All One-loop Maximally Helicity Violating Gluonic Amplitudes in QCD

Abstract

We use on-shell recursion relations to compute analytically the one-loop corrections to maximally-helicity-violating n-gluon amplitudes in QCD. The cut-containing parts have been computed previously; our work supplies the remaining rational parts for these amplitudes, which contain two gluons of negative helicity and the rest positive, in an arbitrary color ordering. We also present formulae specific to the six-gluon cases, with helicities (- + - + + +) and (- + + - + +), as well as numerical results for six, seven, and eight gluons. Our construction of the n-gluon amplitudes illustrates the relatively modest growth in complexity of the on-shell-recursive calculation as the number of external legs increases. These amplitudes add to the growing body of one-loop amplitudes known for all n, which are useful for studies of general properties of amplitudes, including their twistor-space structure.

67 pages, 11 figures, v2 minor corrections, expanded discussion of numerical stability

References in corpus (8)

• Bootstrapping One-Loop QCD Amplitudes with General Helicities
• SUSY Ward identities for multi-gluon helicity amplitudes with massive quarks
• A comparison of efficient methods for the computation of Born gluon amplitudes
• The one-loop amplitude for six-gluon scattering
• The rational parts of one-loop QCD amplitudes I: The general formalism
• The rational parts of one-loop QCD amplitudes III: The six-gluon case
• The rational parts of one-loop QCD amplitudes II: The five-gluon case
• Towards LHC phenomenology at the loop level: A new method for one-loop amplitudes

Cited by in corpus (27)

• Reducing full one-loop amplitudes to scalar integrals at the integrand level
• An Automated Implementation of On-Shell Methods for One-Loop Amplitudes
• Direct extraction of one-loop integral coefficients
• Full one-loop amplitudes from tree amplitudes
• A Numerical Unitarity Formalism for Evaluating One-Loop Amplitudes
• Next-to-Leading Order QCD Predictions for W+3-Jet Distributions at Hadron Colliders
• Polarizing the Dipoles
• Direct Extraction Of One Loop Rational Terms
• Taming Tree Amplitudes In General Relativity
• QCD corrections to tri-boson production
• S@M, a Mathematica Implementation of the Spinor-Helicity Formalism
• One-loop phi-MHV amplitudes using the unitarity bootstrap
• Integral Coefficients for One-Loop Amplitudes
• One-loop amplitudes for W+3 jet production in hadron collisions
• One-loop phi-MHV amplitudes using the unitarity bootstrap: the general helicity case
• The rational parts of one-loop QCD amplitudes I: The general formalism
• One-loop MHV Rules and Pure Yang-Mills
• Polynomial Structures in One-Loop Amplitudes
• NLO QCD corrections to the production of t-tbar-Z in gluon fusion
• Unitarity Method with Spurious Pole
• Massive Quark-Gluon Scattering Amplitudes at Tree Level
• Next-to-Leading-Order Corrections to Weak Boson Production with a Massive Quark Jet Pair at Hadron Colliders
• Automated calculations for multi-leg processes
• Hard QCD at hadron colliders
• One-Loop Six Gluon Amplitude
• MHV Lagrangians for Yang--Mills and QCD
• On perturbative field theory and twistor string theory