# Difference: PolarizationAtlasPartonLevel (1 vs. 91)

Revision 91
Changes from r87 to r91
Line: 1 to 1

 META TOPICPARENT name="SingleTopPolarization"

# Analysis of Single Top Polarization using Parton Level Atlas samples

Line: 39 to 39

### 1. The t-channel

Changed:
<
<
For the t-channel we need the spectator quark, which isn't given in the Truth tree. So we have to use its jets to get information about the original direction of the spectator quark. The jets have a pdgid of 0 or 5, where 5 stands for the b-tagged jets. We use only events that contain two jets and use the one with a pdgid of 0. If we condider the fact that electrons can be misinterpreted as jets, we should use events with three jets and use the first jet that fullfills our requirements.
>
>
For the t-channel we need the spectator quark, which isn't given in the Truth tree. So we have to use its jets to get information about the original direction of the spectator quark. The jets have a pdgid of 0 or 5, where 5 stands for the b-tagged jets. We use only events that contain two jets and use the one with a pdgid of 0. If we consider the fact that electrons can be misinterpreted as jets, we should use events with three jets and use the first jet that fullfills our requirements.

Here is the result for the t-channel, spectator basis.
Line: 89 to 89

At the LHC half the time we guess the wrong direction for the antiquark. Therefore the polarization distribution for the s-channel should look like the sum of the two graphs, assuming the antiquark comes from the right, respectively from the left. That is it should look like the right histogram in the upper graph.

The polarization dsitribution s-channel (AcerMC) for Atlas with the beamline chosen as basis:
>
> The "Degree of Polarization" is:
Line: 102 to 103

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Revision 87
Changes from r83 to r87
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 META TOPICPARENT name="SingleTopPolarization"

# Analysis of Single Top Polarization using Parton Level Atlas samples

Line: 55 to 55

#### Tevatron

To get an idea why the polarization distribution looks the way it does let us take a look at the Tevatron first (ONETOP sample) and what happens when I guess the direction of the incoming d quark wrong.
Changed:
<
< >
> In the left graph we assumed the antiquark would have the same direction as the incoming antiproton, the middle graph assumes an antiquark coming in the proton direction. The histogram on the right hand side is the sum of the two other histograms.
Line: 86 to 86

#### LHC

What does all that mean for the LHC?
Changed:
<
<

At the LHC half teh time we guess the wrong direction for the antiquark. Therefore the polarization distribution for the s-channel should look like the sum of the two graphs, assuming the antiquark comes from the right, respectively from the left. That is it should look like the right histogram in the upper graph.
>
>

At the LHC half the time we guess the wrong direction for the antiquark. Therefore the polarization distribution for the s-channel should look like the sum of the two graphs, assuming the antiquark comes from the right, respectively from the left. That is it should look like the right histogram in the upper graph.

Changed:
<
<

The polarization dsitribution s-channel (AcerMCfor Atlas with the beamline chosen as basis:
>
>

The polarization dsitribution s-channel (AcerMC) for Atlas with the beamline chosen as basis: The "Degree of Polarization" is:
Line: 107 to 107

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>
>
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Revision 83
Changes from r79 to r83
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 META TOPICPARENT name="SingleTopPolarization"

# Analysis of Single Top Polarization using Parton Level Atlas samples

Line: 62 to 62
If I consider the fact that we expect a 100% polarized top quark in the s-channel, the offset in the first histogram must be due to a wrong assumption of the direction of the incoming antiquark. It makes sense that we see this offset, as a certain percentage of the antiquarks do not come from the antiproton but from the quark sea of the incoming proton.

The question is now: Does guessing the wrong side just give me the opposite polarization for the top quark? When we look at the second graph, the answer is no, as in that case we would see exactly the same offset in both the first and the second graph.
Changed:
<
<
%Br% This can be explained by the fact that the polarization is measured not in the restframe of the incoming quarks (which would mean it should be symmetric in exchanging the directions of the antiquark) but in the top quark restframe.
>
>

This can be explained by the fact that the polarization is measured not in the restframe of the incoming quarks (which would mean it should be symmetric in exchanging the directions of the quark and the antiquark) but in the top quark restframe.

