Work Order: Theoretical Calculations Needed for the LHC

1. Work Order: Theoretical Calculations Needed for the LHC Requestor: J. Huston Delivery location: Michigan State University Requested delivery date: before LHC data Total (CHF):free

2. Some references • Also online at ROP http://stacks.iop.org/0034-4885/70/89 Les Houches Physics at TeV colliders 2005, Standard Model and Higgs Working Group: Summary report. C. Buttar et al. hep-ph/0604120 Standard Model benchmarks See www.pa.msu.edu/~huston/ Les_Houches_2005/Les_Houches_SM.html

3. Some background: what to expect at the LHC …according to a theorist

4. What to expect at the LHC • According to a current former Secretary of Defense • known knowns • known unknowns • unknown unknowns …according to a theorist

5. What to expect at the LHC • According to a former Secretary of Defense • known knowns • SM at the Tevatron • (most of) SM at the LHC • known unknowns • some aspects of SM at the LHC • unknown unknowns • ??? …according to a theorist

6. Discovering the SM 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 • SM backgrounds to BSM physics correctly taken into account • ATLAS/CMS will have a program to measure production of SM processes: inclusive jets, W/Z + jets, heavy flavor during first inverse femtobarn • so experimenters need/have a program now of Monte Carlo production and studies to make sure that we understand what issues are important • and we also need tool and algorithm and theoretical prediction developments (such as at NLO)

7. 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 BFKL?

8. Known known: Parton distribution functions • Calculation of production cross sections at the LHC relies upon knowledge of pdf’s in the relevant kinematic region • Pdf’s are determined by global analyses of data from DIS, DY and jet production • Two major groups that provide semi-regular updates to parton distributions when new data/theory becomes available • MRS->MRST98->MRST99 ->MRST2001->MRST2002 ->MRST2003->MRST2004 • CTEQ->CTEQ5->CTEQ6 ->CTEQ6.1->CTEQ6.5(->CTEQ7) • All of the above groups provide ways to estimate the error on the central pdf • methodology enables full characterization of parton parametrization space in neighborhood of global minimum • Hessian method • Lagrange Multiplier • both of above techniques used by CTEQ and MRST • Hessian method accessible to general user • NB: the error estimate only covers experimental sources of errors • theory uncertainties • higher twist/non-perturbative effects • choose Q2 and W cuts to avoid • higher order effects (NNLO) • heavy quark mass effects (not discussed)

9. Parton kinematics • To serve as a handy “look-up” table, it’s useful to define a parton-parton luminosity • this is from the review paper and the Les Houches 2005 writeup • 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

10. Cross section estimates for pT=0.1* sqrt(s-hat) gq gg qQ

11. PDF luminosities as a function of y 6 4 2 0

12. 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 NB: the errors are determined using the Hessian method for a Dc2 of 100 using only experimental uncertainties gq

13. Ratios:LHC to Tevatron pdf luminosities • Processes that depend on qQ initial states (e.g. chargino pair production) have small enchancements • Most backgrounds have gg or gq initial states and thus large enhancement factors (500 for W + 4 jets for example, which is primarily gq) at the LHC • W+4 jets is a background to tT production both at the Tevatron and at the LHC • tT production at the Tevatron is largely through a qQ initial states and so qQ->tT has an enhancement factor at the LHC of ~10 • Luckily tT has a gg initial state as well as qQ so total enhancement at the LHC is a factor of 100 • but increased W + jets background means that a higher jet cut is necessary at the LHC • known known: jet cuts have to be higher at LHC than at Tevatron gg qQ gq

14. The LHC Environment

15. 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-of-view of Sudakov form factors

16. Sudakov form factors • Sudakov form factor gives the probability for a gluon not to be emitted; basis of parton shower Monte Carlos • Consider tT production • In going from the Tevatron to the LHC, you are moving from primarily qQ initial states to gg initial states • …and to smaller values of parton x • so there’s more phase space for gluon emission • So significantly more extra jets associated with the tT final state

