From LoopFest VI: The Road Ahead

1. From LoopFest VI:The Road Ahead David A. KosowerFermilab, April 18, 2007

2. From Geneva (IL) to Geneva (GE) 

3. Hopes • We should hope that commissioning is measured in months not years • We should hope that understanding the detectors is measured in (few) years not decades • Beam energy of 300 Megajoules = 120 Kg TNT, enough to melt ~ a ton of copper Lykken • Beam safety is a critical issue

4. Physics Program • Discover the Higgs (or at least set limits) • Discover new physics truly beyond the Standard Model — or show convincingly it isn’t within the reach of the machine • Discover what underlies electroweak symmetry breaking • Measure its properties, precisely

5. Compare signal to background • Signal is “easy” to compute (so long as one doesn’t need NLO or NNLO) • What about the background?

6. Two Fundamental Philosophies • Get backgrounds from data: “maximal ignorance” • Get backgrounds from fundamental theory (supplemented by models and other measurements only where unavoidable): “maximal prior knowledge” • Perturbative QCD and EW to higher orders • Systematic approximations • Hadronization from data • αsand PDFs from global fits (where’s the lattice?)

7. Heard at the ILC workshop: “6 jets, that’s αs to too high a power to calculate the normalization” Gott isch raffiniert, aber nöd bös — Einstein • First step to doing precision calculations is doing quantitative calculations • In QCD, that demands NLO • For hadronic variables: long development stretching back to Ellis, Ross, Terrano (1981) [shape variable]

8. New NLO calculations Corrections to • production (Melnikovfor Lazopoulos, Melnikov & Petriello) • (Dittmaierfor Dittmaier, Uwer, & Weinzierl) • production in VBF (Jaegerfor Bozzi, Jaeger, Oleari, Zeppenfeld) • Quantitative stability in predictions as renormalization/factorization scales are varied

9. Jaeger Lazopoulos, Melnikov & Petriello

10. Technology Behind the Scenes • “Experimenter-ready” turn-key NLO computer codes rely on a great deal of calculational technology • Virtual corrections • Real-emission corrections: “just” tree amplitudes • Make use of symmetries, color ordering, and the spinor-helicity basis • Combining contributions, canceling IR divergences • In hadron calculations, development started over two decades ago with Ellis & Sexton (1986)

11. Five-point QCD amplitudes 1993 Bern, Dixon, DAK (1993); Kunszt, Signer, Trocsanyi (1994) • Six-point QCD amplitudes 2006 Bern, Berger, Dixon, Forde, DAK (1994–2006); Britto, Buchbinder, Cachazo, Feng, Mastrolia (2005–6); Xiao, Yang, Zhu (2006)Ellis, Giele, Zanderighi (2006) • Six-point EW amplitudes 2005 Dittmaier & Denner (2005) • Slow but steady progress • New technologies ready to go to four final-state objects and beyond

12. Structure of Gauge Theories • Used to thinking of gauge theories in terms of path integral • Perturbative expansion • In recent years, we’ve learned about other representations (so far, mostly for N = 4, but the hints go beyond) • AdS/CFT : strongly-coupled gauge theories have weakly-coupled string representation • Spin-chain model: connection to integrability • Topological string theory: twistor space  new on-shell methods

13. = On-Shell Recursion Relations Britto, Cachazo, Feng, Witten (2005) • Exploit analytic properties: factorization • Key ingredient: complex momenta • Basically reduces any amplitude to cubic vertices

14. Special Case: MHV Rules Dick [Feynman]'s method is this. You write down the problem. You think very hard. Then you write down the answer. — Murray Gell-Mann • Build amplitude out of off-shell continuations of MHV amplitudes (“Parke–Taylor”) and scalar propagators

15. Technology Development • At one loop, one has an integral basis consisting of boxes, triangles, bubbles, and (in massive cases) tadpoles • Instead of doing Passarino-Veltman decomposition of tensors & reduction of higher-point integrals, decompose integrand by solving numerically for coefficients of box, triangle, bubble, tadpole propagator sets (PittauforOssola, Papadopoulos, Pittau) • Equations involve momenta chosen for vanishing propagators  connection to unitarity method • Numerical-stability issues to be studied

