Les Houches SM and NLO multi-leg group: experimental introduction and charge

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Les Houches SM and NLO multi-leg group
experimental introduction and charge

• J. Huston, T. Binoth, G. Dissertori, R. Pittau

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Understanding cross sections at the LHC
LO, NLO and NNLO calculations K-factors
benchmark cross sections and pdf correlations
PDFs, PDF luminosities and PDF uncertainties
underlying event and minimum bias events
Sudakov form factors
jet algorithms and jet reconstruction
Well be dealing with all of these topics in this
session, in the NLM group, in the Tools/MC group
and in overlap.
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Understanding cross sections at the LHC

• Were all looking for BSM physics at the LHC
• Before we publish BSM discoveries from the early
  running of the LHC, we want to make sure that we
  measure/understand SM cross sections
• detector and reconstruction algorithms operating
  properly
• SM physics understood properly
• especially the effects of higher order
  corrections
• SM backgrounds to BSM physics correctly taken
  into account

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Cross sections at the LHC

• Experience at the Tevatron is very useful, but
  scattering at the LHC is not necessarily just
  rescaled scattering at the Tevatron
• Small typical momentum fractions x in many key
  searches
• dominance of gluon and sea quark scattering
• large phase space for gluon emission and thus for
  production of extra jets
• intensive QCD backgrounds
• or to summarize,lots of Standard Model to wade
  through to find the BSM pony

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Goals for this session from wiki page

• Collecting results of completed higher order
  calculations
• Higgs cross sections in and beyond the Standard
  Model
• Identifying/analysing observables of interest
• Identifying important missing processes in Les
  Houches wishlist?
• 6. IR-safe jet algorithms?
• Combination of NLO with parton showers
• leave to tools talk?

• Thomas talk
• 4. Identifying important missing processes in Les
  Houches wishlist
• 5. Standardization of NLO computations
• 7. New techniques for NLO computations and
  automation

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1. Collecting results of completed higher order
calculations

• The primary idea is to collect in a table the
  cross section predictions for relevant LHC
  processes where available. Tree-level results
  should be compared with higher order predictions
  (whatever is known) and K-factors defined for
  specific scale/pdf choices. The table should also
  contain information on scale and pdf
  uncertainties. The inclusive case may be compared
  with standard selection cuts. Producing such a
  table would, of course, include a detailed
  comparison of results originating from different
  groups.

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Some issues/questions

• Once we have the calculations, how do we
  (experimentalists) use them?
• Best is to have NLO partonic level calculation
  interfaced to parton shower/hadronization
• but that has been done only for relatively simple
  processes and is very (theorist) labor intensive
• still waiting for inclusive jets in MC_at_NLO, for
  example
• need more automation look forward to seeing
  progress at Les Houches

• Even with partonic level calculations, need
  public code and/or ability to write out ROOT
  ntuples of parton level events
• so that can generate once with loose cuts and
  distributions can be re-made without the need for
  the lengthy re-running of the predictions
• what is done for example with MCFM for CTEQ4LHC
• but 10s of Gbytes

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CTEQ4LHC/FROOT

• Collate/create cross section predictions for LHC
• processes such as W/Z/Higgs(both SM and
  BSM)/diboson/tT/single top/photons/jets
• at LO, NLO, NNLO (where available)
• new W/Z production to NNLO QCD and NLO EW
• pdf uncertainty, scale uncertainty, correlations
• impacts of resummation (qT and threshold)
• As prelude towards comparison with actual data
• Using programs such as
• MCFM
• ResBos
• Pythia/Herwig/Sherpa
• private codes with CTEQ
• First on webpage and later as a report

Primary goal have all theorists (including
you) write out parton level output into ROOT
ntuples Secondary goal make libraries of
prediction ntuples available

• FROOT a simple interface for writing Monte-Carlo
  events into a ROOT ntuple file
• Written by Pavel Nadolsky (nadolsky_at_physics.smu.ed
  u)
• CONTENTS
• froot.c -- the C file with FROOT functions
• taste_froot.f -- a sample Fortran program writing
  3 events into a ROOT ntuple
• taste_froot0.c -- an alternative top-level C
  wrapper (see the compilation notes below)
• Makefile

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MCFM 5.3 and 5.4 have FROOT built in
store 4-vectors for final state particles event
weights use analysis script to construct any
observables and their pdf uncertainties in
future will put scale uncertainties and pdf
correlation info as well
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Scale uncertainties

