Theory of unitarity bounds and low energy form factors

TL;DR

This paper develops a formalism to derive bounds on form factors using QCD correlators, analyticity, and unitarity, with applications to flavor physics and form factor parameterizations.

Contribution

It introduces a comprehensive method to incorporate various theoretical and lattice inputs into bounds on form factors, including phase and modulus constraints.

Findings

Derived bounds on K_l3 scalar form factor slope and curvature.

Provided a solution to the Meiman problem with multiple interior constraints.

Discussed the implications for flavor physics precision predictions.

Abstract

We present a general formalism for deriving bounds on the shape parameters of the weak and electromagnetic form factors using as input correlators calculated from perturbative QCD, and exploiting analyticity and unitarity. The values resulting from the symmetries of QCD at low energies or from lattice calculations at special points inside the analyticity domain can beincluded in an exact way. We write down the general solution of the corresponding Meiman problem for an arbitrary number of interior constraints and the integral equations that allow one to include the phase of the form factor along a part of the unitarity cut. A formalism that includes the phase and some information on the modulus along a part of the cut is also given. For illustration we present constraints on the slope and curvature of the K_l3 scalar form factor and discuss our findings in some detail. The techniques are useful for checking the consistency of various inputs and for controlling the parameterizations of the form factors entering precision predictions in flavor physics.