# From Loop Fest VI The Road Ahead David

- Slides: 40

From Loop. Fest VI: The Road Ahead David A. Kosower Fermilab, April 18, 2007

From Geneva (IL) to Geneva (GE) From Loop. Fest VI: The Road Ahead, April 18, 2007 2

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 From Loop. Fest VI: The Road Ahead, April 18, 2007 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 From Loop. Fest VI: The Road Ahead, April 18, 2007 5

Compare signal to background Signal is “easy” to compute (so long as one doesn’t need NLO or NNLO) What about the background? From Loop. Fest VI: The Road Ahead, April 18, 2007 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 – – α s and PDFs from global fits (where’s the lattice? ) From Loop. Fest VI: The Road Ahead, April 18, 2007 7

• Heard at the ILC workshop: “ 6 jets, that’s α s 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] • From Loop. Fest VI: The Road Ahead, April 18, 2007 9

• New NLO calculations Corrections to – production (Melnikov for Lazopoulos, Melnikov & Petriello) – (Dittmaier for Dittmaier, Uwer, & Weinzierl) – production in VBF (Jaeger for Bozzi, Jaeger, Oleari, Zeppenfeld) • Quantitative stability in predictions as renormalization/factorization scales are varied From Loop. Fest VI: The Road Ahead, April 18, 2007 10

Lazopoulos, Melnikov & Petriello From Loop. Fest VI: The Road Ahead, April 18, 2007 Jaeger 11

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) From Loop. Fest VI: The Road Ahead, April 18, 2007 12

• 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 • From Loop. Fest VI: The Road Ahead, April 18, 2007 13

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) Ad. S/CFT : strongly-coupled gauge theories have weaklycoupled string representation • Spin-chain model: connection to integrability • Topological string theory: twistor space new on-shell methods • From Loop. Fest VI: The Road Ahead, April 18, 2007 14

On-Shell Recursion Relations Britto, Cachazo, Feng, Witten (2005) • Exploit analytic properties: factorization • Key ingredient: complex momenta • Basically reduces any amplitude to cubic vertices = From Loop. Fest VI: The Road Ahead, April 18, 2007 15

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 From Loop. Fest VI: The Road Ahead, April 18, 2007 16

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 (Pittau for Ossola, Papadopoulos, Pittau) • Equations involve momenta chosen for vanishing propagators connection to unitarity method • Numerical-stability issues to be studied • From Loop. Fest VI: The Road Ahead, April 18, 2007 17

• 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) From Loop. Fest VI: The Road Ahead, April 18, 2007 18

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 • From Loop. Fest VI: The Road Ahead, April 18, 2007 19

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 (Willenbrock for Campbell, Ellis, Maltoni, Willenbrock) • From Loop. Fest VI: The Road Ahead, April 18, 2007 20

Tree-Level Situation • General approach: recursion relations Berends & Giele (1988) • General matrix element generators (some use technology, some ignore it) Mad. Graph – Alp. Gen – Amegic – O’Mega – • Used as black boxes by experimenters From Loop. Fest VI: The Road Ahead, April 18, 2007 21

Tree Level: Recursion Relations Berends & Giele (1988) From Loop. Fest VI: The Road Ahead, April 18, 2007 22

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(2 n ) different helicities: at least exponential complexity • But what about the complexity of each helicity amplitude? From Loop. Fest VI: The Road Ahead, April 18, 2007 23

Complexity of Each Helicity Amplitude Same j-point current appears in calculation of Jn as in calculation of Jm <n • Only a polynomial number of different currents needed • O(n 4) operations • From Loop. Fest VI: The Road Ahead, April 18, 2007 24

On-shell recursion relations: is there an O(n 3) 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 From Loop. Fest VI: The Road Ahead, April 18, 2007 25

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 From Loop. Fest VI: The Road Ahead, April 18, 2007 26

• Longer-term order • Flexibility to deal with new requests on short notice Resources need to accomplish work • From Loop. Fest VI: The Road Ahead, April 18, 2007 27

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 – From Loop. Fest VI: The Road Ahead, April 18, 2007 28

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) SUSY • 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 From Loop. Fest VI: The Road Ahead, April 18, 2007 29

In Memoriam Willy van Neerven 1947– 2007 • • • Ph. D Nijmegen 1975 Pioneer of NNLO calculations: Hamberg, van Neerven, & Matsuura, A Complete calculation of the order α s 2 correction to the Drell-Yan K factor [Nucl. Phys. B 359: 343 (1991), Err. B 644: 403 (2002)] … as well as 2 -loop QED-corrections for LEP; heavy-flavor in DIS; and NLO QCD corrections to top quark cross section From Loop. Fest VI: The Road Ahead, April 18, 2007 30

New NNLO Calculations • Fully-differential W/Z production (Petriello for Melnikov & Petriello, Kilgore) – Use of sector decomposition for real-emission singularities (need analytic form to start with) Analytic work completed Process-specific subtraction scheme Numerics under way Kilgore Melnikov & Petriello • W mass measurement; LHC luminosity; PDFs From Loop. Fest VI: The Road Ahead, April 18, 2007 31

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/Z production Dittmar, Pauss, Zurcher (1997) Limited by theory! • Only real-time monitoring at LHC • From Loop. Fest VI: The Road Ahead, April 18, 2007 32

e+ e− → jets (Heinrich for Gehrmann, Gehrmann-De Ridder, Glover & Heinrich) • Landmark calculation • First NNLO fully-differential jet calculation • Successful extension of antenna subtraction to NNLO • • Improve α s • Forsee extension to hadron environment (Maître for Daleo, Gehrmann, Maître) From Loop. Fest VI: The Road Ahead, April 18, 2007 33

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 (Daleo for Anastasiou, Beerli & Daleo; at NLO, Melnikov) Multiple mass scales – Check on analytic results – From Loop. Fest VI: The Road Ahead, April 18, 2007 34

• 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? From Loop. Fest VI: The Road Ahead, April 18, 2007 35

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 From Loop. Fest VI: The Road Ahead, April 18, 2007 36

Combining Fixed Order and Parton Showers • Existing approaches CKKW for LO – MLM for LO – [email protected] for NLO – Catani, Krauss, Kuhn, & Webber (2001) Mangano (2004) Frixione & Webber (2002) • Inclusion of EW corrections (Montagna) • Pythia & Mad. Event with slicing à la CKKW/MLM (Alwall) • New approach based on antenna factorization (Skands for Giele, DAK, Skands) – – Simple subtraction terms Uniform solution Examine uncertainties due to: finite terms, evolution variable, … Exact massless showering: 2 → 3 From Loop. Fest VI: The Road Ahead, April 18, 2007 37

From Loop. Fest VI: The Road Ahead, April 18, 2007 38

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 • From Loop. Fest VI: The Road Ahead, April 18, 2007 39

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. From Loop. Fest VI: The Road Ahead, April 18, 2007 40

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 • From Loop. Fest VI: The Road Ahead, April 18, 2007 41

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 From Loop. Fest VI: The Road Ahead, April 18, 2007 42