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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 a m for the down and strange quarks (since K = ds). As we mentioned previously, one of the am can always be absorbed by a field redefinition. Therefore only the difference between the quark am’s, d s Dam = rda m- rsam controls the amount of CPT violation and is physically measurable. Here rd,s are coefficients that allow for effects due to the quark bound state [184Jump To The Next Citation Point].

A generic kaon state YK is a linear combination of the strong eigenstates 0 K and --0 K. If we write YK in two component form, the time evolution of the YK wavefunction is given by a Schrödinger equation,

(K0 ) (K0 ) i@t -0 = H --0 , (67) K K
where the Hamiltonian H is a 2 × 2 complex matrix. H can be decomposed into real and imaginary parts, H = M - iG. M and G are Hermitian matrices usually called the mass matrix and decay matrix, respectively. The eigenstates of H are the physically propagating states, which are the familiar short and long decay states KS and KL. CPT violation only occurs when the diagonal components of H are not equal [198]. In the mSME, the lowest order contribution to the diagonal components of H occurs in the mass matrix M, contributions to G are higher order [184]. Hence the relevant observable for this type of CPT violation in the kaon system is the 0 K and -0 K mass difference, DK = |mK0 - mK0-|/mK0.14 In the mSME the deviation DK is (as usual) orientation dependent. In terms of Dam, we have [171]
| | |bmDam | DK ~~ ||------||, (68) mK0
where bm is the four-velocity of the kaon in the observer’s frame. The mass difference DK has been extremely well measured by experiments such as KTeV [234Jump To The Next Citation Point] or FNAL E773 at Fermilab [253]. By looking for sidereal variations or other orientation effects one can derive bounds on each component of am. The best current bounds do not quite achieve this but rather constrain a combination of parameters. A linear combination of Da0 and Daz is bounded at the level of 10- 20 GeV [168] and a combination of Dax and Day is constrained at the 10- 21 GeV [234] level.
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