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, ${\mu }_p{G}_E^p(Q^2)/G_M^p(Q^2)$, 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 $Q^2\le 10.37$GeV${}^2$. The level of confidence increases to $99.9$\% on $Q^2\le 13.06$GeV${}^2$. Significantly, the likelihood that existing data are consistent with the absence of a zero in the ratio on $Q^2\le 14.49$GeV${}^2$ is $1/1$-million.

Comments: 7 pages, 6 figures, 1 table