Bootstrapping One-Loop QCD Amplitudeswith General Helicities

Berger, Carola F. ; Bern, Zvi ; Dixon, Lance J. ; Forde, Darren ; Kosower, David A.

Stanford Linear Accelerator Center

关键词: Phenomenology-Hep,Hepph, Hepth;    Quantum Chromodynamics;    Amplitudes;    Gluons;    71 Classical And Quantum Mechanics, General Physics;   

DOI  :  10.2172/881788
RP-ID  :  SLAC-PUB-11830
RP-ID  :  AC02-76SF00515
RP-ID  :  881788

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来源: UNT Digital Library

【 摘 要 】

The recently developed on-shell bootstrap for computing one-loop amplitudes in non-supersymmetric theories such as QCD combines the unitarity method with loop-level on-shell recursion. For generic helicity configurations, the recursion relations may involve undetermined contributions from non-standard complex singularities or from large values of the shift parameter. Here we develop a strategy for sidestepping difficulties through use of pairs of recursion relations. To illustrate the strategy, we present sets of recursion relations needed for obtaining n-gluon amplitudes in QCD. We give a recursive solution for the one-loop n-gluon QCD amplitudes with three or four color-adjacent gluons of negative helicity and the remaining ones of positive helicity. We provide an explicit analytic formula for the QCD amplitude A{sub 6;1}(1{sup -}, 2{sup -}, 3{sup -}, 4{sup +}, 5{sup +}, 6{sup +}), as well as numerical results for A{sub 7;1}(1{sup -}, 2{sup -}, 3{sup -}, 4{sup +}, 5{sup +}, 6{sup +}, 7{sup +}), A{sub 8;1}(1{sup -}, 2{sup -}, 3{sup -}, 4{sup +}, 5{sup +}, 6{sup +}, 7{sup +}, 8{sup +}), and A{sub 8;1}(1{sup -}, 2{sup -}, 3{sup -}, 4{sup -}, 5{sup +}, 6{sup +}, 7{sup +}, 8{sup +}). We expect the on-shell bootstrap approach to have widespread applications to phenomenological studies at colliders.