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

1. Les Houches SM and NLO multi-leg group: experimental introduction and charge J. Huston, T. Binoth, G. Dissertori, R. Pittau

2. 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.

3. 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

4. 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

5. 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

6. 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.

7. 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 Some issues/questions

8. CTEQ4LHC/FROOT Primary goal: have all theorists (including you) write out parton level output into ROOT ntuples Secondary goal: make libraries of prediction ntuples available • 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

9. 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

10. 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

11. 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

12. Cross section estimates gq gg qQ

13. 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 pdf’s qQ gg W/Z Higgs tT NBIII: tT uncertainty is of the same order as W/Z production 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 gq

14. 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

15. Comparisons of gluons

16. 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

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

18. 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.

19. 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

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 Higgs cross section They use the Harlander- Kilgore code, which is outdated.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

21. 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

22. 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

23. Correlations with Z, tT 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

24. 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 • 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% • 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% tT Z

25. 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

26. 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

27. CTEQ4LHC Higgs webpage

28. Higgs pT distributions

29. Higher order corrections

30. Cross section tables

31. ROOT ntuples 6.6 GB total for real+virtual

32. ROOT ntuples CTEQ6.6 + 44 error pdf’s CTEQ6.6

33. gg

34. K-factors

35. PDF uncertainties and correlations

36. Jet multiplicities

37. 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?

38. 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

39. 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 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

40. 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.

41. 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

42. 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 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

43. 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?

44. 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

45. 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?

46. 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

47. Darren Forde’s talk HT was the variable that gave a constant K-factor

48. 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)

49. 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

50. 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?