the LHCb experiment (2016), searches have been made for sidereal variations during Earth's rotation using B mesons (thus bottom quarks) and their antiparticles. No Lorentz and CPT violating signal were found with upper limits in the range 10−15 − 10−14 GeV. Also top quark pairs have been examined in the D0 experiment (2012). They showed that the cross section production of these pairs doesn't depend on sidereal time during Earth's rotation. Lorentz violation bounds on Bhabha scattering have been given by Charneski et al. (2012). They showed that differential cross sections for the vector and axial couplings in QED become direction dependent in the presence of Lorentz violation. They found no indication of such an effect, placing upper limits on Lorentz violations of . Gravitation The influence of Lorentz violation on gravitational fields and thus general relativity was analyzed as well. The standard framework for such investigations is the Parameterized post-Newtonian formalism (PPN), in which Lorentz violating preferred frame effects are described by the parameters (see the PPN article on observational bounds on these parameters). Lorentz violations are also discussed in relation to Alternatives to general relativity such as Loop quantum gravity, Emergent gravity, Einstein aether theory or Hořava–Lifshitz gravity. Also SME is suitable to analyze Lorentz violations in the gravitational sector. Bailey and Kostelecky (2006) constrained Lorentz violations down to by analyzing the perihelion shifts of Mercury and Earth, and down to in relation to solar spin precession. Battat et al. (2007) examined Lunar Laser Ranging data and found no oscillatory perturbations in the lunar orbit. Their strongest SME bound excluding Lorentz violation was . Iorio (2012) obtained bounds at the level by examining Keplerian orbital elements of a test particle acted upon by Lorentz-violating gravitomagnetic accelerations. Xie (2012) analyzed the advance of periastron of binary pulsars, setting limits on Lorentz violation at the level. Neutrino tests Neutrino oscillations Although neutrino oscillations have been experimentally confirmed, the theoretical foundations are still controversial, as it can be seen in the discussion related to sterile neutrinos. This makes predictions of possible Lorentz violations very complicated. It is generally assumed that neutrino oscillations require a certain finite mass. However, oscillations could also occur as a consequence of Lorentz violations, so there are speculations as to how much those violations contribute to the mass of the neutrinos. Additionally, a series of investigations have been published in which a sidereal dependence of the occurrence