Zero cross-section desired, but a small non-zero, mass- and coupling-dependent value gotten

Hi Nirmal,

I'm worry that we can't do anything about this.

> The only conclusion I can arrive at is that pairs of t-channel gluino or gaugino diagrams are not interfering fully destructively. Some residue is left behind.

My guess is the opposite, the interference is correct but some residue is left behind anyway. Both value are computed in double precision meaning
that the contribution is precise up to 15 digit. But when you do the difference, this precision is not enough and the return value is meaningless.

A beautiful example of such problem is the following function:
(1 + x -1) / x
this function is theoretically equal to one, but if you enter this function in a computer for very small x (x< 1e-15), it will return zero,
and for some specific value it will return 3/2.
In short a computer has trouble with difference a very close number.

If you want to check if this is indeed the problem, you can edit the file
SubProcesses/PXXXXXXXX/matrix1.f
and change the relative sign between the two diagrams.
(in lign of the type : JAMP(1)=+IMAG1*AMP(1)-AMP(2) )
You will see the cross-section to be much much bigger by doing so.

Cheers,

Olivier

On Oct 21, 2012, at 12:01 AM, Nirmal Raj <email address hidden> wrote:

> New question #211856 on MadGraph5:
> https://answers.launchpad.net/madgraph5/+question/211856
>
> I guess this is a very specific issue.
>
> I've been implementing Dirac gluinos and Dirac gauginos. There are two ways I've done this, two ways of modifying the MSSM model given by MG5. They are:
> (i) Include an antiparticle for each gluino/gaugino and change the interactions suitably in vertices.py.
> (ii) Create extra Majorana gluinos and gauginos in particles.py and include suitable vertices and couplings for them. (This is so that I can have a gluino/gaugino with both Dirac and Majorana masses interact like two Majorana states with appropriate couplings and eigen masses.)
>
> Method (ii) enables me to interpolate between the cases "MSSM inos" and "purely Dirac inos" by tuning external parameters. Both methods give cross-sections that are in great agreement with each other, except for the following hitch.
>
> There are certain processes that are supposed to yield a zero cross-section in the pure ino case. Some examples are u u > ul ul and u u > ul ur~ and u d > ul dl, which happen via a t-channel gluino/gaugino. No diagram exists in method (i), whereas in method (ii) there would be two t-channel gluino diagrams that completely destructively interfere.
>
> I do get a zero when I try these processes in method (i) -- in fact it tells me those processes do not exist. But in method (ii), I get a non-zero number, like around 10^-10 for squark production and 10^-14 for antisquark production.
> I have tried to locate the source of this error, but in vain. It's not in the way the couplings are generated using internal parameters, because I tried specifying the couplings by hand and the result was the same.
> When I tried varying the gluino/gaugino mass, the erroneously non-zero cross-section varied accordingly. I tried varying the couplings, once again the cross-section responded accordingly. The only conclusion I can arrive at is that pairs of t-channel gluino or gaugino diagrams are not interfering fully destructively. Some residue is left behind.
>
> And, as I said, the processes that are supposed to yield a non-zero XS, like u u > ul ur, are in excellent agreement in both methods. By which I mean they agree to ~three decimal places.
>
> Could you please help? Where in MG5 might the zero error arise? I need to eliminate it in order to trust the values that interpolate between the scenarios of pure Majorana and pure Dirac.
>
> Thanks in advance.
>
> --
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Thank you for the prompt responses.

Olivier,

I tried changing the relative sign in matrix.1f and I did indeed get a larger cross-section. I also tried retaining the *relative* sign, but flipped the sign for each diagram, and this gave me a smaller cross-section (half the value I used to get before). So I believe your diagnosis is right.

Johan,

Changing the sign of the decay width for the negative-mass Majorana guy did not, unfortunately, change the result. But thanks for bringing this up.

Regards,
Nirmal

Johan!

Instead of changing the decay width's sign in param_card.dat, I made the negative-mass fermion's width an internal parameter and flipped its sign. With this change, I GOT A ZERO CROSS-SECTION.

Thank you *so* much for that insight! It has brought me unparalleled relief.

Nirmal

Thanks Johan Alwall, that solved my question.

Ack! Automated messages!