Transmuting off-shell CHY integrals in the double-cover framework

TL;DR

This paper extends the CHY integral framework to off-shell amplitudes using differential operators, generalizing key relations and verifying the double-cover approach.

Contribution

It introduces a method to link off-shell amplitudes via differential operators within the double-cover CHY framework, generalizing known on-shell amplitude relations.

Findings

Off-shell amplitudes can be linked using differential operators.

Generalization of on-shell amplitude relations to off-shell cases.

Verification of the double-cover construction for off-shell integrals.

Abstract

In this paper, by defining off-shell amplitudes as off-shell CHY integrals, and redefining the longitudinal operator, we demonstrate that the differential operators which link on-shell amplitudes for a variety of theories together, also link off-shell amplitudes in the similar manner. Based on the algebraic property of the differential operator, we also generalize three relations among color-ordered on-shell amplitudes, including the color-ordered reversed relation, the photon decoupling relation, the Kleiss-Kuijf relation, to off-shell ones. The off-shell CHY integrals are chosen to be in the double-cover framework, thus, as a by product, our result also provides a verification for the double-cover construction.