particle physics - Energy of quarks and the mass of the proton

We know that energy of quarks inside the proton can not be exactly fixed because if it,the 'proton decay' must not be exist. My question is if the energy of quarks inside the proton is not exactly fixed than the mass of the proton must be fluctuate because 99% of the proton mass is due to the kinetic energy of the quarks and to the energy of the gluon fields that bind the quarks together. Is this fluctuation in mass really occur or I am missing something. please explain.

Answer

Yes it fluctuates but it is a very small fluctuation. Note that unstable particles have a decay rate or width $\Gamma$ that is related to its lifetime $\tau$ by $$ \Gamma=\frac{\hbar}{\tau} $$ when you measure the mass/energy of such particles in experiments you always get a Lorentzian or Breit-Wigner distribution like this

_{(source: gsu.edu)}

from which you can measure the width and calculate both the mass (with an uncertainty) and the lifetime (from the width measurement). Note that this is for all unstable particles, even fundamental ones, then only stable particles as the electron have a perfectly defined mass.

The issue with the electron is that it's lifetime is very very long (otherwise aggregated matter wouldn't exist), in fact proton decay has never been observed, though theoretical decay modes exist in some models. So it is considered to be effectively stable and both experiments and theoretical calculation set limits for its lifetime. But it still has a lifetime in principle so its mass is not perfectly defined, the fluctuation is really small though.