Gauge dependence

[MailQuestion]

Hi Florian,

We face another trouble with U(1)_Dark extension implementation in SARAH. It seems
that the calcHEP model file generated by SARAH is giving different results for SM Higgs
decay width into Z ZD (ZD = dark photon) channel (i.e. h_SM ---> Z ZD) with and without
enabling the unitary gauge choice.

[FStaub]

Hi,

there can be a problem if you use the rotation matrices with loop corrections as calculated by SPheno. If you use those in CalcHep, which does a pure tree-level calculation, this might spoil gauge invariance.

Cheers
Florian

[arin]

Thanks Florian. Since we are interested in the region MZD (mass of the "dark photon") < MZ,
I have used the following ordering : {{VB,VWB[3],VBp},{VP,VZp,VZ},ZZ} in the gauge sector.
In the pseudoscalar sector I have "{{sigmaH,sigmaB},{Ah,ZA}}," (where sigmaB comes from
the "dark Higgs" and finally Ah[{1}] is assigned as the Goldstone mode corresponding to the
ZD massive boson and Ah[{2}] to the Z boson.

In the SPheno output, in the following files : FlavorKit_Observables_*.f90, LowEnergy_*.f90,
InputOutput_*.f90, and Susymasses_*.f90(SARAH-4.7.0)/ TreeLevelMasses_*.f90 (SARAH-4.9.3)
[* denotes $MODELNAME] I am getting issues with do loops running from a bigger to a
smaller number (i.e. "do i1 = 3, 2 ....") related to the CP-odd sector. Here is an example from
TreeLevelMasses_*.f90 :
! Reorder the physical states by their mass
Do i1=3,2
pos = Minloc(MAh2(i1:2),1) + i1 -1
If (pos.ne.i1) Then
MAhtemp = MAh2
ZAhtemp = ZA
MAh2(i1) = MAhtemp(pos)
ZA(i1,:) = ZAhtemp(pos,:)
MAh2(pos) = MAhtemp(i1)
ZA(pos,:) = ZAhtemp(i1,:)
End if
End do

Do you think that the Goldstone assignment is creating these issues? I tried altering the choice
previously, but some or the other issues kept coming. In case you prefer to look at the model
files, please let me know.

Also, for the gauge choice issue, is there a convenient way to switch off rad. corr. in the gauge boson
(mixing) sector? I am still struggling with it.

[FStaub]

Hi,

In the SPheno output, in the following files : FlavorKit_Observables_*.f90, LowEnergy_*.f90,
InputOutput_*.f90, and Susymasses_*.f90(SARAH-4.7.0)/ TreelevelMasses_*.f90 (SARAH-4.9.3)
[* denotes $MODELNAME] I am getting issues with do loops running from a bigger to a
smaller number (i.e. "do i1 = 3, 2 ....") related to the CP-odd sector.

Yes, some compiler print warnings about this. However, this should be fine: in some loops only physical states should run, i.e. the loop shall start "one generation above the Goldstones". Since you have just pseduo-scalars that means that these loops shouldn't be evaluated at all.

So, all of that should be not connected to your problem about gauge dependent results.

Code: Select all

Also, for the gauge choice issue, is there a convenient way to switch off rad. corr. in the gauge boson 
(mixing) sector? I am still struggling with it.

If you set flag 55 to 0 in the les houhes input, you should get purely tree-level masses and rotation matrices.

Cheers
Florian

[arin]

Thanks for the prompt response again. I have two questions :

We already have flag 55 set to 0. Although the kinetic mixing may originate generally
from loop-induced processes, we are only treating it as a (small) "tree-level" parameter
in this case. There is no particle which is charged both under U(1)_Y and U(1)_D and
in the model file, and therefore I expect no contribution to the kinetic mixing at 1-loop.
I have included the "off-diagonal--gauge couplings" gYD and gDY (and gD) as input
parameters in the SPheno.m file.