• Zoltan Nagy has some ideas for making the
  calculation of the factorization scale
  uncertainty somewhat easier, by simplifying the
  pdf convolutions
• Maybe we can come up with a Les Houches accord
  for its adoption

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Parton kinematics at the LHC

• To serve as a handy look-up table, its useful
  to define a parton-parton luminosity (mentioned
  earlier)
• Equation 3 can be used to estimate the
  production rate for a hard scattering at the LHC
  as the product of a differential parton
  luminosity and a scaled hard scatter matrix
  element

this is from the CHS review paper
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Cross section estimates
gq
gg
qQ
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PDF uncertainties at the LHC
Note that for much of the SM/discovery range,
the pdf luminosity uncertainty is small Need
similar level of precision in theory
calculations It will be a while, i.e. not in
the first fb-1, before the LHC data starts to
constrain pdfs
qQ
gg
W/Z
tT
Higgs
NB I the errors are determined using the Hessian
method for a Dc2 of 100 using only experimental
uncertainties,i.e. no theory uncertainties NB
II the pdf uncertainties for W/Z cross sections
are not the smallest
NBIII tT uncertainty is of the same order as W/Z
production
gq
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gg luminosity uncertainty
You can define the fractional uncertainty of
dL/ds-hat, and for a Higgs of the order of 150
GeV, that is of the order of /- 5, from CTEQ.
Typically, the CTEQ uncertainties are a factor of
2 or so above MSTW, because of the different
choice of Dc2 tolerances. This is not the
cross section uncertainty. That also depends on
sij, and in particular on its as dependence
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Comparisons of gluons
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New MSTW paper

• Here they discuss a prescription for adding in as
  uncertainties, along with the eigenvector
  uncertainties due to experimental data
• Here a difference in philosophy
• CTEQ uses the world average value of as
• as does NNPDF
• MSTW produces the as from the fit as the data
  changes the value of as(mZ) can change, and it
  does, within a small band
• The acceptable range of variation of as is
  determined by the data

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Error prescription

• Since the prescription for dealing with the
  varied as values is a bit complicated, they give
  examples

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Higgs production
For Higgs at the LHC, note the
anti-correlation between the value of as and the
gluon distribution (in the kinematic region
relevant for the production of a 120 GeV Higgs).
Tends to reduce the extra as variation
uncertainty at higher orders. Note also that
the uncertainty range for values of as away
from the center is diminished.
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Gluon uncertainty
The impact of adding in the as variation on
the gluon pdf is to increase the range of
uncertainty but look at the scale
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Higgs cross section
They use the Harlander- Kilgore code, which is
outdated. Can that affect the uncertainty
under discussion.
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Philosophy

• Its fair to attribute the impact of reasonable
  variations in as on the parton distributions as a
  contribution to the effective parton uncertainty
• But its not fair to link the sensitivity of the
  hard matrix element to variations in as as part
  of the pdf uncertainty it is certainly part of
  the total cross section uncertainty
• Also typically we look at the pdf uncertainty
  and the scale uncertainty in evaluating cross
  sections is there double-counting if we also
  include the as variations along with the scale
  uncertainty
• Two arguments/counterarguments
• a change in as is in part an effective change in
  scale, which we are already considering
• but, if the cross section were calculated to all
  orders, there would be no scale dependence, but
  there would still be an as dependence

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PDF correlations

• Consider a cross section X(a), a function of the
  Hessian eigenvectors
• ith component of gradient of X is
• Now take 2 cross sections X and Y
• or one or both can be pdfs
• Consider the projection of gradients of X and Y
  onto a circle of radius 1 in the plane of the
  gradients in the parton parameter space
• The circle maps onto an ellipse in the XY plane
• The angle f between the gradients of X and Y is
  given by
• The ellipse itself is given by

• If two cross sections are very
• correlated, then cosf1
• uncorrelated, then cosf0
• anti-correlated, then cosf-1

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Correlations with Z, tT
tT
Z
Define a correlation cosine between two quantities

• If two cross sections are very
• correlated, then cosf1
• uncorrelated, then cosf0
• anti-correlated, then cosf-1

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Correlations with Z, tT
Define a correlation cosine between two
quantities

