Introduction to Hadronic Final State Reconstruction in Collider Experiments Introduction to Hadronic Final State Reconstruction in Collider Experiments (Part VI) Peter Loch University of Arizona Tucson, Arizona USA Peter Loch University of Arizona Tucson, Arizona USA

2 P. Loch U of Arizona March 09, 2010 Theoretical Requirements For Jet Finders Very important at LHC Very important at LHC Often LO (or even NLO) not sufficient to understand final states Often LO (or even NLO) not sufficient to understand final states Potentially significant K-factors can only be applied to jet driven spectra if jet finding follows theoretical rules Potentially significant K-factors can only be applied to jet driven spectra if jet finding follows theoretical rules E.g., jet cross-section shapes Need to be able to compare Need to be able to compare experiments and theory experiments and theory Comparison at the level of distributions Comparison at the level of distributions ATLAS and CMS will unfold experimental effects and limitations independently – different detector systems Theoretical guidelines Theoretical guidelines Infrared safety Infrared safety Adding or removing soft particles should not change the result of jet clustering Adding or removing soft particles should not change the result of jet clustering Collinear safety Collinear safety Splitting of large pT particle into two collinear particles should not affect the jet finding Splitting of large pT particle into two collinear particles should not affect the jet finding infrared sensitivity (soft gluon radiation merges jets) collinear sensitivity (2) (signal split into two towers below threshold) collinear sensitivity (1) (sensitive to E t ordering of seeds)

3 P. Loch U of Arizona March 09, 2010 Iterative Seeded Fixed Cone Use following jet finder rules: Use following jet finder rules: Find particle with largest pT above a seed threshold Find particle with largest pT above a seed threshold Create an ordered list of particles descending in pT and pick first particle Create an ordered list of particles descending in pT and pick first particle Draw a cone of fixed size around this particle Draw a cone of fixed size around this particle Resolution parameter of algorithm Resolution parameter of algorithm Collect all other particles in cone and re-calculate cone directions from those Collect all other particles in cone and re-calculate cone directions from those Use four-momentum re-summation Use four-momentum re-summation Collect particles in new cone of same size and find new direction as above Collect particles in new cone of same size and find new direction as above Repeat until direction does not change → cone becomes stable Repeat until direction does not change → cone becomes stable Take next particle from list if above pT seed threshold Take next particle from list if above pT seed threshold Repeat procedure and find next proto-jet Repeat procedure and find next proto-jet Note that this is done with all particles, including the ones found in previous cones Note that this is done with all particles, including the ones found in previous cones Continue until no more proto-jets above threshold can be constructed Continue until no more proto-jets above threshold can be constructed The same particle can be used by 2 or more jets The same particle can be used by 2 or more jets Check for overlap between proto-jets Check for overlap between proto-jets Add lower pT jet to higher pT jet if sum of particle pT in overlap is above a certain fraction of the lower pT jet (merge) Add lower pT jet to higher pT jet if sum of particle pT in overlap is above a certain fraction of the lower pT jet (merge) Else remove overlapping particles from higher pT jet and add to lower pT jet (split) Else remove overlapping particles from higher pT jet and add to lower pT jet (split) All surviving proto-jets are the final jets All surviving proto-jets are the final jets

4 P. Loch U of Arizona March 09, 2010 Iterative Seeded Fixed Cone Use following jet finder rules: Use following jet finder rules: Find particle with largest pT above a seed threshold Find particle with largest pT above a seed threshold Create an ordered list of particles descending in pT and pick first particle Create an ordered list of particles descending in pT and pick first particle Draw a cone of fixed size around this particle Draw a cone of fixed size around this particle Resolution parameter of algorithm Resolution parameter of algorithm Collect all other particles in cone and re-calculate cone directions from those Collect all other particles in cone and re-calculate cone directions from those Use four-momentum re-summation Use four-momentum re-summation Collect particles in new cone of same size and find new direction as above Collect particles in new cone of same size and find new direction as above Repeat until direction does not change → cone becomes stable Repeat until direction does not change → cone becomes stable Take next particle from list if above pT seed threshold Take next particle from list if above pT seed threshold Repeat procedure and find next proto-jet Repeat procedure and find next proto-jet Note that this is done with all particles, including the ones found in previous cones Note that this is done with all particles, including the ones found in previous cones Continue until no more proto-jets above threshold can be constructed Continue until no more proto-jets above threshold can be constructed The same particle can be used by 2 or more jets The same particle can be used by 2 or more jets Check for overlap between proto-jets Check for overlap between proto-jets Add lower pT jet to higher pT jet if sum of particle pT in overlap is above a certain fraction of the lower pT jet (merge) Add lower pT jet to higher pT jet if sum of particle pT in overlap is above a certain fraction of the lower pT jet (merge) Else remove overlapping particles from higher pT jet and add to lower pT jet (split) Else remove overlapping particles from higher pT jet and add to lower pT jet (split) All surviving proto-jets are the final jets All surviving proto-jets are the final jets

