Modern Elementary Particle Physics Explaining and Extending the Standard Model

The Standard Model is essentially a complete effective theory of physics at the electroweak scale. It describes all that we see. “See” is taken literally – it does not describe dark matter and other phenomena we do not see. It is also “essentially” complete, in that there are two issues where it is not quite complete, arising from the so-called hierarchy problem and the strong CP problem. This chapter outlines some known areas beyond the Standard Model, and Chapters 23–26 discuss the main current focus of research in each area, so the reader has a very brief introduction to developments that may occur and extend the Standard Model. They comprise the next several short chapters.

The hierarchy problem is a serious, real problem, with two aspects: when the Higgs boson mass is calculated in a quantum field theory, virtual quantum corrections will raise the Higgs boson mass (or equivalently its vacuum expectation value, vev), to the largest scales in the theory, presumably to the order of the Planck mass, of order 1018 GeV. Then all quarks and charged leptons and W, Z masses are raised as well. One attraction of supersymmetry is that it stabilizes the hierarchy since fermionic and bosonic quantum corrections have opposite signs and cancel. But supersymmetry does not predict the value of the electroweak scale, that is, the size of the hierarchy. String theory can do that.

The QCD Lagrangian is allowed to have a term, where. This is equivalent to a term. Such a term violates CP, so the strong interactions, the quarkonium spectra, etc., can violate CP. The strongest limits, from the neutron electric dipole moment, imply θ ≲ 10−10, a remarkable fine tuning for no known reason. One possible solution involves introducing a new particle, called an axion. Explaining the strong CP problem, and the axion solution, both require quantum field theory and some complicated physics, so we do not pursue this topic.

Each of the phenomena described introduces a new scale beyond the electroweak scale. Electroweak scale physics is defined by the Higgs field vev (as described in Chapters 8 and 15), and by the hadron masses. Both are input into the Standard Model. The extension to grand unification of the forces does provide a derivation of the hadron mass scale.