Dilatons Improve (Non)-Goldstones

Roman Zwicky

doi:10.1016/j.nuclphysb.2025.117292

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arXiv · 2306.12914

Dilatons Improve (Non)-Goldstones

Roman Zwicky

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Abstract

Shift symmetry forbids conformal coupling of Goldstone bosons from internal symmetries, but not for spontaneously broken conformal symmetry. Its Goldstone boson, the dilaton $D$, admits and indeed requires, an improvement term $ {\cal L}_R \propto R e^{-2D/F_D}$ as it realises the Goldstone matrix element in the effective theory. The improvement, combined with Weyl-gauging, enables conformal coupling to Goldstone bosons and other particles of arbitrary 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, confirming low-energy constraints. The dilaton decoupling limit further implies that the operator driving spontaneous chiral symmetry breaking has scaling dimension $\Delta= d-2$.

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Roman Zwicky. 2023-06-22. Dilatons Improve (Non)-Goldstones. https://doi.org/10.1016/j.nuclphysb.2025.117292

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