from loopfest vi: the road ahead

From LoopFest VI:The Road Ahead

David A. KosowerFermilab, April 18, 2007

From LoopFest VI: The Road Ahead, April 18, 2007

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From Geneva (IL) to Geneva (GE)


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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


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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


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Compare signal to background

Signal is “easy” to compute (so long as one doesn’t need NLO or NNLO)

What about the background?


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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

– αs and PDFs from global fits (where’s the lattice?)


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• 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]


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• 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


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Lazopoulos, Melnikov & Petriello Jaeger


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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)


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• Five-point QCD amplitudes 1993 Bern, Dixon, DAK (1993); Kunszt, Signer, Trocsanyi (1994)

• Six-point QCD amplitudes 2006Bern, 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 2005Dittmaier & Denner (2005)

• Slow but steady progress• New technologies ready to go to four final-state

objects and beyond


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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


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On-Shell Recursion Relations

Britto, Cachazo, Feng, Witten (2005)

• Exploit analytic properties: factorization

• Key ingredient: complex momenta

• Basically reduces any amplitude to cubic vertices

==


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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


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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


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• 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) 1 2 3 0

Inf ij tc A A A t


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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


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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)


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Tree-Level Situation

• General approach: recursion relationsBerends & Giele (1988)

• General matrix element generators (some use technology, some ignore it)– MadGraph– AlpGen– Amegic– O’Mega

• Used as black boxes by experimenters


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Tree Level: Recursion Relations

Berends & Giele (1988)


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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?


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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(n4) operations


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• 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


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Experimenters’ Work OrderHuston

• 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


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• Longer-term order

• Flexibility to deal with new requests on short notice

• Resources need to accomplish work


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AutomationComputers 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


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Foretaste of Precision

• 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 physicsGiudice, Grojean, Pomarol, Rattazzi (3/2007)

• Need to study high-energy WW scattering

SUSY

I don't want to be interesting. I want to be good. — Mies van der Rohe


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In MemoriamWilly van Neerven

1947–2007

• 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


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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)

• W mass measurement; LHC luminosity; PDFs

Melnikov & Petriello

Analytic work completed

Process-specific subtraction scheme

Numerics under way

Kilgore


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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 productionDittmar, Pauss, Zurcher (1997)

• Limited by theory!• Only real-time monitoring at LHC


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• 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 αs

• Forsee extension to hadron environment (Maître for

Daleo, Gehrmann, Maître)


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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


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• 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?


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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


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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 (Skands for Giele, DAK, Skands)– Simple subtraction terms– Uniform solution– Examine uncertainties due to: finite terms, evolution variable,

…– Exact massless showering: 2 → 3


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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


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GGI WorkshopBrandhuber, 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.


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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


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• 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 loopfest vi: the road ahead

Documents

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precision calculations

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