From Maximal Helicity to Maximal Jets David A

From Maximal Helicity to Maximal Jets David A. Kosower Institut de Physique Théorique, CEA–Saclay and Institute for Advanced Study MHV @ 30 Fermilab, March 16– 19, 2015

A story that starts at • Columbia • Fermilab

Themes • Jet Physics • Amplitudes • Computability

Prehistory (< 1986) • No-one had laptops • No-one had smartphones • Almost no-one had a cell phone • There was no ar. Xiv – Institutions physically mailed preprints to each other!

Prehistory (< 1986) •

A Seed is Planted • Parke–Taylor squared amplitude (1985– 6) showed that there was something simple • Simple expressions should have a simple derivation • With the benefit of hindsight, simple expressions should have many simple derivations

• As a young postdoc, newly arrived at Columbia, what did I start doing? – Those of you who know my advisor — Howard Georgi — and his tastes in physics, can guess… • I knew nothing about QCD beyond what I’d learned in a wonderful course given by John Preskill – Because QCD, of course, was messy and at Harvard, we didn’t do messy things • I started working with a newly-arrived assistant professor, Parameswaran Nair • We derived the five-point QCD amplitude from open strings (along with a Columbia graduate student, B-H Lee) – Color ordering; “simple” single object also Mangano, Parke, Xu (1987) • Connection to perturbative string theory still going strong Stieberger & Taylor, Green & Vanhove, others; Kawai– Lewellen–Tye connection between gravity and gauge theory

• But the most fruitful thing to come out of Columbia in that period was Nair’s observation that the Parke–Taylor amplitude could be thought of as a correlator on CP 1 Nair (1988) • Fifteen years later, Edward Witten would develop it into twistor-string theory, and spark the modern Amplitudes revolution • But what I was doing wasn’t the right thing to be doing at the time

Refinements of Current Recursion •

Onward to Loops! • Thanks to a kind invitation from Jan Ambjorn, I was able to spend a month in 1987 at the Niels Bohr Institute • With Zvi Bern, we started trying to derive one-loop amplitudes in QCD from heterotic string theory • It was a long project! • A lot of elementary objections: – How can you be sure the extra string states decouple? – How can you get a beta function? ? ? String theory is finite! – You can’t get a consistent string theory with SU(N)!

In the Mean time, in Jet Physics •

Five Gluons • Fortified by having Lance Dixon join us, we set off to compute our first new result: the five-gluon amplitude • The first thing we did is to understand the integral basis, and compute integrals, in D dimensions (1993– 4) – Study of integrals & structures underlying them is still an ongoing project at higher loops – Early use of differential equations • String-based calculation (1993)

• Simple results! • Modern form: spinor products polylogs • Other subprocesses (2 q 2 g, 4 q 1 g), with friendly competition Kunszt Signer Trocsanyi (1994– 5)

Impact on Jet Algorithms •

One-Loop All-plus • Simple result at four and five points • Following in the spirit of Parke & Taylor, working with Zvi’s student Gordon Chalmers, we guessed an all-n form • Demonstrated its correctness through allowed analytic structures and collinear limits • Not a derivation • One missing ingredient: complex momenta! – Later supplied by Witten (2003) and Britto, Cachazo, Feng & Witten (2004)

All-n MHV at One Loop in SUSY With Zvi Bern, Lance Dixon, Dave Dunbar • Integral basis • Restricted set of integrals in N = 4 • First: guess based on collinear limits for N = 4 • Then: derivation from unitarity • Later: derivation for N = 1 SUSY • Analytic calculation: required symbolic manipulation • But a powerful new tool

W+4 partons • Applying the unitarity method: the artisinal era • Bern, Dixon, DAK, Weinzierl (1997– 8) • First application of generalized unitarity – Full picture would come later, from Britto, Cachazo, Feng • Computed in parallel by Glover & Campbell: accessible to traditional methods, but the balance of power was shifting – Unitarity provided digestible analytic expressions, softer spurious singularities • Matrix elements used in MCFM to compute W+2 jets Campbell & Ellis (2002)

The Twistor Surge • 2004: a new view of tree-level Yang–Mills as a twistorstring theory Witten (2003) • New people, mostly from a more formal background, coming in to look at amplitudes • Maximal unitarity for the box: a purely numerical approach is possible Britto Cachazo Feng (2004) – Coefficient is a product of trees, which could be computed using Berends–Giele recursion • On-shell methods for tree amplitudes: factorization as a calculational principle • Applicable to more general rational functions, for example purely rational parts of one-loop QCD amplitudes

NLO Revolution • Maximal unitarity picture completed – Forde (for triangles and bubbles) (2007) – by Ellis, Kunszt, Giele, & Melnikov ; and by Badger (2008) for the rational terms • Compute coefficients numerically – At integrand (OPP) or integrated level – Trees are tail ingredient: simple analytic formulae; Berends– Giele recursion; simple formulae from solving N=4 SUSY onshell recursions Dixon, Henn, Plefka, Schuster (2011) • Automation of processes – BLACKHAT for loops, SHERPA for real emission & phase space

NLO Revolution • Lots of revolutionaries roaming the world – BLACKHAT: Berger, Bern, Dixon, Febres Cordero, Forde, Gleisberg, Hoeche, Ita, DAK, Lo Presti, Maître – HELAC-NLO: Ossola, Papadopoulos, Pittau, Actis, Bevilacqua, Czakon, Draggiotis, Garzelli, van Hameren, Mastrolia, Worek & their clients – Rocket: Ellis, Giele, Kunszt, Lazopoulos, Melnikov, Zanderighi – Go. Sam/Samurai: Mastrolia, Ossola, Reiter, Tramontano, Cullen, Greiner, Heinrich, Luisoni – NJet/NGluon: Badger, Biedermann, & Uwer + Sattler & Yundin – Mad. Loop: Hirschi, Frederix, Frixione, Garzelli, Maltoni, & Pittau – Analytics: Anastasiou, Britto, Duhr, Feng, Henn – Loop-Subtraction: Weinzierl, Becker, Goetz, Reuschle

W+5 partons W+3 Jets At the Tevatron… • Third jet in W+3 jets [0907. 1984] • Reduced scale dependence at NLO • Good agreement with CDF data [0711. 4044] • Shape change small compared to LO scale variation • SISCone (Salam & Soyez) vs JETCLU

W+6 partons W+4 Jets •

7 Te. V results from CMS (March 2014) 13 years: from crazy to accomplished & compared with experiment

W+7 partons W+5 Jets Scale-uncertainty bands shrink dramatically Last jet shape is stable, harder jets have steeper spectrum at NLO Last three jet shapes look similar, just getting steeper

ATLAS 7 Te. V [4. 6 fb− 1] results (Sept 2014)

Extrapolation to W+6 Jets

Looking ahead • NLO is now standard • The physics focus is shifting to NNLO for a broad range of processes – Two-loop technologies: maximal unitarity at integrand level & at integrated level – Infrared-cancellation technologies still ripe for development – Computation of integrals – Beginning to understand structure in systems of integrals and in integration by parts: generating vectors which avoid doubled propagators [1009. 0472] provide geometric insight into the systems — Ita [1510. 05626] and Larsen and Zhang [1511. 01071] give the first geometric interpretation of IBP relations • The pace will be faster between now and MHV @ 50!