Normalizing MC

Page maintainer: Rebecca

Important note: This page has not yet been reviewed by an expert! Use the information below with caution. Other pages that have not been reviewed yet can be found in the category FORREVIEW.

Intro

There are two issues concerning proper normalization of MC data:

• relative normalization of events within a MC production using event weights
• normalization of distributions from MC data to compare them to experimental data or other MC productions

Essentials

Event weights

At a fixed beam energy, the kinematics of an inclusive DIS event are defined by two independent variables. MC event generators usually generate events in a Fehler beim Parsen (Konvertierungsfehler. Der Server („https://wikimedia.org/api/rest_“) hat berichtet: „Cannot get mml. Server problem.“): {\displaystyle (x,Q^{2})} (or $(x,y)$ or Fehler beim Parsen (Konvertierungsfehler. Der Server („https://wikimedia.org/api/rest_“) hat berichtet: „Cannot get mml. Server problem.“): {\displaystyle (x,W^{2})} ) plane. A certain group of event generators (LEPTO/PEPSI/disNG, AROMA) generates events distributed with equal probability within such a kinematic box. The kinematic dependence of the cross section is taken into account by weight factors calculated for each event at the true kinematics of the event. This group of event generators is referred to as weighted MC. This procedure has the advantage of a flat distribution of MC statistics even for the tails of cross sections.

The weight factor is stored in g1MEvent.Weight. And this must be used when calculating statistical errors

The PYTHIA generator directly generates events of the different process classes (DIS, PGF, VMD, ...) according to their relative cross section. Thus there is no need for relative weights for the individual events
⇒ g1MEvent.Weight = 1

Normalizing MC to DIS

The easiest way to compare MC data and experimental data is by normalizing the yields to the number of DIS events. However, this only works under certain conditions:

• it is necessary to use gmc_disNG
  

gmc_disNG produces the correct inclusive cross section, which is necessary to use the number of DIS events for normalization.

PYTHIA, on the other hand, does not simulate elastic Bethe-Heitler events. Thus for PYTHIA it is necessary to normalize to the cross section (see next section).

• it is necessary to run the MC without any selectors

Normalizing MC to cross section

Below are some hints at how to normalize MC productions to other MC and to data. This is done in different ways for different analyses so the methods described below may not be right for what you are doing. Proceed with caution...

The information you will need to normalize your MC will likely come from three sources:

• g1MEvent.Weight this uDST variable contains the weight for a given event
  • In PYTHIA the weight is always 1
• extraweight is an additional weight which is output for each MC file and can be found in *.norm.kumac file corresponding to the MC uDST file you are reading (e.g. uDST file pythia6_p_rad_92.smdst.gz --> extraweight is written in pythia6_p_rad_gmc_92.norm.kumac in the same directory)
  • In disNG extraweight is always 1
• IEVGEN is the total number of events thrown in a given MC file, including those that were not calculated because they fall outside the limits of cuts and selectors imposed on the generator. It can also be found in the *.norm.kumac file.

The key to normalizing MC is being able to convert from yields to cross sections:

Fehler beim Parsen (Konvertierungsfehler. Der Server („https://wikimedia.org/api/rest_“) hat berichtet: „Cannot get mml. Server problem.“): {\displaystyle N_{X}=\sigma _{X}*L}

where

$N_{X}$ = number of observed events of process X
$\sigma _{X}$ = cross section of process X
$L$ = luminosity

To get a cross section from MC you need to make use of the three values described above:

Fehler beim Parsen (Konvertierungsfehler. Der Server („https://wikimedia.org/api/rest_“) hat berichtet: „Cannot get mml. Server problem.“): {\displaystyle {\frac {\sum _{i=MCfile}\sum _{j=event}g1MEvent.Weight_{i,j}*extraweight_{i}}{\sum _{k=MCfile}IEVGEN_{k}}}=\sigma } [microbarns]

However, this is only if you have multiple files with the same settings. If this is the case then you will see that extraweight is basically the same in all files. Then you can do

Fehler beim Parsen (Konvertierungsfehler. Der Server („https://wikimedia.org/api/rest_“) hat berichtet: „Cannot get mml. Server problem.“): {\displaystyle {\frac {\sum _{i=MCfile}\sum _{j=event}g1MEvent.Weight_{i,j}}{\sum _{k=MCfile}IEVGEN_{k}}}*<extraweight>=\sigma } [microbarns]

which in practice means you need to calculate the average extraweight and the total IEVGEN from all your files, and then in the end multiply your yields by this fraction:

$\left(\sum _{i=MCfile}\sum _{j=event}g1MEvent.Weight_{i,j}\right){\frac {<extraweight>}{\sum _{k=MCfile}IEVGEN_{k}}}=\sigma$ [microbarns]

• To combine different MC productions you must do a weighted average of the cross sections!

More Info

• For information on how to calculate the cross section of experimental data, look here.
• You may also want to consult Elke's mail on this subject.
• There may one day also be something about this in Bootcamp