# On structure constants with two spinning twist-two operators

## TL;DR

This paper investigates the structure constants of three-point functions involving twist-two operators with spin in N=4 SYM, proposing a conjecture for their spin dependence and computing corrections at one and two loops.

## Contribution

It introduces an empiric conjecture for the spin dependence of structure constants and computes their one- and two-loop corrections in N=4 SYM.

## Key findings

- Proposed a conjecture for structure constants' dependence on spins.
- Fixed infinite sets of one-loop structure constants using the conjecture.
- Calculated two-loop corrections for specific spin values.

## Abstract

I consider three-point functions of one protected and two unprotected twist-two operators with spin in N=4 SYM at weak coupling. At one loop I formulate an empiric conjecture for the dependence of the corresponding structure constants on the spins of the operators. Using such an ansatz and some input from explicit perturbative results, I fix completely various infinite sets of one-loop structure constants of these three-point functions. Finally, I determine the two-loop corrections to the structure constants for a few fixed values of the spins of the operators.