Determine the pole-versus-zero infrared character

Determine whether the light propagator in the sourced symmetric-mass-generation phase has a pole or a Green’s-function zero as $p\to0$.

Background

The symmetry proposition predicts that, under its stated assumptions, a symmetrically gapped light channel has a Green’s-function zero rather than a mass-type pole. The numerical discriminator is the mass-type part of the propagator at zero momentum.

The available lattices do not reach sufficiently small momentum to distinguish these possibilities. The measured odd-part exponent separates phases but does not identify a zero specific to the light half, so an infrared measurement at larger volume is required.

References

the pole-versus-zero character of the light propagator at $p\to0$ is not measured

— Mass as pairing: an explicit Majorana mass on half of a generation does not seesaw in symmetric mass generation  (2610.07735 - Topa, 6 Oct 2026) in Section 6, subsection “What $L\le8$ does not determine”