5 P. Loch U of Arizona March 09, 2010 Iterative Seeded Fixed Cone Use following jet finder rules: Use following jet finder rules: Find particle with largest pT above a seed threshold Find particle with largest pT above a seed threshold Create an ordered list of particles descending in pT and pick first particle Create an ordered list of particles descending in pT and pick first particle Draw a cone of fixed size around this particle Draw a cone of fixed size around this particle Resolution parameter of algorithm Resolution parameter of algorithm Collect all other particles in cone and re-calculate cone directions from those Collect all other particles in cone and re-calculate cone directions from those Use four-momentum re-summation Use four-momentum re-summation Collect particles in new cone of same size and find new direction as above Collect particles in new cone of same size and find new direction as above Repeat until direction does not change → cone becomes stable Repeat until direction does not change → cone becomes stable Take next particle from list if above pT seed threshold Take next particle from list if above pT seed threshold Repeat procedure and find next proto-jet Repeat procedure and find next proto-jet Note that this is done with all particles, including the ones found in previous cones Note that this is done with all particles, including the ones found in previous cones Continue until no more proto-jets above threshold can be constructed Continue until no more proto-jets above threshold can be constructed The same particle can be used by 2 or more jets The same particle can be used by 2 or more jets Check for overlap between proto-jets Check for overlap between proto-jets Add lower pT jet to higher pT jet if sum of particle pT in overlap is above a certain fraction of the lower pT jet (merge) Add lower pT jet to higher pT jet if sum of particle pT in overlap is above a certain fraction of the lower pT jet (merge) Else remove overlapping particles from higher pT jet and add to lower pT jet (split) Else remove overlapping particles from higher pT jet and add to lower pT jet (split) All surviving proto-jets are the final jets All surviving proto-jets are the final jets

6 P. Loch U of Arizona March 09, 2010 Iterative Seeded Fixed Cone Use following jet finder rules: Use following jet finder rules: Find particle with largest pT above a seed threshold Find particle with largest pT above a seed threshold Create an ordered list of particles descending in pT and pick first particle Create an ordered list of particles descending in pT and pick first particle Draw a cone of fixed size around this particle Draw a cone of fixed size around this particle Resolution parameter of algorithm Resolution parameter of algorithm Collect all other particles in cone and re-calculate cone directions from those Collect all other particles in cone and re-calculate cone directions from those Use four-momentum re-summation Use four-momentum re-summation Collect particles in new cone of same size and find new direction as above Collect particles in new cone of same size and find new direction as above Repeat until direction does not change → cone becomes stable Repeat until direction does not change → cone becomes stable Take next particle from list if above pT seed threshold Take next particle from list if above pT seed threshold Repeat procedure and find next proto-jet Repeat procedure and find next proto-jet Note that this is done with all particles, including the ones found in previous cones Note that this is done with all particles, including the ones found in previous cones Continue until no more proto-jets above threshold can be constructed Continue until no more proto-jets above threshold can be constructed The same particle can be used by 2 or more jets The same particle can be used by 2 or more jets Check for overlap between proto-jets Check for overlap between proto-jets Add lower pT jet to higher pT jet if sum of particle pT in overlap is above a certain fraction of the lower pT jet (merge) Add lower pT jet to higher pT jet if sum of particle pT in overlap is above a certain fraction of the lower pT jet (merge) Else remove overlapping particles from higher pT jet and add to lower pT jet (split) Else remove overlapping particles from higher pT jet and add to lower pT jet (split) All surviving proto-jets are the final jets All surviving proto-jets are the final jets

