Form factor decomposition of the off-shell four-gluon amplitudes

Understand

We show how to use the Bern-Kosower master formula, originally a generating functional for on-shell gluon matrix elements, to derive well-organized form factor decompositions of the off-shell one-particle-irreducible N - gluon vertices.

• Two such algorithms are presented which can be used for any N, the first one optimized with respect to the nonabelian gauge invariance, the second one with respect to transversality.
• We give explicit results for the three- and four-gluon cases.
• The second algorithm in the three-point case reproduces precisely the well-known Ball-Chiu decomposition, and in the four-point case a natural generalization thereof.