Gravitational form factors of the $Z$-boson

Matrix elements of the energy-momentum tensor for one-particle states of the $Z$-boson are parameterized in terms of gravitational form factors. One-loop order electroweak corrections to these quantities are calculated. Renormalization and physical interpretation of the obtained results are discussed.

💡 Research Summary

The paper investigates the gravitational structure of the Standard Model Z‑boson by computing its energy‑momentum tensor (EMT) matrix elements for one‑particle states and expressing them in terms of gravitational form factors (GFFs). The authors adopt a parametrisation appropriate for a massive spin‑1 particle, introducing seven independent form factors: (A_0(t), A_1(t), J(t), D_0(t), D_1(t), E(t)) and a set of five antisymmetric structures (F_{1\ldots5}(t)). Unlike the usual treatment for even‑parity systems, the Z‑boson is unstable, so the pole is complex and the residues must be extracted using the LSZ reduction formalism applied to the two‑point function of the EMT with two Z‑fields.

The calculation proceeds at one‑loop order in the electroweak theory. The authors start from the Standard Model Lagrangian (as given in Ref.