1
uv
MRST02
Q2=Mw2
uv – dv
Q2=Mw2
dv
x- range affecting W asymmetry in the measurable
rapidity range
Q2=Mw2
MRST and CTEQ uv – dv distributions are significantly
different : at Q2=MW2 and x~0.006
CTEQ: uv=0.17, dv=0.11, uv-dv=0.06
MRST: uv=0.155, dv=0.11,uv-dv=0.045
dbar
CTEQ6.1
MRST02
dbar-ubar
ubar
Evidence that dbar = ubar for both PDFs at small-x at
Q2=MW2 and x~0.006 MRST and CTEQ dbar=ubar=0.7
So Aw=0.06/(0.28+1.4) = 0.036 CTEQ
Aw=0.045/(0.265+1.4) = 0.027 MRST…pretty close!
But perhaps we need to look more closely at the tiny difference in dbar-ubar–
look at MRST and CTEQ dbar-ubar on a scale blown up by x10
Could this play a role?
Without approximations..but still LO,
Aw = d (uv-dv) +dv Δ
d (uv+dv+2d) -2dΔ –dvΔ
Where Δ=dbar-ubar=0.016 for CTEQ
Aw = 0.7x(0.06) + 0.11x0.016
0.7X(1.68) – 2x0.7x0.016-0.11x0.016
And Δ=0.010 for MRST
AW=0.7x(0.045) + 0.11x0.011
0.7x(1.665) – 2x0.7x0.011-0.11x0.011
The terms involving the difference of ubar and dbar are simply too small to matter
compared to the terms involving the valence difference.
So for the time being I have mocked up some lepton asymmetry data to follow the
prediction of MRST04 with 4% errors and no scatter (!)
Compare to the predictions of ZEUS-S. What if we input these data to the ZEUS-S fit?
The PDF uncertainty is improved by the input of such data – the uncertainty on AW is
reduced from ~8% to ~5% at y=0 (this improvement is spread amongst the valence
parameters, not in any one parameter) -- but the fit is unable to describe the MRST
pseudodata unless the valence params are extended.
The valence parametrisations at Q20 become xuv = Au xau (1-x)bu(1+du √x + cu x) ,
xdv = Ad xad (1-x)bd (1+dd√x + cd x)- 16 rather than 14 parameters are needed to fit
MRST pseudodata
MRST02 pseudodata
ZEUS-S prediction
Conclusion we have valence PDF discrimination, and will be able to
measure valence distributions at x~0.005 on proton targets for the first time
……………………..
•Data on the low-x valence distributions comes only from the CCFR/NuTeV data on
Fe targets. The data extend down to x~0.01, but are subject to significant
uncertainties from heavy target corrections in the low-x region.
•HERA neutral current data at high-Q2, involving Z exchange, make valence
measurements on protons- but data are not yet very accurate and also only extend
down to x~0.01
•Current PDFs simply have prejudices as to the low-x valence distributions - coming
from the input parametrisations. The PDF uncertainties at low x do not actually reflect
the real uncertainty (horse’s mouth- Thorne)
•LHC W asymmetry can provide new information and constraints in the x region
0.0005 < x <0.05
Example of how
PDF uncertainties
matter for BSM
physics– Tevatron
jet data were
originally taken as
evidence for new
physics--
Theory CTEQ6M
These figures show inclusive jet cross-sections
i
compared to predictions in the
form (data - theory)/ theory
Today Tevatron jet data are considered to lie within PDF uncertainties
And the largest uncertainty comes from the uncertainty on the high x gluon
Such PDF uncertainties the jet cross sections
compromise the LHC potential for discovery.
E.G. Dijet cross section potential sensitivity to
compactification scale of extra dimensions (Mc)
reduced from ~6 TeV to 2 TeV. (Ferrag et al)
Mc = 2 TeV,
no PDF error
SM
2XD
4XD
6XD
Mc = 2 TeV,
with PDF error
And it could get much better…
HERA now in second stage of
operation (HERA-II)
substantial increase in luminosity
possibilities for new measurements
Gluon fractional error
HERA-II projection shows significant
improvement to high-x PDF uncertainties
 relevant for high-scale physics
at the LHC
 where we expect new physics !!
x
Inputting data to a PDF fit needs a prediction for the cross-section which can be
easily obtained analytically –true for DIS inclusive cross-section. But many NLO
cross-sections can only be computed by MC and can take 1-2 CPU days to
compute. This cannot be done for every iteration of a PDF fit.
