Mass of Z' in spectrum file

[ahmedthabt]

Hello Florian,

When I write a large mass for Z' in the input LesHouches file I find the Z' mass calculated by SPheno in the spectrum file correct. However, when I input smaller masses (less than 100 GeV), I find the calculated mass in the spectrum file very different, and for smaller masses it always gives 9.04108035E+01

What is the cause of this problem?

[FStaub]

Hi,

1) If you have M_Z' < M_Z you need to exchange the definition of the fields in the SARAH model file

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{{VB,VWB[3],VBp},{VP,VZ,VZp},ZZ},

to

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{{VB,VWB[3],VBp},{VP,VZp,VZ},ZZ},

2) For small masses, there might be largish loop corrections depending on the model. All mixing effects between Z and Z' can play a role in the case of degenerated masses. Both might not be included in the used relations between Z' mass and VEV used in the input.

Cheers
Florian

[ahmedthabt]

Thanks so much Florian, this solved the problem.

I manipulated the parameters file so that SPheno displays ZZ (the mixing angle between photon, Z, and Z'), and I get this matrix in the spectrum:

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  1  1     8.74665974E-01   # Real(ZZ(1,1),dp)
  1  2     3.27597270E-04   # Real(ZZ(1,2),dp)
  1  3    -4.84726032E-01   # Real(ZZ(1,3),dp)
  2  1     4.84726143E-01   # Real(ZZ(2,1),dp)
  2  2    -5.91134167E-04   # Real(ZZ(2,2),dp)
  2  3     8.74665774E-01   # Real(ZZ(2,3),dp)
  3  1     0.00000000E+00   # Real(ZZ(3,1),dp)
  3  2    -9.99999772E-01   # Real(ZZ(3,2),dp)
  3  3    -6.75839903E-04   # Real(ZZ(3,3),dp)

Looking at the third row, I would expect ZZ(3,2) and ZZ(3,3) to be positive, so why are they negative here?

Also when I look at the branching ratio of (higgs->Z' Z') I find it very different from what I calculated by hand by many orders of magnitude. My calculations used the the vertex expression computed by SARAH and the values of ZZ displayed by SPheno. Do you have an idea of what may have gone wrong here?

[FStaub]

Looking at the third row, I would expect ZZ(3,2) and ZZ(3,3) to be positive, so why are they negative here?

Also when I look at the branching ratio of (higgs->Z' Z') I find it very different from what I calculated by hand by many orders of magnitude. My calculations used the the vertex expression computed by SARAH and the values of ZZ displayed by SPheno. Do you have an idea of what may have gone wrong here?

That's just an arbitrary phase which doesn't play.

Also when I look at the branching ratio of (higgs->Z' Z') I find it very different from what I calculated by hand by many orders of magnitude. My calculations used the the vertex expression computed by SARAH and the values of ZZ displayed by SPheno. Do you have an idea of what may have gone wrong here?

Can you give some numbers?

[ahmedthabt]

Hello Florian,

First thanks for your reply.

This is the h-Z'-Z' vertex generated by SARAH:

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{1/2 I (16 vp (4 + zu)^2 ZH[2, 2] (g1p1 ZZ[1, 2] + g1p ZZ[3, 2])^2 + v1 ZH[2,1] (-g1 ZZ[1, 2] + 2 g1p1 (1 + zu) ZZ[1, 2] + g2 ZZ[2, 2] - g11p ZZ[3, 2] + 2 g1p ZZ[3, 2] + 2 g1p zu ZZ[3, 2])^2), g[lt2, lt3]}}
 

The higgs mixing matrix from SPheno is:

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  1  1     6.37989416E-08   # ZH(1,1)
  1  2    -1.00000000E+00   # ZH(1,2)
  2  1    -1.00000000E+00   # ZH(2,1)
  2  2    -6.37989416E-08   # ZH(2,2)

We want the hh_2 which is the standard model higgs. Plugging in the numbers from SPheno, with zu=-3.5, g11p=g1p1=0, g1p=10^-4, vp~v1=244.9
this vertex is of order 10^-13

Multiplying by polarization, squaring, and integrating over phase space (assuming mass of Z' << mass of higgs) we get a factor of 10^-2 and 1/HiggsMass, which eventually give a decay width of order 10^-30 GeV. And since the total decay width of higgs is of order 10^-3 GeV, we expect a branching ratio of order 10^-27

However the branching ratio calculated by SPheno is 1.90931670E-03

[ahmedthabt]

Hi Florian,

Now when I turned off the Calculate loop corrected masses option, I got an answer that's pretty much close to my own calculation: 1.21570125E-26

But I think it's a coincidence, since I tried to input other parameters and it printed a very different result than mine.

By the way, I noticed that in the file "DecayFunction.f90" the "coup" in Subroutine ScalarToTwoVectorbosons is not the same as the vertex computed by SARAH for the tree-level process.

Also the formula of decay width:

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x = mSsq / mV1sq
    kappa = Sqrt( 1._dp - 4._dp / x )
    width = oo64Pi * Abs(coup)**2 * kappa * (x*x - 4._dp*x + 12._dp) / mS 

is different from my calculation. I roughly have

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width = oo64Pi * Abs(coup)**2 * kappa

without the last bracket and last mS.

I need to know if there is a problem in the SPheno code and its formulas, or the problem is rather in my calculation, since this has been a source of much confusion.

Thanks Florian.

[FStaub]

By the way, I noticed that in the file "DecayFunction.f90" the "coup" in Subroutine ScalarToTwoVectorbosons is not the same as the vertex computed by SARAH for the tree-level process.

Do you mean the numerical value? There shouldn't be big differences.

Also the formula of decay width:

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x = mSsq / mV1sq
    kappa = Sqrt( 1._dp - 4._dp / x )
    width = oo64Pi * Abs(coup)**2 * kappa * (x*x - 4._dp*x + 12._dp) / mS 

is different from my calculation. I roughly have

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width = oo64Pi * Abs(coup)**2 * kappa

without the last bracket and last mS.

Your result must be wrong because it has as units GeV^2.

[ahmedthabt]

Do you mean the numerical value? There shouldn't be big differences.

When the "Calculate loop corrected masses" was turned on, it gave a value of 10^-9 while the value from SARAH is 10^-13. These two values I calculated totally based on the SPheno code. I manipulated the DecayFunctions file to print "coup" instead of the whole width. And the SARAH vertex expression I retrieved from Subroutine CouplinghhVZpVZpT(gt1,g1,g2,gp,gBY,gYB,v,vp,ZZ,ZH,res) in the Couplings file of my model. All I did is substituting the numbers from the spectrum file.

Your result must be wrong because it has as units GeV^2.

Sorry, my result includes the last mS but not the last bracket. I checked my calculations many times and of course checked the units.

[FStaub]

Hi,

the loop corrections can affect the mixing, so I guess that the differences in the vertex come from the changes in the Higgs rotation matrix.

I would need to double check the expression, because I haven't coded it. However, this won't work out this work. Sorry.

Florian

[ahmedthabt]

I would need to double check the expression, because I haven't coded it. However, this won't work out this work. Sorry.

Thank you I'm looking forward to hearing your response about this. After some investigations I figured out the discrepancy happens because the significant figures that I read from the spectrum file are not precise enough to get an accurate result for such very small couplings... when I tried it for larger coupling constant both numbers agreed.

Regarding the decay width expression, I checked your guide 1703.09237 section 2.1 and figured out my mistake. I ignored the longitudinal polarization thinking it won't make a difference, but I carefully repeated my calculations including the longitudinal polarization and it gives exactly the same expression written in DecayFunctions.