16. In the unitarity method, cutting four legs freezes all momenta, giving an algebraic expression for the coefficient in terms of trees with complex momentum arguments Britto, Cachazo, Feng (2004) • For triangles & bubbles, triple or ordinary cuts don’t freeze integrand completely; but one can use analytic properties to obtain coefficients directly, without solving equations (Forde)

17. Combining Real & Virtual • Formalisms for isolating IR divergences, cancelling them off, and producing manifestly finite ingredients have been known for over a decade Giele & Glover (1992); Giele, Glover, & DAK (1993) Frixione, Kunszt, & Signer (1995) Catani & Seymour (1996) Sector decomposition (Binoth & Heinrich 2004) could in principle be used as well

18. So Why Are Deliveries to Experimenters So Slow? • Bespoke calculations • Need to move to “industrial production” of amplitudes • Need “prefabricated” modules implementing subtraction scheme into which new amplitudes can be plugged in • Should be as simple as plugging a new USB device into your laptop • MCFM (Campbell & Ellis,1999) only example of multiprocess program so far • Backgrounds to single top (Willenbrockfor Campbell, Ellis, Maltoni, Willenbrock)

19. Tree-Level Situation • General approach: recursion relations Berends & Giele (1988) • General matrix element generators (some use technology, some ignore it) • MadGraph • AlpGen • Amegic • O’Mega • Used as black boxes by experimenters

20. Tree Level: Recursion Relations Berends & Giele (1988)

21. Computational Complexity of Tree Amplitudes • How many operations (multiplication, addition, etc.) does it take to evaluate an amplitude? • Textbook Feynman diagram approach: factorial complexity • Color ordering  exponential complexity • O(2n) different helicities: at least exponential complexity • But what about the complexity of each helicity amplitude?

22. Complexity of Each Helicity Amplitude • Same j-pointcurrent appears in calculation of Jn as in calculation of Jm<n • Only a polynomial number of different currents needed • O(n4) operations

23. On-shell recursion relations: is there an O(n3) algorithm? • Good for analytic results: but still exponential complexity, because there is no reuse of subexpressions • Loop level: polynomial complexity attained for box coefficients, not yet elsewhere • But with tractable expressions available for tree amplitudes with up to seven legs, the technology can go well beyond current limits

24. Experimenters’ Work Order Huston • Need to cut our teeth on SM physics before we attack BSM • Intensive QCD backgrounds: increase in gg and gq channels  increased W + jets  higher jet cut • Hard to extrapolate backgrounds for low cross section final states and/or final states where a clear separation of signal and background regions is difficult Short-term order: Speed up computer program production from new matrix elements

25. Longer-term order • Flexibility to deal with new requests on short notice • Resources need to accomplish work

26. Automation Computers are useless. They can only give you answers. — Pablo Picasso • Automation is good; but what automation? Brute-force automation vs Intelligent automation If you know how to do something analytically & generally, and it reduces computational complexity, do that. Only otherwise numerically • Loop integrals • Singular Factors & their integrals

27. Foretaste of Precision I don't want to be interesting. I want to be good. — Mies van der Rohe • Electroweak corrections (Metzler, Reuter, Weiglein, Awramik, Becher, Passarino, Martin, Schoefbeck) • & to QCD/hadron processes (Scharf, Montagna, Schulze) • Additional QCD corrections to Higgs production (Muehlleitner, Daleo) • But why only SUSY? • It’s not the only physics beyond the standard model: Little Higgs, Holographic Higgs, etc. • Light Higgs is not a sign of weakly-coupled physics Giudice, Grojean, Pomarol, Rattazzi (3/2007) • Need to study high-energy WW scattering SUSY

28. In MemoriamWilly van Neerven1947–2007 • PhD Nijmegen 1975 • Pioneer of NNLO calculations: Hamberg, van Neerven, & Matsuura, A Complete calculation of the order αs2 correction to the Drell-Yan K factor [Nucl. Phys. B359:343 (1991), Err. B644:403 (2002)] • … as well as 2-loop QED-corrections for LEP; heavy-flavor in DIS; and NLO QCD corrections to top quark cross section

29. New NNLO Calculations • Fully-differential W/Z production (Petriellofor Melnikov & Petriello, Kilgore) • Use of sector decomposition for real-emission singularities (need analytic form to start with) • W mass measurement; LHC luminosity; PDFs Analytic work completed Process-specific subtraction scheme Numerics under way Kilgore Melnikov & Petriello

