# Scalar radius of the pion and zeros in the form factor

## TL;DR

This paper reanalyzes the pion scalar radius, resolving discrepancies between previous methods by considering zeros in the form factor, leading to a more consistent value with experimental phase shift uncertainties.

## Contribution

It introduces a method that accounts for zeros in the scalar form factor, reconciling different calculations of the pion scalar radius.

## Key findings

- Revised scalar radius value: 0.65±0.05 fm^2.
- Identification of zeros in the form factor for certain T-matrices.
- Main uncertainties stem from experimental phase shifts and asymptotic phase behavior.

## Abstract

The quadratic pion scalar radius, \la r^2\ra^\pi_s, plays an important role for present precise determinations of \pi\pi scattering. Recently, Yndur\'ain, using an Omn\`es representation of the null isospin(I) non-strange pion scalar form factor, obtains \la r^2\ra^\pi_s=0.75\pm 0.07 fm^2. This value is larger than the one calculated by solving the corresponding Muskhelishvili-Omn\`es equations, \la r^2\ra^\pi_s=0.61\pm 0.04 fm^2. A large discrepancy between both values, given the precision, then results. We reanalyze Yndur\'ain's method and show that by imposing continuity of the resulting pion scalar form factor under tiny changes in the input \pi\pi phase shifts, a zero in the form factor for some S-wave I=0 T-matrices is then required. Once this is accounted for, the resulting value is \la r^2\ra_s^\pi=0.65\pm 0.05 fm^2. The main source of error in our determination is present experimental uncertainties in low energy S-wave I=0 \pi\pi phase shifts. Another important contribution to our error is the not yet settled asymptotic behaviour of the phase of the scalar form factor from QCD.