Method for measuring the charge radii of charged hyperons from the time-like region

TL;DR

This paper introduces a new experimental method to measure the charge radii of charged hyperons using Dalitz decays, enabling precise measurements in the time-like region and offering a cross-check for proton radius determinations.

Contribution

It proposes a novel approach leveraging Dalitz decays to measure hyperon charge radii, including the first potential measurements for $oldsymbol{oldsymbol{ ext{Σ}}^+}$ and $oldsymbol{oldsymbol{ ext{Ξ}}^-}$ hyperons.

Findings

Charge radii can be measured with 0.2 fm precision at BES extsuperscript{3}

Future facilities could improve accuracy by an order of magnitude

Method also applicable to proton charge radius measurements

Abstract

We propose a novel method for measuring the charge radii of charged stable hadrons, with which the first measurement of the charge radii of the $\Sigma^+$ and the $\Xi^-$ is foreseen. The method explores the facts that the Dalitz decay $\psi(2S) \to Y\bar{Y}e^+e^-$ contains the hyperon form factors and the lowest measurable four-momentum transfer squared can be as low as $\sim 4m_e^2= 1.05\times10^{-6}\,{\rm GeV^2}$ in the time-like region. We identify a kinematic region where the hyperon form factors are essential and propose a method for subtracting the background from the data. It is estimated that the hyperon charge radii can be measured to a precision of about {0.2~fm} with the BES\Rom{3} experiment and one order of magnitude better at the future Super $\tau$-Charm Facility. Moreover, the same method can be used to measure the charge radius of the proton, which provides an independent cross-check on the extraction of proton radius from elastic $ep$ scattering or leptonic hydrogen spectroscopy.