Problems with 2HDM in SARAH

[oscarvives]

Hi Florian,

> Hi Oscar,
>
> thank you for your message. First, just to clarify: you refer to the
> value \alpha written in HMIX 11 in the SPheno.spc?

Yes, this is the value we refer to

>
> This value is calculated is (see parameters.m under "scalar mixing angle")
>
> DependenceSPheno -> ArcCos[ZH[1,2]]
>
> where ZH[1,2] is the (1,2) element of the matrix which diagonalises
> the CP even mass matrix which is parametrised in SARAH by
>
> {{-Sin[\[Alpha]],Cos[\[Alpha]]},
> {Cos[\[Alpha]],Sin[\[Alpha]]}}

We thought the reason for the positive values of alpha we are getting all the time could be your different
convention in m12.
The usual convention is very nicely explained in Appendix A of:
Higgs Bosons in Supersymmetric Models. 2. Implications for Phenomenology
J.F. Gunion (UC, Davis), Howard E. Haber in Nucl.Phys. B278 (1986) 449,

Here they choose positive M12 that appears with negative sign in the scalar potential, while you have positive sign in the potential and then M12 must be negative. They have a very nice Table 2 that shows the obtained signs of alpha, beta, etc.

But, in SARAH's conventions nothing should change if you use negative M12 as you (and we) do... so, we should get negative alpha, but it is not the results we are getting.

> In the calculation in SPheno, ZH is calculated numerically. Now, the
> point is that each matrix which is diagonalised by ZH is also
> diagonalised by -ZH, i.e. there is some (random) overall sign returned
> by the numerical routine. This explains the two values A and Pi -A
> which you get for alpha which result from ArcCos[Cos[A]] and
> ArcCos[-Cos[A]]. There are no further conventions applied to restrict
> the value to some specific range. (Maybe, it would be good to add that
> option in the future).

I am afraid this is not the full explanation of the two values and the positive sign.

In fact, if you fix alpha only with ZH[[1,2]] as ArcCos[Cos[A]], you have two possible values for A: A and (2Pi -A) giving the same Cos[A].
Then for some strange reason, SARAH/SPheno seems to take only the positive values of ArcCos[Cos[A]] and you end up with A for ZH and Pi-A for
-ZH. Does this make sense??

Obviously this would not be correct, this would not give the correct matrix. I guess that is not all SARAH is doing. What is happening?

Best,
Oscar

> I hope that clarifies the conventions and the "randomness" in alpha.
>
> Cheers,
> Florian
>
>
>
>> Dear Florian and Manuel,
>>
>> As you may remember, we are working now in Valencia in collaboration with
>> Ipsita Saha in a 2HDM defined at high scale with SUSY boundary conditions.
>>
>> We are using SARAH to obtain the 2 loop RGEs and then use SPheno to run a
>> scan. Manuel helped us (Ipsita) to configure SARAH files correctly.
>>
>> However, now we are having a problem with your conventions and more exactly
>> with the values of alpha (the scalar mixing) we obtain. In fact, if we do a
>> scan, all masses seem right, but we get two different values of alpha for
>> very similar input parameters. These values are related as A and (Pi -A)
>> and moreover both are positive. We think the problem may be the convention
>> you are using for M12, which appears in your scalar potential with positive
>> sign.
>>
>> According to the usual MSSM conventions, or the definitions in "the Higgs
>> hunter guide", M12 appears with negative sign and if v1< v2 and (mh+mH) > 2
>> MZ, we will have -Pi/2< alpha< 0 and cos (beta-alpha) < 0.
>>
>> This is not what we are getting and could be due to a problem with SARAH's
>> conventions. In the recent Florian's paper, 1705.03677, you say that you get
>> negative tan alpha, but we have tried with low scale input, using the last
>> version of SARAH and either the default input file or the values you give
>> below Fig 3 of your paper and we get always positive alpha.
>>
>> Are we doing something wrong??
>>
>> Best,
>>
>> Ipsita and Oscar
>>
>>
>>
>>

[oscarvives]

Indeed, this is exactly what happens. It is not enough to use ArcCos(Cos(A)) to obtain A, apart from the global sign problem. I just plotted
(SCALARMIX[1, 2], Cos[HMIX[11]]) and (SCALARMIX[1, 1], Sin[HMIX[11]]) and this is what I get:

So, with the alpha SPheno gets, I can not reproduce the mixing matrix (just 1/4 of the times...). This should be corrected. alpha ahoud be between 0 and -Pi/2, i.e. Cos alpha > 0 and Sin alpha <0. I can correct it by hand, but...

[FStaub]

Hi,

yes, there is a problem how alpha is extracted. What is (for sure) correct is the block ZH which contains the rotation matrix for the scalars. And this is also the only parameter which is used in SPheno throughout the calculation. The value of alpha is only calculated when writing the output file.
(I never recognised this problem, because I'm always looking at the rotation matrix and not at the value given in HMIX[11]). Anyway, I think, it would be better to calculated alpha as ArcTan[ZH[1,1]/ZH[1,2]] which then also should have no longer a 'random' sign because it cancels out. Do you agree?

Cheers,
Florian

[oscarvives]

Hi Florian,

I think it could be correct, if you use the function ATan which gives results between (-Pi/2 and Pi/2), or something similar. The only thing is that you should do ATan ( ZH[2,2]/ZH[1,2]) as ZH[1,1] is (-Sin(alpha) ).

Thanks a lot for your help.

Oscar

[FStaub]

Hi Oscar,

thank you to you for pointing out this issue.

Best,
Florian