## Stop decay widths in UDD RPV

Questions concerning the different calculations performed by SARAH and the output of the information into other formats
jmontejo
Posts: 4
Joined: 12. Jul 2017, 11:30

### Stop decay widths in UDD RPV

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
Posts: 719
Joined: 13. Apr 2016, 14:05

### Re: Stop decay widths in UDD RPV

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
Posts: 4
Joined: 12. Jul 2017, 11:30

### Re: Stop decay widths in UDD RPV

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
Posts: 719
Joined: 13. Apr 2016, 14:05

### Re: Stop decay widths in UDD RPV

Hi,

I was quickly looking at the code which reads

Code: Select all

Do gt1= 1, 3  Do gt2= gt1, 3m1out = 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
Posts: 4
Joined: 12. Jul 2017, 11:30

### Re: Stop decay widths in UDD RPV

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
Posts: 719
Joined: 13. Apr 2016, 14:05

### Re: Stop decay widths in UDD RPV

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
Posts: 1
Joined: 23. Jan 2018, 22:49

### Re: Stop decay widths in UDD RPV

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, 4m1out = 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
Posts: 719
Joined: 13. Apr 2016, 14:05

### Re: Stop decay widths in UDD RPV

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
Attachments
processes.m

jmontejo
Posts: 4
Joined: 12. Jul 2017, 11:30

### Re: Stop decay widths in UDD RPV

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