Connected formulas for amplitudes in standard model

TL;DR

This paper extends twistor-string inspired connected formulas to include QCD tree amplitudes with massless quarks and Higgs bosons, providing new representations for more realistic Standard Model processes.

Contribution

It introduces connected formulas for QCD and Higgs amplitudes in four dimensions, generalizing previous pure-gluon formulas to include quarks and massive Higgs bosons.

Findings

Connected formulas for quark-gluon amplitudes include a flavor-dependent Jacobian.

Higgs amplitudes are represented by two additional massless legs, modeling the Higgs effectively.

First twistor-string/connected formula for form factors is presented.

Abstract

Witten's twistor string theory has led to new representations of S-matrix in massless QFT as a single object, including Cachazo-He-Yuan formulas in general and connected formulas in four dimensions. As a first step towards more realistic processes of the standard model, we extend the construction to QCD tree amplitudes with massless quarks and those with a Higgs boson. For both cases, we find connected formulas in four dimensions for all multiplicities which are very similar to the one for Yang-Mills amplitudes. The formula for quark-gluon color-ordered amplitudes differs from the pure-gluon case only by a Jacobian factor that depends on flavors and orderings of the quarks. In the formula for Higgs plus multi-parton amplitudes, the massive Higgs boson is effectively described by two additional massless legs which do not appear in the Parke-Taylor factor. The latter also represents the first twistor-string/connected formula for form factors.