Q1. While running the SPheno spectrum generator, should we set flag 60 ("include possible
kinetic mixing") to "1" or to "0" in the LesHousches.in file (considering that in our case kinetic
mixing is already included by gYD and gDY input parameters at tree-level, and there is
no one-loop contribution expected)?

Using the spectrum generated (with flag 55 and flag 60 both set to "0") to compute
h_SM--> ZD ZD (using CalcHEP) I find no gauge dependence, only h_SM--> Z ZD is
showing it. I have used the following parametrisation for the gauge boson mixing matrix :
{ZZ, { Dependence -> {{Cos[ThetaW], -Sin[ThetaW] Sin[ThetaWp], Sin[ThetaW] Cos[ThetaWp]},
{Sin[ThetaW],Cos[ThetaW] Sin[ThetaWp],-Cos[ThetaW] Cos[ThetaWp]},
{0, Cos[ThetaWp], Sin[ThetaWp]}},
LaTeX -> "Z^{\\gamma Z Z'}",
LesHouches -> ZMx,
OutputName -> ZZ}},
where,
{ThetaWp, { Real -> True,
LaTeX -> "{\\Theta'}_W",
DependenceSPheno -> ArcCos[Abs[ZZ[3,2]]],
OutputName-> TWp,
LesHouches -> {ANGLES,10}}},
Since I have been following {{VB,VWB[3],VBp},{VP,VZp,VZ},ZZ} order for the gauge and mass eigenbasis
respectively, I have interchanged the 2nd and the 3rd column of the ZZ specified for your B-L model
already implemented in SARAH. In spite of mentioning "LesHouches -> ZMx," in the above description
for the mixing matrix ZZ in SPheno.m file, when I run the the generated output with SPheno, the output
spectrum file doesn't print ZMx block.

Q2. Could you suggest a way to print the gauge mixing matrix ZZ explicitly in the Spheno generated output
file? That would help a lot, thanks again.

[FStaub]

Hi,

1) if you have tree-level gYD and gDY you should put flag 60 to 1. Otherwise, those are set to zero to speed up the calculation.

2) You would need to remove Dependence of ZZ at all to see it in the les houches output. Then, all vertices are expressed in terms of ZZ and ThetaW, ThetaWp won't show up at all. Maybe, that might help to reduce the number of potential problems. To see ZZ, the simplest option is to add a write command in TreeMasses_MODEL.f90

Cheers
Florian

[arin]

Thanks Florian. But even when I remove the dependence for ZZ, the block is not written
in the SPheno output file. Now I have the following description for ZZ in the parameters.m
file :
{ZZ, { LaTeX -> "Z^{\\gamma Z Z'}",
LesHouches -> ZMx,
OutputName -> ZZ}},
But this matrix is not present in the SPheno output file. I can print it from the Treemasses+*.f90
though. But it would be very convenient if the output file had this block (e.g. for CHep or madgraph
analysis). Please let me know if you have any suggestions.

[FStaub]

Hi,

sorry for the confusion; I also needed to check what goes on. The reason for the problem was a buggy check for the correct entry of ZZ in the parameters file. Two possible fixes
1) Put the definition of ZZ before the one of ThetaW in parameters.m
2) Edit SPhenoTreeMasses.m and replace

Code: Select all

Position[paraDef, Last[mixVB[[i]]]]

by

Code: Select all

Position[Transpose[paraDef][[1]], Last[mixVB[[i]]]]

Cheers,
Florian

[arin]

Thanks again. Now it prints the block ZZ. I have removes the
Theta_Wp parametrization of ZZ as well. However, while h_SM-> ZD ZD
shows about the same value (less than 10% off) in both gauges,
h_SM-> Z ZD turns out to be very different (by 3 orders of magnitude)
in CalcHEP. I am in the process of analytically checking the relevant
vertices and gauge fixing. Any other suggestions are very welcome.