Effective field theory amplitudes the on-shell way: scalar and vector couplings to gluons

• Published in: The journal of high energy physics Vol. 2019; no. 2; pp. 1 - 26
• Main Authors: Shadmi, Yael, Weiss, Yaniv
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.02.2019; Springer Nature B.V; SpringerOpen
• Subjects: Amplitudes; Beyond Standard Model; Classical and Quantum Gravitation; Couplings; Effective Field Theories; Elementary Particles; Field theory; Gluons; High energy physics; Mathematical analysis; Operators; Particle decay; Photons; Physics; Physics and Astronomy; Polynomials; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; Space-Time Symmetries; String Theory; Effective Field Theories; Beyond Standard Model; Space-Time Symmetries
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP02(2019)165

A bstract We use on-shell methods to calculate tree-level effective field theory (EFT) amplitudes, with no reference to the EFT operators. Lorentz symmetry, unitarity and Bose statistics determine the allowed kinematical structures. As a by-product, the number of independent EFT operators simply follows from the set of polynomials in the Mandelstam invariants, subject to kinematical constraints. We demonstrate this approach by calculating several amplitudes with a massive, SM-singlet, scalar ( h ) or vector ( Z ′ ) particle coupled to gluons. Specifically, we calculate hggg , hhgg and Z ′ ggg amplitudes, which are relevant for the LHC production and three-gluon decays of the massive particle. We then use the results to derive the massless- Z ′ amplitudes, and show how the massive amplitudes decompose into the massless-vector plus scalar amplitudes. Amplitudes with the gluons replaced by photons are straightforwardly obtained from the above.