If we assume the top to be produced at rest (which can be achieved by putting a cut onto the top PT), we therefore expect that guessing the wrong side just means opposite polarization for the top quark. As a consequence our offset would give us directly the number of antiquark whose direction we guessed wrong and therefore directly the percentage of antiquarks coming from the quark sea of the proton. Furthermore we would expect the two left graphs to have the same offset and the sum to be a horizontal line.
Changed:
<
<
On the other hand by applying a minimum cut on the top PT we expect the effect to be bigger.
>
>

On the other hand by applying a minimum cut on the top PT we expect the assymetry between the two left graphs to be bigger and therefore the sum to show a steeper curve, a larger "Degree of Polarization". Here we put a PT cut on the top quark, Px>100 GeV. If we compare the "Degree of Polarization" of the sum without and the sum with the cut, we get:
Changed:
<
<

D(without cut)=0.102
>
>
D(without cut)=0.102

D(with cut)=0.55

So how does the momentum of the topquark effect the polarization measurement?
Revision 79
Changes from r75 to r79
Line: 1 to 1

 META TOPICPARENT name="SingleTopPolarization"

# Analysis of Single Top Polarization using Parton Level Atlas samples

Line: 7 to 7

## 1. Abstract

I looked at polarization distributions of Atlas parton level samples in the Optimal/Spectator basis for the s-channel and the t-channel.
Changed:
<
<
Trying to do this I ran into missing information and had to reconstruct quarks. This effects the polarization distributions, in a way that is described below.
>
>
Trying to do this I ran into missing information and had to reconstruct quarks.

## 2. Parton Level Samples

Line: 31 to 31 ## 4. Optimal basis/ Spectator basis

>
>

For the Spectator basis in the t-channel use spectator quark and the antilepton in the CM frame of the top quark.

For the Optimal basis (s-channel) you have to take the incoming antiquark and the antilepton in the CM-frame of the top quark.
The Optimal Basis in the s-channel corresponds to the Spectator basis in the t-channel.
Deleted:
<
<

For the Spectator basis in the t-channel use spectator quark and the antilepton in the CM frame of the top quark.

### 1. The t-channel

Changed:
<
<
For the t-channel we need the spectator quark, which isn't given in the Truth tree, either. So we have to use its jets to get information about the original direction of the spectator quark. The jets have a pdgid of 0 or 5, where 5 stands for the b-tagged jets. We use only events that contain two jets and use the one with a pdgid of 0. If we condider the fact that electrons can be misinterpreted as jets, we should use events with three jets and use the first jet that fullfills our requirements.
>
>
For the t-channel we need the spectator quark, which isn't given in the Truth tree. So we have to use its jets to get information about the original direction of the spectator quark. The jets have a pdgid of 0 or 5, where 5 stands for the b-tagged jets. We use only events that contain two jets and use the one with a pdgid of 0. If we condider the fact that electrons can be misinterpreted as jets, we should use events with three jets and use the first jet that fullfills our requirements.

Here is the result for the t-channel, spectator basis.
Line: 59 to 59

In the left graph we assumed the antiquark would have the same direction as the incoming antiproton, the middle graph assumes an antiquark coming in the proton direction. The histogram on the right hand side is the sum of the two other histograms.
Changed:
<
<
If I consider the fact that we expect a 100% polarized top quark in the s-channel, the offset in the first histogram must be due to a wrong assumption of the direction of the incoming antiquark. It makes sense, that we see this offset, as a certain percentage of the antiquarks do not come from the antiproton but from the quark sea of the incoming proton.
>
>
If I consider the fact that we expect a 100% polarized top quark in the s-channel, the offset in the first histogram must be due to a wrong assumption of the direction of the incoming antiquark. It makes sense that we see this offset, as a certain percentage of the antiquarks do not come from the antiproton but from the quark sea of the incoming proton.

The question is now: Does guessing the wrong side just give me the opposite polarization for the top quark? When we look at the second graph, the answer is no, as in that case we would see exactly the same offset in both the first and the second graph. %Br% This can be explained by the fact that the polarization is measured not in the restframe of the incoming quarks (which would mean it should be symmetric in exchanging the directions of the antiquark) but in the top quark restframe.
Revision 75
Changes from r71 to r75
Line: 1 to 1

 META TOPICPARENT name="SingleTopPolarization"

# Analysis of Single Top Polarization using Parton Level Atlas samples

Line: 47 to 47

### 2. The s-channel

Deleted:
<
< For the Optimal basis, s-channel, we need the direction of the incoming antiquark (the d quark). At the Tevatron we collide protons and antiprotons. Therefore the guess that the antiquark has the same direction as the antiproton is right in most cases, but not in all as there is a certain percentage of events in which the antiquark has its origins in the quark sea of the proton.
Line: 72 to 71 Changed:
<
<
Here we put a PT cut on the top quark, PT>100 GeV.
>
>
Here we put a PT cut on the top quark, Px>100 GeV.
If we compare the "Degree of Polarization" of the sum without and the sum with the cut, we get:

D(without cut)=0.102
Line: 95 to 94
The "Degree of Polarization" is:
D=0.63 +/- 0.02
Changed:
<
<
Here we see a much higher "degree of polarization" than in the graphs above. This means we have a greater assymetry between guessing the right direction for the antitop and guessing the wrong direction for the antitop. An explanation for this could be a higher top PT, which makes sense, as the Atlas samples in contrast to the ONETOP samples have cuts on the minimum PT.
>
>
The high "degree of polarization" means we have a big assymetry between guessing the direction of the incoming antiquark right/ wrong. This means we have a high top PT, which makes sense, as the Atlas samples in contrast to the ONETOP samples have cuts on the minimum PT.

