### 5.8 Constraints on the Higgs sector

Since the constraints on various parameters of the mSME are so tight, one can derive interesting
indirect constraints on unmeasured sectors by considering loop effects. Such an approach has been
recently taken in [28], where loop corrections to mSME coefficients from Lorentz violation in the
Higgs sector are considered. Such an approach could be used with any particle, but since the
Higgs is an observationally hidden sector, such an analysis is more important as direct tests
are unlikely any time soon. There are four parameters in the Higgs sector of the mSME (see
Section 4.1.1).
Constraints on the antisymmetric part of , which we denote , and
come from the birefringence constraints on photon propagation (see Section 6.3). Here the loop corrections
to the photon propagator induce a non-zero , which can be directly constrained. This yields a
constraint on all three coefficients of order . A bound can be derived from the
cyclotron frequencies of hydrogen ions and anti-protons. Bounds on the CPT violating term come
from both the spin polarized torsion balance experiments and the noble gas maser. The torsion
experiments bound the and components (where is parallel to the earth’s rotation axis)
at the level of and the transverse components at . The
maser system gives a better, although less clean, bound on the transverse components of order
.