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Symmetries of space time, and Lorentz and CPT symmetry in particular, are a cornerstone of modern physics and lie at the foundation of quantum field theory (QFT) and Einstein's theory of general relativity, the two most successful theories in physics which together describe the four fundamental forces of nature. However, the inability to incorporate gravity as described by general relativity into the QFT standard model of particle physics, which very successfully combines the electromagnetic, strong and weak interactions, has led to the development of alternative so-called Grand Unified Theories (GUTs) or theories of quantum gravity. Since many of these theories break Lorentz symmetry at some small level [1-4], experimental searches for Lorentz-violating effects could help shed light on new physics beyond the standard model (SM) and provide clues as to the nature of quantum gravity. Parameterization of such effects within the Lorentz-violating Standard Model Extension (SME) developed by A. Kostelecky [5] has allowed direct comparison of many experiments, ranging from table-top precision measurements to observations of ultra-high energy cosmic and gamma rays to astrophysical observations. The SME has proven to be a remarkable tool in the search for Lorentz violation across the landscape of experimental physics. Up until the present, experimental results have taken the form of upper bounds on the SME coefficients and are tabulated in the Data Tables for Lorentz and CPT Violation [6]. On a closer look, however, Lorentz invariance has been tested poorly in the weak interaction [7, 8], which is all the more surprising since violations of fundamental symmetries could be observed only in the weak sector:

The first discovery of a violation of presumed (discrete) space-time symmetry was that of parity violation in nuclear β decay [9]. C. S. Wu and her collaborators found that when a specific nucleus (60Co) was placed in a magnetic field, electrons from the beta decay were preferentially emitted in the direction opposite that of the aligned angular momentum of the nucleus. When it is possible to distinguish these two cases in a mirror, parity is not conserved. If the mirror not only reverses spatial direction but also changes matter to antimatter, then the experiment in front of the mirror would look just like its mirror image. The separate violations of P symmetry and C symmetry cancel to preserve CP symmetry. These symmetry violations arise only from the weak interaction, not from the strong and electromagnetic interactions, and therefore shows up strongly only in beta decay. Until 1964 it was thought that the combination CP was a valid symmetry of the Universe. That year, Christenson, Cronin, Fitch, and Turlay performed their historic experiment to see if the long-lived neutral K meson could occasionally decay to π+ π. They found that indeed it did [10]! And the observed CP violation implies, by CPT invariance, violations of T-symmetry as well.

Recently, a new project was initiated at the Kernfysisch Versneller Instituut (KVI), Groningen [11] to test Lorentz invariance in the weak interaction while searching for a dependence of the decay rate of spin-polarized nuclei on the orientation of their spin with respect to a fixed absolute galactical reference frame. An observation of such a dependence would imply a violation of Lorentz invariance. In a phenomological description, the ß-decay rate, if there is a preferred direction in space, is expected to be of the form:

  • display math(1)

where p and E are the momentum and energy of the β-particle, I is the nuclear spin, and inline image is proportional to the lifetime of the nucleus. The first term in (1) describes the SM contribution to the decay rate including the parity-violating parameter A of the weak interaction. The quantity inline image contains the hypothetical field that violates Lorentz invariance by defining a “preferred” reference frame and requires a non-zero average polarisation of inline image along the quantization axis. It measures the dependence of the lifetime on orientation.

As reported in the paper of H. W. Wilschut et al. [12], one uses a beam of short-lived alkali isotopes produced with the AGOR cyclotron at KVI. The isotopes are stopped in a buffer gas cell, where their spins are subsequently oriented via optical pumping using a weak magnetic field and circularly polarized laser light. Changing the circular polarization of the laser light will reverse the nuclear polarization. Detecting a change in the decay lifetime when changing the direction of nuclear polarization by 180° would indicate a non-zero value of inline image. A change in lifetime can be investigated by detecting the rates of β-particles (or the corresponding annihilation photons at 511 keV for β+ decays) or prompt gamma rays from decays of excited daughter particles. In general, alkali isotopes are good candidates because their hyperfine structure makes them ideally suited for efficient optical pumping. At KVI the availability of a strong pumping laser for sodium atoms allowed to study Lorentz violation in the decay of 20Na (τ1/2 = 0.448s). The lifetimes of 20Na for the two polarization directions are measured by detecting the γ-radiation from the decay of the 20Ne daughter nucleus with two NaI-detectors placed perpendicularly to the polarization axis. Wilschut et al. tested Lorentz invariance of 20Na searching for a difference in the lifetimes inline image for different orientations of the nuclear polarization. This is done by fitting the rate spectra in Fig. 1 for t > 1s with an exponential decay function. A difference in the lifetimes for different nuclear spin directions due to Lorentz invariance violation would be confirmed if the difference shows an oscillation period of the sidereal day because the earth rotates with respect to a fixed galactical reference frame. The function

  • display math(2)

has been fitted to the data, where inline image. The parameters As and Ac parameterize the sidereal variations of τ due to Lorentz symmetry breaking effects. Preliminary results from the analysis of unpolarized decays show that a statistical sensitivity on sidereal variations of lifetime changes of 10−3–10−4 can be reached, and that systematic effects from ambient temperature and pressure changes are well under control. In a recent paper [13], entitled “Lorentz violation in neutron decay and allowed nuclear β decay”, Wilschut et al. provide a general theoretical framework that should be used for designing and interpreting β-decay experiments that search for Lorentz violation. In particular, it determines the kind of experiments that are necessary to probe different parameters that quantify Lorentz violation, and it establishes their sensitivity. In this respect, there is a certain analogous to the famous paper of Lee and Yang [14], where they stated: “To decide unequivocally whether parity is conserved in weak interactions, one must perform an experiment to determine whether weak interactions differentiate the right from the left”.

image

Figure 1. γ rates detected with a NaI detector for different helicity states of the laser light with a pulsed beam of 20Na (1s “on”, 1s “off”). Rates have been averaged over a data taking period of 35 min (figure from: Hyperfine Interact. 215, 1–3, pp. 31–38 (2013), Lorentz invariance on trial in the weak decay of polarized atoms, Stefan E. Müller, Fig. 4a. With kind permission from Springer Science and Business Media, see [11]).

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