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 [1691]. 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.