Stop decay widths in UDD RPV

[jmontejo]

Dear Florian,
I'm using SPheno+SARAH with the MSSMBpV model to study stop pair production with subsequent stop->bs or stop->tN1 decays.
When comparing to other results (1601.03737) I noticed I get a different BR for stop->bs. The partial width for stop->tN1 agrees but the width for stop->bs differs by a factor 2. I find this extremely surprising since I would expect a difference in convention leading to a factor 4 difference.

As an example, I use a purely right-handed stop, a bino-like LSP and m(stop)=620 GeV, m(N1)=200 GeV, lambda’’323=0.1
I get back Width(stop->bs)=0.49 GeV and Width(stop->tN1)=0.91. From the formula A.1 in 1601.03737 I get half the width for bs.

Would you have some insight on this? The convention seems to be the same so I would expect the results to match but maybe I'm overseeing some detail.

Cheers
Javier

[FStaub]

Hi,

did you try to compare with another reference? For instance, using the UFO output and calculate the width with MG. If this doens't agree with SARAH/SPheno, I need to check. However, I have hardly time right now. Sorry.

Florian

[jmontejo]

Hi Florian,
running the same scenario through Madgraph I reproduce the numbers in 1601.03737, so factor of 2 disagreement with SARAH.

Cheers
Javier

[FStaub]

Hi,

I was quickly looking at the code which reads

Code: Select all

Do gt1= 1, 3
  Do gt2= gt1, 3
m1out = MFd(gt1)
m2out = MFd(gt2)
coupL = cplcFdcFdcSuL(gt1,gt2,i1)
coupR = cplcFdcFdcSuR(gt1,gt2,i1)
Call ScalarToTwoFermions(m_in,m1out,m2out,coupL,coupR,gam) 
If (gt1.ne.gt2) gam = 2._dp*gam 
gPartial(i1,i_count) = 2*gam 
gT(i1) = gT(i1) + gPartial(i1,i_count) 
i_count = i_count +1 
  End Do 
End Do 

Does the width into two identical states (i.e. bb or ss) agree with your expectations? In that case, the relevant line is

Code: Select all

If (gt1.ne.gt2) gam = 2._dp*gam 

i.e. SARAH multiplies the width into q_i q_j with a factor of 2 for i =! j. This factor is there, because it doesn't calculate q_i q_j and q_j q_i individually as you can so on the do-loops (gt1,gt2 are generation indices of the external states). Does this make sense...?

Cheers,
Florian

[jmontejo]

Hi Florian,
I'm not familiar with the code so there might be some context I'm missing here, apologies if I misunderstood the code.
This is a UDD decay so the case where gt1==gt2 should always be zero, how would I get stop->bb?
When gt1!=gt2 it seems that you are multiplying twice by 2, there is a second one just after the If, is this intended? maybe the color factor?

Reading through the appendices in 1601.03737 and 0406039 what I understand is that the convention lambda''/2 UDD is chosen so that the antisymmetry in the coupling is already taken into account and there would be no need to for

Code: Select all

If (gt1.ne.gt2) gam = 2._dp*gam 

Cheers
Javier

[FStaub]

Hi,

of course, the decay into identical states is forbidden. Yes, the other factor of 2 is just the colour as you say.
However, the factor of 2 for non-identical generation indices has nothing do to with the coupling. It would also be there for decays H->h_i h_j for multi-Higgs models for i =! j.

Cheers,
Florian

[amonteux]

Hi Florian,
Javier invited me to try to figure this out (we were in contact as the author of 1601.03737).

I am not sure I understand this line:

Code: Select all

If (gt1.ne.gt2) gam = 2._dp*gam 

When calculating the width for a scalar decaying to two fermions, one simply writes down the feynman diagram for $\phi > f1 f2$ and there is no ambiguity unless the fermions are identical, in which case one adds a 1/2! into the amplitude to avoid double-counting when integrating the phase space.

The RPV decay to q_i q_j (i!=j) is in that sense no different than the RPC decay to t chi. So apart from the color factor in the averaged squared amplitude (which is $\delta_a^a/N_c=1$ for RPC decays and $\epsilon_abc \epsilon^abc/N_c=(N_c-1)=2$ for RPV decays), there should be no difference in the expressions. If I look at SusyDecays_MSSMBpV.f90, I find the lines responsible for the RPC decays:

Code: Select all

! ----------------------------------------------
! Fu, Chi
! ----------------------------------------------
Do gt1= 1, 3
  Do gt2=1, 4
m1out = MFu(gt1)
m2out = MChi(gt2)
coupL = cplChiFucSuL(gt2,gt1,i1)
coupR = cplChiFucSuR(gt2,gt1,i1)
Call ScalarToTwoFermions(m_in,m1out,m2out,coupL,coupR,gam) 
gPartial(i1,i_count) = 1*gam 
gT(i1) = gT(i1) + gPartial(i1,i_count) 
i_count = i_count +1 
  End Do 
End Do 

Here the offending line about different final states is not appearing. I agree with the analytical expression here (given the definition of ScalarToTwoFermions()), and I think the RPV decay should be the same (apart from the extra factor of 2 from the color sum).

This error would explain why Javier was getting partial widths which are a factor of 2 bigger for the RPV case only.
Moreover, I should point out that the RPVMSSM UFO generated with Feynrules agrees with my analytical expressions (and disagrees with the SARAH/Spheno results).

Cheers,
Angelo,

[FStaub]

Hi,

thank you for your comments. I was checking the code and found a code how the symmetry factor is determined. Actually, the factor 2 which we discussed right now is correct with the conventions how the code is set up. However, a factor 1/2 for identical particle families in the final states was missing. A patch is attached.

Best,
Florian

[jmontejo]

Hi Florian,
thanks for providing a patch so fast. I can confirm that with new code the widths are in perfect agreement.
Thanks so much for your support

Cheers
Javier