### 5.5 Neutral mesons

Mesons have long been used to probe CPT violation in the standard model. In the framework of the
mSME, CPT violation also implies Lorentz violation. Let us focus on kaon tests, where most of the work
has been done. The approach for the other mesons is similar [169, 1]. The relevant parameter for CPT and
Lorentz violation in neutral kaon systems is for the down and strange quarks (since ). As we
mentioned previously, one of the can always be absorbed by a field redefinition. Therefore only the
difference between the quark ’s, controls the amount of CPT violation and is
physically measurable. Here are coefficients that allow for effects due to the quark bound
state [184].
A generic kaon state is a linear combination of the strong eigenstates and . If we write
in two component form, the time evolution of the wavefunction is given by a Schrödinger
equation,

where the Hamiltonian is a complex matrix. can be decomposed into real and imaginary
parts, . and are Hermitian matrices usually called the mass matrix and decay
matrix, respectively. The eigenstates of are the physically propagating states, which are the familiar
short and long decay states and . CPT violation only occurs when the diagonal components of
are not equal [198]. In the mSME, the lowest order contribution to the diagonal components of
occurs in the mass matrix , contributions to are higher order [184]. Hence the relevant observable
for this type of CPT violation in the kaon system is the and mass difference, =
.
In the mSME the deviation is (as usual) orientation dependent. In terms of , we have [171]
where is the four-velocity of the kaon in the observer’s frame. The mass difference has been
extremely well measured by experiments such as KTeV [234] or FNAL E773 at Fermilab [253].
By looking for sidereal variations or other orientation effects one can derive bounds on each
component of . The best current bounds do not quite achieve this but rather constrain a
combination of parameters. A linear combination of and is bounded at the level of
[168] and a combination of and is constrained at the [234]
level.