CalcHEP negative BR

[AntonK]

Dear Florian,

First of all, sorry for a messy question but I believe that you can shed light on the problem. As I am a new user to SARAH, this is hopefully something trivial.

I am working with an extend SM Higgs sector, more specifically 3HDM where one of the doublets is inert. The main purpose of using SARAH was to generate a CalcHEP model files. Everything works fine in micrOMEGAs 5.0.4 in the unitary gauge, i.e. ForceUG=1, the default option, but when setting ForceUG=0 in the output I noticed that some of the branching ratios are negative. I took a look at this topic (http://stauby.de/sarah_userforum/viewtopic.php?t=307) and if I got it correctly, both "1/0" switches should function correctly, am I right? Afterwards I took a look at the CalcHEP forums, especially at (https://bugs.launchpad.net/calchep/+bug/1647774 and https://answers.launchpad.net/calchep/+question/675273). A. Belyaev noted that: "negative width in t'Hooft-Feynman gauge is the sign of absense of gauge invariance."

If both switches "1/0" should function properly here is a continuation. Afterwards I took a look at the "problematic" decays and noticed that those included decays with Goldstone bosons, i.e. CP-odd and charged Higgs bosons. CheckModel[ ] didn't output any errors. I tried playing around with the charged sector, but was getting an error in SARAH due to the charge conservation. In this specific model all neutral Higgs gauge components mix to form physical states; to be more specific here is a link to PDF so it would be easier to understand what I am talking about. In the SARAH model file I wrote down a single mixing matrix {{phi1, phi2, sigma1, sigma2}, {hh, ZH}} for both CP-even/odd sectors. I assume that this might be one of the issues? I took a look at the "Model implementation in SARAH" section but failed to find topics which could explain this.

Another interesting observation is that in SARAH, for example, the coupling for vertex h1-h2-h4 is zero (using Vertex[{hh[{i}], hh[{j}], hh[{k}]}] function), while in CalcHEP branching ratio for h4-> h1 h2 is 1.04E-30, I enclose this benchmark point in data file. Couplings generated by SARAH are in agreement with the ones derived before. In principle such terms can be deleted by hand in lgrng1.mdl file, but this might indicate a possible issue? Thus decided to include this comment.

P.S. To export to CalcHEP I am using the following command: MakeCHep[SLHAinput -> False, CalculateMasses -> False].

With best regards,
Anton

[FStaub]

Hi,

one problem might be indeed the ordering of your scalars, more precisely this part in particles.m:

PDG -> {25, 35, 0, 36},

The unphysical states (Goldstones) should appear at the very beginning, i.e. it should be

PDG -> {0, 25, 35, 36},

Moreover, as long as you don't have CP violaiton, it might be better to split CP even and CP odd Higgs. That should result in a much faster code. The reason is that in general the triple Higgs vertex h_i h_j h_k only exists if it is allowed by CP. Thus, you are summing now over all i,j,k, because your states have no definite CP, while SARAH will recognise that h_i-h_j-A_k always zero if h/A have definite CP.

Cheers,
Florian

[AntonK]

Dear Florian,

First of all, I tried re-ordering scalar states so that the Goldstone boson would appear first. Unfortunately this did not work. I checked vertices and those are in agreement with previous results. Also, just to be sure, I changed the Goldstone field in the Z section. In CalcHEP I was getting error ¨Cannot calculate constraint Wh2¨, this corresponds to the CP-odd scalar. The only decay process was h2 -> Wm WP with ¨-NAN¨ branching ratio. Number of Lagrangian terms was consistent with the mixing used before.

