# Cross section in NLO production (gridpack mode)

Dear Experts,

I am curious about the cross section in NLO gridpack production. It seems that the final value of the cross section and uncertainty is related to the value shown after calculating the upper envelope if we increase the event number. (With low event number they could be different)

In mg265 generating gridpack. e.g.

cards: https:/

the value after calculating the upper envelope: 1.039e+05 +- 9.7e+01 pb

final results: 1.034e+05 +- 9.7e+01 pb

But in lhe production, no matter how much events I generate, in lhe file, It seems that the value would not change and it is related to the intermediate result in gridpack.

e.g.

1k events in lhe file:

<init>

2212 2212 0.65000000E+04 0.65000000E+04 -1 -1 325500 325500 -4 1

1.039320782028E+05 9.741180631555E+01 1.178599179620E+05 0

</init>

10k events in lhe file:

<init>

2212 2212 0.65000000E+04 0.65000000E+04 -1 -1 325500 325500 -4 1

1.039320782028E+05 9.741180631555E+01 1.178599179620E+05 0

</init>

So My questions:

1) Why the lhe production choose this value? It seems that this is the intermediate value rather than the final value.

2) It seems that LO didn't have this issue. So I would like to know if this limit in NLO is caused by some theoretical reason, which also means that we can not suppress the statistical uncertainty by generating more events in gridpack mode. Or does it mean the cross section in NLO and it's uncertainty are limited once the gridpack is produced?

3) It seems that the branching ratio from madspin decay is not taken into consideration.

Could you give me some information for these value? I am not sure if I understand these value properly. Thanks a lot!

Best,

Sen

## Question information

- Language:
- English Edit question

- Status:
- Solved

- Assignee:
- Rikkert Frederix Edit question

- Solved by:
- SEN DENG

- Solved:
- 2020-11-16

- Last query:
- 2020-11-16

- Last reply:
- 2020-11-16

## This question was reopened

- 2020-11-15 by SEN DENG

Concerning MadSpin,

Looks like your BR should be one since you ask all decay from the W ...

So I do not understand your third question

Olivier

SEN DENG (sdeng) said : | #2 |

Thanks Olivier Mattelaer, that solved my question.

SEN DENG (sdeng) said : | #3 |

But for Q1 and Q2, I am still confused

Rikkert Frederix (frederix) said : | #4 |

Dear Sen,

For NLO running, the 2nd step in the integration (i.e., the determination of the upper envelope) typically gives the most precise value of the integral and therefore this one is used. The "final value" is the value computed from the generation of events step. This value can be less precise if not so many events are requested. Hence, when writing out these events, it's the cross section given is the one obtained after the determination of the upper envelope.

Now, in practice, these two should be statistically equivalent. If there are large differences between them, that this is a sign of something going completely wrong in the code and potentially a serious bug somewhere.

The overall statistical accuracy for the events that can be generated with the gridpack is given by the accuracy with which the gridpack was created. In your case, this has been set to 0.001 (in the run_card), and 1/sqrt(0.001) = 1 million. So, this gridpack should be easily good enough for the generation of 1 million events to not be limited whatsoever to the statistical uncertainty in the creation of the gridpack. In practice, even many more (like ~10 million) are also okay with this gridpack, since during the event generation step there is another randomisation process which reduces this statistical uncertainty somewhat -- but this is hard to quantify. However, at some point, the statistical fluctuations in the final result will be dominated by the statistical uncertainty that was present in the creation of the gridpack.

In any case, there are other sources of uncertainties (theoretical systematic uncertainties from renormalisation and factorisation scale dependence, PDF uncertainties, etc.) that are typically much larger than this statistical uncertainty.

Note that the NLO code works quite a bit differently from the LO code in this respect. When running the code at LO, this distinction between "grid setup", "determination of upper envelope", "generating events" is not needed, because the integrals to be computed are simpler. Hence, it is more efficient to do these three steps in one go and update all of them together every time more phase-space points are used. Hence, at LO, it's really the final results that is always the most precise.

Best,

Rikkert

SEN DENG (sdeng) said : | #5 |

Dear Rikkert,

Thanks a lot for you information! It is really useful.

Best,

Sen