Generalized Fierz Identities and Applications to Spin-3/2 Particles

Understand

We study the most general Fierz identities for a pair of non-contracted Dirac matrices both in the standard basis and for chiral spinors.

• These identities are useful in building independent effective operators of fermions that involve derivatives or sextuple and more fields.
• We apply them to construct independent effective four-fermion interactions that contain one to three spin-3/2 chiral fields.
• These operators could be relevant to physics of higher-spin baryons and phenomenology of a neutral, massive spin-3/2 particle as a dark matter candidate.