What is the Weinberg angle at Planck energy?

Question

Many papers show how the Weinberg angle (the weak mixing angle in the electroweak interaction) changes with energy / momentum transfer. One is https://arxiv.org/abs/1107.4683 and shows that sin^2 theta_W starts at 0.238 at low energy, reduces to 0.232 at around 100 GeV and goes back to 0.238 at 1000 GeV.

But the curves stop at around 1000 GeV. Is there a theoretical prediction about how the value changes for higher energies / momentum transfers? I am looking for a curve that ideally would go up to Planck energy - or at least to the GUT scale.

Answer 1

The running value of any constant is not known beyond the latest LHC energy. There are predictions from Grand Unification Theories, most notably Supersymmetry, that state the value of sin² theta_W of 3/8 for the GUT energy scale however that is close to the Planck scale but not exactly there. The GUT energy scale is estimated around 10¹⁶ GeV and the Planck scale is around 10¹⁹ GeV.