Editing Fine-structure constant (section)

== Variation with energy scale ==
In [[quantum electrodynamics]], the more thorough quantum field theory underlying the electromagnetic coupling, the [[renormalization group]] dictates how the strength of the electromagnetic interaction grows [[logarithm]]ically as the relevant [[energy scale]] increases. The value of the fine-structure constant {{mvar|α}} is linked to the observed value of this coupling associated with the energy scale of the [[electron mass]]: the electron's mass gives a lower bound for this energy scale, because it (and the [[positron]]) is the lightest charged object whose [[Quantum electrodynamics#Renormalizability|quantum loops]] can contribute to the running. Therefore, {{sfrac|1| 137.03600 }} is the asymptotic value of the fine-structure constant at zero energy. 
At higher energies, such as the scale of the [[Z boson]], about 90&nbsp;[[GeV]], one [[Coupling constant#QED and the Landau pole|instead]] measures an ''effective'' {{mvar|α}} ≈ 1/127.<ref>
{{cite journal
 |last=Fritzsch |first=Harald
 |year=2002
 |title=Fundamental constants at high energy
 |journal=Fortschritte der Physik
 |volume=50 |issue=5–7 |pages=518–524
 |doi=10.1002/1521-3978(200205)50:5/7<518::AID-PROP518>3.0.CO;2-F
 |arxiv=hep-ph/0201198 |bibcode=2002ForPh..50..518F |s2cid=18481179
}}</ref>

As the energy scale increases, the strength of the electromagnetic interaction in the [[Standard Model]] approaches that of the other two [[fundamental interaction]]s, a feature important for [[grand unification]] theories. If quantum electrodynamics were an exact theory, the fine-structure constant would actually diverge at an energy known as the [[Landau pole]] – this fact undermines the consistency of quantum electrodynamics beyond [[perturbative]] expansions.