17. NLO corrections • NLO is the first order for which the normalization, and sometimes the shape, is believable • NLO is necessary for precision comparisons of data to theory • Sometimes backgrounds to new physics can be extrapolated from non-signal regions, but this is difficult to do for low cross section final states and/or final states where a clear separation of a signal and background region is difficult

18. NLO corrections Sometimes it is useful to define a K-factor (NLO/LO). Note the value of the K-factor depends critically on its definition. K-factors at LHC (mostly) similar to those at Tevatron. K-factors may differ from one because of new subprocesses/contributions at higher order and/or differences between LO and NLO pdf’s

19. Counterexample: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 • 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 • see extra slides for discussion as to why

20. Another example, from the Tevatron • Suppose you measure the high mtT region looking for new physics • Suppose that your measurement agrees well with Pythia • Have you missed something? • Yes, because NLO prediction at high mass is about half of LO prediction • partially pdf’s • partially matrix elements

21. What about tT at the LHC? • The cross section is dominated by the gg subprocess so the K-factor is approximately constant and > 1 • unlike the Tevatron

22. Now we come to the “maligned” experimenter’s NLO wishlist almost 6 years to the day and yet not a single calculation finished!Shame

23. NLO calculation priority list from Les Houches 2005: theory benchmarks G. Heinrich and J. Huston + * + + * *completed since list +people are working What about time lag in going from availability of matrix elements to having a parton level Monte Carlo available? See e.g. H + 2 jets. Other processes are going to be just as complex.

24. tTj • An important calculation at NLO that would have made the list, except we knew that Dittmaier, Uwer and Weinzierl were alread working on it • see Stefan’s talk on Wed • NLO corrections are small with scale choice near mt • Bonus feature: tTj asymmetry at Tevatron small at NLO bonus because tT and tTj asymmetries in opposite directions

25. From LHC theory initiative white paper Uli Baur Fermilab W&C Aug 18

26. Higgs production Perhaps no surprise that many of the calculations on the list relate to Higgs production and backgrounds thereof.

27. WWj • In addition to backgrounds to SUSY processes, WWj is also one of primary backgrounds to Higgs(->WW)+jet • where both W’s decay semi-leptonically • We’ve seen that the Higgs is often accompanied by a jet, plus we want to make use of all channels (H+0 jet, H+1 jet, and H+2 jets) in searching for a Higgs signal • ATLAS plan is to extrapolate from background-rich region • primarily Dfll>1.2 • + some other cuts • to signal-rich region • primarily Dfll <1.2 • + some other cuts • By far the largest systematic uncertainty in this analysis comes from the LO nature of the WWj background and the extrapolation into the signal region • Improvement of this uncertainty from 20% to 5% would significantly improve discovery potential

28. VBF production of Higgs is an important process that will allow measurements of Higgs couplings to vector bosons Larger cross section, though, from QCD production of Higgs plus two jets Large scale dependence at LO Little shape change in going from LO to NLO (K-factor of ~1.25, similar to Higgs+1 jet) but renormalization scale dependence still large different scales for as at top/bottom and middle vertices? Higgs + 2 jets production (Campbell, Ellis, Giele, Zanderighi) A cut of 40 GeV/c has been placed on each of the Jets. For lower pT jets, the renormalization scale dependence is even greater (and sHiggs+3 jets > sHiggs+2jets)

29. tTbB and tTjj CMS Physics TDR • tTH(->bB) is a tough business, but may be useful for discovery of a low mass Higgs • For one W decaying semi-leptonically and the other hadronically, the final state has at least 6 jets, a lepton and missing transverse momentum • Large backgrounds from tTbB and tTjj and important to understand them well • In order to suppress latter, require 4 b-tagged jets in event • Even without backgrounds, large combinatorics from signal alone

