Hello
I have some (probably) very basic questions, some of them I have an idea but I want to ask you just to be sure about your notation:
1.- When I run the command CalcRGEs[Options], the solutions are saved, for example in the case of the MSSM, in SARAH-x.xx.x/Output/MSSM/RGEs/. I saw that if I wanted to use some of the results I would have to write
BetaGauge=<<SARAH-x.xx.x/Output/MSSM/RGEs/BetaGauge.m;
BetaYijk=<<SARAH-x.xx.x/Output/MSSM/RGEs/BetaYijk.m;
RunRGEs==<<SARAH-x.xx.x/Output/MSSM/RGEs/RunRGEs.m;
is it right? is it essetial to write the first part of those expressions, i.e. BetaGauge=, BetaYijk= and RunRGEs== or what is the purpose of those parts?
2.- In some manuals, as well as in the wiki, it is said that
“The first entry consists of BetaYijk[ [1,1]]: Ye[i1,i2] ,i.e. this entry contains the β-functions for the electron Yukawa coupling”
also they mention that BetaYijk[ [1,2]] is for 1-loop correction and BetaYijk[ [1,3]] for 2-loop. In my case BetaYijk[ [1,1]]: Yd[i1,i2] instead of Ye[i1,i2], so I suppose the order has been changed. Since the evolution of beta-functions is calculated up to 2-loops, and then only BetaYijk[ [1,2]] and BetaYijk[ [1,3]] are relevant, what is the importance of BetaYijk[ [1,1]]? I mean, is it only used to know what kind of particle is associated with? or is it useful in a calculation?
3.- Yukawa couplings are in general matrices, so I suppose that in your notation Yu[a,b], Yd[a,b] and Ye[a,b] (where a=1,2,3 and b=1,2,3) represent the elements of those matrices, am I right?. Then I can imagine only when those matrices are diagonal the elements Yu[1,1], Yu[2,2], Yu[3,3], Yd[1,1], Yd[2,2], Yd[3,3], Ye[1,1], Ye[2,2] and Ye[3,3] I could interpret (in some sense multiplying by the vev) as proportional to the mass of the up, charm, top, down, strange, down, electron, muon, tau. Am I correct?
4.- If I want to calculate a numerical solution for the Yukawa couplings I need to write
solution=RunRGEs[{Yu[1,1]->value, Yu[2,2]->value, Yu[3,3]->value, Yd[1,1]->value, Yd[2,2]->value, Yd[3,3]->value, Ye[1,1]->value, Ye[2,2]->value, Ye[3,3]->value,g1->value,g2->value, g3->value}, Log[10,value], Log[10,value], TwoLoop->True][[1]]
what does the [[1]] means? is it essential or necessary?
5.- As I have said before, after CalcRGEs[Options] all the information is saved. Particularly, in SARAH-x.xx.x/Output/MSSM/EWSB/TeX/MSSM-EWSB.pdf is located the pdf created by the tex file. When I look for the Yukawa Beta-functions, I realize that the 1 and 2-loop corrections only depends of Yu, Yd, Ye, g1, g2 and g3 and there’s nothing like for instance anomalous dimension or gaugino mass parameters. So, like in the previous question, running the command RunRGEs, in general if want a complete solution I have to give the initial condition not only of the diagonal elements of Yu, Yd and Ye (like Yu[1,1], Yu[2,2], Yu[3,3] and the same for Yd and Ye), but also the no-diagonal elements like Yu[1,2], Yu[1,3], Yu[2,1], Yu[2,3], Yu[3,1], Yu[3,2] and the same for Yd and Ye. Is it right? And in the same sense those would be all the elements of my initial conditions because as I said, there’s nothing else like anomalous dimension or gaugino mass parameters, or do I have to consider something else?
6.- What happens if I don’t set the initial value of a parameter in RunRGEs?
7.- I saw (I don’t remember where) that SARAH is able to calculate the masses of all the particles up to tree level. Then I suppose that there is not any way in which I can calculate them up to 2-loops with SARAH, at least only with a single command, is there?
Is there a better option in SARAH to calculate those masses if I have some initial values of Yukawa couplings, instead of starting with those initial values and then using the RGEs up to the desired scale?
8.- In my work I need to go from MSSM to SM. As it has been mention before in the post, RGEs for SM work using MS(bar) renormalization scheme and MSSM using DR(bar). Going from one scheme to the other brings some corrections. Is there any simple way in which SARAH takes into account those corrections (mainly in Yukawa and gauge couplings)? and if this is the case, what is the order of those corrections?
Finally, I want to tank you for all your support