Likelihood of a zero in the proton elastic electric form factor

Abstract

Working with the 29 available data on the ratio of proton electric and magnetic form factors, ${\mu }_p{G}_E^p\left(Q^2\right)/G_M^p\left(Q^2\right)$, and independent of any model or theory of strong interactions, we use the Schlessinger point method to objectively address the question of whether the ratio possesses a zero and, if so, its location. Our analysis predicts that, with 50% confidence, the data are consistent with the existence of a zero in the ratio on $Q^2\le 10.37$ GeV². The level of confidence increases to 99.9% on $Q^2\le 13.06$ GeV². Significantly, the likelihood that existing data are consistent with the absence of a zero in the ratio on $Q^2\le 14.49$ GeV² is 1/1-million.