Constraining Form Factors with the Method of Unitarity Bounds

TL;DR

This paper reviews the method of unitarity bounds, a mathematical technique that constrains form factors using bounds on integrals of their modulus, and discusses recent advances incorporating phase and modulus information for precise predictions.

Contribution

It provides a comprehensive review of the unitarity bounds method and introduces recent developments that enhance its capability to include phase and modulus data.

Findings

The method effectively constrains form factors inside the analyticity domain.

Inclusion of phase and modulus information improves the precision of form factor predictions.

The technique can exclude zeros in specific regions of the complex plane.

Abstract

The availability of a reliable bound on an integral involving the square of the modulus of a form factor on the unitarity cut allows one to constrain the form factor at points inside the analyticity domain and its shape parameters, and also to isolate domains on the real axis and in the complex energy plane where zeros are excluded. In this lecture note, we review the mathematical techniques of this formalism in its standard form, known as the method of unitarity bounds, and recent developments which allow us to include information on the phase and modulus along a part of the unitarity cut. We also provide a brief summary of some results that we have obtained in the recent past, which demonstrate the usefulness of the method for precision predictions on the form factors.