7 P. Loch U of Arizona March 09, 2010 Iterative Seeded Fixed Cone Use following jet finder rules: Use following jet finder rules: Find particle with largest pT above a seed threshold Find particle with largest pT above a seed threshold Create an ordered list of particles descending in pT and pick first particle Create an ordered list of particles descending in pT and pick first particle Draw a cone of fixed size around this particle Draw a cone of fixed size around this particle Resolution parameter of algorithm Resolution parameter of algorithm Collect all other particles in cone and re-calculate cone directions from those Collect all other particles in cone and re-calculate cone directions from those Use four-momentum re-summation Use four-momentum re-summation Collect particles in new cone of same size and find new direction as above Collect particles in new cone of same size and find new direction as above Repeat until direction does not change → cone becomes stable Repeat until direction does not change → cone becomes stable Take next particle from list if above pT seed threshold Take next particle from list if above pT seed threshold Repeat procedure and find next proto-jet Repeat procedure and find next proto-jet Note that this is done with all particles, including the ones found in previous cones Note that this is done with all particles, including the ones found in previous cones Continue until no more proto-jets above threshold can be constructed Continue until no more proto-jets above threshold can be constructed The same particle can be used by 2 or more jets The same particle can be used by 2 or more jets Check for overlap between proto-jets Check for overlap between proto-jets Add lower pT jet to higher pT jet if sum of particle pT in overlap is above a certain fraction of the lower pT jet (merge) Add lower pT jet to higher pT jet if sum of particle pT in overlap is above a certain fraction of the lower pT jet (merge) Else remove overlapping particles from higher pT jet and add to lower pT jet (split) Else remove overlapping particles from higher pT jet and add to lower pT jet (split) All surviving proto-jets are the final jets All surviving proto-jets are the final jets

8 P. Loch U of Arizona March 09, 2010 Iterative Seeded Fixed Cone Use following jet finder rules: Use following jet finder rules: Find particle with largest pT above a seed threshold Find particle with largest pT above a seed threshold Create an ordered list of particles descending in pT and pick first particle Create an ordered list of particles descending in pT and pick first particle Draw a cone of fixed size around this particle Draw a cone of fixed size around this particle Resolution parameter of algorithm Resolution parameter of algorithm Collect all other particles in cone and re-calculate cone directions from those Collect all other particles in cone and re-calculate cone directions from those Use four-momentum re-summation Use four-momentum re-summation Collect particles in new cone of same size and find new direction as above Collect particles in new cone of same size and find new direction as above Repeat until direction does not change → cone becomes stable Repeat until direction does not change → cone becomes stable Take next particle from list if above pT seed threshold Take next particle from list if above pT seed threshold Repeat procedure and find next proto-jet Repeat procedure and find next proto-jet Note that this is done with all particles, including the ones found in previous cones Note that this is done with all particles, including the ones found in previous cones Continue until no more proto-jets above threshold can be constructed Continue until no more proto-jets above threshold can be constructed The same particle can be used by 2 or more jets The same particle can be used by 2 or more jets Check for overlap between proto-jets Check for overlap between proto-jets Add lower pT jet to higher pT jet if sum of particle pT in overlap is above a certain fraction of the lower pT jet (merge) Add lower pT jet to higher pT jet if sum of particle pT in overlap is above a certain fraction of the lower pT jet (merge) Else remove overlapping particles from higher pT jet and add to lower pT jet (split) Else remove overlapping particles from higher pT jet and add to lower pT jet (split) All surviving proto-jets are the final jets All surviving proto-jets are the final jets

