# A Running coupling of the Higgs potential

1. Sep 27, 2016

### spaghetti3451

Why is the coupling constant of the Higgs potential not a constant, but is a running constant?

In other words, $\lambda (h) \sim \lambda_{0} - \frac{y_{t}}{16\pi^{2}}\text{ln}\big(\frac{h^{2}}{m^{2}}\big) + \frac{\lambda_{0}^{2}}{16\pi^{2}}\text{ln}\big(\frac{h^{2}}{m^{2}}+\cdots$,

where $\lambda_{0}$ is the bare coupling and $y_{t}=\frac{m_{t}}{VEV}$, $m_{t}$ is the mass of the top quark and VEV is the HIggs vacuum expectation value?

2. Sep 27, 2016

### vanhees71

Look for "renormalization group equation".