# Roadmap for measuring b-jet cross section using a muon tag

## Introduction

The final goal is to measure the b-jet cross section, using muons to tag
the b-jets. To achieve this, different steps in the analysis have to be
taken. The formula for measuring the cross section is:

$\sigma = \frac{N}{\varepsilon \cdot A \cdot L}$

\(1\)

where:

-   σ is the cross section

-   N is the number of signal jets (background jets are taken out)

-   ε is the total efficiency with which b-jets are tagged. This
    efficiency is broken down in different other efficiencies, explained
    below.

-   A is the kinematic acceptance of the bbbar producing process

-   L is the total luminosity measured.

Each of these terms have their own errors and correlations which all
have to be taken into account in the final measurement of the cross
section.

## N: Number of signal jets

This is simply the number of jets that are tagged as a b-jet by the muon
tagger. The b-tagging efficiency of this tagger is taken into account in
ε. The purity of this tagger is not 100%, which causes the tagged number
of jets to be higher than the real number of b-jets. Thus, the number of
signal jets measured needs to be divided by the purity:

$N = \frac{N_{\text{meas}}}{\text{purity}}$

\(2\)

The error on this purity needs to be determined, and propagated to the
error on the number of b-jets measured. *How can we measure the purity
in a good way? How can we measure the error on the purity in a good
way?*

## L: Luminosity

The luminosity is a number we get from 'somebody else' (*who? How can I
get the luminosity for a certain run, or for all runs? Is this one
number, or is this different for every run...?)*. The error on the
luminosity has to be propagated in the cross section.

## A: Acceptance

This is the kinematic acceptance of the detector for the bbbar physics
process. We use some cuts, like \|η~μ~\| \<2, which cut away a certain
number of events. To calculate how many events are cut away, and thus to
determine what the acceptance of these cuts are, we can do a MC study.
This study uses MC parton information, and counts how many events pass
the cuts that we apply. Current cuts are:

-   \|η~μ~\| \< 2;

-   \|η~jet~\| \< 2

> I currently do not know if these are reasonable cuts, but they are
> easily changed after providing a good start. *How can we get a handle
> on the error on this acceptance?* I do not know what happens at the
> borders of this cut: what happens to a muon that is originally outside
> the cut, but due to the reconstruction it is reconstructed inside the
> cut? Do I have to look at the reconstructed distribution and see how
> many events now pass the cuts, to calculate the 'reconstructed'
> acceptance?

## ε: Efficiency

As said, the efficiency is broken up in different efficiencies, each
with (or without) correlations:

-   ε~L1μ~: L1 muon trigger efficiency

-   ε~L1jet~: L1 jet trigger efficiency

-   ε~L2μ~: L2 muon trigger efficiency

-   ε~L2jet~: L2 jet trigger efficiency

-   ε~L3μ~: L3 muon trigger efficiency

-   ε~L3jet~: L3 jet trigger efficiency

-   ε~off,\ μ~: Offline muon reconstruction efficiency

-   ε~off,\ jet~: Offline jet reconstruction efficiency

-   ε~tag~: B-tag efficiency

Folded into these efficiencies is the detector coverage. *However, I am
not sure in which efficiency this folds in. Is it L1, L2, or L3? Or
offline?* Each of these efficiencies has to be measured separately, then
correlations between them have to be investigated. For example, there is
probably a correlation between the jet reconstruction efficiency and the
muon reconstruction efficiency. In Run I, this was solved by looking at
the muon reconstruction efficiency as a function of the δR separation
between the jet and the muon.

### L1 muon trigger efficiency

We have to measure the efficiency of the trigger used and the error on
that efficiency. To measure this efficiency, we can do two things:

1.  Use MC -- this is not preferred, but can be the only option if there
    is no trigger available with any looser requirements;

2.  Use a trigger with looser requirements, e.g. a lower p~T~ threshold.
    This trigger will pass all events (*hmmm... how to calculate the
    efficiency of this trigger??)*, so the efficiency of the used
    trigger can be determined.

*How can we get a handle on the error of the trigger efficiency?*
Currently, the L1 muon trigger simulator is not in a good state and not
usable. Plans however are to make turn-on curves for the triggers used,
and look at efficiencies of the different triggers

### L1 jet trigger efficiency, L2 triggers, L3 triggers

Not much thought has gone into this, but we have to calculate the
efficiency + error for each of these triggers...

### Offline muon reconstruction efficiency

We can measure the muon offline reconstruction efficiency by using a MC
file and calculating how many muons are reconstructed. The distribution
of this efficiency is hopefully flat as a function of p~T~. If not, we
need to calculate the efficiency for each p~T~ bin, and we cannot simply
calculate the cross section anymore.

### Offline jet reconstruction efficiency

I have to put some thoughts in on how we can calculate this.

### B-tag efficiency

This can be calculated in two ways:

1.  Running on large bbbar samples (with normalized cross sections!)

2.  Calculate it with respect to other taggers, or 2 tagged jets vs. one
    tagged jet in bbbar events. Calculating it with respect to other
    taggers might prove difficult, for this requires an intimate
    knowledge of the other taggers.

For inclusive bbbar samples, some efficiencies are already available.
*How can I calculate the error on the b-tag efficiency?*

### Correlations

A lot of thought has to go into the correlations in these efficiencies.
A couple of possible correlations:

-   Muon detector coverage (not sure if this is a correlation)

-   Muon reconstruction on L3 and muon reconstruction offline (uses same
    software...)

-   Muon reconstruction and jet reconstruction efficiency