Dilatons Improve (Non)-Goldstones

Shift symmetry forbids conformal coupling of Goldstone bosons from internal symmetries, but not for spontaneously broken conformal symmetry. Its Goldstone boson, the dilaton 𝐷, requires the improvement term L 𝑅 ∝ 𝑅𝑒−2𝐷∕𝐹𝐷 to realise the Goldstone matrix element in the effective theory. The dilaton can be used for Weyl-gauging and conformally couple to particles of any Weyl-weight. While improvement does not affect scattering amplitudes in flat space, it impacts gravitational form factors decisively, giving rise to the dilaton pole in the spin-zero channel. We
compute leading-order scalar, fermion, pion and dilaton form factors, including the treatment soft breaking by a relevant perturbation. We show that a pion low-energy theorem enforces the operator driving spontaneous chiral symmetry breaking to be of scaling dimension Δ = 𝑑 − 2 at the fixed point.