Next I tried to split CP-even and CP-odd mixing matrices, but here comes another issue. Suppose that the neutral Higgs components are given by:

Code: Select all

 DEFINITION[EWSB][VEVs]= 
  {     {H10, {v , 1/2}, {sigma1, I/Sqrt[2]},{phi1, 1/Sqrt[2]}},
        {H20, {v , 1/2}, {sigma2, I/Sqrt[2]},{phi2, 1/Sqrt[2]}},
        {HS0, {0, 0},    {sigmaS, I/Sqrt[2]},{phiS, 1/Sqrt[2]}}  
        };

In our model the Goldstone boson is a mixture of sigma1 and sigma2, while the CP-odd Higgs state - mixture of phi1 and phi2. On the other hand, in order to get the CP-even states, you need to mix all 4 components. I tried to apply several different ideas but everything seemed to fail, or at least I defined it in a wrong way. Here are some of the possibilities I tried:
1) Going into the Higgs basis, so that the CP-odd sector is automatically defined and then for the CP-even sector you need only 2 fields. This would require to use something like this:

Code: Select all

 DEFINITION[EWSB][VEVs]= 
  {    {H10, {v , 1/2}, {(A+B), I/Sqrt[2]},{(C+D), 1/Sqrt[2]}},
        ...
       };

2) Instead of using all 4 gauge eigenstates for a diagonalization procedure, combine them into pairs:
DEFINITION[EWSB][MatterSector]=

Code: Select all

     { {{(sigma1+sigma2), (phi1 + phi2)}, {hh, ZH}},
          ...
       }; 

3) Trying to diagonalize using a non-squared matrix, i.e. of dimension 4 x 2, so that you still get 2 CP states while mixing all 4 gauge eigenstates.

Unfortunately none of the aforementioned assumptions worked and could not successfully load model . Is there a valid possibility in this case? Or should I just mix in the following way:

Code: Select all

DEFINITION[EWSB][MatterSector]=   
    { {{sigma1, sigma2, phi1, phi2}, {hh, ZH}},
      {{sigma1, sigma2, phi1, phi2}, {Ah, ZA}},
       ...
      } ;

with both ZH and ZA of dimension 4 x 4 and then by-hand delete redundant states. (Just found out that it is impossible to use {sigma1, sigma2, phi1, phi2} twice)

With best regards,
Anton

[FStaub]

Hi,

yes, the approaches 1)-3) won't be understood by SARAH. Thus, it might be really the best to stick to the very first implementation. I just made a quick check:

Code: Select all

Start["3HDM"]
sol = Solve[TadpoleEquations[EWSB] == 0, {\[Mu]12}][[1]]
FullSimplify[
 MassMatrix[hh] //. sol /. RXi[_] -> 0 //. 
   Select[subNumDependences, FreeQ[#[[1]], v] &] /. \[Sigma] -> 0 ] 
FullSimplify[Eigenvalues[%]]

If everything would be consistent, I just should get the masses as eigenvalues. However, I find:

Code: Select all

{0, Mh1^2 + Mh4^2, 
 Mh2^2 Sqrt[((Mh1 - Mh2) (Mh1 + Mh2) (Mh2 - Mh4) (Mh2 + Mh4))/(
  Mh2^2 (Mh1^2 - Mh2^2 + Mh4^2))], 
 Mh2^2 (-1 + Sqrt[1 - (Mh1^2 Mh4^2)/(Mh2^2 (Mh1^2 - Mh2^2 + Mh4^2))])}

Thus, there might be something wrong with your definitions of the parameters.

Another comment: I never put the complex phase into the Lagrangian, but usually define it later, see for instance MSSM/CPV or NMSSM/CPV. It might work the way you do it, but that wasn't checked thoroughly and there is no guarantee from my side.

Cheers,
Florian

[AntonK]

Dear Florian,

First of all, I decided to get rid of all DependenceNum-> for the scalar potential so that the mass eigenvalues would be expressed in terms of couplings; talking about the code provided above. It did not help.

I am not sure about the second comment. I got:

Code: Select all

DEFINITION[GaugeES][Phases]= 
{    {H1p, Exp[I \[Sigma]]},
     {H10, Exp[I \[Sigma]]}
    }; 

where I got this from the THDMCPV model. The same structure is in MSSM-CPV and NMMSM-CPV. Also just a note, I do get correct trilinear and quartic couplings it is just that something seems to be wrong with the Goldstone bosons.

Currently I am trying to "fix" by hand negative branching ratios by introducing additional "-" sign in the "Factor" column. The issue is that with different input parameters it seems that you need to introduce this "-" at different places.

With best regards,
Anton