2014/05/31 by Brando Bellazzini, Luca Martucci, Riccardo Torre
Mathematics · Physics and Astronomy · #Amplitude #Black Holes and Theoretical Physics #Boson #Electroweak interaction #Gauge boson #Gauge theory #Geometry #Global symmetry #Goldstone boson #Higgs boson #Homogeneous space #Invariant (physics) #Mathematical physics #Mathematics #Particle physics #Particle physics theoretical and experimental studies #Physics #Quantum Chromodynamics and Particle Interactions #Quantum chromodynamics #Quantum mechanics #Scattering amplitude #Spontaneous symmetry breaking #Sum rule in quantum mechanics #Symmetry breaking #Symmetry group #Theoretical physics #Unitarity #hep-ph #hep-th
paper · pdf · doi:10.1007/jhep09(2014)100
50 pages, 5 figures, 5 appendices; several typos fixed, discussions improved, references added; results unchanged
arxiv created 2014/07/09 · openalex publication_date 2014/09/01 · arxiv updated 2015/06/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
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 Goldstone bosons in spontaneously broken gauge theories. We discuss explicit examples that are relevant for WW-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.