QCD at the LHC: What needs to be done?. Part 2: Higher Order QCD. West Coast LHC Meeting Zvi Bern, UCLA. Outline. General overview Examples of importance of higher order QCD Experimenters’ wish lists What is the problem? Evils of unphysical formalisms.
Part 2: Higher Order QCD
West Coast LHC Meeting
Zvi Bern, UCLA
QCD at hadron collider involves a number of complex
Steve Ellis’ talk
Purpose: After discovery of Higgs Boson measure HWW coupling
Background uncertainty can be reduced with an NLO calculation.
ALPGEN vs PYTHIA
It is important to merge NLO with parton showering.
First example of
merging NLO with shower Monte Carlo
See Dave Soper
Les Houches 2005
Bold action is required even for this
Five point is still state-of-the art in QCD:
Brute force calculations give GB expressions – numerical stability?
Amusing numbers: 6g: 10,860 diagrams, 7g: 168,925 diagrams
Much worse difficulty: integral reduction generates nasty determinants
To attack the wish list need new ideas:
Promising recent progress.
Binoth and Heinrich Kaur; Giele, Glover, Zanderighi
Binoth, Guillet, Heinrich, Pilon, Schubert;
Soper and Nagy; Ellis, Giele and Zanderighi;
Anastasiou and Daleo; Czakon;
Binoth, Heinrich and Ciccolini
Bern, Dixon, Dunbar, Kosower; Bern and Morgan; Cachazo, Svrcek and Witten;
Bern, Dixon, Kosower;
Bedford, Brandhuber, Spence, Travaglini;
Bern, Dixon, Del Duca and Kosower;
Britto, Cachazo, Feng and Witten;
Berger, Bern, Dixon, Kosower, Forde
gauge-dependent off-shell states.
This is the origin of the complexity.
-- MHV vertices
-- on-shell recursion
Bern, Dixon, Dunbar, Kosower
Bern and Morgan
Cachazo, Svrcek Witten
Britto, Cachazo, Feng, Witten
Bern, Dixon, Kosower
Forde and Kosower;
Berger, Bern, Dixon, Forde amd Kosower
Spinor helicity for gluon polarizations in QCD:
Penrose Twistor Transform:
Early work from Nair
Witten’s remarkable twistor-space link:
QCD scattering amplitudes Topological String Theory
Witten; Roiban, Spradlin and Volovich
Key implication: There are simple structure in gauge theory amplitudes
Witten Conjectured that in twistor –space gauge theory
amplitudes should be supported on curves of degree:
These structures imply
an amazing simplicity
in the scattering amplitudes.
MHV vertices for
Cachazo, Svrcek and Witten
Bern and Morgran (1995)Loop Amplitudes
Three- particle cut:
Generalized triple cut:
Should be interpreted as demanding that cut propagators do not cancel.
Unitarity method combines very effectively with twistor-inspired ideas.
Bern, Dixon, Kosower
Key problems preventing widespread applications:
New representations of tree amplitudes from IR consistency of one-loop amplitudes in N = 4 super-Yang-Mills theory.
Bern, Del Duca, Dixon, Kosower;
Roiban, Spradlin, Volovich
With intution from twistors and generalized unitarity:
Britto, Cachazo, Feng
Britto, Cachazo, Feng and Witten
Consider shifted amplitude :
At tree level we know all the residues:
Bern, Dixon Kosower;
Forde and Kosower;
Berger, Bern, Dixon, Forde, Kosower,
Pure phase for real momenta
Assume we already have log terms computed from D = 4 cuts.
The most challenging part was rational function terms.
Only one non-vanishing recursive diagram:
Only two overlap diagrams:
The rational function terms are as easy to get as at tree level!
Large z behavior of loop amplitudes.
General understanding of unreal poles.
Complex factorization of amplitudes.
Carola Berger’s presentation
Badger, Glover, Khoze, Svrcek
Chalmers and Siegel; Vaman and Yao
Many theoretical and practical aspects
Bern, Rozowsky, Yan; Anastasiou,Bern, Dixon, Kosower;
Bern, Dixon, Smirnov; Buchbinder and Cacazho; Cachazo, Spradlin,Volovich
Howe and Stelle; Bern, Bjerrum-Bohr, DunbarOther Applications
A method is even more important than a discovery, since
the right method will lead to new and even more important
— L.D. Landau
On-shell method have been applied to a variety of problems.
Experimenters’ wish list awaits us.