Will-be-set-by-IN-TECHIn this section a summary of the current formulation of the SM is presented: the elementary particles and the fundamental interactions of the SM, and then the basic problem inherent in the SM.
Elementary particles of the SMIn the SM the elementary particles that are the constituents of matter are assumed to be the six leptons: electron neutrino (ν e ), electron (e − ), muon neutrino (ν µ ), muon (µ − ), tau neutrino (ν τ ), tau (τ − ) and the six quarks: up (u), down (d), charmed (c), strange (s), top (t) and bottom (b), together with their antiparticles. These twelve particles are all spin-1 2 particles and fall naturally into three families or generations:Each generation consists of two leptons with charges Q = 0 and Q = −1 and two quarks with charges Q =+ 2 3 and Q = − 1 3 . The masses of the particles increase significantly with each generation with the possible exception of the neutrinos, whose very small masses have yet to be determined.In the SM the leptons and quarks are allotted several additive quantum numbers: charge Q, lepton number L, muon lepton number L µ , tau lepton number L τ , baryon number A, strangeness S, charm C, bottomness B and topness T. These are given in Table 1. For each particle additive quantum number N, the corresponding antiparticle has the additive quantum number −N. Table 1. SM additive quantum numbers for leptons and quarks Table 1 demonstrates that, except for charge, leptons and quarks are allotted different kinds of additive quantum numbers so that this classification of the elementary particles in the SM is non-unified.The additive quantum numbers Q and A are assumed to be conserved in strong, electromagnetic and weak interactions. The lepton numbers L, L µ and L τ are not involved in strong interactions but are strictly conserved in both electromagnetic and weak interactions. The remainder, S, C, B and T are strictly conserved only in strong and electromagnetic interactions but can undergo a change of one unit in weak interactions.The quarks have an additional additive quantum number called "color charge", which can take three values so that in effect we have three kinds of each quark, u, d, etc. These are often