Pion electromagnetic form factor at spacelike momenta.

TLDR: The analysis shows that hard contributions to the pion form factor dominate for Q²≳8 GeV², but, even so, the magnitude of Q²F(π)(Q²) reflects the scale of dynamical chiral symmetry breaking, a pivotal emergent phenomenon in the standard model.

Abstract: A novel method is employed to compute the pion electromagnetic form factor, ${F}_{\ensuremath{\pi}}({Q}^{2})$, on the entire domain of spacelike momentum transfer using the Dyson-Schwinger equation (DSE) framework in QCD. The DSE architecture unifies this prediction with that of the pion's valence-quark parton distribution amplitude (PDA). Using this PDA, the leading-order, leading-twist perturbative QCD result for ${Q}^{2}{F}_{\ensuremath{\pi}}({Q}^{2})$ underestimates the full computation by just 15% on ${Q}^{2}\ensuremath{\gtrsim}8\text{ }\text{ }{\mathrm{GeV}}^{2}$, in stark contrast to the result obtained using the asymptotic PDA. The analysis shows that hard contributions to the pion form factor dominate for ${Q}^{2}\ensuremath{\gtrsim}8\text{ }\text{ }{\mathrm{GeV}}^{2}$, but, even so, the magnitude of ${Q}^{2}{F}_{\ensuremath{\pi}}({Q}^{2})$ reflects the scale of dynamical chiral symmetry breaking, a pivotal emergent phenomenon in the standard model.