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

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 ($n\ge 4$) 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.

Latex, 35 pages, 6 figures; v2: typos corrected; v3: published version

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