Conformal anomaly of generalized form factors and finite loop integrals

TL;DR

This paper uncovers a new conformal symmetry breaking mechanism in generalized form factors involving massless particles, revealing hidden singularities and their impact on finite loop integrals across dimensions.

Contribution

It introduces a novel conformal anomaly mechanism at Born level due to collinear singularities, distinct from known holomorphic anomalies, with applications to loop integrals and conformal Ward identities.

Findings

Identification of a new conformal anomaly mechanism in form factors.

Derivation of second-order differential equations for loop integrals.

Application to finite loop integrals like the four-dimensional scalar double box.

Abstract

We reveal a new mechanism of conformal symmetry breaking at Born level. It occurs in generalized form factors with several local operators and an on-shell state of massless particles. The effect is due to hidden singularities on collinear configurations of the momenta. This conformal anomaly is different from the holomorphic anomaly of amplitudes. We present a number of examples in four and six dimensions. We find an application of the new conformal anomaly to finite loop momentum integrals with one or more massless legs. The collinear region around a massless leg creates a contact anomaly, made visible by the loop integration. The anomalous conformal Ward identity for an $\ell-$loop integral is a 2nd-order differential equation whose right-hand side is an $(\ell-1)-$loop integral. We show several examples, in particular the four-dimensional scalar double box.