Recently grid techniques have been developed to include DIS jet cross-sections in
PDF fits (ZEUS-JETs fit)
This technique has been extended to LHC high-ET jet cross-sections
Use data at lower PT and higher η-where new physics is not expected
Dan Clements, Glasgow
Claire Gwenlan, Oxford
T. Carli
Effect Of Increased Statistics on PDF Fits
Gluon Fractional Error
Gluon Fractional Error
Increase 10×statistics
•Increasing the statistics from 1fb-1 to 10fb-1 has little effect on improving
the constraining of PDFs at ATLAS.
Dan Clements- DIS2006 –Structure Functions and Low x WG
Such PDF uncertainties on the jet cross sections
compromise the potential for discovery.
E.G. Dijet cross section potential sensitivity to
compactification scale of extra dimensions (Mc)
reduced from ~6 TeV to 2 TeV. (Ferrag et al)
Mc = 6 TeV,
no PDF error
The reduced uncertainties can then be used in background
calculations for new physics signals
Summary
At the LHC high precision (SM and BSM) cross section
predictions require precision Parton Distribution
Functions (PDFs)
PDF uncertainties affect discovery physics
Higgs cross-sections
high ET jets..contact interactions/extra dimensions
Investigate ‘standard candle’ processes are not SO
insensitive to PDF uncertainties
We can make measurements at ATLAS which will
improve the PDF uncertainty
LHC is a low-x machine (at least
for the early years of running)
Low-x information comes from
evolving the HERA data
Is NLO (or even NNLO) DGLAP good
enough?
The QCD formalism may need
extending at small-x
BFKL ln(1/x) resummation
High density non-linear effects etc.
(Devenish and Cooper-Sarkar, ‘Deep
Inelastic Scattering’, OUP 2004,
Section 6.6.6 and Chapter 9 for
details!)
Thorne will talk about this
MRST have produced a set of PDFs derived from a fit without low-x data –ie do
not use the DGLAP formalism at low-x- called MRST03 ‘conservative partons’.
These give VERY different predictions for W/Z production to those of the
‘standard’ PDFs.
Z
W+
WMRST02
Z
W+
WMRST03
Differences persist in the decay lepton spectra and even in their ratio and
asymmetry distributions
Reconstructed Electron Pseudo-Rapidity Distributions (ATLAS fast simulation)
200k events of W+- -> e+- generated with HERWIG 6.505 + NLO K factors
Reconstructed e-
Reconstructed e+
6 hours
running
MRST02
MRST02
MRST03
MRST03
h
Reconstructed e+- e- Asymmetry
h
Reconstructed e- / e+ Ratio
MRST02
MRST03
MRST02
MRST03
h
Interesting recent calculation of how lack of pt ordering at low-x may affect the
pt spectra for W and Z production at the LHC
(See hep-ph/0508215)
•
The values of cross section of the process
moves in the range 0 – 10% of the cross section obtained with CTEQ6ll
depending on the cuts and PDFs used
• The shape of distributions of kinematic quantities of Z boson and its
secondaries
seems to be very similar at the current(very preliminary) level of investigation.
This has to be confirmed/disconfirmed by more
quantitative analysis.
• There are differences between the shapes of distributions of
kinematic quantities of Z boson and its secondaries obtained
with Herwig/Jimmy and Pythia.
Physics Motivations for Z+ b-jet
•
Measurement of the b-quark PDF
– Process sensitive to b content of
the proton
(bb->Z @ LHC is ~5% of entire Z production -> Knowing σZ to
about 1% requires a b-pdf precision of the order of 20%
• Differences in total Z+b cross-section from current PDFs are of
the order of 5%
Pt b (MeV/c)
Conclusions II
•
•
Z+b measurement in ATLAS will be possible with high statistics and
good purity of the selected samples with two independent tagging
methods
We will have data samples to control systematic errors related to btagging at the few-% level over the whole jet Pt distribution
– b-tagging efficiency
– Mistagging: from W+jet
The measurement of Z+b should be more interesting at
LHC than at Tevatron:
• Signal cross-section larger (x80), and more
luminosity
• Relative background contribution smaller (x5)
Now study PDF effects
< pT(W) >
Same pattern
dMW(fit)
~no correlation
RMS(yW)
Set#
Summary
•
Raw dMW from pdf uncertainties as of today, when using pT(e), is ≥50 MeV
•
However, measuring pT(Z) with 10 fb-1, gives

dpT(W) ~ 3 MeV

dMW (fit) ~ 1 MeV (slope)  2.5 MeV (residuals, from y(W) distortions)
~ 2.7 MeV
This is obtained using pT(e), and should be true a fortiori when using
MT(W), which is less sensitive to pT(W)
•
Are pdf’s trustworthy to this level (i.e should we believe the correlation so
blindly?)
