RGEs in leptoquark model

[grazor]

Hi there
I try and run the RGEs for the scalar leptoquark model file

I run the command
Rl = {g1 -> 0.46, g2 -> 0.63, g3 -> 1.05, \[Lambda] -> 0.277,
Yu[3, 3] -> 0.9, Yu[2, 2] -> 0.1, Yu[1, 1] -> 0.1, Yd[1, 1] -> 0.1,
Yd[2, 2] -> 0.1, Yd[3, 3] -> 0.1, Ye[1, 1] -> 0.1, Ye[2, 2] -> 0.1,
Ye[3, 3] -> 0.1, mu2 -> -18000, MPhi2 -> 1000^2, gHP -> 0.1,
LPhi -> 0.1 , MS2 -> 0.1, gSH -> 0.1, LS3 -> 0.1, LS4 -> 0.1,
KSP -> 0.1, KSH -> 0.1, gSP -> 0.1, lamL[1, 1] -> 0.02,
lamL[2, 2] -> 0.02, lamL[3, 3] -> 0.02, gSC[1, 1] -> 0.02,
gSC[2, 2] -> 0.02, lamR[1, 1] -> 0.02,
lamR[2, 2] -> 0.02, lamR[3, 3] -> 0.02, MChi[1, 1] -> 0.1,
MChi[2, 2] -> 0.1 , v -> 274, vS -> 0.1}


sol = RunRGEs[Rl, 2, 12][[1]]

And I get the error

Encountered non-numerical value for a derivative at t == 2.`

doing the analogous thing for other model files works fine. For example doing this for the SM and SSM works fine. I'm not sure what I'm doing wrong.

[FStaub]

Hi,

hard to say. You can try the following: After RunRGEs[...] output

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(Take[equations, {1, Length[equations]/2}] /.  A_[t] -> A[2] ) /. {Take[equations, {Length[equations]/2 + 1, Length[equations]}] /. (a_ == b_) -> (a -> b)}

That should show you what non-numerical piece is present on the right hand side of the equations.

Cheers,
Florian

[grazor]

Hi! Thanks for your reply

When I add that line I get this message

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ReplaceAll::reps: "{\.05\ (mu2[2]->-18000),\.05\ (MS2[2]->0.1),\.05\ (MPhi2[2]->1000000),\.05\ (LS3[2]->0.1),\.05\ (KSH[2]->0.1),\.05\ (KSP[2]->0.1),\.05\ (v[2]->274),\.05\ (vS[2]->0.1),\.05\ (g1[2]->0.46),\.05\ (g2[2]->0.63),\.05\ (g3[2]->1.05),\.05\ (Yu[1,1][2]->0.1),\.05\ (Yu[2,2][2]->0.1),\.05\ (Yu[3,3][2]->0.9),\.05\ (Yd[1,1][2]->0.1),\.05\ (Yd[2,2][2]->0.1),\.05\ (Yd[3,3][2]->0.1),\.05\ (Ye[1,1][2]->0.1),\.05<<1>><<1>>,\.05\ (Ye[3,3][2]->0.1),\.05\ (lamL[1,1][2]->0.02),\.05\ (lamL[2,2][2]->0.02),\.05\ (lamL[3,3][2]->0.02),\.05\ (gSC[1,1][2]->0.02),\.05\ (gSC[2,2][2]->0.02),\.05\ (lamR[1,1][2]->0.02),\.05\ (lamR[2,2][2]->0.02),\.05\ (lamR[3,3][2]->0.02),\.05\ (MChi[1,1][2]->0.1),\.05\ (MChi[2,2][2]->0.1),\.05\ (\[Lambda][2]->0.277),\.05\ (LS4[2]->0.1),\.05\ (gSH[2]->0.1),\.05\ (gSP[2]->0.1),\.05\ (gHP[2]->0.1),\.05\ (LPhi[2]->0.1)} is neither a list of replacement rules nor a valid dispatch table, and so cannot be used for replacing."

followed by a huge output that look like

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{{Derivative[1][mu2][2] ==equations etc.

where there are 32 such equations. The first few terms on the RHS look like

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(Log[10] (-2 KSH[2]^2 - 6 gHP[2] MPhi2[2] - 2 gSH[2] MS2[2] - 
   9/10 g1[2]^2 mu2[2] - 9/2 g2[2]^2 mu2[2] + 6 mu2[2] \[Lambda][2] + 
   6 mu2[2] (Yd[1, 1][2]^2 + Yd[2, 2][2]^2 + Yd[3, 3][2]^2) + 
   2 mu2[2] (Ye[1, 1][2]^2 + Ye[2, 2][2]^2 + Ye[3, 3][2]^2) + 
   6 mu2[2] (Yu[1, 1][2]^2 + Yu[2, 2][2]^2 + 
      Yu[3, 3][2]^2)))/(16 \[Pi]^2)

And there appears to be nothing unusual. There are some parameters that appear in the DEs but don't have a DE associated with them. Assigning them a value doesn't help

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cHF = 1; cH3 = 1; cHY = 1; cHYbar = 1; cHS = 1;

Even stranger if I literally turn the output into NDSolve I get this error message (and modify the format slightly to be compatible with NDSolve)

NDSolve::derlen: "The length of the derivative operator Derivative[1] in \!\(\*SuperscriptBox[\"mu2\", \"\[Prime]\",
MultilineFunction->None][t]\) is not the same as the number of arguments"

But when I count the equations and arguments I get 32 for each

[FStaub]

I guess, I found the problem. Can you try to replace the file in Package/RGEs/ with the one attached.

Cheers,
Florian

[grazor]

Hi there!
Thanks for that

That seems to fix the problem!