Likelihood of a zero in the proton elastic electric form factor

TL;DR

This study uses a model-independent method to analyze proton form factor data, predicting a high likelihood of a zero in the ratio at certain momentum transfers, which has implications for understanding proton structure.

Contribution

It applies the Schlessinger point method to proton form factor data to objectively assess the existence and location of a zero in the ratio, independent of strong interaction models.

Findings

Data are consistent with a zero in the ratio at Q^2 ≤ 10.37 GeV^2 with 50% confidence.

Confidence increases to 99.9% for Q^2 ≤ 13.06 GeV^2.

The probability of no zero up to Q^2 ≤ 14.49 GeV^2 is one in a million.

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 $Q^2 \leq 10.37\,$GeV$^2$. The level of confidence increases to $99.9$\% on $Q^2 \leq 13.06\,$GeV$^2$. Significantly, the likelihood that existing data are consistent with the absence of a zero in the ratio on $Q^2 \leq 14.49\,$GeV$^2$ is $1/1$-million.