Symmetry and Naturalness

We said before that physicists are often uncomfortable with numbers that are not O(1) . However, this is not always the case. Physicists will accept an exceedingly small number if it is very close to a symmetric point and if the symmetry of the physical system would get enhanced if that number were to vanish (i.e., go to zero). We might consider such a very small number natural because it’s so near to the symmetric point. In such cases we would say that number is “protected” by the symmetry, and we would treat it as if it is literally at the symmetric point.