-- SarahHeim - 10 Mar 2008
Line: 103 to 102

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Revision 71
Changes from r67 to r71
Line: 1 to 1

 META TOPICPARENT name="SingleTopPolarization"

# Analysis of Single Top Polarization using Parton Level Atlas samples

Line: 53 to 53

At the LHC protons are collided with protons, which means that there is no preferred direction for the antiquark. The guess that the antiquark comes, let's say from the right, should lead to the correct result in 50% of all events.
>
>

#### Tevatron

To get an idea why the polarization distribution looks the way it does let us take a look at the Tevatron first (ONETOP sample) and what happens when I guess the direction of the incoming d quark wrong. Line: 67 to 68
If we assume the top to be produced at rest (which can be achieved by putting a cut onto the top PT), we therefore expect that guessing the wrong side just means opposite polarization for the top quark. As a consequence our offset would give us directly the number of antiquark whose direction we guessed wrong and therefore directly the percentage of antiquarks coming from the quark sea of the proton. Furthermore we would expect the two left graphs to have the same offset and the sum to be a horizontal line.
>
>
On the other hand by applying a minimum cut on the top PT we expect the effect to be bigger.

Changed:
<
< >
> Changed:
<
<
Here we put an energy cut on the top quark, of 197 GeV. If we compare the "Degree of Polarization" of the sum without and the sum with the cut, we get:
>
>
Here we put a PT cut on the top quark, PT>100 GeV. If we compare the "Degree of Polarization" of the sum without and the sum with the cut, we get:

Changed:
<
<

D(without cut)=0.102 +/- 0.010
D(with cut)=0.192 +/- 0.011
This is a small effect, but visible.
>
>

D(without cut)=0.102
D(with cut)=0.55

So how does the momentum of the topquark effect the polarization measurement? For the Optimal basis the angle between the incoming antiquark and the decay lepton is measured in the top quark restframe.
Line: 83 to 85 Thus our basis is not optimal any more and we cannot expect to see full polarization.
Changed:
<
<
What does all that mean for Atlas?
>
>

#### LHC

What does all that mean for the LHC?
At the LHC half teh time we guess the wrong direction for the antiquark. Therefore the polarization distribution for the s-channel should look like the sum of the two graphs, assuming the antiquark comes from the right, respectively from the left. That is it should look like the right histogram in the upper graph.

Changed:
<
<

The polarization dsitribution s-channel for Atlas with the beamline chosen as basis:
>
>

The polarization dsitribution s-channel (AcerMCfor Atlas with the beamline chosen as basis: >
>
The "Degree of Polarization" is:
D=0.63 +/- 0.02

Here we see a much higher "degree of polarization" than in the graphs above. This means we have a greater assymetry between guessing the right direction for the antitop and guessing the wrong direction for the antitop. An explanation for this could be a higher top PT, which makes sense, as the Atlas samples in contrast to the ONETOP samples have cuts on the minimum PT.
-- SarahHeim - 10 Mar 2008

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Revision 67
Changes from r63 to r67
Line: 1 to 1

 META TOPICPARENT name="SingleTopPolarization"

# Analysis of Single Top Polarization using Parton Level Atlas samples

Line: 80 to 81
Guessing the wrong direction for the antiquark doesn't affect our distribution as long as the topquark is close to rest, as then we have a totally symmetric situation and simply get the opposite polarization for the top quark. If our top quark has PT momentum and we guess the wrong direction, the situation is not symmetric any more but the chosen reference axis (which is the direction of the antiquark) is off by a certain angle compared to the direction of the optimal reference axis which is the direction of the quark. Changed:
<
<
%Br%Thus our basis is not optimal any more and we cannot expect to see full polarization.
>
>

Thus our basis is not optimal any more and we cannot expect to see full polarization.

What does all that mean for Atlas?