30. Luminosity Measurement at LHC • Required for all physics measurements • Comparison with theory • Comparison with other experiments • Extraction of physics parameters • Forward detectors for elastic scattering, Roman pots/scintillators/thin-gap ionization chambers • W/Zproduction Dittmar, Pauss, Zurcher (1997) • Limited by theory! • Only real-time monitoring at LHC

31. e+ e− → jets (Heinrichfor Gehrmann, Gehrmann-De Ridder, Glover & Heinrich) • Landmark calculation • First NNLO fully-differential jet calculation • Successful extension of antenna subtraction to NNLO • Improve αs • Forsee extension to hadron environment (Maître for Daleo, Gehrmann, Maître)

32. Higher-Loop Technology • Find Master Integrals • Integration by parts equations (Tkachov & Chetyrkin 1981) • Lorentz invariance equations (Gehrmann & Remiddi 1999) • Laporta algorithm to solve (Laporta 2001) • Evaluate Master Integrals • Mellin-Barnes technique (Smirnov) MB package (Czakon 2005) • or differential equations • Numerical alternative using sector decomposition + contour deformation (Daleofor Anastasiou, Beerli & Daleo; at NLO, Melnikov) • Multiple mass scales • Check on analytic results

33. Successful for a variety of calculations • But a long ways from the one-loop situation • Is there a standard choice of basis at two loops? • Can one compute amplitudes using maximal unitarity & analytic properties?

34. Three Different Approaches • General parton-level fixed-order calculations • Numerical jet programs: general observables • Systematic to higher order/high multiplicity in perturbation theory • Parton-level, approximate jet algorithm; match detector events only statistically • Parton showers • General observables • Leading- or next-to-leading logs only, approximate for higher order/high multiplicity • Can hadronize & look at detector response event-by-event • Semi-analytic calculations/resummations • Specific observable, for high-value targets • Checks on general fixed-order calculations

35. Combining Fixed Order and Parton Showers • Existing approaches • CKKW for LO Catani, Krauss, Kuhn, & Webber (2001) • MLM for LO Mangano (2004) • MC@NLO for NLO Frixione & Webber (2002) • Inclusion of EW corrections (Montagna) • Pythia & MadEvent with slicing à la CKKW/MLM (Alwall) • New approach based on antenna factorization (Skandsfor Giele, DAK, Skands) • Simple subtraction terms • Uniform solution • Examine uncertainties due to: finite terms, evolution variable, … • Exact massless showering: 2 → 3

37. Precision Top Quark Mass • Need careful analysis & separation of different scales in perturbative and non-perturbative region (Hoang) • Application of soft-collinear effective theory • e+ e− now, hadrons later

38. GGI Workshop Brandhuber, Del Duca, Glover, DAK, Passarino, Spence, Travaglini, Zeppenfeld • This fall in the beautiful Tuscan hills overlooking Florence • Advancing Collider Physics: from Twistors to Monte Carlos ( August 27 - October 26) Physics Challeges • Jet observable at NNLO: Average thrust for e+e− → 3 jets • All one loop amplitudes for pp → 4 jets, pp → W+ 3 jets. • Full one-loop top production with decays folded in. Unstable particles within loop. • Evaluator for higher-loop integrals: program or web page where you feed in kinematics, get back a number. Compilation of known results.

39. Physics Challenges II • at one loop. • Parton showers merging with fixed order: at LO, with W + 3 partons; at NLO, with W + 1 and W + 2 partons • Automated program to construct IR subtraction counterterms for evaluating cross sections: • Plug in color ordered amplitudes out come differential cross sections. • Plug and play with standard interface. • Flexibility to add new physics. • Electroweak corrections to W + jet production • Two-loop renormalization of electroweak Lagrangian in the complex pole (mass) scheme

40. Experimenters’ work order • Turn-key programs and industrial production for NLO • Matching to parton showers • Next-generation two-loop technology on the one-loop model I often say that when you can measure what you are speaking about, and express it in numbers, you know something about it; but when you cannot express it in numbers, your knowledge is of a meagre and unsatisfactory kind; it may be the beginning of knowledge, but you have scarcely, in your thoughts, advanced to the stage of Science, whatever the matter may be. — Lord Kelvin