CPT invariance

The recent advances in producing, trapping and cooling antiprotons and positrons opened the possibility of antihydrogen formation in laboratory. This may allow the studies of antimatter and tests of fundamental physical principles such as charge - parity - time ( CPT ) invariance or the weak equivalence principle (WEP) for antiparticles. Such experiments are planned at the newly built CERN AD (Antiproton Decelerator) within ASACUSA, ATRAP and ATHENA projects, which have just started their operations. 

There are both theoretical and experimental reasons to search for CPT violations. The strong theoretical incentive is that, even though the CPT invariance is required to formulate a quantum field theory consistent with special relativity, it turns out to be difficult to construct a gravitational relativistic quantum field theory of the GUT type with the CPT symmetry maintained. In other words it is difficult to incorporate the CPT invariance in the GUT-type extensions of the Standard Model. 

The most perceptible experimental reason is the evident asymmetry of the Universe. The CP violation alone, on the level allowed by the Standard model, is not sufficient to explain the excess of matter in the Universe [18]. Finding a suitable extension of the Standard Model is not easy not only do the GUT theories tend to violate CPT invariance but they are also difficult to test. Specifically they can not be tested by means of the particle accelerator experiments, which so far have been very successful in extending our knowledge of Physics. This is because the GUT energy is some 1013 times larger than what we can now days produce in the most powerful accelerators. Consequently we must look for the low-energy manifestations of GUT and CPT invariance. Interestingly some possibilities for such tests lie within the realm of atomic and molecular physics. 

What can be tested As mentioned before, CPT invariance guarantees the equality of masses, charges and lifetimes of particles and antiparticles. This means that the experimental investigations of masses, charges, etc. of particle - antiparticle pairs are tests of CPT symmetry. Such experiments are not easy to do with the charged particles themselves (because of their interactions with stray fields). Comparison of neutral atom - antiatom pairs is much more convenient. In particular, the fine structure, hyperfine structure and Lamb shifts of atoms and antiatoms should be identical - and can be tested in laboratory. 

But what precision is required The answer to this question is two-fold. One scale of precision is set by the previous experimental tests of CPT invariance the new tests must simply have better accuracy in order to be interesting. The so far best (albeit indirect) experimental test has been obtained from the comparison of the masses of neutral kaons K° and K°, which are known to be equal with the accuracy of 1 part in 1018 (i.e. (mKo — mxo)/mKo < 10 18) [22]. 

Here and throughout this paper, all uncertainties are standard uncertainties, i.e., one standard deviation estimates.) Assuming CPT invariance holds, we take... 

In the discussion of Kostelecky et al. on testing for Lorentz and CPT invariance using their extension of the standard model, the experiment on 7Li is designated as a clock comparison type experiment which tests for spatial anisotropy. Recent experiments of this type have greatly improved the bounds on parameters for Lorentz violation to 10-27 GeV for the proton (as indicated in Table 1), to 10 3° GeV for the neutron. 

Abstract. CPT invariance is a fundamental property of quantum field theories in flat space-time. Principal consequences include the predictions that particles and their antiparticles have equal masses and lifetimes, and equal and opposite electric charges and magnetic moments. It also follows that the fine structure, hyperfine structure, and Lamb shifts of matter and antimatter bound systems should be identical. 

CPT invariance is a fundamental property of quantum field theories in flat space-time which results from the basic requirements of locality, Lorentz invariance and unitarity [1,2,3,4,5]. A number of experiments have tested some of these predictions with impressive accuracy [6], e.g. with a precision of 10-12 for the difference between the moduli of the magnetic moment of the positron and the electron [7] and of 10-9 for the difference between the proton and antiproton charge-to-mass ratio [8],... 

Hydrogen Hyperfine Structure and Related CPT Invariant Quantities... 

When describing arbitrary two-body systems fully relativistically, one would expect that the formalism produces explicitly CPT-invariant results. CVT-invariance requires symmetry of the terms under change of the sign of the system s total energy E + E% = E <— —E, also for bound states where the individual energies Ei and E% are not conserved. This means that the decisive equations should contain only even powers of E. 

In the following, an approach is presented that reproduces the main part of the recoil and hyperfine corrections without any nonrelativistic approximation and therefore with full CPT-invariance. 

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