quantum chromodynamics - Is the QCD potential really monotonic ? How does it prevent two quarks from meson to annihilate?

The QCD potential is made of two terms -(4/3) * alpha_s / r that describes the short distance

and the term +k*r that describes the long distance

Of course, alpha is a function of energy, so it is a function of radius.

But in the measurements of QCD potential, I always see that the graphical potential VQCD=f(r) is monotonic, so I would think that it only attracts the two quarks.

So what does prevent the two quarks of the meson to annihilate from the QCD potential. Remark : in the word 'QCD potential', there is Q=quantum, so normally this potential should take into account the quantum effects. Does it take it into account ?

Does the potential stops decreasing at a low radius value ? At which value ? Why the measurements have not been made down to this low r value.

Thank you for your help.