On gauge amplitudes first appearing at two loops

Program Document · Sat Jul 20 04:00:00 EDT 2024

OSTI ID:2404879

Dixon, Lance J ^[1]; Morales, Anthony ^[2]

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1. SLAC National Accelerator Laboratory (SLAC), Menlo Park, CA (United States), FPD Theory Elem Particle Phys
2. Physics Department, Stanford University

We study scattering amplitudes in massless non-abelian gauge theory where all outgoing gluons have positive helicity. It has been argued recently by Costello that for a particular fermion representation (8 fundamentals plus one antisymmetric-tensor representation in SU(N)) the one-loop amplitudes vanish identically. We show that this vanishing leads to previously-observed identities among one-loop color-ordered partial amplitudes. We then turn to two loops, where Costello has computed the all-plus amplitudes for this theory, as rational functions of the kinematics for any number of gluons using the celestial chiral algebra (CCA) bootstrap. We show that in dimensional regularization, these two-loop amplitudes are not rational, and they are not even finite as ϵ → 0. However, the finite remainder for four gluons agrees with the formula by Costello. In addition, we provide a mass regulator for the infrared-divergent loop integrals; with this regulator, the CCA bootstrap formula is recovered exactly. Finally, we use the CCA bootstrap to compute the double-trace terms in the theory at two loops for an arbitrary number of gluons.

• Research Organization: SLAC National Accelerator Laboratory (SLAC), Menlo Park, CA (United States)
• Sponsoring Organization: USDOE Office of Science (SC)
• DOE Contract Number: AC02-76SF00515
• OSTI ID: 2404879
• Country of Publication: United States
• Language: English