•
Next time :
– check if the correlation is preserved to this level with ResBos
– uncertainty from missing higher orders (vary Qren, Qfac in MCatNLO)
extras
And how do PDF uncertainties affect the Higgs discovery potential?
q
g
W/Z
t
H
W/Z
g
S Ferrag
q
W/Z
H
Standard Model side: Theoretical Uncertainties
• Generator level MC@NLO:
 computed by 100 GeV bin
200 GeV < invMass< 2500 GeV
• Sources of uncertainties:
-Factorisation and Renormalisation scales
1/p * m t < m < p* m t
-PDFs: CTEQ6
Energy scale
variation
40 CTEQ6
pdfs
S. Ferrag
Invariant mass(GeV)
• Fully simulation level:
Sample Zee M>150: 5114
So for the time being I have mocked up some lepton asymmetry data to follow each of
the predictions of CTEQ6.1, MRST02 and ZEUS-S with 4% errors and no scatter (!) .
In the plots below each of these pseudodata sets are compared to the predictions of
ZEUS-S
Cteq6.1 pseudodata
ZEUS-S prediction
MRST02 pseudodata
ZEUS-S prediction
ZEUS-S pseudodata
ZEUS-S prediction
It is clear that the MRST pseudodata do not agree with the ZEUS PDF prediction
even within PDF errors
What if we input these data to the ZEUS-S fit?
But it is possible that dbar and ubar could be more different for other PDFs
MRST
CTEQ
Alekhin
There are many difference between these PDF sets so I have made two toy PDFs (based on ZEUS-S) in which
the only difference is dbar-ubar as x → 0. Standard dbar-ubar = 0.24 x0.5 (1-x)9 at Q20 ~ 7 GeV2
and
Extreme dbar-ubar = 0.005x-0.16(1-x)13 (1+100x) at Q20 ~ 7 GeV2
ZEUS standard
ZEUS extreme
ALL with E866 dbar-ubar data
superimposed
W lepton
asymmetry from
ZEUS standard
Dbar-ubar
Clearly even this more extreme difference in
dbar-ubar has had no visible impact on the
lepton asymmetry
W lepton
asymmetry from
ZEUS extreme
The basic reason is that dbar and ubar are
themselves quite large ~ O(1) at x=0.006 and
Q2=MW2- since they have evolved from small
values at low Q2 BUT
Dbar-ubar
The difference dbar-ubar has become relatively
negligible - O(10-2) because it does NOT
evolve – we could only see it if we could
measure at the sub percent level of accuracydbar
dbar-ubar
.
A large difference in dbar-ubar at
Q2=MW2 would involve putting it in
as similarly large at the starting scale
Q2~ 7 GeV2 –incredible fine tuning
For ZEUS- extreme
How to constrain PDFs at LHC
We can improve our knowledge on PDF’s at LHC measuring
the vector boson production: photons, W’s, and Z’s
Direct g production:
(LO contributions)
Compton:
(~90%)
Annihilation:
(~10%)

u
d

W
W production:
(main contributions) du  W 
Z production: uu  Z
(main contributions)
dd  Z
At the EW scale we will have dominantly sea and gluon parton interactions at low-x
And at Q2~M2W/z the sea is driven by the gluon which is far less precisely determined
for all x values
How to constrain gluon-PDFs at LHC
direct g production (Ivan Hollins, Birmigham Univ.)
 Sensitive to PDF differences:
 CTQE6L-MRST01E ~ +16-18% disagreement
on Jet and g PT distributions
Typical Jet + g event
Jet and photon are back to back
 At this stage the aim is to establish the degree to which
signal can be seen (photon identification, fake photon rejection etc.): g selection efficiency >91%
 Investigate methods for reducing background
Prompt photon cross-sections may also be amenable to this treatment –compare
photon pt and η distributions for Cteq61 up and down eigenvector 15 -emphasizing
the uncertainties in the high-x gluon (PT > 330 GeV)
Ivan Hollins Birmingham
•
2) Differences I saw between pdf
sets
Plots are for photon distributions only
– ~700k events in each ~ 100fb-1 at 330 GeV
– Plots look only at the shape, no comparison made to absolute numbers
PT
g - distributions for
MRST2004 and Cteq61.
PT > 330 GeV
h
At ~350 GeV, h = 0, xT~0.05
Is this caused by
1)
High x uncertainly in the quark
2)
Mid x uncertainty in the gluon
3)
A v large uncertainly in the
high x gluon?
4)
A poor LO cal?