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Misure di Funzioni di Struttura ad LHC

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Title: Misure di Funzioni di Struttura ad LHC


1
Misure di Funzioni di Struttura ad LHC
  • by
  • Alessandro Tricoli
  • Rutherford-Appleton Laboratory and
  • University of Oxford

Workshop sui Monte Carlo, la Fisica e le
Simulazioni ad LHC Frascati, 23 Maggio 2006
2
Overview
  • Introduction
  • What are Parton Distribution Functions (PDFs)?
  • How they determined
  • How the PDF Uncertainties are estimated
  • Why the accurate knowledge of PDFs is vital for
    the LHC
  • Impact of PDF Uncertainty on the discovery of
    New Physics signals
  • Higgs, Extra Dimensions etc.
  • Impact of PDF Uncertainty on SM measurements
    sensitive to New Physics
  • Inclusive Jet cross-section, Drell-Yan
    cross-section
  • How to constrain PDF at LHC, some examples
  • Inclusive jet cross section
  • W and Z rapidity distributions
  • Conclusions


3
What are PDF distributions?
  • PDFs are parameterizations of the partonic
    content of the proton
  • i uv, dv, g and sea
  • x pparton / Ebeam parton momentum fraction
  • Q2 momentum transfer
  • How are PDFs determined from global Fits?
  • QCD predicts the scale dependence of fi(x,Q2)
    through the DGLAP
  • evolution equations, BUT does not accurately
    predict the x-dependence
  • which has non-perturbative origin.
  • x-dependence is parameterised at a fixed scale
    Q02 1-7 GeV2
  • Valence Quarks f xl (1-x)h P(x)
  • Sea/Gluon f x-l (1-x)h P(x)
  • Different people use different parameterisations
    with different no. of
  • free parameters
  • fi(x,Q2) is evolved from Q02 to any other Q2 by
    numerically solving the
  • conventional DGLAP equations to various orders
    (LO,NLO, NNLO)
  • The free parameters are determined by fit to
    data from exp. observables
  • DIS processes (fixed target and HERA), DY
    lepton pair production
  • High Et jets (CDF, D0), W rapidity asymmetry
    (CDF)

fi(x,Q2)
4
PDF uncertainties
  • Theoretical Uncertainties
  • Theoretical Formalism perturbative
    calculations,
  • i.e
    DGLAP approx., higher order truncation, etc.
  • Model Assumptions non-perturbative
    parameterisations (x-depedence)
  • i.e.
    assumptions to limit the no. of free parameters
  • Experimental Uncertainties
  • Statistical and Systematic Uncertainties on
    experimental data inputs
  • Correlated Systematic Uncertainties on data
    points

The theoretical uncertainties are estimated
varying the theoretical assumptions, But only
recently the correlated syst. on data points are
properly considered PDF sets after year 2000
provide UNCERTAINTIES fi(x,Q2) d
fi(x,Q2) use a modified c2 -gt c2 DT2 to
consider non-gaussian syst. errors and their

correlations. T tolerance
  • Offset Method the correlated syst. errors
    affect only the determination of the PDF
  • uncertainty, NOT
    the best fit (centre value) e.g. ZEUS-S DT249
  • Hessian method the collective effect of the
    correlated syst. errors can also modify
  • the values of
    the best fit e.g. CTEQ6 DT2100, MRST01 DT250

5
Why PDFs are vital at LHC ?
  • At Hadron Colliders every Cross-Section
    calculation is a convolution of the cross-section
    at parton level and PDFs
  • PDFs are vital for reliable predictions
  • for new physics signal (Higgs, Super- Symmetry,
    Extra Dimensions etc.)
  • and background cross-section
  • at LHC.

6
A lesson from Tevatron on the importance of PDFs
PDF Uncertainties must be properly taken into
account or SM physics features could be
misinterpreted as new physics signal
Tevatron Jet data were originally taken as
evidence of New Physics Since Proton Structure
Uncertainty was not properly considered
(Data-Theory)/Theory
CDF Run I
7
LHC Kinematic regime
Kinematic regime for LHC much broader than
currently explored
Test of QCD
  • Test DGLAP evolution at small x
  • Is NLO DGLAP evolution sufficient
  • at so small x ?
  • Are higher orders
  • important?
  • Improve information of high x gluon distribution

