VL leptons with mixings between generations

[Amin]

Dear Florian,

I am implementing a vectorlike extension to the MSSM and I am using "NMSSM+VL-5+10plets.m" as a template to do so. Now the extra thing in my model is the presence of mixings between the vectorlike generation and the first three generations.
For example, if we take the fields, as defined in the file:

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SuperFields[[2]] = {l,  3, {vL,  eL},   -1/2, 2, 1, RpM,1};
SuperFields[[12]] = {l5p,  1, {conj[eL5p],  conj[vL5p]},    1/2, 2, 1, RpM,-1};

There will be terms in the superpotential as

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Yf l5p.l + Yfp e.e10p , ... etc

where Yf and Yfp are matrices containing the complex couplings with the three generations. So my questions are:
1) Does this set up make sense to SARAH? If yes, how can I define the matrices Yf and Yfp?
2) Those mixings will bring about a change in the lepton mass eigenvalues and so they must be chosen carefully to avoid spoiling the lepton masses. Would that work with SPheno and is there a way to check that the lepton masses are not off?

Thanks a lot,
Amin

[FStaub]

Hi,

yes, the setup seems to make sense. You can define the new couplings as input for SPheno. SPheno should then determine the 'standard' Yukawas in a way that the SM data is reproduced. In principle, the algorithm for that should be quite generic, but might fail in the case that the mixing becomes too large.

Cheers,
Florian

[Amin]

Hi Florian,

Sounds great. I have yet to try it and hopefully it runs smoothly.
Thanks a lot.

Best,
Amin

[Amin]

Hi Florian,

I believe most of the model is working fine except for some nuisances coming from the terms:

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Yf l5p.l + Yfp e.e10p , ... etc.

1) Those terms violate global Z2 symmetry, defined as ExtraZ2 in the file. What is that ExtraZ2 and should I worry about that?
2) There are three couplings between each of the three generations and the vectorlike one. How can I explicitly have those couplings with out having to undergo flavour decomposition? Defining Yf and Yfp as matrices does not work (or maybe I am making a mistake in their definition!).

Thank you,
Amin

[FStaub]

Hi,

- the ExtraZ2 is just there to forbid them mixing between SM and VL states.
- Did you check Vectorlike/SusyTop/Vectorlike-SusyTop.m where such mixing terms for quarks are included? Thus, it works without flavour decomposition.

Cheers,
Florian

[Amin]

Thanks Florian. I did check the model you suggested but the couplings are the same for all generations. Here's what I meant:
Say the lepton doublet is \psi_{\alpha,L} = (\nu_{\alpha, L}, \ell_{\alpha, L}) with \alpha being the generation index and the vectorlike "mirror" doublet is \chi^c = (E^c_L, N^c_L). I want expressions in the superpotential to have this form:

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... + f_3 Epsilon[i,j] \chi^c^i \psi^j_{1,L} + f'_3 Epsilon[i,j] \chi^c^i \psi^j_{2,L} + f''_3 Epsilon[i,j] \chi^c^i \psi^j_{3,L} + ...

So I want the couplings between each generation and the vectorlike one to be different.

Hope this makes it clear.

Thanks a lot,
Amin

[FStaub]

Sure, they are by default.

In the same way in which

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Yu H.u.q

leads to a 3x3 Yukawa matrix Yu,

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Yt H.u.qPrime

gives a 3-vector Yt. See also http://stauby.de/sarah_wiki/index.php?t ... al#Example

Cheers,
Florian

[Amin]

I see. So I can define the couplings in SPheno as Yt[1], Yt[2] and Yt[3] by giving them different values as f_3, f'_3 and f''_3.
Does that sound right?

Thank you,
Amin

[FStaub]

Yes, therefore my proposal to check the SusyTop model where you find in SPheno.m

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BoundarySUSYScale={
{Yt,0},
{Yt[3],YTinput}
};

Thus, here we couple the VL states only to the third generation.

[Amin]

Got it. The initial run, Start["Model"] now works fine with no errors or warnings.
I am going to work on SPheno now.

Thanks for the help, Florian.
Amin