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

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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 PDF s, PDF luminosities and PDF uncertainties benchmark cross sections and pdf correlations 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 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 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. IR-safe jet algorithms 8. Combination of NLO with parton showers leave to tools talk

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 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 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 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

8 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 (q T 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@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 toplevel 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 gg gq qq

13 PDF uncertainties at the LHC gg Note that for much of the SM/discovery range, the pdf luminosity uncertainty is small qq Higgs tt 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 W/Z 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 Δχ 2 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

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 Δχ 2 tolerances. This is not the cross section uncertainty. That also depends on σ ij, and in particular on its α s 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 α s as does NNPDF MSTW produces the α s from the fit; as the data changes the value of α s (m Z ) can change, and it does, within a small band The acceptable range of variation of α s is determined by the data

17 Since the prescription for dealing with the varied α s values is a bit complicated, they give examples Error prescription

18 Higgs production For Higgs at the LHC, note the anti-correlation between the value of α s and the gluon distribution (in the kinematic region relevant for the production of a 120 GeV Higgs). Tends to reduce the extra α s variation uncertainty at higher orders. Note also that the uncertainty range for values of α s away from the center is diminished.

19 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

20 They use the Harlander- Kilgore code, which is outdated.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

21 Philosophy It s fair to attribute the impact of reasonable variations in α s 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 α s 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 α s variations along with the scale uncertainty Two arguments/counterarguments a change in α s 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 α s dependence

22 PDF correlations Consider a cross section X(a), a function of the Hessian eigenvectors i th 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 If two cross sections are very correlated, then cosφ~1 uncorrelated, then cosφ~0 anti-correlated, then cosφ~-1 The ellipse itself is given by

23 Correlations with Z, tt Define a correlation cosine between two quantities Z tt If two cross sections are very correlated, then cosφ~1 uncorrelated, then cosφ~0 anti-correlated, then cosφ~-1

24 Correlations with Z, tt Define a correlation cosine between two quantities If two cross sections are very correlated, then cosφ~1 uncorrelated, then cosφ~0 anti-correlated, then cosφ~-1 tt Z 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(σ W +/σ Z )~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(σ H /σ Z )~8%

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 p T distributions

29 Higher order corrections

30 Cross section tables

31 ROOT ntuples 6.6 GB total for real+virtual

32 ROOT ntuples CTEQ6.6 CTEQ error pdf s

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 Other benchmarks besides W/Z production? 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.

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 (m top =172 GeV) NLO 14 TeV CTEQ6.6: 829 pb CTEQ6M: 852 pb MSTW2008: 902 pb CT09: 839 pb CT09 (but with MSTW α s ): 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->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 Simplistic rule C i1 + C i2 C f,max Casimir for biggest color representation final state can be in L. Dixon Casimir color factors for initial state

43 W + 3 jets Consider a scale of m W 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 m Higgs for Higgs + jets.) Is the K-factor (at m W ) at the LHC surprising?

44 Is the K-factor (at m W ) at the LHC surprising? The K-factors for W + jets (p T >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 m W ; 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 m W ) at the LHC surprising? The K-factors for W + jets (p T >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 m W ; 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,q 2 range along with varying mixture of gg,gq,and qq subprocesses PDF uncertainties are significant at high p T Over limited range of p T 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 H T 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 µ<p T, positive for µ>p T Third term is negative for factorization scale M < p T 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 p T, 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 µ<p T, positive for µ>p T Third term is negative for factorization scale M < p T 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 p T, and are positive for larger scales NLO parabola moves out towards higher scales for forward region Scale of E T /2 results in a K-factor of ~1 for low E T, <<1 for high E T for forward rapidities at Tevatron Related to why the K-factor for W + 3 jets is so small and why H T 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?

51 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

52 The LHC will be a very jetty place Total cross sections for tt and Higgs production saturated by tt (Higgs) + jet production for jet p T values of order 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-ofview of Sudakov form factors

53 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.

54 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, k T, anti-k T (my suggestions)

55 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 p T 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 R cone 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 p T increases (and α s decreases) at NLO the k T algorithm corresponds to Region I (for D=R); thus at parton level, the cone algorithm is always larger than the k T algorithm d z=p T2 /p T1 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.

56 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

57 Some recommendations from jet paper 4-vector kinematics (p T,y and not E T,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

58 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

59 Extras Update to NLO pdf s recent Tevatron data arxiv: eigenvector tools arxiv: 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

60 Some references CHS arxiv: Dec 14, 2007