30. VVV critical for SUSY trilepton and other new physics involving multiple leptons, jets and missing ET in final state • Calculated by Lazopoulos, Melnikov and Petriello • see Kirill’s talk on Monday on ZZZ • Large increase in cross section, partially due to pdf’s and partially to large virtual corrections • Scale dependence of LO does not give indication of size of NLO corrections • but similar to VV corrections at NLO • Small shape changes at NLO, so K-factor works

31. What if we don’t finish every process on the Les Houches list in time? and/or we think of new ones Can we make some generalizations based on type of reaction, initial state partons, kinematics gg s-channel reactions have large K-factors? past experience tTg->tTbB? and (LO) data/theory at the Tevatron? Can we learn anything more about NLO multi-jet cross sections from threshold resummation? Calculate soft and collinear approximations to NLO (George Sterman)? collinear regions in phase and loop space universal (and fairly simple) soft gluon regions change with number of jets, but are also simple generate a relatively simple approximation to NLO following from same factorization formulas used to prove threshold resummation Some issues/questions

32. 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 need more automation Even with partonic level calculations, need ability to write out ROOT ntuples of parton level events so that cuts/distributions can be changed without the need for the lengthy re-running of the predictions what I do for example with MCFM 10’s of Gbytes Some issues/questions

33. Something (easy) for the Tevatron:Wcj • A relatively simple process, Wcj production, is still known only at LO • sensitive to the strange quark distribution • Crucial for understanding W + jets, where one or more jets has been tagged as originating from heavy flavor • Agreement is within systematics but not as good as we’d like to see in the one and two jet bins

34. Don’t forget • NNLO: we need to know some processes (such as inclusive jet production) at NNLO • Resummation effects: affect important physics signatures • mostly taken into account if NLO calculations can be linked with parton showering Monte Carlos

35. BFKL logs: will we finally see them at the LHC? EW logs: aWlog2(pT2/mW2) can be a big number at the LHC …and

36. Jet algorithms CDF Run II events • For some events, the jet structure is very clear and there’s little ambiguity about the assignment of towers to the jet • But for other events, there is ambiguity and the jet algorithm must make decisions that impact precision measurements • If comparison is to hadron-level Monte Carlo, then hope is that the Monte Carlo will reproduce all of the physics present in the data and influence of jet algorithms can be understood • more difficulty when comparing to parton level calculations

37. Jet algorithms at NLO • Remember at LO, 1 parton = 1 jet • At NLO, there can be two 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

38. Jets and you • There is a need/desire to have available the results of more than one jet algorithm when analyzing an event • A student of mine and I have assembled some jet algorithms together in a routine that runs on 4-vector files • So far, the routine runs JetClu, Midpoint, kT (inclusive and exclusive), Cambridge/Aachen algorithm, SISCone and simple Pythia UA-1 type algorithm (CellJet) • in a UA-1 type algorithm, the center of the jet is taken as the location of the highest pT tower; a cone is drawn around the jet and those towers are eliminated from the remaining jet clustering • User specifies the parameters for the jet reconstruction (including whether to pre-cluster the 4-vectors together into towers), whether to add in extra min bias events (pending), and whether to make lego plots (with user-specified tower granularity) • Available from www.pa.msu.edu /~huston/lhc_jet/lhc_jet.html

39. Jet sample with pTmin>2 TeV/c (from website) …except for exclusive kT (where jets are explicitly broken up) high ET distributions look similar

40. Jet masses from 2 TeV/c sample • It’s often useful to examine jet masses, especially if the jet might be some composite object, say a W/Z or even a top quark • very popular in recent literature, LHC Olympics • For 2 TeV jets, peak mass (from dynamical sources) is on order of 125 GeV/c2, but with long tail • Sudakov suppression for low jet masses • fall-off as 1/m2 due to hard gluon emission • algorithm suppression at high masses • jet algorithms tend to split high mass jets in two

