Wing Sheung Chan

18 The Standard Model and lepton flavour violation Some of these unsolved problems are: Quantum gravity Despite being one of the four known fundamental forces of Nature, gravity is not a part of the SM. Currently, the best theory that describes gravity is the general theory of relativity (GR). Even though GR is a classical field theory like electromagnetism in classical mechanics, attempts to construct a corresponding quantum field theory like it was done for QED has been met with two main obstacles. The first of which is the fact that spacetime is dynamic in GR, while quantum field theory depends on a fixed spacetime background (Minkowski spacetime). The second is that gravity seems to be non-renormalisable in perturbation theory, suggesting that infinitely many independent parameters are needed to meaningfully define the theory [24] . Dark matter There is an abundance of evidence that the universe consists of not only ordinary baryonic matter, but also some kind of invisible matter that does not interact, or only interact extremely weakly, with the ordinary matter [25– 27] . This unknown, hypothetical type of matter is referred to as dark matter, and there is no particle candidate for such matter in the SM. The existence of dark matter can only be inferred by astronomically or cosmologically observed gravitational phenomena. This implies that dark matter could be just a manifestation of our possibly inaccurate understanding of gravity, instead of undiscovered particles. In all cases, it is clear that the dark matter phenomena cannot be explained by the SM. The hierarchy problem As also mentioned in Section 1.2.2, the mass of the Higgs boson is expected to be comparable with the Planck mass due to quantum corrections. The fact that it is not poses a fine-tuning problem known as the hierarchy problem. Since the Planck mass is defined using the gravitational constant as a natural unit, the hierarchy problem can therefore also be understood as the question of why the gravitational force is so much weaker than the electroweak force. The matter-antimatter asymmetry It is apparent that the observable universe consists of radically more (baryonic) matter than antimatter. Extrapolating back in time, this implies an asymmetry in the matter and antimatter generation process in the early universe. To create such an asymmetry, baryon-generating interactions must satisfy three criteria known as the Sakharov conditions [28] : they violate baryon number conservation, they violate the charge (C) and charge-parity (CP) symmetries, and they must be out of thermal equilibrium. Baryon number and CP are indeed violated in the SM. However, the violation as we understand it is too small to account for the observed asymmetry. Neutrino mass With the observation of neutrino oscillations, it is now evident that neu- trinos have finite rest masses. Nonetheless, the mechanism responsible for neutrinos to acquire mass still remains unknown. It is possible that neutrinos acquire their masses in a way similar to the other SM fermions. However, if that is indeed the case, extra explanation will be needed for the huge difference between the neutrino masses and the other SM fermion masses, which turns it into another fine-tuning problem.