Abstract
The purely on-shell approach to effective field theories requires the construction of independent contact terms. Employing the little-group-covariant massive-spinor formalism, we present the first systematic derivation of independent four-point contact terms involving massive scalars, spin-1/2 fermions, and vectors. Independent three-point amplitudes are also listed for massive particles up to spin-3. We make extensive use of the simple relations between massless and massive amplitudes in this formalism. Our general results are specialized to the (broken-phase) particle content of the electroweak sector of the standard model. The (anti)symmetrization among identical particles is then accounted for. This work opens the way for the on-shell computation of massive four-point amplitudes.
Highlights
The remainder of the four-point amplitude consists of pole-free non-factorizable contact terms which map to higher-dimensional operators in a Lagrangian formulation
We addressed the construction of contact-term bases required to form massive on-shell three- and four-point amplitudes
Some of the techniques we described apply to higher-spin and higher-point contact terms
Summary
A massive amplitude carries 2si symmetrized little-group indices for each external particle of spin si. We identify the sets of independent spinor structures {S{I}} from which contact-term bases can be generated by multiplying each element S{I} by Lorentz invariants. For the purpose of constructing an SCT basis, a spinor structure is redundant if it can be expressed as a linear combination of the other structures, with prefactors involving only non-negative powers of Lorentz invariants and masses (in the massive case). Inverse powers of the masses are only required in the i [i/mi combinations appearing in the polarization vectors of particles of spin-1 and higher Another basis of interest is the spinor-structure basis, which can be used to span a generic amplitude. Using the massless relations between spinor products, including Schouten identities, it is straightforward to identify SCT bases for massless amplitudes [16]
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