The polarization dsitribution s-channel for Atlas with the beamline chosen as basis: -- SarahHeim - 10 Mar 2008
Revision 63
Changes from r59 to r63
Line: 1 to 1

 META TOPICPARENT name="SingleTopPolarization"

# Analysis of Single Top Polarization using Parton Level Atlas samples

Line: 71 to 71 Here we put an energy cut on the top quark, of 197 GeV. If we compare the "Degree of Polarization" of the sum without and the sum with the cut, we get:
Changed:
<
<
D(without cut)=0.102 +/- 0.010 D(with cut)=0.192 +/- 0.011 This is a small effect, but visible.
>
>

D(without cut)=0.102 +/- 0.010
D(with cut)=0.192 +/- 0.011
This is a small effect, but visible.

So how does the momentum of the topquark effect the polarization measurement? For the Optimal basis the angle between the incoming antiquark and the decay lepton is measured in the top quark restframe. Guessing the wrong direction for the antiquark doesn't affect our distribution as long as the topquark is close to rest, as then we have a totally symmetric situation and simply get the opposite polarization for the top quark. If our top quark has PT momentum and we guess the wrong direction, the situation is not symmetric any more but the chosen reference axis (which is the direction of the antiquark) is off by a certain angle compared to the direction of the optimal reference axis which is the direction of the quark.
Changed:
<
< Thus our basis is not optimal any more and we cannot expect to see full polarization.
>
> %Br%Thus our basis is not optimal any more and we cannot expect to see full polarization.

-- SarahHeim - 10 Mar 2008
>
>
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>
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Revision 59
Changes from r55 to r59
Line: 1 to 1

 META TOPICPARENT name="SingleTopPolarization"

# Analysis of Single Top Polarization using Parton Level Atlas samples

Line: 13 to 13

The used parton samples are generated by AcerMC for the Atlas Single Top analysis. The parton level samples can be found in the Truth tree. This truth tree doesn't contain the initial particles, nor the spectator quark for the t-channel. This complicates things, as explained in the following.
Changed:
<
<

>
>

## 3. Degree of Polarization

The degree of polarization is defined as D=(N--N+)/(N-+N+) where N- is the number of events with a negative polarized top and N+ is the number of events with a positive polarized top.

There are two ways to get the N- and the N+ from the histogram: The first method means you just take the number of events at the left and right corner of the histogram (cos(θ)=-1 and cos(θ)=1 respectively). In the second method you actually count events and plug the total number of events with negative/positive polarized tops. This requires a fit.

The first method works as D is a ratio and using the actual number of N-/N+ we can simplify it by cancelling, so that we end up with the values at cos(θ)=-1 and cos(θ)=1.

Although half of the time we use the wrong direction of the antiquark, it is interesting to look at the s-channel and see the degree of polarization as a function of the number of jets in our event. ## 4. Optimal basis/ Spectator basis

For the Optimal basis (s-channel) you have to take the incoming antiquark and the antilepton in the CM-frame of the top quark.
The Optimal Basis in the s-channel corresponds to the Spectator basis in the t-channel.
Line: 38 to 55

To get an idea why the polarization distribution looks the way it does let us take a look at the Tevatron first (ONETOP sample) and what happens when I guess the direction of the incoming d quark wrong.
Changed:
<
< >
> In the left graph we assumed the antiquark would have the same direction as the incoming antiproton, the middle graph assumes an antiquark coming in the proton direction. The histogram on the right hand side is the sum of the two other histograms.
Line: 47 to 64
The question is now: Does guessing the wrong side just give me the opposite polarization for the top quark? When we look at the second graph, the answer is no, as in that case we would see exactly the same offset in both the first and the second graph. %Br% This can be explained by the fact that the polarization is measured not in the restframe of the incoming quarks (which would mean it should be symmetric in exchanging the directions of the antiquark) but in the top quark restframe.
Changed:
<
<
If we assume the top to be produced at rest (which can be achieved by putting a cut onto the top PT), we therefore expect the two left graphs to have the same offset and the sum to be a horizontal line.

## 4. Degree of Polarization

The degree of polarization is defined as D=(N--N+)/(N-+N+) where N- is the number of events with a negative polarized top and N+ is the number of events with a positive polarized top.

There are two ways to get the N- and the N+ from the histogram: The first method means you just take the number of events at the left and right corner of the histogram (cos(θ)=-1 and cos(θ)=1 respectively). In the second method you actually count events and plug the total number of events with negative/positive polarized tops. This requires a fit.

The first method works as D is a ratio and using the actual number of N-/N+ we can simplify it by cancelling, so that we end up with the values at cos(θ)=-1 and cos(θ)=1.

