Computation of Multi-Jet QCD Amplitudes at NLO
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Carola Berger (SLAC), Zvi Bern (UCLA), Lance Dixon (SLAC), Darren Forde (SLAC), David Kosower (Saclay), Daniel Maitre (SLAC), Yorgos Sofianatos (SLAC).
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Precise QCD amplitudes are needed to maximise the discovery potential of the LHC (2008).
NLO amplitudes 1-loop amplitudes.
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“Famous” Les Houches experimentalist wish list, (2005)
Six or more legs, until recently a bottleneck
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Calculating using Feynman diagrams is Hard!
Factorial growth in the number of Feynman diagrams.
Known results much simpler than would be expected!
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Unitarity cutsK3
K2K1
A3
A2
A1
On-shell recurrence relations
ji
“Glue” together trees to produce loops
Recycle results of amplitudes with fewer legs
Use the most efficient approach for each piece,
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On-shell recursion relations originally developed for massless tree amplitudes (Phys.Rev.Lett.94-Britto,Cachazo,Feng,Witten) Very general, proof relies only on Factorization properties of
amplitudes and Cauchy’s theorem. Extended to massive particles, (JHEP 0507-
Badger,Glover,Khoze,Svrcek) All-plus and single-minus all-multiplicity amplitudes for a pair of
massive scalars, An(φ,+,…,±,…,+, φ). (Phys.Rev.D73-Forde,Kosower)
Extended to one-loop amplitudes with no cut pieces. All-plus and single-minus helicity amplitudes, An(±,+,+,…,+), Just gluons, (Phys.Rev.D71-Bern, Dixon, Kosower) Both quarks and gluons with an arbitrary number of legs,
(Phys.Rev.D71-Bern, Dixon, Kosower)
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Amplitudes with two or more negativity helicity legs contain cut terms.
Apply unitarity bootstrap; cut terms previously calculated (Nucl.Phys.B435&B425-Bern,Dixon,Dunbar,Kosower)
Adjacent 2-minus with 6 legs, (Phys.Rev.D73-Bern, Dixon, Kosower)
Minimal growth in “complexity” of solution with arbitrary numbers of legs, An(-,-,+,…,+), (Phys.Rev.D73 -Forde, Kosower)
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Non-adjacent 2-minus amplitude, An(-,+,…,-,…,
+), (Phys.Rev.D75-Berger, Bern, Dixon, Forde, Kosower)
Three minus adjacent amplitude, An(-,-,-,+,…,+), (Phys.Rev.D74-Berger, Bern, Dixon, Forde, Kosower)
Important contributions to the recently derived complete six gluon amplitude. (Bern,Dixon,Kosower) (Berger,Bern,Dixon,Forde,Kosower) (Xiao,Yang,Zhu) (Bedford,Brandhuber,Spence,Travaglini) (Britto,Feng,Mastrolia) (Bern,Bjerrum-Bohr,Dunbar,Ita).
A Higgs boson plus arbitrary numbers of gluons or a pair of quarks for the all-plus and one-minus helicity combinations, An(φ,+,…,±,…,+ ). (Phys.Rev.D74-Berger, Del Duca, Dixon)
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Do better - use generalised unitarity for cut terms,
New techniques produce “compact” results in a direct manner.
Generally applicable, including “wish list” processes.
i ij ijki ij ijk
b c d
Quadruple cuts, give box coefficients(Nucl.Phys.B725-Britto, Cachazo, Feng)Two-particle and triple cuts,
give bubble and triangle coefficients(Phys.Rev.D-Forde)
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