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

PDF’s, PDF luminosities and PDF uncertainties

Sudakov form factors underlying event and minimum bias events

LO, NLO and NNLO calculations K-factors

jet algorithms and jet reconstruction

benchmark cross sections and pdf correlations

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 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.

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 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 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

  FROOT: a simple interface for writing Monte-Carlo events into a ROOT ntuple file

  Written by Pavel Nadolsky (nadolsky@physics.smu.edu)

  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

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

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

qQ

gg

PDF uncertainties at the LHC

gg

gq

qQ 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 pdf’s

NB I: the errors are determined using the Hessian method for a Δχ2 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

W/Z

NBIII: tT uncertainty is of the same order as W/Z production

tT Higgs

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 Δχ2 tolerances.

This is not the cross section uncertainty. That also depends on σij, and in particular on its αs 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 αs

▲  as does NNPDF ◆  MSTW produces the αs

from the fit; as the data changes the value of αs(mZ) can change, and it does, within a small band

◆  The acceptable range of variation of αs is determined by the data

Error prescription

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

Higgs production For Higgs at the LHC, note the anti-correlation between the value of αs and the gluon distribution (in the kinematic region relevant for the production of a 120 GeV Higgs). Tends to reduce the extra αs variation uncertainty at higher orders.

Note also that the uncertainty range for values of αs away from the center is diminished.

Gluon uncertainty

The impact of adding in the αs variation on the gluon pdf is to increase the range of uncertainty… but look at the scale

Higgs cross section

They use the Harlander- Kilgore code, which is outdated. Can that affect the uncertainty under discussion.

Philosophy   It’s fair to attribute the impact of reasonable variations in αs 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 αs 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 αs variations along with the scale uncertainty

  Two arguments/counterarguments ◆  a change in αs 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 αs 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 φ between the gradients of X and Y is given by

  The ellipse itself is given by

• If two cross sections are very correlated, then cosφ~1 • …uncorrelated, then cosφ~0 • …anti-correlated, then cosφ~-1

Correlations with Z, tT

• If two cross sections are very correlated, then cosφ~1 • …uncorrelated, then cosφ~0 • …anti-correlated, then cosφ~-1

Define a correlation cosine between two quantities Z tT

Correlations with Z, tT

• If two cross sections are very correlated, then cosφ~1 • …uncorrelated, then cosφ~0 • …anti-correlated, then cosφ~-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 φ > 0;e.g. Δ(σW+/σZ)~1%

• If cos φ < 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%; Δ(σH/σZ)~8%

Define a correlation cosine between two quantities

Z

tT

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 + 44 error pdf’s CTEQ6.6

gg

K-factors

PDF uncertainties and correlations

Jet multiplicities

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 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 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?

W/Z agreement

CTEQ6.5(6)

  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

MSTW08

Alekhin and Blumlein

Some tT cross section comparisons (mtop=172 GeV)

 NLO ◆  14 TeV ◆  CTEQ6.6: 829 pb ◆  CTEQ6M: 852 pb ◆  MSTW2008: 902 pb ◆  CT09: 839 pb ◆  CT09 (but with MSTW αs): 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

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

mod LO PDF

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->γγ ◆  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 compared to background

Ci1 + Ci2 – Cf,max

Simplistic rule

Casimir color factors for initial state

Casimir for biggest color representation final state can be in

L. Dixon

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 µ<pT, positive for µ>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 µ<pT, positive for µ>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

  σ W+3 jets > σ 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-of-view 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 (=ΔR)

  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 αs 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

z=pT2/pT1

d

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,η) 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 ▲  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

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

arXiv:07122447 Dec 14, 2007

CHS