Symmetries, sum rules and constraints on effective field theories

Brando Bellazzini (1, 2) , Luca Martucci (3, 2) , Riccardo Torre (4, 2, 3)

1 IPHT - Institut de Physique Théorique - UMR CNRS 3681
2 Dipartimento di Fisica e Astronomia "Galileo Galilei"
3 INFN, Sezione di Padova
4 SISSA and INFN Sezione di Trieste

Using unitarity, analyticity and crossing symmetry, we derive universal sum rules for scattering amplitudes in theories invariant under an arbitrary symmetry group. The sum rules relate the coefficients of the energy expansion of the scattering amplitudes in the IR to total cross sections integrated all the way up to the UV. Exploiting the group structure of the symmetry, we systematically determine all the independent sum rules and positivity conditions on the expansion coefficients. For effective field theories the amplitudes in the IR are calculable and hence the sum rules set constraints on the parameters of the effective Lagrangian. We clarify the impact of gauging on the sum rules for Gold-stone bosons in spontaneously broken gauge theories. We discuss explicit examples that are relevant for W W-scattering, composite Higgs models, and chiral perturbation theory. Certain sum rules based on custodial symmetry and its extensions provide constraints on the Higgs boson coupling to the electroweak gauge bosons.

Keywords: Beyond Standard Model; Sum Rules; Chiral Lagrangians; Global Symmetries

Domains: High Energy Physics - Theory [hep-th]; High Energy Physics - Phenomenology [hep-ph]

Brando Bellazzini, Luca Martucci, Riccardo Torre. Symmetries, sum rules and constraints on effective field theories. Journal of High Energy Physics, 2014, 2014 (9), ⟨10.1007/JHEP09(2014)100⟩. ⟨cea-01236289⟩