• The optimization of values of \(\alpha_1,\alpha_2,\alpha_3\) of HYP blocking is done by maximizing the minimum value of plaquette on 500 of gauge configurations of \(4^4\) lattice. This reduces the maximum fluctuation of plaquette over a choosen gauge configurations and smoothes the gauge configuration.
• scaling violations is probably lattice artifacts.
• If we are to exclude the fictitious time direction then we can define the HYP blocking in 3 possible ways.
  1. We can say that we will not include any projection from fictitious time links to smearing of other links, and proceed with 2 level HYP smearing with 2 link staples in 2nd level rather than 4.
  2. Since we are ignoring smearing of fictitious time links we can still include SU(3) projection of APE smearing of time like links in smearing of spatial links and proceed with 2 level APE smearing with 2nd level and 1st level containing only 4 staples per link.
  3. We can still ignore smearing of fictitious time links and still have 3 level HYP smearing, by having 4 staples in top most level, 2 in middle level and 2 in most basic level, with each level excluding the smeared fictitious time links (but in basic level using time links as they are not smeared).

Now only question remains is to use which definition of HYP smearing for our case, also what shall be values of alpha2 with 2nd method which I have used?