At the EW scale cross section predictions for LHC
are dominated by low-x gluon uncertainty (i.e.
W and Z masses) gt see later slides At TeV scale
New Physics cross section predictions are
dominated by high-x gluon uncertainty (not
sufficiently well constrained by PDF fits) gt see
later slides
8
Impact of PDF uncertainty on New Physics Higgs
_
H
Djouadi Ferrag, Phys. Lett. B 586 345352
(2004)
9
Impact of PDF uncertainty on New Physics Extra
Dimensions
Ferrag, hep-ph/0407303 (2004)
An E.D. Model di-jets cross section in the E.D.
regime is a continuity of the Standard Model one
with new as running
(mb)
Mc 8 TeV
Mc 2 TeV
SM
2XD
4XD
6XD
Pt(GeV)
Pt(GeV)
10
Impact of PDF uncertainty on SM Drell-Yan cross
section
Sensitive to New Physics
PDF Relative Uncertainty
MC_at_NLO
40 CTEQ6 PDFs
Mll GeV
High mass dileptons ? Uncertainties at high-x
important (up to 10)
11
Impact of PDF uncertainty on SM Inclusive Jet
cross-section
A SM measurement sensitive to New Physics
compositeness, Black Holes etc.
D. Clements, C. Butter, A. Moraes
  • Experimental and theoretical errors can distort
    the measurements and predictions
  • creating false signals of new physics
  • PDF Uncertainty (gluon),
  • Renormalisation and Factorisation scale
    uncertainty,
  • Experimental Jet Energy scale uncertainty.

12
Impact of PDF uncertainty on SM Inclusive Jet
cross-section
  • Can we constrain PDF with jets at LHC as done by
    Tevatron?
  • The large PDF uncertainty indicates that we might
    be able to constrain
  • the high-x gluon with high ET jets up to 1
    TeV even with 1 fb-1 luminosity.

13
How to constrain PDFs at low-x at LHC?
We can improve our knowledge of PDFs at LHC
measuring the vector boson production Ws, Zs
(and photons?)
At the EW scale cross sections are dominated by
sea and/or gluon interactions at low-x.
Furthermore, at Q2M2W/Z the sea is driven by
the gluon (via gluon splitting) which is far less
precisely determined for all x values.
14

How to constrain low-x PDFs at LHC single Z and
W Productions
15
W -gt e n rapidity distributions (1)
Experimentally we detect e- from W decays W-
-gt e-
A. Tricoli hep-ex/0511020, A. Tricoli, A.
Cooper-Sarkar, C. Gwenlan,
CERN-2005-014, hep-ex/0509002
HERWIG MC Simulations with NLO Corrections
At y0 the total PDF uncertainty is 5.2 from
ZEUS-S 3.6 from MRST01E 8.7 from
CTEQ6.1M ZEUS-S to MRST01E central value
difference 5 ZEUS-S to CTEQ6.1 central value
difference 3.5
16
W -gt e n rapidity distributions (2)
Effect of including the ATLAS W Rapidity
pseudo-data in global PDF Fits how much can
we reduce the PDF errors when LHC is up and
running?
Simulate real experimental conditions Generate
1M data sample with CTEQ6.1 PDF through
ATLFAST detector simulation and then include this
pseudo-data (with imposed 4 error) in the
global ZEUS PDF fit (with Det.-gtGen. level
correction). Central value of ZEUS-PDF prediction
shifts and uncertainty is reduced

h
In few day stat. of LHC at low Luminosity
NB in ZEUS-PDF fit the e Normalisation is left
free gt no assumption on Luminosity measurement
17
W Charge Asymmetry measurement (1)
Experimentally we measure e- charge asymmetry
from W decays W- -gt e-
e - e- asymmetry
HERWIG MC Simulations with NLO Corrections
  • In the Asymmetry experimental uncertainties and
    the gluon/sea PDF Uncertainty
  • mostly cancel out 5 PDF error within each
    PDF set
  • But MRST02 predicts Asym. 15 lower than the
    other PDF sets, WHY?

