Missing variance term in likelihood estimation In Murphy(2007), equation (10)

Why did the author ignore the term containing $s^2$.( Here, $s^2$ denotes the variance of the of the observed data).
From the looks of it , it doesn't seem like the term is actually constant yet the author has dropped the term. Any help is appreciated

As clarified by @dipetkov in the comments, we can calculate the sample variance directly from the data and hence it is an constant.