• If two cross sections are very
• correlated, then cosf1
• uncorrelated, then cosf0
• anti-correlated, then cosf-1
• Note that correlation curves to Z
• and to tT are mirror images of
• each other
• By knowing the pdf correlations,
• can reduce the uncertainty for a
• given cross section in ratio to
• a benchmark cross section iff
• cos f gt 0e.g. D(sW/sZ)1
• If cos f lt 0, pdf uncertainty for
• one cross section normalized to
• a benchmark cross section is
• larger

tT
Z
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New CTEQ technique

• With Hessian method, diagonalize the Hessian
  matrix to determine orthonormal eigenvector
  directions 1 eigenvector for each free parameter
  in the fit
• CTEQ6.6 has 22 free parameters, so 22
  eigenvectors and 44 error pdfs
• CT09 NLO pdfs have 24 free parameters
• Each eigenvector/error pdf has components from
  each of the free parameters
• Sum over all error pdfs to determine the error
  for any observable
• But,we are free to make an additional orthogonal
  transformation that diagonalizes one additional
  quantity G

• In these new coordinates, variation in a given
  quantity is now given by one or a few
  eigenvectors, rather than by all 44 (or however
  many)
• G may be the W cross section, or the W rapidity
  distribution or a tT cross section, depending on
  how clever one wants to be
• In principle these principal error pdfs could be
  provided as well, for example in CTEQ4LHC ntuples
  

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2. Higgs cross sections in and beyond the
Standard Model

• This issue is too important to be just a sub-part
  of point 1. Note that in former workshops a
  separate Higgs working group did exist. Special
  attention will be given to higher order
  corrections of Higgs observables in BSM scenarios
  (coordinated with the BSM group).
• Clearly tied to tools/MC groups as well

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CTEQ4LHC Higgs webpage
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Higgs pT distributions
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Higher order corrections
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Cross section tables
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ROOT ntuples
6.6 GB total for realvirtual
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ROOT ntuples
CTEQ6.6 44 error pdfs
CTEQ6.6
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gg
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K-factors
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PDF uncertainties and correlations
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Jet multiplicities
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4. Identifying/analysing observables of interest

• Of special interest are observables which have an
  improved scale/pdf dependence, e.g. ratios of
  cross sections. Classical examples are W/Z and
  the dijet ratio (and Wjets/Zjets). New ideas
  and proposals are welcome. Another issue is to
  identify jet observables which have no strong
  dependence on the absolute jet energy, as this
  will not be measured very precisely during the
  early running. Recent examples are jet
  sub-structure, boosted tops, dijet delta-phi
  de-correlation... This topic has some overlap
  with the BSM searches and inter-group activity
  would be welcome.

Other benchmarks besides W/Z production?
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W/Z agreement

• Inclusion of heavy quark mass effects affects DIS
  data in x range appropriate for W/Z production at
  the LHC
• but MSTW2008 also has increased W/Z cross
  sections at the LHC
• now CTEQ6.6 and MSTW2008 in good agreement

CTEQ6.5(6)
MSTW08
Alekhin and Blumlein
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Some tT cross section comparisons (mtop172 GeV)

• NLO
• 14 TeV
• CTEQ6.6 829 pb
• CTEQ6M 852 pb
• MSTW2008 902 pb
• CT09 839 pb
• CT09 (but with MSTW as) 863 pb
• 10 TeV
• CTEQ6.6 375 pb
• CT09 382 pb
• MSTW2008 408 pb

• LO
• 14 TeV
• CTEQ6L1 617 pb
• CTEQ6L 533 pb
• CTQE6.6 569 pb
• CT09MC1 804 pb
• CT09MC2 780 pb
• 10 TeV
• CTEQ6L1 267 pb
• CTEQ6L 229 pb
• CTE09MC2 342 pb

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4. Identifying important missing processes

• The Les Houches wishlist from 2005/2007 is
  filling up slowly but progressively. Progress
  should be reported and a discussion should
  identify which key processes should be added to
  the list.This discussion includes experimental
  importance and theoretical feasibility. (and
  may also include relevant NNLO corrections.) This
  effort will result in an updated Les Houches
  list. Public code/ntuples will make the
  contributions to this wishlist the most
  useful/widely cited.
• See Thomas talk for more details.

