Bug (sign errors) in MadGraph's R-parity violating part

[Nikolai Wyderka]

Hello!

We generated events from a FeynRule generated model. This model is based
on RPV-MSSM and includes a Majorana fermion 'psi' (a singlet under the SM)
and a much heavier charged colored scalar 'sigma'. The complete model
files are attached.
The 'psi'-particle can decay into three SM quarks by violating R-parity.
The decay is mediated by an off-shell 'sigma' particle. To study the
hadronization after the decay of 'psi', we generated the process with
MadGraph: psi > u d d. We then launched the event generator and examined
the LHE - output.
The resulting energy spectrum of up-type -quarks does not have the
expected shape — it increases with raising energy which is not a physical
behavior.
In this case it's also possible to analytically calculate the differential
decay rate of the produced up-type quark yielding dN/dE ~ E^2*(M_psi-2*E)
in the limit of massless SM quarks. At least the analytical calculation of
the squared matrix element was also performed in [Baltz, Gondolo. Physical
Review D, 57(5):2969, 1998] (for RPV neutralino decays) and disagrees with
the result from MadGraph.
Later we figured out that we could reproduce the MadGraph spectrum by
changing the sign between the two contributing Feynman diagrams in the
analytical calculation.
Thus, the problem seems to appear in the calculation of the squared matrix
element. We therefore analyzed the 'matrix1.f' file created in the
'SubProcesses -> P1_psi_udd' sub-folder of the MadGraph output. We were
able to find the correct spectrum by either deleting all negative signs in
front of the stored color factors in the 'COLOR DATA' table or by deleting
all negative signs occurring in the definition of each 'JAMP' beneath this
color table. We cannot say for sure what the actual source of the error
is.
Interestingly, the total decay width calculated with MadWidth and the
command "compute_width psi" yields the correct value.
Although we have already found a pragmatic solution to our problem, this
issue becomes more important in the further treatment of the created
model. We are trying to generate decays where the up-type quark is a top
resulting in a five-body final state where an analytic expression for any
differential decay rate is out of range and the correction of signs in the
matrix element file seems to be too cumbersome. Therefore we would be very
grateful for any kind of help.

We are using MadGraph5 v. 2.3.3

Steps to reproduce:
1. Put attachment's content into MadGraph's model directory
2. Start MadGraph, import model MinDecDM_Model
3. Generate psi > u d d, output and launch
4. wait......
5. Analyze the energy spectrum of the LHE event file

Sincerely,
Nikolai Wyderka on behalf of Christopher Eckner and Michael Gustafsson

[Olivier Mattelaer (olivier-mattelaer)]

Thanks for the report.
I have succeeded to reproduce the different behavior for MadWidth and MadEvent and indeed the associated matrix-element is different in both cases.
I’m investigating to understand what the problem is and how to fix this.

Cheers and thanks,

Olivier

> On Nov 25, 2015, at 15:48, Nikolai Wyderka <email address hidden> wrote:
>
> Public bug reported:
>
> Hello!
>
> We generated events from a FeynRule generated model. This model is based
> on RPV-MSSM and includes a Majorana fermion 'psi' (a singlet under the SM)
> and a much heavier charged colored scalar 'sigma'. The complete model
> files are attached.
> The 'psi'-particle can decay into three SM quarks by violating R-parity.
> The decay is mediated by an off-shell 'sigma' particle. To study the
> hadronization after the decay of 'psi', we generated the process with
> MadGraph: psi > u d d. We then launched the event generator and examined
> the LHE - output.
> The resulting energy spectrum of up-type -quarks does not have the
> expected shape — it increases with raising energy which is not a physical
> behavior.
> In this case it's also possible to analytically calculate the differential
> decay rate of the produced up-type quark yielding dN/dE ~ E^2*(M_psi-2*E)
> in the limit of massless SM quarks. At least the analytical calculation of
> the squared matrix element was also performed in [Baltz, Gondolo. Physical
> Review D, 57(5):2969, 1998] (for RPV neutralino decays) and disagrees with
> the result from MadGraph.
> Later we figured out that we could reproduce the MadGraph spectrum by
> changing the sign between the two contributing Feynman diagrams in the
> analytical calculation.
> Thus, the problem seems to appear in the calculation of the squared matrix
> element. We therefore analyzed the 'matrix1.f' file created in the
> 'SubProcesses -> P1_psi_udd' sub-folder of the MadGraph output. We were
> able to find the correct spectrum by either deleting all negative signs in
> front of the stored color factors in the 'COLOR DATA' table or by deleting
> all negative signs occurring in the definition of each 'JAMP' beneath this
> color table. We cannot say for sure what the actual source of the error
> is.
> Interestingly, the total decay width calculated with MadWidth and the
> command "compute_width psi" yields the correct value.
> Although we have already found a pragmatic solution to our problem, this
> issue becomes more important in the further treatment of the created
> model. We are trying to generate decays where the up-type quark is a top
> resulting in a five-body final state where an analytic expression for any
> differential decay rate is out of range and the correction of signs in the
> matrix element file seems to be too cumbersome. Therefore we would be very
> grateful for any kind of help.
>
> We are using MadGraph5 v. 2.3.3
>
> Steps to reproduce:
> 1. Put attachment's content into MadGraph's model directory
> 2. Start MadGraph, import model MinDecDM_Model
> 3. Generate psi > u d d, output and launch
> 4. wait......
> 5. Analyze the energy spectrum of the LHE event f...

[Olivier Mattelaer (olivier-mattelaer)]

Dear Nikolai,

I'm back on this after the season of application.
I'm actually not sure that the sign is wrong in madevent.
I have check all those signs and they are all correct,
The minus sign in the matrix came from the epsilon_ijk color structure
while the minus sign in the JAMP definition cames from the permutation of two fermions.

On the other hand, I have found a bug in MadWith (it was only using one Feynman Diagram and was not considering the symmetric one). The fact that it was returning the correct value was just pure coincidence.

I have also looked at the paper and if I'm correct:
1) in Equation 17. We can drop the first line since this correspond to some mixing which are not present in your model.
2) They have the same epsilon factor (\epsilon^{\alpha\beta\gamma})for all the line.
Personally, I would have expect to have the following factor
\epsilon^{\beta\gamma\alpha}
\epsilon^(\alpha\gamma\beta)
\epsilon^(\alpha\beta\gamma)
for each line.

I therefore think that the problem is in MadWith and in the analytical paper rather than in the "standard" event generation.

Do you agree with me?

Cheers,

Olivier

[Nikolai Wyderka (nikolai-wyderka)]

Dear Olivier,

thank you for your effort! We had a look at the calculations in the paper. The comment you made on the colour structure of the amplitude in this particular paper is true and we came to the conclusion that the signs in MG5 must be the correct ones.

Greetings,
Nikolai Wyderka