Abstract
Beyond-the-standard-model (BSM) particles should be included in effective field theory in order to compute the scattering amplitudes involving these extra particles. We formulate an extension of Higgs effective field theory which contains an arbitrary number of scalar and fermion fields with arbitrary electric and chromoelectric charges. The BSM Higgs sector is described by using the nonlinear sigma model in a manner consistent with the spontaneous electroweak symmetry breaking. The chiral-order counting rule is arranged consistently with the loop expansion. The leading-order Lagrangian is organized in accord with the chiral-order counting rule. We use a geometrical language to describe the particle interactions. The parametrization redundancy in the effective Lagrangian is resolved by describing the on-shell scattering amplitudes only with the covariant quantities in the scalar/fermion field space. We introduce a useful coordinate (normal coordinate), which simplifies the computations of the on-shell amplitudes significantly. We show that the high-energy behaviors of the scattering amplitudes determine the ``curvature tensors'' in the scalar/fermion field space. The massive spinor--wave function formalism is shown to be useful in the computations of on-shell helicity amplitudes.
Highlights
Four seemingly independent fundamental energy scales that we know about in elementary particle physics, the Planck scale ≃1.2 × 1019 GeV, the cosmological constant ≃ð2.2 meVÞ4(accelerated expansion of the Universe), the weak scale v ≃246 GeV, and the QCD scale ≃300 MeV.Among these four known fundamental energy scales, the most well understood one is the QCD scale
We have proposed the generalized Higgs effective field theory (GHEFT) framework [37], in which arbitrary number of spin-0 resonances/
In our previous paper on GHEFT [37], we showed that
Summary
Four seemingly independent fundamental energy scales that we know about in elementary particle physics, the Planck scale ≃1.2 × 1019 GeV (energy scale of gravitational interaction), the cosmological constant ≃ð2.2 meVÞ4. For strongly interacting BSM, we can use the Higgs effective field theory (HEFT) [16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31], in which the electroweak symmetry SUð2Þ × Uð1Þ is realized nonlinearly. GHEFT (electroweak resonance chiral perturbation theory) can be described by using the covariant tensors of the scalar manifolds, which allows us to parametrize the particle scattering amplitudes and the quantum corrections in a covariant manner under the changes of effective field variables (coordinates) [48,49]. The scattering amplitude formulas given in this paper can be compared to the formulas computed in other equivalent formulation of fermionic resonance electroweak chiral perturbation theories. Appendix C is for the explicit computations of higher-order coefficients in the normal coordinate expansion, as well as a proof of Bianchi identity
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