# Analysis of Single Top Polarization using Parton Level Atlas samples

## 1. Abstract

## 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.

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

_{+})
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.

## 5. ONETOP-samples

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SarahHeim - 10 Mar 2008