# Hilbert Transforms and Sum Rules of Bessel Moments

## TL;DR

This paper uses Hilbert transforms to derive sum rules for Bessel moments, confirming and extending previous conjectures related to integrals in quantum field theory.

## Contribution

It introduces new linear relations among Bessel moments using Hilbert transforms, generalizing prior conjectures in the field.

## Key findings

- Established two families of sum rules for Bessel moments.
- Verified and generalized two conjectures by Bailey-Borwein-Broadhurst-Glasser and Broadhurst-Mellit.
- Connected Bessel moments with Feynman diagram integrals in quantum field theory.

## Abstract

Using Hilbert transforms, we establish two families of sum rules involving Bessel moments, which are integrals associated with Feynman diagrams in two-dimensional quantum field theory. With these linear relations among Bessel moments, we verify and generalize two conjectures by Bailey-Borwein-Broadhurst-Glasser and Broadhurst-Mellit.