Difference between nominal xs and avg event weight for interference calculation

The value Cross-section : 8.587e-05 +- 4.837e-06 pb
is before the event selection while the value
actual average event weight from the LHE file, which is
9.93e-05
So the second number has a second source of uncertainty which is related to probability to "over-sample" the positive or the negative events.

>And actually, the cross-section should be zero, I think, this being the interference of the SM with a CP-odd contribution - but it's not, quite significantly.

Integrating vanishing zero is always tricky and naturally subject to numerical issue.

So if you expect zero, from a computation of the type A-A, then the output should typically be of the order of 2* delta(A).
So in order to see if indeed you have a zero compatible result or not, you need to know what is the contribution of the positive contribution (and what is the associated error on it).

Cheers,

Olivier

Hi Olivier,

I am not sure I follow.

What causes the oversampling of positive weights?

On the vanishing cross-section: I count 101699 positive weight and 98301 negative weight events. Then A is 100000 and delta(A)~300? Well, at least of the level of number of events. On the cross-section level it is not clear to me how I get the positive contribution? We use event_norm = average, so the event weight is determined by the size of the nominal xs (which is only noise), right?

Cheers,
Hannes

> What causes the oversampling of positive weights?

It is just random.
If your absolute cross-section is 2A+epsilon (assuming here zero error on that number/expression)
and that you cross-section is epsilon
(i.e. positive contribution is A+epslion and negative contribution is epsilon)

Then when you N generate events you,
You do expect that the number of positive events being
N* (A+epsilon)/(2*A+epsilon) +- sqrt(N* (A+epsilon)/(2*A+epsilon))

so in 50% of your sample you will have too many positive event and in 50% of your samples you will get too few positive events.
So in 50% of the sample your average of the weight will over-estimate the cross-section and in 50% you will under-estimate it. As said above this assumes in top of that that you have a zero error on the absolute cross-section (i.e this is another source of uncertainty due to the event generation in presence of negative weight).

> On the cross-section level it is
> not clear to me how I get the positive contribution?

You can get that from the absolute value of the weight.

> We use event_norm =
> average, so the event weight is determined by the size of the nominal xs
> (which is only noise), right?

No the norm of the weight will be associated to the integral of the absolute value of the cross-section.

Cheers,

Olivier

> On 12 Apr 2022, at 18:30, Hannes <email address hidden> wrote:
>
> Question #701317 on MadGraph5_aMC@NLO changed:
> https://answers.launchpad.net/mg5amcnlo/+question/701317
>
> Hannes posted a new comment:
> Hi Olivier,
>
> I am not sure I follow.
>
> What causes the oversampling of positive weights?
>
> On the vanishing cross-section: I count 101699 positive weight and 98301
> negative weight events. Then A is 100000 and delta(A)~300? Well, at
> least of the level of number of events. On the cross-section level it is
> not clear to me how I get the positive contribution? We use event_norm =
> average, so the event weight is determined by the size of the nominal xs
> (which is only noise), right?
>
> Cheers,
> Hannes
>
> --
> You received this question notification because you are an answer
> contact for MadGraph5_aMC@NLO.

Hi,

thanks, yes that was nonsense what I said on the meaning of the weight!

So taking into account the sampling error (which is something like 1e-05) the cross-section from summing up event weights, 9.93e-05, is compatible with the one quoted by mg: " Cross-section : 8.587e-05 +- 4.837e-06 pb".

But why is the cross-section significantly non-zero, both considering the quoted error 4.837e-06 pb and considering the sampling error (which shouldn't apply for the first number?)? That is down to an issue with the integration?

Cheers,
Hannes

Hi,

This I can not comment,
The first question is that if the non zero component is not related to
1) cuts
2) running of alpha_s (if the scale is not the same in the two part of the phase-space for some reason.

It can also be an issue of the phase-space integrator where the code is not designed/optimized for such type of computation (so we start from a poor efficiency).
The typical way to check that is
- running with multiple seed
- changing sde_strategy from one to two (or the opposite)
- using the parameter hard_survey to one, two or three

and in all cases observe the stability of the result, if they all give the exact same non zero value, then one can assume that the phase-space integrator is quite stable.

Cheers,

Olivier

Hi Olivier,

thanks a lot, we will try to vary the seed and integration parameters.
I don't think cuts play a role, you should only see something when cutting on a CP-odd observable.

Cheers,
Hannes