# Two-loop Doubly Massive Four-Point Amplitude Involving a half-BPS and Konishi Operator

## TL;DR

This paper analytically computes a two-loop four-point amplitude involving a half-BPS and Konishi operator in maximally supersymmetric Yang-Mills theory, verifying UV behavior and IR divergence exponentiation.

## Contribution

It provides the first explicit two-loop amplitude involving a half-BPS and a Konishi operator, revealing unique transcendental structures and verifying key theoretical properties.

## Key findings

- Verified the ultraviolet behavior of the unprotected operator.
- Confirmed the exponentiation of infrared divergences with universal anomalous dimensions.
- Discovered lower transcendental weight terms in the amplitude.

## Abstract

The two-loop four-point amplitude of two massless SU(N) colored scalars and two color singlet operators with different virtuality described by a half-BPS and Konishi operators is calculated analytically in maximally supersymmetric Yang-Mills theory. We verify the ultraviolet behaviour of the unprotected composite operator and exponentiation of the infrared divergences with correct universal values of the anomalous dimensions in the modified dimensional reduction scheme. The amplitude is found to contain lower transcendental weight terms in addition to the highest ones and the latter has no similarity with similar amplitudes in QCD.