Landau Pole - Phenomenological Aspects

Phenomenological Aspects

In a theory intended to represent a physical interaction where the coupling constant is known to be non-zero, Landau poles or triviality may be viewed as a sign of incompleteness in the theory. For example, QED is usually not believed to be a complete theory on its own, and the Landau pole could be a sign of new physics entering via its embedding into a Grand Unified Theory. The grand unified scale would provide a natural cutoff well below the Landau scale, preventing the pole from having observable physical consequences.

The problem of the Landau pole in QED is of pure academic interest. The role of in Eqs.1,2 is played by the fine structure constant α ≈ 1/137 and the Landau scale for QED is estimated as 10283keV/c2, which is far beyond any energy scale relevant to observable physics. For comparison, the maximum energies accessible at the Large Hadron Collider are of order 1013 eV, while the Planck scale, at which quantum gravity becomes important and the relevance of quantum field theory itself may be questioned, is only 1028 eV.

The Higgs boson in the Standard Model of particle physics is described by theory. If the latter has a Landau pole, then this fact is used in setting a "triviality bound" on the Higgs mass. The bound depends on the scale at which new physics is assumed to enter and the maximum value of the quartic coupling permitted (its physical value is unknown). For large couplings, non-perturbative methods are required. Lattice calculations have also been useful in this context.