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K-factor table from CHS paper
mod LO PDF
Note K-factor for W lt 1.0, since for this table
the comparison is to CTEQ6.1 and not to
CTEQ6.6, i.e. corrections to low x PDFs due to
treatment of heavy quarks in CTEQ6.6 built-in
to mod LO PDFs
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Go back to K-factor table

• Some rules-of-thumb
• NLO corrections are larger for processes in which
  there is a great deal of color annihilation
• gg-gtHiggs
• gg-gtgg
• K(gg-gttT) gt K(qQ -gt tT)
• NLO corrections decrease as more final-state legs
  are added
• K(gg-gtHiggs 2 jets) lt
  K(gg-gtHiggs 1 jet) lt
  K(gg-gtHiggs)
• unless can access new initial state gluon channel
  
• Can we generalize for uncalculated HO processes?
• What about effect of jet vetoes on K-factors?
  Signal processes compared to background

Casimir for biggest color representation final
state can be in
Simplistic rule
Ci1 Ci2 Cf,max
L. Dixon
Casimir color factors for initial state
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W 3 jets
Consider a scale of mW for W 1,2,3 jets.
We see the K-factors for W 1,2 jets in the
table below, and recently the NLO corrections
for W 3 jets have been calculated, allowing us
to estimate the K-factors for that process.
(Lets also use mHiggs for Higgs jets.)
Is the K-factor (at mW) at the LHC surprising?
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Is the K-factor (at mW) at the LHC surprising?
The K-factors for W jets (pTgt30 GeV/c) fall
near a straight line, as do the K-factors for the
Tevatron. By definition, the K-factors for Higgs
jets fall on a straight line. Nothing special
about mW just a typical choice. The only way to
know a cross section to NLO, say for W 4 jets
or Higgs 3 jets, is to calculate it, but in
lieu of the calculations, especially for
observables that we have deemed important at Les
Houches, can we make rules of thumb? Something
Nicholas Kauer and I are interested in. Anyone
else? Related to this is - understanding the
reduced scale dependences/pdf uncertainties for
the cross section ratios we have been
discussing -scale choices at LO for cross
sections uncalculated at NLO
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Is the K-factor (at mW) at the LHC surprising?
The K-factors for W jets (pTgt30 GeV/c) fall
near a straight line, as do the K-factors for the
Tevatron. By definition, the K-factors for Higgs
jets fall on a straight line. Nothing special
about mW just a typical choice. The only way to
know a cross section to NLO, say for W 4 jets
or Higgs 3 jets, is to calculate it, but in
lieu of the calculations, especially for
observables that we have deemed important at Les
Houches, can we make rules of thumb? Something
Nicholas Kauer and I are interested in. Anyone
else? Related to this is - understanding the
reduced scale dependences/pdf uncertainties for
the cross section ratios we have been
discussing -scale choices at LO for cross
sections uncalculated at NLO
Will it be smaller still for W 4 jets?
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Shape dependence of a K-factor

• Inclusive jet production probes very wide x,Q2
  range along with varying mixture of gg,gq,and qq
  subprocesses
• PDF uncertainties are significant at high pT
• Over limited range of pT and y, can approximate
  effect of NLO corrections by K-factor but not in
  general
• in particular note that for forward rapidities,
  K-factor ltlt1
• LO predictions will be large overestimates

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Darren Fordes talk
HT was the variable that gave a constant K-factor
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Aside Why K-factors lt 1 for inclusive jet
production?

• Write cross section indicating explicit
  scale-dependent terms
• First term (lowest order) in (3) leads to
  monotonically decreasing behavior as scale
  increases
• Second term is negative for mltpT, positive for
  mgtpT
• Third term is negative for factorization scale M
  lt pT
• Fourth term has same dependence as lowest order
  term
• Thus, lines one and four give contributions which
  decrease monotonically with increasing scale
  while lines two and three start out negative,
  reach zero when the scales are equal to pT, and
  are positive for larger scales
• At NLO, result is a roughly parabolic behavior

(1)
(2)
(3)
(4)
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Why K-factors lt 1?

• First term (lowest order) in (3) leads to
  monotonically decreasing behavior as scale
  increases
• Second term is negative for mltpT, positive for
  mgtpT
• Third term is negative for factorization scale M
  lt pT
• Fourth term has same dependence as lowest order
  term
• Thus, lines one and four give contributions which
  decrease monotonically with increasing scale
  while lines two and three start out negative,
  reach zero when the scales are equal to pT, and
  are positive for larger scales
• NLO parabola moves out towards higher scales for
  forward region
• Scale of ET/2 results in a K-factor of 1 for low
  ET, ltlt1 for high ET for forward rapidities at
  Tevatron
• Related to why the K-factor for W 3 jets is so
  small and why HT works well as a scale for W 3
  jets

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Multiple scale problems

• Consider tTbB
• Pozzorini Loopfest 2009
• K-factor at nominal scale large (1.7) but can be
  beaten down by jet veto
• Why so large? Why so sensitive to jet veto?
• What about tTH? What effect does jet veto have?

