Journal Club Notes 09/03/19 (Patrick on Jets and Jet Stuff)

Really Fundamental Thing About Jets:

Ex: e+e- ->qqbar easy at leading order
Ex: e+e- ->qqbar at NLO, there exists an IR divergence, leading to a infinite cross section

Adding LO to NLO diagram we get a correction to the cross section.
Divergence is dependent on inclusivity.

Important Question about Jets:
What gets grouped together into one jet?
What are the important observables of your jet clusturing algorithm?

Could take a Delta R and call everything within it as belonging to a jet.

Major issue with dealing with jets is divergences that can be eliminated using Resummation.

Soft Colinear Effective Field Theory : If we ignore the loop diagrams, the IR divergences come from the 
region in which the gluon is either very soft (p_g ~ 0) or if the angle between the quark and the gluon -> 0.

Feynman Propagator of quark-gluon leg = 1 / 2 * E_q * E_g * [1 - cos(theta)]
Also known as the Structure of QCD.

UV digergences usually take the form of ln(Lamda)
The key thing in IR Divergences is it takes the form of ln^2(Lambda) so you cannot use the
usual renormalization.

Cone Algorithms:

Older algorithms based on cone algorithms where you select a Delta R and find away to cluster objects 
within that Delta R. Starts with clustering around a hard object and working your way out.
Cone Algorithms are not IRC safe.

Could be mitigated by using Thrust (Calculating along axis of the back to back jets)

Figure 2 shows the danger of using non-IRC safe algorithms.

What we currently use (most of the time) is the Sequential Jet Algorithm.
Section 2.2.1 - Jade Algorithm: Objects group by defining a metric of a distance between two particles.
If the value of the metric is below a threshold when grouping objects together, you expand the jet.
This can tend to group two back to back soft particles into one jet.

As time goes on the metrics used are less intuitive but more robust.

kT Algorithm replaced Jade Algorithm by taking the min of the square of the two object energies.

In ATLAS we use the Anti-kT Algorithm which uses the min of square of pT of particles times the fractional R spread.

Figure 7: Great plot for how the different algorithms cluster objects into jets.

Perturbative Properties of Jets:
How the pT of the jet and invariant mass affected by the radius of the jet.
Though naively we would expect the pT of the jet to closely match the pT of the parton in the jet, it
highly depends on radius and algorithm dependent and hadronization.

Underlying Events and Pileup will also change the energy and shape of your jet if an underlying event occurs 
in the same proton collision or if an occurance in another part of the detector ends up in the 
area you are clustering in.

Jet Area is defined as the susceptibility to soft radiation in your jet clustering.

Cambridge-Achen methods are angular ordered and serve to resolve jet substructure (something we'll talk about next week).