18
W Charge Asymmetry measurement (2)
A. Cooper-Sarkar
  • At LO the Asymmetry is dominated by uv dv
    parameter
  • uv dv parameter is not well constrained by data
    at very low-x
  • current PDFs simply have prejudices as to the
    low-x valence distributions
  • coming from the input parameterisations.
  • The small PDF uncertainties at low x
  • do NOT actually reflect the real
    uncertainty.

at Q2MW2 and x0.006 (corresponging to y0 at
LHC) MRST uV dV is 25 lower than other PDF
sets which reflects on A(y) measurement.
For the first time with the LHC we will have
valence PDF discrimination measuring valence
distributions at x0.005 on proton targets
19
W -gt e n rapidity distributions to detect new
low-x physics scenarios
Comparison between a conventional PDF set,
CTEQ61, which INCLUDEs very low-x data (down to
x6 10-5 ) and a toy PDF set MRST03 which
EXCLUDES HERA low-x data (x gt 5 10 -3 )
e- rapidity
CTEQ6.1 MRST2003
e - e- asymmetry
CTEQ6.1 MRST2003
e rapidity
  • Shows what would be our predictions w/o low-x
    HERA data
  • warning against premature extrapolations of our
    knowledge to new kinematic regions
  • Shows the impact of low-x data on current LHC
    predictions
  • Since the validity of the DGLAP formalism is
    not certain at such low-x, the LHC
  • should be able to detect new low-x scenarios
    right in the central rapidity region

20
Can we compute the PDF Uncertainty with MC in a
fast way PDF Re-weighting
  • The computation of PDF uncertainties on MCs is
    time consuming
  • To estimate the full PDF uncertainty for MRST01,
    ZEUS-S, CTEQ61
  • we have to generate 92 event samples,
    since
  • 30 sub-sets (15 eigenvectors)
    provide the full MRST02 PDF uncertainty
  • 22 sub-sets (11 eigenvectors)
    provide the full ZEUS-S PDF uncertainty
  • 40 sub-sets (20 eigenvectors)
    provide the full CTEQ61 PDF uncertainty
  • TOO LONG generation time
  • The PDF re-weighting technique is useful tool to
    quickly evaluate the
  • full PDF uncertainties for many PDF sets,
    saving generation time
  • only 1 event sample is generated with one PDF
    set
  • each event is re-weighted off-line with a second
    PDF set,
  • applying an Event Weight calculated (for the
    moment) from the hard scatter
  • parameters x1, x2, Q2 only

21
Can we use PDF re-weighting to simulate other
PDFs? - OK for RAPIDITY distributions
Events generated with HERWIG MRST02 and
re-weighted with CTEQ61 are compared to Events
generated with HERWIG CTEQ61
W-
W
W-
W
Relative difference between Re-weighted and
Generated distributions
Weighted mean on whole y-range
  • Accuracy of 0.5 in rapidity and no evidence of
    a y-dependent bias.
  • For the PT distribution its more complex
  • it needs re-weighting of the Parton Shower
    (Sudakov Form factors)

22
Conclusions
  • Precision Parton Distribution Functions are
    crucial for new physics discoveries at LHC
  • PDF uncertainties can compromise the potential
    for discovery
  • At LHC we are not limited by statistic but by
    systematic uncertainties
  • To discriminate between conventional PDF sets we
    need to
  • reach high experimental accuracy ( few)
  • LHC experiments are currently working hard to
    understand better and improve
  • the detector performances to determine and
    reduce systematic errors.
  • The SM processes like Z, W productions, Jet
    productions (and hopefully Direct Photon) are
    good candidates to constrain PDFs at the LHC
  • LHC can significantly constrain PDFs, especially
    the gluon distribution
  • with unprecedented precision
  • The W charge asymmetry can constrain for the
    first time valence distributions at very low-x
  • New low-x physics scenarios can be easily
    accessible by the LHC with early data
  • From now to the LHC start up, 2007, our PDF
    knowledge might improve
  • HERA-II substantial increase in luminosity,
    possibilities for new measurements
  • Projection significant improvement to high-x PDF
    uncertainties (high-scale physics at the LHC)

23
EXTRAS
24
How to constrain PDFs at mid-low-x at LHC?
We can improve our knowledge of PDFs at LHC
measuring the vector boson production Ws, Zs
(and photons?)
At the EW scale cross sections are dominated by
sea and/or gluon interactions at low-x.
Furthermore, at Q2M2W/Z the sea is driven by
the gluon (via gluon splitting) which is far less
precisely determined for all x values.
25
Why do we measure the b-PDF?
How to constrain gluon-PDFs at LHC Z b-jet (1)
Also background to Higgs searches
Sensitive to b content of the proton
(J.Campbell et al. Phys.Rev.D67095002,2003)
(J.Campbell et al. Phys.Rev.D69074021,2004)
  • bb-gtZ _at_ LHC is 5 of entire Z production
  • Knowing sZ to about 1 requires
  • a b-PDF precision of the order of 20