Although half of the time we use the wrong direction of the antiquark, it is interesting to look at the s-channel and see the degree of polarization as a function of the number of jets in our event. >
>
If we assume the top to be produced at rest (which can be achieved by putting a cut onto the top PT), we therefore expect that guessing the wrong side just means opposite polarization for the top quark. As a consequence our offset would give us directly the number of antiquark whose direction we guessed wrong and therefore directly the percentage of antiquarks coming from the quark sea of the proton. Furthermore we would expect the two left graphs to have the same offset and the sum to be a horizontal line. Here we put an energy cut on the top quark, of 197 GeV. If we compare the "Degree of Polarization" of the sum without and the sum with the cut, we get: D(without cut)=0.102 +/- 0.010 D(with cut)=0.192 +/- 0.011 This is a small effect, but visible.

So how does the momentum of the topquark effect the polarization measurement? For the Optimal basis the angle between the incoming antiquark and the decay lepton is measured in the top quark restframe. Guessing the wrong direction for the antiquark doesn't affect our distribution as long as the topquark is close to rest, as then we have a totally symmetric situation and simply get the opposite polarization for the top quark. If our top quark has PT momentum and we guess the wrong direction, the situation is not symmetric any more but the chosen reference axis (which is the direction of the antiquark) is off by a certain angle compared to the direction of the optimal reference axis which is the direction of the quark. Thus our basis is not optimal any more and we cannot expect to see full polarization.

-- SarahHeim - 10 Mar 2008

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>
>
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>
>
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Revision 55
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Line: 1 to 1

 META TOPICPARENT name="SingleTopPolarization"

# Analysis of Single Top Polarization using Parton Level Atlas samples

Line: 36 to 36

At the LHC protons are collided with protons, which means that there is no preferred direction for the antiquark. The guess that the antiquark comes, let's say from the right, should lead to the correct result in 50% of all events.
Changed:
<
<
To get an idea why the polarization distribution looks the way it does let us take a look at the Tevatron first and what happens when I guess the direction of the incoming d quark wrong.
>
>
To get an idea why the polarization distribution looks the way it does let us take a look at the Tevatron first (ONETOP sample) and what happens when I guess the direction of the incoming d quark wrong. >
>
In the left graph we assumed the antiquark would have the same direction as the incoming antiproton, the middle graph assumes an antiquark coming in the proton direction. The histogram on the right hand side is the sum of the two other histograms.

>
>
If I consider the fact that we expect a 100% polarized top quark in the s-channel, the offset in the first histogram must be due to a wrong assumption of the direction of the incoming antiquark. It makes sense, that we see this offset, as a certain percentage of the antiquarks do not come from the antiproton but from the quark sea of the incoming proton.

The question is now: Does guessing the wrong side just give me the opposite polarization for the top quark? When we look at the second graph, the answer is no, as in that case we would see exactly the same offset in both the first and the second graph. %Br% This can be explained by the fact that the polarization is measured not in the restframe of the incoming quarks (which would mean it should be symmetric in exchanging the directions of the antiquark) but in the top quark restframe.

If we assume the top to be produced at rest (which can be achieved by putting a cut onto the top PT), we therefore expect the two left graphs to have the same offset and the sum to be a horizontal line.

Line: 71 to 78

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>
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 META TOPICPARENT name="SingleTopPolarization"

# Analysis of Single Top Polarization using Parton Level Atlas samples

Line: 30 to 30

### 2. The s-channel

Changed:
<
< >
> For the Optimal basis, s-channel, we need the direction of the incoming antiquark (the d quark). At the Tevatron we collide protons and antiprotons. Therefore the guess that the antiquark has the same direction as the antiproton is right in most cases, but not in all as there is a certain percentage of events in which the antiquark has its origins in the quark sea of the proton.

At the LHC protons are collided with protons, which means that there is no preferred direction for the antiquark. The guess that the antiquark comes, let's say from the right, should lead to the correct result in 50% of all events.
Changed:
<
<
To get an idea why our
>
>
To get an idea why the polarization distribution looks the way it does let us take a look at the Tevatron first and what happens when I guess the direction of the incoming d quark wrong. Line: 67 to 71

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>
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Revision 47
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 META TOPICPARENT name="SingleTopPolarization"

# Analysis of Single Top Polarization using Parton Level Atlas samples

Line: 7 to 7

## 1. Abstract

I looked at polarization distributions of Atlas parton level samples in the Optimal/Spectator basis for the s-channel and the t-channel.
Changed:
<
<
Trying to do this I ran into missing information and had to reconstruct quarks. This effects the polarization distributions, that is, it increases the offset, in a way that I haven't looked at quantitatively so far.
>
>
Trying to do this I ran into missing information and had to reconstruct quarks. This effects the polarization distributions, in a way that is described below.

