Diferences between MadGraph cross-section and theoretical result

Does the cross-section of
AAB correct compare to your theory?
does
A A B --> (A --> a a) correct?
does
A A B --> (B --> b b) correct?

Did you check the following FAQ?

Cheers,

Olivier
FAQ #2442: “why production and decay cross-section didn't agree.”.

>>Does the cross-section of AAB correct compared to your theory?

Yes, the cross-section for producing AAB matches the theory.

>> The cross-section for A A B --> (A --> a a) is correct?

>> The cross-section for A A B --> (B --> b b) correct?

I've checked and one of the Cross-sections don't match the theory, it is the case where we have a h --> b b~

It might be the cause of the error. Do you know why specifically this decay channel have this problem?

Also, I've just checked the FAQ you mentioned and tried all the possible solutions, the only one that worked was changing the Higgs total width from the default value to another (on the param card). But this other value is different from the PDG width for Higgs.

If you want that a LO computation gives you the LO Branching Ratio then you have to set the width to the LO width for the Higgs, (with the ambiguity for the loop-induced decay in the above statement).

Now the PDG will not give you the LO width. So here you have to decide what you want to preserve either the shape of the events or the branching ratio (for the Higgs, many argue that the width is too small to care about shape effect).

Cheers,

Olivier

let me give me more detail here:

The phase-space integral that madgraph computes is on |M|^2
If you select a subset diagram such that all of them have a single diagram in common, you can write the amplitude like (here the case for vector boson in unitary gauge)
\mathcal{M} = \mathcal{M}_P^\mu \frac{g_{\mu\nu}+\frac{p_\mu p_\nu}{M^2}}{p^2-M^2+iM\Gamma} \matcal{M}_D^\nu

where \mathcal{M} is the amplitude
\matcal{M}_P is (the offshell) amplitude of the production matrix element --without polarisation vector for the propagator particle--
g_{\mu\nu} the minkowski metric
M the mass of the particle
\Gamma the (total width of the particle)
and \matcal{M}_D^\nu is (the offshell) amplitude of the production matrix element --without polarisation vector for the propagator particle--

MadGraph performs the numerical computation of the above amplitude (without any additional hypothesis) with
1) a phase-space cut to enforce that the particle is not too offshell (where the narrow-width approximation that typically justify the fact that all amplitude can be written in the above form is not valid anymore)
2) potential cut on the decaying particle (presence of such cut will automatically break the formula that the full cross-section is the one of production times branching ratio). (default is that all such cut are de-activated)

So here you can note that --in general--:
1) the amplitude depends on the width only via the propagator (typically the width will not enter directly --or only midly-- in the production/decay matrix-element)
2) partial width/branching ratio do not enter anywhere in the above computation at all.
(We do not assume/use any of those points in the computation, and none of the point below depends on it, so you do not have to worry if you have an example where one of the point above is not True).

Now if NWA is valid (which implies no cut)
then
\int dp^2 \frac{1}{|p^2-M^2+iM\Gamma|^2 = 1/(M\Gamma) \delta(q^2-M^2) +\mathcal{O}(\Gamma/M)
Which means that the full integral split into two pieces
\int dp_P dp_D dp^2 |M|^2 = \int dp_P |M_P|^2 \pi/(M\Gamma) \int dp_D |M_D|^2
(here the M_P and M_D contains the polarization vector that handle the numerator of the propagator)
( I did not check/include the needed Jacobian in the above formula).

Note that such formula, is missing the spin-correlation (which is preserve with the above one)
and is also missing any breit-wigner (so spread in the invariant mass and any potential deviation to it).
Obviously, for the Higgs decay, none of those effect are relevant (this is a spin 0 so no spin-correlation between production and decay) and the width is too small to have any spread relevant.

The piece \pi/M \int dp_D |M_D|^2 correspond (to a factor of 2\pi --which should be absorbed by one of the jacobian that I omitted here--) to the partial width. (equation 1 from https://arxiv.org/pdf/1402.1178.pdf). Lets note that partial width as \Gamma_{decay}

So if you provide to MG5aMX a process/amplitude/cut where the NWA is valid,
we will compute the full computation on the phase-space, but having NWA being valid such computation will return (up to correction term proportional to \Gamma/M)
\sigma_{production) * \Gamma_{decay}/\Gamma

where \sigma_{production) and \Gamma_{decay} are the one computed at LO , while the \Gamma is the full width taken from the param_card.

Given those point, you should be able to decide what you want to preserve
- if you want offshell effect to be correct then you have to set the total width to his observed value and then correct the total cross-section via a flat change to the cross-section.
- if you care about LO consistency then you should set everything to LO value including the total width and then you will get (up to \Gamma/M) exactly the branching ratio between the different computation.

Now as a general comment --without knowing all the details of what you try to do--, for the Higgs production case
- you do not care about offshell effect (too small)
- you do not care the LO cross-section prediction (too large correction from NLO and higher order)
While Higgs prediction is an extreme example where LO cross-section is so far off, the general statement is still to not trust LO computation for their cross-section (at LHC at least) given their large theoretical uncertainty --again with all the precaution needed since this can depend a lot in what you try to do in practise--.

Hope this clarify points.

Olivier