Now we have only HERA measurements, far from
this precision
26
How to constrain gluon-PDFs at LHC Z b-jet (PDF
Uncertainty)
HERWIG with MRST03CNNLO, CTEQ5M1, Alehkin1000
S. Diglio, A. Tonazzo and M. Verducci (2005)
  • PDF Differences in total
  • Zb cross-section are
  • of the order of 5 to 10

ATLAS
Number of events
  • Event selection only Z?mm-
  • Two isolated muons with high PT
  • inclusive b-tagging of jet

27
How to constrain gluon-PDFs at LHC direct g
production
Typical Jet ? event Jet and photon are back to
back
In NLO cross-section calculations discrepancy
between different PDF set predictions up to 20
ATLAS
Kumar et al. Physics Review D 67
  • Good candidate to constrain PDFs on a wide pT
    range
  • smaller energy scale uncertainty than jets, no
    jet-finder bias
  • sensitivity to high-x comes with high-pt and
    high-h photons
  • Problems
  • Large background (especially at low PT)
  • Can the Theoretical-Experimental Discrepancy in
    PT distribution be well understood?

I. Hollins (2005)
28
Differences between PDF sets
  • different data sets in fit
  • different sub-selection of data
  • different treatment of exp. sys. errors
  • different choices of
  • tolerance to define ? ? fi (CTEQ ??2100,
    MRST ??250 Alekhin ??21)
  • parametric form Axa(1-x)b.. etc
  • theoretical assumptions about sea flavour
    symmetry
  • factorisation/renormalisation scheme/scale
  • Q02
  • aS
  • treatment of heavy flavours

29
PDF Re-weighting Implementation
  • I generate a MC event with one specific PDF set,
    say pdf set n.1
  • This event happens to have
  • One hard process scale (QMW)
  • Two primary partons with two specific
    flavours(flav1,flav2)
  • Momentum fractions x1, x2 of the two primary
    partons (calculated at the Hard Process, before
    the Parton Shower in the backward evolution is
    applied in the MC) according to the probability
    (i.e. xf) estimated by the PDF they are generated
    with (say pdf set n.1)
  • Offline (with LHAPDFv3) I evaluate the
    probability, i.e. xf, of picking up the same
    flavoured partons with the same momentum
    fractions x1,x2, according to a second PDF set,
    i.e. PDF set n.2, at the same energy scale, i.e.
    Q.
  • Then I perform the Ratio

30
PDF scenario at LHC start up (2007) might be
different
  • In most of the relevant x regions
  • accessible at LHC
  • HERA data are most important source of
  • information in PDF determinations
  • (low-x sea and gluon PDFs)
  • HERA now in second stage of operation (HERA-II)
  • ? substantial increase in luminosity
  • ? possibilities for new measurements
  • HERA-II projection shows significant improvement
    to high-x PDF uncertainties
  • relevant for high-scale physics at the LHC
  • ? where we expect new physics !!

- significant improvement to valence-quark
uncertainties over all-x - significant
improvement to sea and gluon uncertainties at
mid-to-high-x - little visible improvement to sea
and gluon uncertainties at low-x
C. Gwenlan, A. Cooper-Sarkar,C. Targett-Adams,
hep-ph/0509220 (2005)
31
Impact of PDF uncertainty on New Physics Extra
Dimensions (Theory)
Hierarchy problem
  • EW symmetry breaking scale 102 GeV
  • GUT scale 1016
    GeV
  • Planck scale 1019
    GeV

Alternative
1 fondamental scale few tens TeV and
13d time-space structure
Parameters number of extra-dimensions d
compactification scale Mc
Phenomenological aspects
  • Possibility to produce Gravitons at LHC low
    Planck scale
  • Kaluza Klein (KK)excitations d compactified
    extra dimensions
  • Violation of the expected (MS)SM evolution
    behavior of aem,w,s
  • (E. Dudas, R. Dienes, T. Ghergetta,
    hep/ph9803466 and hep/ph9807522)

MSSMXD
MGUT 30 TeV (42)D, R1/10 Tev-1
Exerimentally Evolution of as by measuring
di-jets cross section on a large energy range
32
How to constrain gluon-PDFs at LHC Z b-jet
(Measurement)
Signal
Background
  • Event selection only Z?mm-
  • Two isolated muons (Pt gt 20 GeV/c, opposite
    charge, invariant mass close to Mz)
  • inclusive b-tagging of jet (total Z b selection
    efficiency 15, purity 53 )

