Quantum Gravity and Lorentz Invariance Violation in the Standard Model

The most important problem of fundamental physics is the quantization of the gravitational field. A main difficulty is the lack of available experimental tests that discriminate among the theories proposed to quantize gravity. Recently, Lorentz invariance violation by quantum gravity (QG) has been the source of growing interest. However, the predictions depend on an ad hoc hypothesis and too many arbitrary parameters. Here we show that the standard model itself contains tiny Lorentz invariance violation terms coming from QG. All terms depend on one arbitrary parameter $\alpha$ that sets the scale of QG effects. This parameter can be estimated using data from the ultrahigh energy cosmic ray spectrum to be $|\alpha |<\sim {10}^{-22}-{10}^{-23}$.