The standard model of particle physics for describing the basic interactions of microscopic particles consists of two parts: quantum chromodynamics (QCD) for describing strong interactions and electroweak unified theory for describing electromagnetic interactions and weak interactions.
QCD is the SU (3) gauge interaction theory of the color freedom of quarks, which transfers strong interactions by gluons. A large number of experimental results have supported this theory. The unified theory of electroweak is the SU (2) × U (1) gauge theory of the flavor freedom of quarks, which transfers the electromagnetic effect, W ± and Z0 bosons by photons. The experiment shows that W ± and Z0 have mass. This theory encounters more complex problems. If the theory is assumed to have complete SU (2) × U (1) symmetry, the theory is renormalized and can be accurate to the calculation of any order perturbation, but the mass of W ± and Z0 in the theory is zero, which is inconsistent with the experiment.
If the mass terms W ± and Z0 are added to the theoretical Lagrangian (equation of motion), the SU (2) × U (1) symmetry will be broken, and the renormalization of the theory will be broken, resulting in uncontrollable infinity in higher-order perturbation calculation. The possible solution to this contradiction is to add new physical content to the Lagrangian and maintain its SU (2) × U (1) gauge symmetry (renormalization), but the vacuum state (the lowest energy state) determined by it does not have SU (2) × U (1) symmetry, so that the physically observed W ± and Z0 have mass. This is often referred to as spontaneous symmetry breaking. The phenomenon of spontaneous symmetry breaking has precedents in QCD and condensed matter physics. The mass of all particles in the standard model is generated through this mechanism.
Therefore, this mechanism involves the origin of all masses, which is a very basic and profound problem in physics. The specific method of the standard model of particle physics is to introduce a scalar field called Higgs field into the Lagrangian, and assume that its self acting form can lead to spontaneous breaking of the weak symmetry. The neutral scalar particles excited by the Higgs field are called Higgs particles or Higgs bosons. The key to test this theory is to detect the information of such particles from experiments. Up to now, a large number of experiments have supported the SU (2) × U (1) gauge action part of the electroweak unified theory, but the Higgs boson has not been found. Experiments have determined that the mass limit of the Higgs boson is greater than 114.3 GeV. In addition, it is found that the introduction of the basic Higgs field will bring theoretical defects to the standard model.
After careful study of the higher-order correction of the standard model, it is found that if the standard model is assumed to be applicable to the full energy range, the effective self interaction strength of the Higgs field is actually zero, so it is impossible to produce a symmetric spontaneous breaking. This means that the standard model is actually only applicable below a certain energy scale Λ, beyond which new physical laws must play a role. A natural energy scale Λ is the Planck energy scale when gravity becomes important. However, if Λ is Planck energy standard, the parameters in the standard model must be accurate to 34 digits to obtain the W boson mass in line with the experiment. This requirement cannot be realized in physics. It can be seen that the standard model is not perfect, and we need to find a better new physical theory.
Many new physical models above λ energy scale have been conceived. They can be roughly divided into two categories.
① Keep the existing structure of the standard model, and introduce new symmetry and new particles to offset the defects caused by the Higgs field. The most popular is the minimal supersymmetry model. This model assumes that the Lagrangian has supersymmetry (Fermi Bose symmetry), so every existing particle has a supersymmetric partner whose spin is 1/2 different from its spin. The above defects are offset by the supersymmetric partner of Higgs. No supersymmetry partner has been found in the experiment, so the supersymmetry partner can only be very heavy, that is, the supersymmetry is broken. In this way, the offset of the above defects is not complete. The remaining defects must be small enough to be not serious before this model can be accepted. This requires that the mass of the supersymmetric partner does not exceed 1 teraelectron volt, that is, Λ of this model is about 1 teraelectron volt. In addition, there are five observable Higgs bosons in this theory, of which the lightest mass does not exceed 135 GeV.
② The structure of the standard model is modified, and the basic Higgs field is abandoned and a new strong interaction is introduced, which results in the electroweak symmetry breaking of dynamics (by virtue of QCD and superconductivity theory). In this way, the defects caused by the basic Higgs field are completely eliminated. Most of these models do not contain light Higgs bosons, but some contain light composite Higgs bosons. In order to obtain the correct W ±, Z0 boson masses naturally, the energy scale Λ of this new strong interaction should also be about 1 teraelectron volt. The detection capabilities of the new LHC collider of CERN and the future electron positron linear collider can reach the range of 1 teraelectron volt, so all the models mentioned above will be tested soon. It is also possible to find unexpected new phenomena on the new collider. Experiments on new colliders in the future are the key to understanding the basic interaction laws, which may lead to new breakthroughs in understanding. [1]
