Abstract
It has been suggested a long time ago by W. Bardeen that non-vanishing of the one-loop same helicity YM amplitudes, in particular such an amplitude at four points, should be interpreted as an anomaly. However, the available derivations of these amplitudes are rather far from supporting this interpretation in that they share no similarity whatsoever with the standard triangle diagram chiral anomaly calculation. We provide a new computation of the same helicity four-point amplitude by a method designed to mimic the chiral anomaly derivation. This is done by using the momentum conservation to rewrite the logarithmically divergent four-point amplitude as a sum of linearly and then quadratically divergent integrals. These integrals are then seen to vanish after appropriate shifts of the loop momentum integration variable. The amplitude thus gets related to shifts, and these are computed in the standard textbook way. We thus reproduce the usual result but by a method which greatly strengthens the case for an anomaly interpretation of these amplitudes.
Highlights
In [7] William A
The purpose of this paper is to provide a new computation of the result (1.1) by a method that does not require going to additional dimensions and mimics the textbook triangle diagram chiral anomaly computation
We perform all computations for massless QED, but in appendix we review the version of the Feynman rules for self-dual YM (SDYM) that makes it manifest that the SDYM amplitudes are multiples of those in massless QED
Summary
All computations in this paper are performed for massless QED, as the Feynman rules are simplest in this case. We adopt spinor index-free notation of bras and kets. A 4-momentum lμ, where μ is the usual spacetime index, becomes the spinorial object lM M It can “act” on a primed spinor λM returning an object lM M λM that is an unprimed spinor. In index-free notation the primed spinor λM is represented by a ket |λ], where the square bracket indicates that this is a primed spinor. The umprimed spinor lM M λM gets represented as the result of action of l on the ket |λ], which we write as l|λ] This can be contracted with an arbitrary unprimed spinor μM. We label external momenta on any diagram as k1, k2, It is very convenient, when no confusion can arise, to drop the letter k and refer to the momentum just by its number.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
