With the discovery of the Higgs boson in 2012, a major voyage was successfully over, and a variety of new opportunities began to emerge. The mass (and properties) of the Higgs boson points toward how to extend the Standard Model, strengthen its foundations, and work toward an “ultraviolet completion,” a theory valid to near or at the Planck scale. Surprisingly, the data seems to allow more than one qualitatively different interpretation. In this chapter we describe the data and some of the interpretations.

We have already described the properties the Higgs field needed to have to make the Standard Model a complete effective theory of the world we see at the electroweak scale and below in Chapter 8, and the Higgs mechanism that led to breaking the electroweak symmetry to allow masses simultaneously for gauge bosons, quarks, and charged leptons. In this chapter we describe the successful search for the Higgs boson experimentally, its production at LHC, how it was detected, and the tests so far that it is indeed the Higgs boson. Its properties, such as its mass and decay branching ratios, are somewhat surprising and ironic, and have implications for physics beyond the Standard Model. Some, but not all, people think the results imply that the correct interpretation is the supersymmetric extension of the Standard Model.

The Higgs boson h0 was difficult to observe because its couplings are proportional to mass, as we have seen, so they are small for the light particles that are most copiously available in beams. Another reason is that the mass of h0 is unknown in the Standard Model theory. As we have seen, mh depends on the coefficient λ of the Higgs self-interaction in the Higgs potential. Since there is no understanding in the Standard Model of the physical origin of λ, its numerical value is not known. Nor does any other observable depend on λ in a way that allows λ to be extracted.

Since mh was unknown, searches had to be planned for all mh, which is much more difficult than designing an experiment to look for h at a specific mass. Different techniques work best for different mass ranges.

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.