On-Shell Methods in Field Theory. David A. Kosower International School of Theoretical Physics, Parma, September 10-15, 2006 Lecture III. Factorization in Gauge Theory. Collinear limits with splitting amplitudes. Twistors and CSW. On-Shell Recursion Relation. =.
Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.
David A. Kosower
International School of Theoretical Physics, Parma, September 10-15, 2006
Collinear limits with splitting amplitudes
Let’s compute it with complex momenta chosen so that
so we have to compute
but gauge invariant nonetheless,
and exactly the n=3 case of the general Parke–Taylor formula!
Pick a shift, giving one diagram
Three-point vertices with z-dependent momentum flow ~ z
Four-point vertices with z-dependent momentum flow ~ 1
Propagators with z-dependent momentum flow ~ 1/z
(one more vertex than propagators & two εs)
Compute the (1−,j−) amplitude: choose shift
Other diagrams vanish because
Consider NMHV amplitude: 3 negative helicities m1, m2, m3, any number of positive helicities
Momenta are still on shell, and
because of the Schouten identity
Bjerrum-Bohr, Dunbar, Ita, Perkins & Risager, th/0509016
unphysical singularity— cancels between terms
Grisaru, Pendleton & van Nieuwenhuizen (1977)