Conformal Symmetry and Pion Form Factor: Space- and Time-like Region

TL;DR

This paper extends conformal symmetry constraints on the pion electromagnetic form factor to the time-like region, demonstrating the importance of quark spin and mass effects in reproducing vector meson dominance features.

Contribution

It introduces an analytic continuation approach for the pion form factor from space-like to time-like regions under conformal symmetry constraints.

Findings

Time-like form factor satisfies dispersion relation.

Quark spin and mass effects are essential for realistic vector meson dominance.

Analytic continuation accurately models form factor behavior.

Abstract

We extend a recent analysis of the pion electromagnetic form factor constrained by the conformal symmetry to explore the time-like region. We show explicitly that the time-like form factor obtained by the analytic continuation of the space-like form factor correctly satisfies the dispersion relation. Our results indicate that the quark spin and dynamical mass effects are crucial to yield the realistic features of the vector meson dominance phenomena.