Twistor-Inspired Construction of Electroweak Vector Boson Currents

TL;DR

The paper addresses the challenge of efficiently computing tree-level amplitudes with both colored QCD partons and electroweak vector bosons. It extends the Cachazo–Svrček–Witten CSW (twistor-inspired) framework by introducing off-shell vector-boson currents with new basic vertices, enabling construction of NMHV and higher-current amplitudes with one quark pair and any number of gluons. The authors show consistency with known results for Z, W, gamma* -> q qbar + n gluons up to n=3 and validate against Berends–Giele recursion up to high multiplicities, including non-abelian triple-vector-boson couplings. This work broadens the applicability of CSW rules to mixed QCD–EW processes and suggests avenues for multi-vector-boson and colored-vector currents in collider phenomenology. The approach offers a potentially efficient tool for collider physics involving electroweak vector bosons.

Abstract

We present an extension of the twistor-motivated MHV vertices and accompanying rules presented by Cachazo, Svrvcek and Witten to the construction of vector-boson currents coupling to an arbitrary source. In particular, we give rules for constructing off-shell vector-boson currents with one fermion pair and n gluons of arbitrary helicity. These currents may be employed directly in the computation of electroweak amplitudes. The rules yield expressions in agreement with previously-obtained results for Z,W,γ^* --> qbar q + n gluons (analytically up to n=3, beyond via the Berends--Giele recursion relations). We also confirm that the contribution to a seven-point amplitude containing the non-abelian triple vector-boson coupling obtained using the next-to-MHV currents matches the previous result in the literature.

Figures (4)

• Figure 1: The stripped diagrams for 3 minus helicity amplitudes with vector boson exchange between two fermion pairs. Legs 1 and 2 correspond to the leptons and the legs 3 and $n$ to the quarks. Lines with arrows represent quarks and those without arrows represent either vector bosons or gluons.
• Figure 2: The NMHV vector boson current in terms of diagrams where positive helicity gluon lines have been stripped.
• Figure 3: The two Feynman diagrams contributing the seven point amplitude with a triple vector boson self coupling. Wavy lines represent gauge bosons such as the $W$ or $Z$ and curly lines gluons.
• Figure 4: The Feynman diagram for the electroweak vector boson current with a non-abelian triple vector boson self interaction. We may couple this to the QCD vector boson current determined using CSW diagrams.