ATLAS
33
Impact of PDF uncertainty on SM Inclusive Jet
cross-section
D. Clements, C. Butter, A. Moraes
C. Gwenlan, A. Cooper-Sarkar, C. Targett-Adams,
hep-ph/0509220 (2005)
  • Can we constrain PDF with jets at LHC as done by
    Tevatron?
  • The large PDF uncertainty indicates that we
    might be able to constrain
  • the high-x gluon with high ET jets up to 1
    TeV even with 1 fb-1 luminosity.
  • PDF error is dominant at high pT , but low stat.
  • PDF error negligible at low pT w.r.t. other
    syst. uncertainty sources
  • Fact.Ren. Scale uncertainty 14 at 1 TeV
  • 1 (10) exp. energy scale uncertainty gt 6
    (70) incl. jet x-sec. error

34
Higgs production and decays at LHC
Higgs production mechanisms
Higgs decays
35
Parton Luminosity uncertainty
J. Stirling
PDF uncertainties encoded in parton-parton
luminosity functions
Note high x gluon should become better
determined from Run 2 Tevatron data
LHC (Alekhin 2002)
Tevatron (Alekhin 2002)
36
High ET jet cross section at LHC (James Stirling)
37
Impact of PDF uncertainty on SM Inclusive Jet
cross-section (Syst.)
Jet Energy scale uncertainty this systematic
error is stat. significant, particularly for low
pT jets
Factorisation and Renormalisation scale
uncertainty dominant theoretical uncertainty at
low pT being overtaken by pdf uncertainties at a
leading jet pT of 1TeV
38
Impact of PDF uncertainty on SM Inclusive Jet
cross-section (NLO/LO)
The ratio of the inclusive jet cross-section as
calculated for pdfs CTEQ6L1(LO) to CTEQ6m (NLO)
using PYTHIA
ckin(3) PT min of hard scatter
39
Impact of PDF uncertainty on SM D.-Y.
production.
uncertainty
uncertainty
5
5
-5
-5
CTEQ6.1E
x
x
Q2 104
x
x
High mass dileptons ? Uncertainties at high x
important
40
Direct g production
Photon PT spectrum
I. Hollins (2005)
Pythia v6.221
41
W Production at LHC
LHC
pp -gt W
W
p
p
Cabibbo Suppressed
Cabibbo Suppressed Contribution 1-3 at LHC
42
W -gt e n rapidity distributions
Signal vs Background
Small Background contamination 1 gt Very clean
measurement
43
A. Cooper-Sarkar
  • Data on the low-x valence distributions comes
    only from the CCFR/NuTeV data on Fe targets. The
    data extend down to x0.01, 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 x0.01
  • 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 (horses mouth- Thorne)
  • LHC W asymmetry can provide new information and
    constraints in the x region 0.0005 lt x lt0.05

44
Z b-jet Background and Systematic uncertainties
  • Efficiency of b-tagging
  • we can expect ?eb/eb 5
  • Background from mistag
  • Check mis-tagging on a sample where no b-quark
    jets should be present we use W jets.
  • Precision will be dominated by other sources of
    systematics
  • Luminosity measurement
  • Jet reconstruction and energy resolution
  • It is likely that the overall precision will be
    some-, comparable to uncertainty on theoretical
    prediction

45
It has been known that dbar ? ubar in the sea,
since the violation of the Gottfried sum-rule in
1992. More recently, E866 Drell-Yan data have
measured the shape of dbar-ubar. This difference
is usually fitted as a valence-like quantity
dbar-ubar?0 as x ? 0 e.g. dbar-ubar 0.24 x0.5
(1-x)9 at Q20 7 GeV2
James Stirling
46
The measured difference between dbar and ubar is
actually very small, and is negligible at the Q2
of interest at the LHC. But the question has been
raised what if dbar-ubar ? 0 as x ? 0 ? Could
this be significant for W production at LHC?
ubar
x (dbar-ubar)
dbar
E866
47
Try the parametrisation 0.005x-0.16(1-x)13
(1100x) at Q20 7 GeV2 inspired by the shape of
the gluon
x (dbar-ubar)
dbar
ubar
dbar and ubar difference still negligible at the
Q2 of interest at the LHC dbar-ubar DOES NOT
EVOLVE in Q2 the way that the singlet quantities
gluon and sea do, it doesnt even evolve in the
more modest way that a non-singlet valence
quantity does- it is the difference between two
quantities which evolve in the same way. To get
it to matter at LHC Q2 it would have to be
fine-tuned at the starting scale
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