On MHV Form Factors in Superspace for $\mathcal{N}=4$ SYM Theory

TL;DR

This paper develops a supersymmetric unitarity cut method for form factors in $ =4$ SYM, providing explicit expressions and analyzing loop corrections, soft, and collinear limits for MHV form factors.

Contribution

It introduces a supersymmetric approach to compute MHV form factors in $ =4$ SYM, including explicit tree- and one-loop formulas and a two-loop ansatz, advancing computational techniques in the field.

Findings

Explicit $ =4$ covariant expressions for n-point tree- and one-loop MHV form factors.

Verification of the relation between superform factors and superamplitudes at tree and one-loop levels.

Proposal of a two-loop three-point MHV superform factor in the planar limit.

Abstract

In this paper we develop a supersymmetric version of unitarity cut method for form factors of operators from the chiral truncation of the the $\mathcal{N}=4$ stress-tensor current supermultiplet $T^{AB}$. The relation between the superform factor with supermomentum equals to zero and the logarithmic derivative of the superamplitude with respect to the coupling constant is discussed and verified at tree- and one-loop level for any MHV $n$-point ($n \geq 4$) superform factor involving operators from chiral truncation of the stress-tensor energy supermultiplet. The explicit $\mathcal{N}=4$ covariant expressions for n-point tree- and one-loop MHV form factors are obtained. As well, the ansatz for the two-loop three-point MHV superform factor is suggested in the planar limit, based on the reduction procedure for the scalar integrals suggested in our previous work. The different soft and collinear limits in the MHV sector at tree- and one-loop level are discussed.