Not All Tree Level Minima Found

[Kfirdolev]

So I could add to the Lagrangian a term like a*(Re[\phi1])^2?

[benoleary]

Oh dear, I was wrong.

I had somehow misread the mixing term in the potential as being proportional to v1I * v2^2.

In that case, there would be a ring of extrema for v2 = 0. As it is though, the term v1I * v2 * M12 should be sufficient to break the degeneracy everywhere. I think that I was also fooled by the first 6 digits being the same around |v1| = 1017.42... and thought that the rest was numerical jitter.

Back to square 1. It seems to be a problem with HOM4PS2. The model should work correctly with the homotopy continuation algorithm, but apparently it is not working with HOM4PS2. Maybe the parameter breaking the degeneracy is too numerically small for the numerics of HOM4PS2. I would be surprised though.


Apologies,
Ben

[KfirDolev]

Hey Ben,

Whenever V2=0, V1->phase*V1 is a symmetry of the Lagrangian, because only terms like H1*.H1 and (H1*.H1)^2 remain, so I think you were initially right. I'm trying to add a term like Mre*Re[H1].Re[H1] into the lagrangian, but the vin file doesn't seem to change.

[FStaub]

Hi,

Yes, Re[x] won't be understood by SARAH. So, you'll need to write the term for instance as (M1 H1.H1 + h.c.) + 2 M2 H1.conj[H1] and put M1=M2.

Cheers,
Florian

[KfirDolev]

Hey, thanks again for all of the help.

I tried adding these terms. When starting the model in SARAH I get a warning that says this term break hypercharge. When I make Vevacious, only the M2 term shows up in the tadpole equations. The symmetry breaking term H1.H1 is ignored completely. Is there a way to fix this?

[FStaub]

Hi,

ok, it seems that I added some checks to prevent 'such mistakes' in the potential. Now, I went back to the tadpole equations themselves, and actually I think the problem are not the degenerated minima. I set up the model and included also the imaginary part for v2 (called v2I), i.e. I get four equations. In the limit v2->0, v2I->0 they read

Code: Select all

v1 (M112 + Lambda1 (v1^2 + v1I^2))=0
rM12 v1 + iM12 v1I=0
v1I (M112 + Lambda1 (v1^2 + v1I^2))=0
-iM12 v1 + rM12 v1I} =0

which simpifies further for real M12 - as you are using for your point - to

Code: Select all

v1 (M112 + Lambda1 (v1^2 + v1I^2))=0
rM12 v1=0, 
v1I (M112 + Lambda1 (v1^2 + v1I^2))=0
rM12 v1I=0

Now, you don't have the last equations, which looks crucial: the second equations gives v1=0, and then the third equation can be used to solve for v1I what gives the result you see. However, this contradicts the fourth equation which you don't have.

However, I'm still not sure why HOM4PS2 fails to find the solution when you feed it with only the first three equations: even if there is a degeneracy in the potential, this seems not to be reflected by the tadpoles unless you drop the second equation as well.

[benoleary]

Just to mention: even in scenarios where there is a ring of degenerate minina, homotopy continuation should find at least a complex solution on the ring (the problem being that the ring might suck in paths which should go to other minima, leading to the other minima not being found). I don't know what is up with HOM4PS2 for this set of equations.

[KfirDolev]

Hey Florian,

Which model did you use? I think the tadpole equations should depend on Lambda2, Lambda3, Lambda4, Lambda5 as well. Perhaps you are using a simplified 2HDM?