Fermi Geometry of the Higgs Sector

Abstract

We develop the field space geometry of scalar-fermion effective field theories as a vector bundle supermanifold. We further establish a Fermi normal coordinate system on the bundle that clarifies the geometric content in scattering amplitudes, particularly the imprints of field space non-analyticities. Specializing to the Standard Model Higgs sector, we examine the geometric consequences of custodial symmetry violation, including implications for the physical Higgs field as a distinguished scalar axis and deformations in the fermionic sector. Our results enable a systematic and realistic geometric interpretation of Higgs sector phenomenology.

35 pages, 1 figure. v2: Journal version, a fermion amplitude corrected