# Presentation: 143348

## From LoopFest VI:The Road Ahead 

- David A. KosowerFermilab, April 18, 2007

## From Geneva (IL) to Geneva (GE)

-                                                 

- 40 talks
*The secret of managing is to keep the guys who hate you away from the guys who are undecided. — Casey Stengel*

## 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

## 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

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

## 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?)

## Challenges

- Do the physics
- Improve sophistication of theoretical analyses
- Win mind-share amongst experimenters

- 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]

- 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

- Lazopoulos, Melnikov & Petriello

- Jaeger

## 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)

- 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

## 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

## On-Shell Recursion Relations

- Britto, Cachazo, Feng, Witten (2005)
- Exploit analytic properties: factorization
- Key ingredient: complex momenta
- Basically reduces any amplitude to cubic vertices

## 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
*     *

## 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

- 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)

## 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

## 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)

## 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

## Tree Level: Recursion Relations

- Berends & Giele (1988)

## 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?

## Complexity of Each Helicity Amplitude

*Same **j*-point* *current appears in calculation of *J**n* as in calculation of *J**m*<*n*
- Only a polynomial number of different currents needed
- O(*n*4) operations

- 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

## 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

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

## 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

## 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 physics
- Giudice, 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*

## In MemoriamWilly van Neerven1947–2007

- PhD 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. 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

## 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

## 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

- 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)

## 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

- 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?

## 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

## 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

## 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

## 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.

## 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

-    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*