Massless particles in loop

[jjonesperez]

Hi Florian,

I am building a model with two heavy neutrinos N_i (which do not decouple). Here, the SM neutrinos are massless, the heavy neutrinos are Dirac, but there do exist Yukawa couplings between the SM nus and the N_i (such that they mix).

As I want the final state fermions to be Dirac after EWSB, as I need to define left-handed (LH) and right-handed (RH) states. To keep things simple, I specify that only nu_e has Yukawa couplings with N_2 (all other Yukawas being zero) and, set the {nu_e, N_1} and {nu_mu, N_2} forming the LH and RH components of the two final Dirac neutrinos. That part of the model works well, with the first eigenstate being massless and the second one having a large mass which includes the Yukawa coupling and the original heavy Dirac mass.

The issue is that the nu_tau is left alone, and even though SARAH does recognize it as massless, on the SPheno code I get functions depending on "MFvt". This variable appears as (for example):

Complex(dp), Intent(in) :: MFvt(0),MFvt2(0)

The worst part is that it appears everywhere on the code, and doesn't go away even if I specify that the mass is zero in particles.m

It is likely that I am complicating things too much at the SARAH level, but I am not sure how to define this model in any other way. This passes all SARAH tests that i know.

Do you think this can have a solution? Thanks in advance,

Joel

[FStaub]

Hi Joel,

I'm not sure if this a problem because it's massless. It seems more to be a problem with the number of generations because for M(X), X should be the number of states. Right now, I'm not totally sure what might the origin. Maybe, it would help to get a brief look at the model file.

Cheers,
Florian

[jjonesperez]

Sure!

I did have to split generations to make only the nu_e interact. This is how I did it (I only show the parts involving leptons):

Code: Select all

FermionFields[[2]] = {le, 1, {veL0, eL0},    -1/2, 2,  1};
FermionFields[[6]] = {v1c, 1, vR1,     0, 1,  1};
FermionFields[[7]] = {v2, 1, conj[vR2],     0, 1,  1};
FermionFields[[8]] = {lmu, 2, {vL, lL},    -1/2, 2,  1};

The relevant Lagrangian was:

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LagHC =  -(Yd conj[H].d.q + Yu H.u.q + Ye1 conj[H].e.le + Ye2 conj[H].e.lmu + Yv H.v2.le  + Mv v1c.v2 );

To build the Dirac spinor, I needed to choose a specific generation within lmu (this is the part that worries me). This was done with:

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DEFINITION[EWSB][Flavors]= {
  {lL, {muL0, tauL0}}, 
  {vL, {vmuL0, vtauL0}}
}

The rotation into mass eigenstates is done with:

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DEFINITION[EWSB][MatterSector]=   
    {{{{eL0, muL0, tauL0}, {conj[eR]}}, {{EL,Ve}, {ER,Ue}}},
     {{{veL0,vR1},{conj[vmuL0],conj[vR2]}},{{NuL,VvL}, {NuR,VvR}}}
    };  

Finally, the Dirac spinor is obtained with:

Code: Select all

DEFINITION[EWSB][DiracSpinors]={
 Fv ->{  NuL, conj[NuR]},
 Fvt -> { vtauL0, 0}
};

[FStaub]

Hi,

yes, the problem is the part with the Flavors. If I remember correctly, this is not supported in the SPheno output. So, it might be better to just keep all flavours and chose the numerical values in a way that only some states get masses.

Cheers,
Florian

[jjonesperez]

Right, but the problem there is that the reconstructed mass matrix ends up being Majorana, and I need it to be Dirac.

What about not using the Flavour option, and separating the lmu states into two families from the start?

[FStaub]

What about not using the Flavour option, and separating the lmu states into two families from the start?

Yes, that should work.

[jjonesperez]

Ok, it didn't work.

Now SARAH does recognize that the nu_tau is massless. However, I now get MNeutrino and MNeutrino2 variables within LoopCouplings, FlavorKit_QFV and SPheno subroutines. These variables are generally undefined, except in FlavorKit_QFV, where they appear as:

Complex(dp),Intent(in) :: MNeutrino(0),MNeutrino2(0)

In addition, there is a problem on the Model_Data subroutine, as Ye1, Ye2 and Ye3 are not properly inserted. One gets things like "ElectronYukawa = YeSM". This is easily solvable, though.

I am attaching the model file in full, just in case you want to have a look.

[FStaub]

Hi,

hm... I guess you have not added the keyword "Neutrino" to any of your fields in particles.m? The problem is that SARAH needs to insert at some places the neutrinos (in LoopCouplings for the calculation for Delta_VB, in FlavorKit for all meson decays into neutrinos).

However, I'm not sure what would be correct in your model. I guess, you should define the Fv in your model as 'Neutrino'. This should be at least correct for Delta_VB and many flavour observables. But of course not for observables like B->tau nu. Moreover, if you need flavour observables where the sum over all neutrinos are taken even if they don't appear as different generations of the same state, then I guess you need to work a bit to get a suitable implementation of these flavour observables via FlavorKit.

Cheers,
Florian

[jjonesperez]

Excellent! I had defined them as "Dirac Neutrinos", but once changing them to "Neutrinos", and fixing some issues with the ElectronYukawa variable appearing every here and there, the code compiled.

Many thanks, let's hope that I find no problems when doing the tests. :-O