RGEs in SARAH

[Kugard]

I want to use the renormalization group equations (RGEs) to determine the value of the yukawa couplings from the Grand Unification scale to the electroweak scale.

My question is:
Can Sarah work with the RGEs starting from the grand unification scale to the electroweak scale or going from low to high energies, ie from the electroweak scale to the grand unification scale?

How can I do that?

[FStaub]

Sure, that can be done. Please check for these questions either the manual or the wiki, e.g.

http://stauby.de/sarah_wiki/index.php?title=RGEs
http://stauby.de/sarah_wiki/index.php?t ... athematica

[Kugard]

Ok, I have read the wiki pages that you gave me and I tried to do the example. I think the example of the wiki has different the order of the input in

http://stauby.de/sarah_wiki/index.php?t ... athematica

and should be
solution = RunRGEs[{g1 -> 0.45, g2 -> 0.63, g3 -> 1.04}, 3, 16, TwoLoop -> False]

I did this one and then I ploted it but I only had one line in the plot (for g1)

{g1[16], g2[16], g3[16]} /. solution[[1]];
Plot[g1[x] /. solution[[1]], {x, 3, 16}]


After that, ok you are right about everything you have said to me and I have to use RunRGEs[ ] . However the example was RunRGEs[] for the gauge coplings and it was used g1, g2 and g3 and I was thinking how I can do the same thing but for the yukawa couplings and the vev's . What do I have to use instead of g1, g2 and g3? it could be Y1, Y2, Y3 and v1, v2 y v3? or maybe something else?

[FStaub]

You can you the same syntax for all other parameters. For tensors add indices in squared brackets, e.g. {Yu[3,3]->0.95...}

Cheers,
Florian

[Kugard]

I have writen as an example

solution1 =
RunRGEs[{Yu[1, 1] -> 0.90, Yu[2, 2] -> 0.80, Yu[3, 3] -> 0.70,
Yd[1, 1] -> 0.60, Yd[2, 2] -> 0.50, Yd[3, 3] -> 0.40,
Ye[1, 1] -> 0.30, Ye[2, 2] -> 0.20, Ye[3, 3] -> 0.10},
Log[10^(16)], Log[246], TwoLoop -> True]

And I have gotten

{{B[\[Mu]] -> InterpolatingFunction[{{5.50533, 36.8414}}, <>],
T[Yd][1, 1] -> InterpolatingFunction[{{5.50533, 36.8414}}, <>],
T[Yd][2, 2] -> InterpolatingFunction[{{5.50533, 36.8414}}, <>],
...
g1 -> InterpolatingFunction[{{5.50533, 36.8414}}, <>],
g2 -> InterpolatingFunction[{{5.50533, 36.8414}}, <>],
g3 -> InterpolatingFunction[{{5.50533, 36.8414}}, <>],
Yd[1, 1] -> InterpolatingFunction[{{5.50533, 36.8414}}, <>],
Yd[2, 2] -> InterpolatingFunction[{{5.50533, 36.8414}}, <>],
Yd[3, 3] -> InterpolatingFunction[{{5.50533, 36.8414}}, <>],
Ye[1, 1] -> InterpolatingFunction[{{5.50533, 36.8414}}, <>],
Ye[2, 2] -> InterpolatingFunction[{{5.50533, 36.8414}}, <>],
Ye[3, 3] -> InterpolatingFunction[{{5.50533, 36.8414}}, <>],
Yu[1, 1] -> InterpolatingFunction[{{5.50533, 36.8414}}, <>],
Yu[2, 2] -> InterpolatingFunction[{{5.50533, 36.8414}}, <>],
Yu[3, 3] ->
InterpolatingFunction[{{5.50533, 36.8414}}, <>], \[Mu] ->
InterpolatingFunction[{{5.50533, 36.8414}}, <>]}}

What is all that?

I thought that I would have a numeric result for the Yu[1, 1] , Yu[2, 2] , Yu[3, 3],
Yd[1, 1], Yd[2, 2], Yd[3, 3] ,
Ye[1, 1], Ye[2, 2] , Ye[3, 3]
at the value of Log[246]

**then, how can I get the numerical result?

Also I wrote

{Yu[1, 1][16], Yu[2, 2][16], Yu[3, 3][16], Yd[1, 1][16], Yd[2, 2][16],
Yd[3, 3][16], Ye[1, 1][16], Ye[2, 2][16], Ye[3, 3][16]} /.
solution1[[1]];
Plot[{Yu[1, 1][x], Yu[2, 2][x], Yu[3, 3][x], Yd[1, 1][x], Yd[2, 2][x],
Yd[3, 3][x], Ye[1, 1][x], Ye[2, 2][x], Ye[3, 3][x]} /.
solution1[[1]], {x, Log[10^(16)], Log[246]},
PlotLegends -> "Expressions"]

And ok I didn't set well the legends but I got a plot with the 9 lines that sounds good.


For the vev's I wrote

solutionvev =
RunRGEs[{vu -> 0.9, vd -> 0.93}, Log[10^(16)], Log[246],
TwoLoop -> False];

{vu[16], vd[16]} /. solutionvev[[1]];
Plot[{vu[x], vd[x]} /. solutionvev[[1]], {x, Log[10^(16)], Log[246]},
PlotRange -> {0.8, 1}]

And basically I got a pair of constants at the value that I set as the initial value.


So, the main question could be "**then, how can I get the numerical result?" for the yukawa's and de vev's and not only a result for a plot



===Thank you==

[FStaub]

Please check the Mathematica handbook how to use InterpolatingFunction.

Florian

[Kugard]

I have gotten the result of the problem (I think), but I still have a question


Are the results obtained with SARAH in DR (dimensional reduction) or MS (minimal subtraction)?

[FStaub]

SUSY RGEs are in DR, non-SUSY RGEs in MS.

[Kugard]

I want to use SUSY Yukawas and non-SUSY yukawas as only one expresion for both and ploting. I'm running one of the models (for example MSSM) and set the values of yukawas and after that I run the other model (for example SM=standard model) and their yukawas and then I put together both using the comand piecewise of mathematica. However, when I run SM after MSSM, it takes so much time (comparing with the time used for running SM before than MSSM). So, can you recommend me something better?


Also, I have to run the models each time I want to work with them and then I have to calculate the 2 loop calculations at the same time

[FStaub]

Hi,
do you really mean that you run the models all the time via SARAH to get the RGEs? That won't work, you must always quit the kernel before running a new model. Moreover, it's sufficient to calculate the RGEs once, because the results are stored in the output directory,

Cheers,
Florian