Problems of the Sensitivity Parameter and Its Relation to the Time-varying Fundamental Couplings Problems
Abstract
The sensitivity parameter is widely used for quantifying fine tuning. However, examples show it fails to give correct results under certain circumstances. We argue that these problems only occur when calculating the sensitivity of a dimensionful mass parameter at one energy scale to the variation of a dimensionless coupling constant at another energy scale. Thus, by mechanisms such as dynamical symmetry breaking etc, the high sensitivity of the energy scale parameter () to the dimensionless coupling constant can affect the reliability of the sensitivity parameter through the renormalization invariant factor of the dimensionful parameter. Theoretically, These phenomena are similar to the problems associated with the time-varying coupling constant discovered recently. We argue that, the reliability of the sensitivity parameter can be improved if it is used properly.