## 2. Parton Level Samples

Line: 20 to 20

For the Spectator basis in the t-channel use spectator quark and the antilepton in the CM frame of the top quark.
>
>

Changed:
<
<

### 1. The s-channel

At the LHC protons are collided with protons (unlike the Tevatron which collides protons and antiprotons). That means at the LHC we have a totally symmetric situation, that is the probability for our incoming antiquark to come in positive z-direction is as big as the probability to come in negative z-direction.
>
>
For the t-channel we need the spectator quark, which isn't given in the Truth tree, either. So we have to use its jets to get information about the original direction of the spectator quark. The jets have a pdgid of 0 or 5, where 5 stands for the b-tagged jets. We use only events that contain two jets and use the one with a pdgid of 0. If we condider the fact that electrons can be misinterpreted as jets, we should use events with three jets and use the first jet that fullfills our requirements.

Changed:
<
<
As we don't have information about the incoming antiquark we have to use the beamline as reference axis. This means have of the time, we assume the wrong direction, so we cannot expect to see a total polarization any more.
>
>
Here is the result for the t-channel, spectator basis.

Changed:
<
<
Here is the result for the s-channel, with a messed up Optimal basis that is effectively a beamline basis now and therefore not optimal any more.
>
> ### 2. The s-channel For the Optimal basis, s-channel, we need the direction of the incoming antiquark (the d quark). At the Tevatron we collide protons and antiprotons. Therefore the guess that the antiquark has the same direction as the antiproton is right in most cases, but not in all as there is a certain percentage of events in which the antiquark has its origins in the quark sea of the proton.

At the LHC protons are collided with protons, which means that there is no preferred direction for the antiquark. The guess that the antiquark comes, let's say from the right, should lead to the correct result in 50% of all events.

To get an idea why our

Deleted:
<
< ### 2. The t-channel

Deleted:
<
<
For the t-channel we need the spectator quark, which isn't given in the Truth tree, either. So we have to use its jets to get information about the original direction of the spectator quark. The jets have a pdgid of 0 or 5, where 5 stands for the b-tagged jets. We use only events that contain two jets and use the one with a pdgid of 0. If we condider the fact that electrons can be misinterpreted as jets, we should use events with three jets and use the first jet that fullfills our requirements.

Deleted:
<
<
Here is the result for the t-channel, spectator basis.

Deleted:
<
< ## 4. Degree of Polarization

The degree of polarization is defined as D=(N--N+)/(N-+N+)
Line: 53 to 58
Although half of the time we use the wrong direction of the antiquark, it is interesting to look at the s-channel and see the degree of polarization as a function of the number of jets in our event. Deleted:
<
<

## 5. ONETOP-samples

Using ONETOP samples for the s-channel that had been generated with the updated LHC-code, there was no information about incoming particles either, so that we get an offset here, too, which can simply be explained by the fact that half the time we guess the direction of the incoming antiquark wrong. This was tested by using the updated code, but with Tevatron setting. Here no offset was seen. -- SarahHeim - 10 Mar 2008
Revision 43
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 META TOPICPARENT name="SingleTopPolarization"

# Analysis of Single Top Polarization using Parton Level Atlas samples

Line: 22 to 22

### 1. The s-channel

Changed:
<
<
At the LHC we collide protons with protons (unlike the Tevatron which collides protons and antiprotons). That means at the LHC we have a totally symmetric situation, that is the probability for our incoming antiquark to come in positive z-direction is as big as the probability to come in negative z-direction.
>
>
At the LHC protons are collided with protons (unlike the Tevatron which collides protons and antiprotons). That means at the LHC we have a totally symmetric situation, that is the probability for our incoming antiquark to come in positive z-direction is as big as the probability to come in negative z-direction.

As we don't have information about the incoming antiquark we have to use the beamline as reference axis. This means have of the time, we assume the wrong direction, so we cannot expect to see a total polarization any more.
Line: 55 to 55 ## 5. ONETOP-samples

Changed:
<
<
Using ONETOP samples for the s-channel that had been generated with the updated LHC-code, there was no information about incoming particles either, so that we get an offset here, too, which can simply be explained by the fact that half the time we guess the direction of the incoming antiquark wrong. IThis was tested by using the updated code, but with Tevatron setting. Here no offset was seen.
>
>
Using ONETOP samples for the s-channel that had been generated with the updated LHC-code, there was no information about incoming particles either, so that we get an offset here, too, which can simply be explained by the fact that half the time we guess the direction of the incoming antiquark wrong. This was tested by using the updated code, but with Tevatron setting. Here no offset was seen. -- SarahHeim - 10 Mar 2008
Line: 64 to 64

