Transcript QCD Working Group Goals…and welcome J. Huston Michigan

Les Houches SM and NLO multi-leg
group: experimental introduction and
charge
J. Huston, T. Binoth, G. Dissertori, R. Pittau
Understanding cross sections at the LHC
LO, NLO and NNLO calculations
K-factors
benchmark cross
sections and pdf
correlations
PDF’s, PDF luminosities
and PDF uncertainties
underlying event
and minimum
bias events
Sudakov form factors
jet algorithms and jet reconstruction
We’ll be dealing with all of these topics in this session,
in the NLM group, in the Tools/MC group and in overlap.
Understanding cross sections at the LHC
 We’re 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
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
Goals for this session: from wiki page
1. Collecting results of
completed higher order
calculations
2. Higgs cross sections in and
beyond the Standard Model
3. Identifying/analysing
observables of interest
4. Identifying important missing
processes in Les Houches
wishlist
6. IR-safe jet algorithms
8. 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
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 Kfactors 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.
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@NLO, for
example
need more automation;
look forward to seeing
 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 remade without the need for
the lengthy re-running of
the predictions
what is done for example
with MCFM for
CTEQ4LHC
 but 10’s of Gbytes
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
([email protected])
 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 toplevel C wrapper (see the compilation
notes below)
 Makefile
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
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
Parton kinematics at the LHC
 To serve as a handy “look-up”
table, it’s 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
Cross section estimates
gq
gg
qQ
PDF uncertainties at the LHC
gg
Higgs tT
Note that for much of the
SM/discovery range, the pdf
luminosity uncertainty is small
Need similar level of precision in
theory calculations
qQ
W/Z
It will be a while, i.e. not in the
first fb-1, before the LHC
data starts to constrain pdf’s
NBIII: tT uncertainty is of
the same order as W/Z
production
gq
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
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
Comparisons of gluons
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
Error prescription
 Since the prescription
for dealing with the
varied as values is a
bit complicated, they
give examples
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.
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
Higgs cross section
They use the
HarlanderKilgore code,
which is
outdated. Can
that affect the
uncertainty under
discussion.
Philosophy
 It’s fair to attribute the impact of reasonable variations in as on the
parton distributions as a contribution to the effective parton
uncertainty
 But it’s 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
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 pdf’s
 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 cosf~1
•…uncorrelated, then cosf~0
•…anti-correlated, then cosf~-1
Correlations with Z, tT
Z
Define a correlation cosine between two quantities
•If two cross sections are very
correlated, then cosf~1
•…uncorrelated, then cosf~0
•…anti-correlated, then cosf~-1
tT
Correlations with Z, tT
Define a
correlation
cosine between
two quantities
•If two cross sections are very
correlated, then cosf~1
•…uncorrelated, then cosf~0
•…anti-correlated, then cosf~-1
•Note that correlation curves to Z
and to tT are mirror images of
each other
tT
•By knowing the pdf correlations,
can reduce the uncertainty for a
given cross section in ratio to
a benchmark cross section iff
cos f > 0;e.g. D(sW +/sZ)~1%
Z
•If cos f < 0, pdf uncertainty for
one cross section normalized to
a benchmark cross section is
larger
•So, for gg->H(500 GeV); pdf
uncertainty is 4%; D(sH/sZ)~8%
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 pdf’s
CT09 NLO pdf’s have 24 free
parameters
 Each eigenvector/error pdf has
components from each of the free
parameters
 Sum over all error pdf’s 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 pdf’s could
be provided as well, for example in
CTEQ4LHC ntuples
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
CTEQ4LHC Higgs webpage
Higgs pT distributions
Higher order corrections
Cross section tables
ROOT ntuples
6.6 GB total for real+virtual
ROOT ntuples
CTEQ6.6
CTEQ6.6 + 44 error pdf’s
gg
K-factors
PDF uncertainties and correlations
Jet multiplicities
4. Identifying/analysing
observables of interest
 Of special interest are
Other benchmarks besides W/Z production?
observables which have an
improved scale/pdf dependence,
e.g. ratios of cross sections.
Classical examples are W/Z and
the dijet ratio (and W+jets/Z+jets).
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 substructure, boosted tops, dijet
delta-phi de-correlation... This
topic has some overlap with the
BSM searches and inter-group
activity would be welcome.
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
Alekhin and Blumlein
CTEQ6.5(6)
MSTW08
Some tT cross section comparisons
(mtop=172 GeV)
 NLO


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



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
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.
K-factor table from CHS paper
mod LO PDF
Note K-factor
for W < 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
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->Higgs
 gg->gg
 K(gg->tT) > K(qQ -> tT)
 NLO corrections decrease as
more final-state legs are added
 K(gg->Higgs + 2 jets)
< K(gg->Higgs + 1 jet)
< K(gg->Higgs)
 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
Casimir for biggest color
representation final state can
be in
Simplistic rule
Ci1 + Ci2 – Cf,max
L. Dixon
Casimir color factors for initial state
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. (Let’s also use mHiggs
for Higgs + jets.)
Is the K-factor (at mW) at the LHC surprising?
Is the K-factor (at mW) at the LHC surprising?
The K-factors for W + jets (pT>30 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
Is the K-factor (at mW) at the LHC surprising?
The K-factors for W + jets (pT>30 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?
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
<<1
 LO predictions will be
large overestimates
Darren Forde’s talk
HT was the variable that gave
a constant K-factor
Aside: Why K-factors < 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 m<pT,
positive for m>pT
 Third term is negative for factorization
scale M < 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)
Why K-factors < 1?
 First term (lowest order) in (3) leads
to monotonically decreasing behavior
as scale increases
 Second term is negative for m<pT,
positive for m>pT
 Third term is negative for factorization
scale M < 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, <<1 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
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?
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
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 W+3 jets > s W+2 jets
 indication that can expect interesting
events at LHC to be very jetty
(especially from gg initial states)
 also can be understood from point-ofview of Sudakov form factors
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.
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 there’s 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
 There’s 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)
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
 Let’s 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
D=R); thus at parton level,
the cone algorithm is always
larger than the kT algorithm
d
z=pT2/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.
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
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
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 us…understanding
before discovery
 …but perhaps not the most
exciting
 Plans for Les Houches
 collecting results of completed
higher order calculations






special interest in higher order
corrections of Higgs observables
missing processes for wishlist
standardization of NLO
computations



tables, plots and ntuples a la
CTEQ4LHC
common format for storing parton
level information in the ntuples
scale variations stored
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
Extras
•Update to NLO pdf’s
•recent Tevatron data
•arXiv:0904.2424
•eigenvector tools
•arXiv:0904.2425
•In the near future, CTEQ
will also have
•modified LO pdf’s
•several types
•combined (x and qt) pdf fits
•useful for precision
measurements such
as W mass
•NNLO pdf’s
•will then make the
relevant Higgs ntuples
 All of our work was made
possible by the insight and
inspiration of our late colleague
Wu Ki Tung
Some references
CHS
arXiv:07122447 Dec 14, 2007