Constraining the low energy Pion electromagnetic form factor with space-like and phase of time-like data

TL;DR

This paper constrains the low-energy pion electromagnetic form factor's Taylor coefficients using analyticity, phase information from time-like data, and space-like measurements, providing tighter bounds and comparisons with theoretical predictions.

Contribution

It introduces a method using Lagrange multipliers to derive bounds on the pion form factor's coefficients incorporating phase and space-like data, improving existing constraints.

Findings

Stringent constraints on the coefficient c consistent with chiral perturbation theory

Estimated d coefficient around 10 GeV^{-6} when c is fixed to theoretical values

Results agree with previous literature and theoretical predictions

Abstract

The Taylor coefficients c and d of the Pion EM form factor are constrained using analyticity, knowledge of the phase of the form factor in the time-like region, 4 m_pi^2 \le t \le \tin and its value at one space-like point, using as input the (g-2) of the muon. This is achieved using the technique of Lagrange multipliers, that gives a transparent expression for the corresponding bounds. We present a detailed study of the sensitivity of the bounds to the choice of time-like phase and errors present in the space-like data, taken from recent experiments. We find that our results constrain c stringently. We compare our results with those in literature and find agreement with the chiral perturbation theory results for $c$. We obtain d \sim O(10)GeV^{-6} when c is set to the chiral perturbation theory values.