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Difficult calculations
I know that the multi-loop and multi-leg
calculations are very difficult but just
compare them to the complexity of the sentences
that Sarah Palin used in her run for the
vice-presidency.
loops
legs
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The LHC will be a very jetty place

• Total cross sections for tT and Higgs production
  saturated by tT (Higgs) jet production for jet
  pT values of order 10-20 GeV/c
• s W3 jets gt s W2 jets
• indication that can expect interesting events at
  LHC to be very jetty (especially from gg initial
  states)
• also can be understood from point-of-view of
  Sudakov form factors

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6. IR-safe jet algorithms

• Detailed understanding of jet algorithms will
  play an important role in the LHC era. Much
  progress has been made in the last several years
  concerning IR-safe jet algorithms. Studies and
  comparisons of different jet algorithms in the
  NLO context are highly welcome. Of particular
  interest is how the observables map from the
  parton level inherent in the pQCD approach to the
  particle/detector level.

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Jet algorithms

• Most of the interesting physics signatures at the
  LHC involve jets in the final state
• For some events, the jet structure is very clear
  and theres little ambiguity about the assignment
  of towers/particles to the jet
• But for other events, there is ambiguity and the
  jet algorithm must make decisions that impact
  precision measurements
• There is the tendency to treat jet algorithms as
  one would electron or photon algorithms
• Theres a much more dynamic structure in jet
  formation that is affected by the decisions made
  by the jet algorithms and which we can tap in
• Analyses should be performed with multiple jet
  algorithms, if possible

CDF Run II events
SISCone, kT, anti-kT (my suggestions)
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Jet algorithms at NLO

• Remember at LO, 1 parton 1 jet
• At NLO, there can be two (or more) partons in a
  jet and life becomes more interesting
• Lets set the pT of the second parton z that of
  the first parton and let them be separated by a
  distance d (DR)
• Then in regions I and II (on the left), the two
  partons will be within Rcone of the jet centroid
  and so will be contained in the same jet
• 10 of the jet cross section is in Region II
  this will decrease as the jet pT increases (and
  as decreases)
• at NLO the kT algorithm corresponds to Region I
  (for DR) thus at parton level, the cone
  algorithm is always larger than the kT algorithm

d
zpT2/pT1
Are there subtleties being introduced by the more
complex final states being calculated at NLO? in
data (and Monte Carlo), jet reconstruction does
introduce more subtleties.
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ATLAS jet reconstruction

• Using calibrated topoclusters, ATLAS has a chance
  to use jets in a dynamic manner not possible in
  any previous hadron-hadron calorimeter, i.e. to
  examine the impact of multiple jet
  algorithms/parameters/jet substructure on every
  data set

similar to running at hadron level in Monte
Carlos
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Some recommendations from jet paper

• 4-vector kinematics (pT,y and not ET,h) should be
  used to specify jets
• Where possible, analyses should be performed with
  multiple jet algorithms
• For cone algorithms, split/merge of 0.75
  preferred to 0.50

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Summary

• Physics will come flying hot and heavy when LHC
  turns on in 2009
• Important to establish both the SM benchmarks and
  the tools we will need to properly understand
  this flood of data
• Having (only) 200 pb-1 of data at 10 TeV may be
  the best thing for usunderstanding before
  discovery
• but perhaps not the most exciting

• Plans for Les Houches
• collecting results of completed higher order
  calculations
• tables, plots and ntuples a la CTEQ4LHC
• common format for storing parton level
  information in the ntuples
• scale variations stored
• special interest in higher order corrections of
  Higgs observables
• missing processes for wishlist
• standardization of NLO computations
• minimal agreement on color and helicity
  management and on passing IR subtraction terms
  could lead to transportable modules for virtual
  corrections
• new techniques for NLO computations
• IR safe jet algorithms

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Extras

• All of our work was made possible by the insight
  and inspiration of our late colleague Wu Ki Tung

• Update to NLO pdfs
• recent Tevatron data
• arXiv0904.2424
• eigenvector tools
• arXiv0904.2425
• In the near future, CTEQ
• will also have
• modified LO pdfs
• several types
• combined (x and qt) pdf fits
• useful for precision
• measurements such
• as W mass
• NNLO pdfs
• will then make the
• relevant Higgs ntuples

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Some references
CHS
arXiv07122447 Dec 14, 2007