The weak mixing angle, also known as the Weinberg angle or θW, is a parameter in the electroweak theory that characterizes the mixing between the weak force and the electromagnetic force. The value of the weak mixing angle depends on the energy scale at which it is measured.
At the low-energy scale, such as in experiments involving particle interactions at low energies, the weak mixing angle has been experimentally measured to be approximately 28.7 degrees. This value corresponds to the so-called "on-shell" measurement, where the particles involved are on their mass shells.
However, at higher energy scales, the weak mixing angle is expected to run, meaning its value changes with the energy scale at which it is measured. The running of the weak mixing angle is described by the renormalization group equations in quantum field theory.
The precise upper bound for the weak mixing angle depends on the specific theoretical framework and assumptions. In the Standard Model of particle physics, which incorporates the electroweak theory, there is no theoretical upper bound for the weak mixing angle. Its value is a free parameter that is determined experimentally.
It's worth noting that theories beyond the Standard Model, such as Grand Unified Theories (GUTs) or theories with extended gauge symmetries, can introduce constraints or predictions on the weak mixing angle at high energies. However, these constraints or predictions depend on the specific details and assumptions of those theories.
In summary, within the context of the Standard Model, there is no theoretical upper bound for the weak mixing angle. Its value is experimentally determined and is known to be approximately 28.7 degrees at low energies.