41. Event from J8 file (5017, 49120) • MidPoint Jets Et eta phi n mass 2622 -0.348 2.92 26 174.5 2509 0.442 6.05 14 59.8 15.5 -0.033 0.40 9 4.7 9.03 -1.55 1.53 13 2.79 • A 2.6 TeV/c jet with the mass of a top quark • But a real top quark would probably have jet energy distributed differently • separate W and b clusters • Need to be able to look inside structure of jet as well

42. LHC jet study • We’ve started an LHC working group on jets, with the intent to have ATLAS and CMS (and interested theorists) work on • commonality of jet algorithms • jet benchmarks • we’re running common events through the ATLAS/CMS machinery to note any differences • continuing the work begun at the MC4LHC workshop last summer • http://mc4lhc06.web.cern.ch/mc4lhc06/ • to be continued at Les Houches 2007 • plus establishing the machinery to allow jet re-clustering to be easily done at the ntuple level (so no excuse not to compare the results of several different jet algorithms) • See www.pa.msu.edu/~huston/lhc_jet/lhc_jet.html

43. Summary • Physics will come flying hot and heavy when LHC turns on at full energy in 2008 • Important to establish both the SM benchmarks and the tools we will need to properly understand this flood of data • and in particular, the needed NLO calculations

44. WGNLO Multi-leg will address the issue of the theoretical predictions for multileg processes, in particular beyond leading order, and the possibility of implementing these calculations in Monte Carlos. This working group aims at a cross breeding between novel approaches (twistors, bootstraps,..) and improvements in standard techniques. • Dave Soper, Borut Kersevan and I are leading a group dealing with NLO calculations and their use • WGSM Handles and Candles  will review and critically compare existing tools for SM processes, covering issues in pdf, jets and Higgs physics. • WGNew Physics  is a beyond SM group, subdivided into SUSY and new models of symmetry breaking. It will also address the issue of model reconstruction and model independent searches based on topologies. • There will also be an intergroup dedicated to Tools and Monte Carlos. This intergroup  will liaise with all  WG with the task of incorporating some of the issues and new techniques developed in these groups in view of improving Monte Carlos and setting standards and accords among the simulation codes to better meet the experimental needs. http://lappweb.in2p3.fr/conferences/LesHouches/Houches2007/

45. CTEQ LHC Workshop • May 14-15 Kellogg Biological Station*, Michigan State University • Program * The LHC environment * Benchmark QCD measurements * W/Z production as luminosity monitor * W/Z/photon+light/heavy-flavor jets * ttbar/single-top production * Simulation tools: from parton-level to full event * Next generation of parton shower models * The Tevatron reach to new physics * New physics searches with 1 fb-1 * Theory tools for new physics searches http://tigger.uic.edu/~varelas/cteq_lhc_workshop/ *no medical experiments will be performed on participants

46. Extra slides

47. Known known: underlying event at the Tevatron • Define regions transverse to the leading jet in the event • Label the one with the most transverse momentum the MAX region and that with the least the MIN region • The transverse momentum in the MAX region grows as the momentum of the lead jet increases • receives contribution from higher order perturbative contributions • The transverse momentum in the MIN region stays basically flat, at a level consistent with minimum bias events • no substantial higher order contributions • Monte Carlos can be tuned to provide a reasonably good universal description of the data for inclusive jet production and for other types of events as well • multiple interactions among low x gluons

48. Known unknown: underlying event at the LHC • There’s a great deal of uncertainty regarding the level of underlying event at 14 TeV, but it’s clear that the UE is larger at the LHC than at the Tevatron • Should be able to establish reasonably well with the first collisions in 2008 • Rick Field is working on some new tunes • fixing problems present in Tune A • tunes for Jimmy • tunes for CTEQ6.1 (NLO) • see TeV4LHC writeup for details

49. Aside: Why K-factors < 1 for inclusive jet prodution? • 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)

50. 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