Anti-##k_T## algorithm for jets

In summary, the anti-##k_T## algorithm is an iterative clustering algorithm that uses a momentum-weighted distance parameter to merge protojets into larger jets. The distance is defined by the transverse momenta of the protojets and their angular distance, with a set boundary ##L##. The algorithm starts with the protojet with the highest energy as the seed and continues until all protojets are merged. The parameter ##\Delta R## is a measured value and smaller distances between jets are more likely to lead to merging.
  • #1
ChrisVer
Gold Member
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First I'll try to give a summary of what I understand about the anti-##k_T## algorithm (as a continuation for a particle flow algorithm)...
The algorithm uses an iterative clustering with transverse momentum ##p_T## weighted distance parameter and is applying a selection on the "protojets". For particle flow jets every PF object is a protoject except for those that have been identified as electrons or muons. The anti-##k_T## algorithm takes the protojet with the highest energy and merges it with the next nearest one into a new protojet if the distance is within some boundary. Let's call that boundary set by us as ##L##. This is done until there are no more protojets left. Then the algorithm restarts with the highest of the remaining protojets as the seed.
The distance is defined as:
##d_{ij}= min(k_{Ti}^{2p}, k_{Tj}^{2p}) \frac{(\Delta R)^2}{r^2}##
Where ##r,p## are parameters ( for anti-##k_T## we set ##p=-1##), ##k_{Ti}## are the transverse momenta of the ##i##-th protojet, and ##\Delta R## are the protojets ##(\eta,\phi)## distance.

My Question:
Suppose I have the protojet with the highest energy ##k_{T1}=20GeV##.
And the nearest to it protojet has an energy ##k_{T2}=10GeV##.
In that case the momentum-weighed distance is:
##d_{12}= min (\frac{1}{400}, \frac{1}{100} ) \frac{(\Delta R)^2}{r^2} = \frac{(\Delta R)^2}{400 r^2}##
In order for this distance to be within the set boundary we have
##\frac{(\Delta R)^2}{(20r)^2}= d_{12} < L##
The problem:
I believe that ##\Delta R## should be set very small to keep this inequality. And the strange thing is that any protojet with energy smaller than 20GeV should satisfy this smallness for ##\Delta R##...I feel that this is unreasonable? For example if the 1 protojet has energy 20GeV and the 2nd nearest has 3GeV I don't find a reason they can't "exist" together in a larger cone to form the jet...In other words the energy of the 1st protojet is always going to rule out any other choice of "nearest" ones due to the min() function.
Where am I wrong?
 
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  • #2
You don't set ##\Delta R##, it is a measured value. Smaller distances between the jets are more likely to lead to merging.

You can have two completely unrelated jets going in the same direction, but this is unlikely and there is no way to notice this experimentally.
 

1. What is the purpose of the Anti-##k_T## algorithm for jets?

The Anti-##k_T## algorithm is used to cluster jets in particle physics experiments. It is designed to be more robust against soft radiation compared to other jet clustering algorithms, making it a powerful tool for studying high-energy collisions.

2. How does the Anti-##k_T## algorithm work?

The algorithm starts by calculating the distance between all particles in the event. It then merges the two closest particles and recalculates the distance between the new merged particle and all other particles. This process continues until all particles have been clustered into jets.

3. What are the advantages of using the Anti-##k_T## algorithm?

The algorithm is less sensitive to soft radiation, meaning it can better distinguish between jets and background noise. It also tends to produce more circular-shaped jets compared to other algorithms, making it easier to interpret and analyze the data.

4. Are there any limitations to using the Anti-##k_T## algorithm?

One limitation is that the algorithm can be computationally expensive, especially for larger events with a high number of particles. It also assumes that the particles are massless, which may not always be the case in certain experiments.

5. How is the Anti-##k_T## algorithm used in practice?

The Anti-##k_T## algorithm is commonly used in high-energy physics experiments, such as those at the Large Hadron Collider. It is also used in simulations to help researchers understand the dynamics of jet formation and to compare theoretical predictions with experimental results.

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