• Vector-like Lepton Model

Hello everyone,

I am trying to implement the vector-like lepton model from https://arxiv.org/abs/1705.07007 in SARAH (for use in FlexibleSUSY),
but am running into an issue with the SSV vertices.

My first question is about the field definition. Following the vector-like quark examples I added

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FermionFields[[6]] = {ve1, 1, conj[veL], -1, 1,  1};
FermionFields[[7]] = {ve2, 1, conj[veR],  1, 1,  1}; 
FermionFields[[8]] = {vl1, 1, {lL0, lLm},    -1/2, 2,  1}; 
FermionFields[[9]] = {vl2, 1, {-lRm, lR0},    1/2, 2,  1};

...
LagHC = -(Yd conj[H].d.q + Yu H.u.q + Ye conj[H].e.l + mE ve1.ve2 + mL vl1.vl2 + BLmda H.ve1.vl2 + Lmda conj[H].ve2.vl1 + LmdaE conj[H].ve2.l + LmdaL conj[H].e.vl1);
...

DEFINITION[GaugeES][DiracSpinors]={
 ...
 FE ->{veL, conj[veR]},
 FLm ->{lLm, conj[lRm]},
 FL0 ->{lL0, conj[lR0]}
};

Is there a way to avoid this "by hand" conjugation? Ideally I would like the model file to match exactly the established conventions,
however, all my attempts so far always resulted in Hypercharge violation errors.

Second, when running CheckModel[] in Mathematica I get a suggestion about additional terms I could add like {vl1,conj[H],conj[ve1]}, which should however not appear, because both fields are supposed to be "right-handed". I was hoping that the definition of the GaugeES spinors takes care of this, but it seems not. Also, there is a warning about possible mixing between VP and VZ

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Lagrangian::PossibleMixing: Possible mixing between VP and VZ induced by the term: -(1/4) e^2 v^2 (Sec[ThetaW] ZZ[1,1]-Csc[ThetaW] ZZ[2,1]) (Sec[ThetaW] ZZ[1,2]-Csc[ThetaW] ZZ[2,2])

Can I ignore these messages, or are these actual problems with the implementation?

Other than that, the model passes all checks, which brings me to the main issue.
When I generate the FeynArts model file I get the following warnings

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Vertex::ChargeViolating: Non-zero result for {Ah,Hp,VWp} vertex which violates charge. (This might just be a problem with simplifying the vertex, but could also point towards a mistake in the implementation.)

Vertex::ChargeViolating: Non-zero result for {Ah,conj[Hp],conj[VWp]} vertex which violates charge. (This might just be a problem with simplifying the vertex, but could also point towards a mistake in the implementation.)

Vertex::ChargeViolating: Non-zero result for {hh,Hp,VWp} vertex which violates charge. (This might just be a problem with simplifying the vertex, but could also point towards a mistake in the implementation.)

General::stop: Further output of Vertex::ChargeViolating will be suppressed during this calculation.

The additional VL leptons mix with the SM leptons, which modifies the FFV and FFS couplings, but the scalar gauge interactions
should not be affected by that. In the FeynArts model file I can remove these unwanted vertices by hand, but in FlexibleSUSY this wont
be feasible and I therefore need the generation to work correctly.

Any suggestions or insights on these questions would be very helpful and I am happy to provide further information on the model implementation
if necessary.

Best regards,
Kilian

Hello Kilian,

per default all the spinors in SARAH are left-handed Weyl spinors to start with. This is one of the reasons why one has to add the conjugation at various places. Therefore I do not fully understand your second comment that vl1 and ve1 are right-handed.
The warning about the mixing you can in general ignore. However, you should check that the given expression indeed vanishes because of either unitarity or orthogonality of the matrix. Unfortunately, Mathematica does not know these matrices are orthogonal or unitary which is the reason for the warning.

Best,
Werner

Hello Werner,

thanks a lot for your reply!

You are right, the warnings can be safely ignored. In fact, after adding the explicit expressions
for the rotation matrices in the parameters.m file the warnings do not appear anymore.

I think your first comment also solves my other issue, but I have to read up again on what Conj[]
does exactly and perhaps check my implementation.

Best regards,
Kilian

Vector-like Lepton Model

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