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>
>
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 META TOPICPARENT name="SingleTopPolarization"

# Analysis of Single Top Polarization using Parton Level Atlas samples

Line: 52 to 52

Although half of the time we use the wrong direction of the antiquark, it is interesting to look at the s-channel and see the degree of polarization as a function of the number of jets in our event.
Changed:
<
< >
> ## 5. ONETOP-samples

>
>
Using ONETOP samples for the s-channel that had been generated with the updated LHC-code, there was no information about incoming particles either, so that we get an offset here, too, which can simply be explained by the fact that half the time we guess the direction of the incoming antiquark wrong. IThis was tested by using the updated code, but with Tevatron setting. Here no offset was seen.

-- SarahHeim - 10 Mar 2008

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>
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<
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Revision 35
Changes from r31 to r35
Line: 1 to 1

 META TOPICPARENT name="SingleTopPolarization"

# Analysis of Single Top Polarization using Parton Level Atlas samples

## 1. Abstract

>
>

I looked at polarization distributions of Atlas parton level samples in the Optimal/Spectator basis for the s-channel and the t-channel. Trying to do this I ran into missing information and had to reconstruct quarks. This effects the polarization distributions, that is, it increases the offset, in a way that I haven't looked at quantitatively so far.

## 2. Parton Level Samples

The used parton samples are generated by AcerMC for the Atlas Single Top analysis. The parton level samples can be found in the Truth tree. This truth tree doesn't contain the initial particles, nor the spectator quark for the t-channel. This complicates things, as explained in the following.
Line: 46 to 50

The first method works as D is a ratio and using the actual number of N-/N+ we can simplify it by cancelling, so that we end up with the values at cos(θ)=-1 and cos(θ)=1.
>
>
Although half of the time we use the wrong direction of the antiquark, it is interesting to look at the s-channel and see the degree of polarization as a function of the number of jets in our event. ## 5. ONETOP-samples

-- SarahHeim - 10 Mar 2008

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>
>
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Line: 1 to 1

 META TOPICPARENT name="SingleTopPolarization"

# Analysis of Single Top Polarization using Parton Level Atlas samples

Line: 7 to 7

## 2. Parton Level Samples

Changed:
<
<
The used parton samples are generated by AcerMC for the Atlas Single Top analysis. The parton level samples can be found in the Truth tree. This truth tree doesn't contain the initial particles, nor the spectator quark for the t-channel. This complicates things, as explained in the following.
>
>
The used parton samples are generated by AcerMC for the Atlas Single Top analysis. The parton level samples can be found in the Truth tree. This truth tree doesn't contain the initial particles, nor the spectator quark for the t-channel. This complicates things, as explained in the following.

## 3. Optimal basis/ Spectator basis

Line: 24 to 24

Here is the result for the s-channel, with a messed up Optimal basis that is effectively a beamline basis now and therefore not optimal any more.
Changed:
<
<
>
> ### 2. The t-channel

For the t-channel we need the spectator quark, which isn't given in the Truth tree, either. So we have to use its jets to get information about the original direction of the spectator quark. The jets have a pdgid of 0 or 5, where 5 stands for the b-tagged jets. We use only events that contain two jets and use the one with a pdgid of 0. If we condider the fact that electrons can be misinterpreted as jets, we should use events with three jets and use the first jet that fullfills our requirements.

Here is the result for the t-channel, spectator basis.
Changed:
<
<
>
> ## 4. Degree of Polarization

The degree of polarization is defined as D=(N--N+)/(N-+N+)
Line: 50 to 50

-- SarahHeim - 10 Mar 2008
Changed:
<
<
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>
>
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Revision 27
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 META TOPICPARENT name="SingleTopPolarization"
Changed:
<
<

>
>

# Analysis of Single Top Polarization using Parton Level Atlas samples

## 2. Parton Level Samples

>
>

The used parton samples are generated by AcerMC for the Atlas Single Top analysis. The parton level samples can be found in the Truth tree. This truth tree doesn't contain the initial particles, nor the spectator quark for the t-channel. This complicates things, as explained in the following.

## 3. Optimal basis/ Spectator basis

For the Optimal basis (s-channel) you have to take the incoming antiquark and the antilepton in the CM-frame of the top quark.
Line: 10 to 13

For the Optimal basis (s-channel) you have to take the incoming antiquark and the antilepton in the CM-frame of the top quark.
The Optimal Basis in the s-channel corresponds to the Spectator basis in the t-channel.
>
>

For the Spectator basis in the t-channel use spectator quark and the antilepton in the CM frame of the top quark.
>
>

### 1. The s-channel

At the LHC we collide protons with protons (unlike the Tevatron which collides protons and antiprotons). That means at the LHC we have a totally symmetric situation, that is the probability for our incoming antiquark to come in positive z-direction is as big as the probability to come in negative z-direction.

As we don't have information about the incoming antiquark we have to use the beamline as reference axis. This means have of the time, we assume the wrong direction, so we cannot expect to see a total polarization any more.

Here is the result for the s-channel, with a messed up Optimal basis that is effectively a beamline basis now and therefore not optimal any more.

### 2. The t-channel

For the t-channel we need the spectator quark, which isn't given in the Truth tree, either. So we have to use its jets to get information about the original direction of the spectator quark. The jets have a pdgid of 0 or 5, where 5 stands for the b-tagged jets. We use only events that contain two jets and use the one with a pdgid of 0. If we condider the fact that electrons can be misinterpreted as jets, we should use events with three jets and use the first jet that fullfills our requirements.

Here is the result for the t-channel, spectator basis.

## 4. Degree of Polarization

The degree of polarization is defined as D=(N--N+)/(N-+N+)
Revision 23
Changes from r19 to r23
Line: 1 to 1

 META TOPICPARENT name="SingleTopPolarization"

# Analysis of Single Top Polarization using Parton Level Atlas samples

Line: 21 to 21 Changed:
<
<
The first method means you just take the number of events at the left and right corner of the histogram (cos(&sigma)=-1 and cos(&sigma)=1 respectively).
>
>
The first method means you just take the number of events at the left and right corner of the histogram (cos(θ)=-1 and cos(θ)=1 respectively). In the second method you actually count events and plug the total number of events with negative/positive polarized tops. This requires a fit.

The first method works as D is a ratio and using the actual number of N-/N+ we can simplify it by cancelling, so that we end up with the values at cos(θ)=-1 and cos(θ)=1.

## 5. ONETOP-samples

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 META TOPICPARENT name="SingleTopPolarization"

# Analysis of Single Top Polarization using Parton Level Atlas samples

Line: 14 to 14

## 4. Degree of Polarization

Changed:
<
<
The degree of polarization is defined as
>
>
The degree of polarization is defined as D=(N--N+)/(N-+N+) where N- is the number of events with a negative polarized top and N+ is the number of events with a positive polarized top.

Changed:
<
<
D=(N--N+<\SUB>)
>
>
There are two ways to get the N- and the N+ from the histogram: >
>
The first method means you just take the number of events at the left and right corner of the histogram (cos(&sigma)=-1 and cos(&sigma)=1 respectively).

## 5. ONETOP-samples

-- SarahHeim - 10 Mar 2008
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 META TOPICPARENT name="SingleTopPolarization"

# Analysis of Single Top Polarization using Parton Level Atlas samples

Line: 14 to 14

## 4. Degree of Polarization

Changed:
<
<
\hbar
>
>
The degree of polarization is defined as

D=(N--N+<\SUB>) Revision 11
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 META TOPICPARENT name="SingleTopPolarization"

# Analysis of Single Top Polarization using Parton Level Atlas samples

Line: 13 to 13

For the Spectator basis in the t-channel use spectator quark and the antilepton in the CM frame of the top quark.

## 4. Degree of Polarization

Changed:
<
< >
>

\hbar ## 5. ONETOP-samples

-- SarahHeim - 10 Mar 2008
Changed:
<
<
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>
>
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 META TOPICPARENT name="SingleTopPolarization"

# Analysis of Single Top Polarization using Parton Level Atlas samples

>
>

## 3. Optimal basis/ Spectator basis

For the Optimal basis (s-channel) you have to take the incoming antiquark and the antilepton in the CM-frame of the top quark.
The Optimal Basis in the s-channel corresponds to the Spectator basis in the t-channel.
For the Spectator basis in the t-channel use spectator quark and the antilepton in the CM frame of the top quark.

## 4. Degree of Polarization ## 5. ONETOP-samples

-- SarahHeim - 10 Mar 2008 \ No newline at end of file
>
>

 META FILEATTACHMENT attachment="degreepolarization.jpg" attr="" comment="" date="1206124250" name="degreepolarization.jpg" path="degreepolarization.jpg" size="26195" stream="degreepolarization.jpg" user="Main.SarahHeim" version="1"
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Changed:
<
<
>
>

# Analysis of Single Top Polarization using Parton Level Atlas samples

-- SarahHeim - 10 Mar 2008
Deleted:
<
<
bla
\ No newline at end of file

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