9 P. Loch U of Arizona March 09, 2010 Iterative Seeded Fixed Cone Use following jet finder rules: Use following jet finder rules: Find particle with largest pT above a seed threshold Find particle with largest pT above a seed threshold Create an ordered list of particles descending in pT and pick first particle Create an ordered list of particles descending in pT and pick first particle Draw a cone of fixed size around this particle Draw a cone of fixed size around this particle Resolution parameter of algorithm Resolution parameter of algorithm Collect all other particles in cone and re-calculate cone directions from those Collect all other particles in cone and re-calculate cone directions from those Use four-momentum re-summation Use four-momentum re-summation Collect particles in new cone of same size and find new direction as above Collect particles in new cone of same size and find new direction as above Repeat until direction does not change → cone becomes stable Repeat until direction does not change → cone becomes stable Take next particle from list if above pT seed threshold Take next particle from list if above pT seed threshold Repeat procedure and find next proto-jet Repeat procedure and find next proto-jet Note that this is done with all particles, including the ones found in previous cones Note that this is done with all particles, including the ones found in previous cones Continue until no more proto-jets above threshold can be constructed Continue until no more proto-jets above threshold can be constructed The same particle can be used by 2 or more jets The same particle can be used by 2 or more jets Check for overlap between proto-jets Check for overlap between proto-jets Add lower pT jet to higher pT jet if sum of particle pT in overlap is above a certain fraction of the lower pT jet (merge) Add lower pT jet to higher pT jet if sum of particle pT in overlap is above a certain fraction of the lower pT jet (merge) Else remove overlapping particles from higher pT jet and add to lower pT jet (split) Else remove overlapping particles from higher pT jet and add to lower pT jet (split) All surviving proto-jets are the final jets All surviving proto-jets are the final jets

10 P. Loch U of Arizona March 09, 2010 Iterative Seeded Fixed Cone Use following jet finder rules: Use following jet finder rules: Find particle with largest pT above a seed threshold Find particle with largest pT above a seed threshold Create an ordered list of particles descending in pT and pick first particle Create an ordered list of particles descending in pT and pick first particle Draw a cone of fixed size around this particle Draw a cone of fixed size around this particle Resolution parameter of algorithm Resolution parameter of algorithm Collect all other particles in cone and re-calculate cone directions from those Collect all other particles in cone and re-calculate cone directions from those Use four-momentum re-summation Use four-momentum re-summation Collect particles in new cone of same size and find new direction as above Collect particles in new cone of same size and find new direction as above Repeat until direction does not change → cone becomes stable Repeat until direction does not change → cone becomes stable Take next particle from list if above pT seed threshold Take next particle from list if above pT seed threshold Repeat procedure and find next proto-jet Repeat procedure and find next proto-jet Note that this is done with all particles, including the ones found in previous cones Note that this is done with all particles, including the ones found in previous cones Continue until no more proto-jets above threshold can be constructed Continue until no more proto-jets above threshold can be constructed The same particle can be used by 2 or more jets The same particle can be used by 2 or more jets Check for overlap between proto-jets Check for overlap between proto-jets Add lower pT jet to higher pT jet if sum of particle pT in overlap is above a certain fraction of the lower pT jet (merge) Add lower pT jet to higher pT jet if sum of particle pT in overlap is above a certain fraction of the lower pT jet (merge) Else remove overlapping particles from higher pT jet and add to lower pT jet (split) Else remove overlapping particles from higher pT jet and add to lower pT jet (split) All surviving proto-jets are the final jets All surviving proto-jets are the final jets

11 P. Loch U of Arizona March 09, 2010 Iterative Seeded Fixed Cone Use following jet finder rules: Use following jet finder rules: Find particle with largest pT above a seed threshold Find particle with largest pT above a seed threshold Create an ordered list of particles descending in pT and pick first particle Create an ordered list of particles descending in pT and pick first particle Draw a cone of fixed size around this particle Draw a cone of fixed size around this particle Resolution parameter of algorithm Resolution parameter of algorithm Collect all other particles in cone and re-calculate cone directions from those Collect all other particles in cone and re-calculate cone directions from those Use four-momentum re-summation Use four-momentum re-summation Collect particles in new cone of same size and find new direction as above Collect particles in new cone of same size and find new direction as above Repeat until direction does not change → cone becomes stable Repeat until direction does not change → cone becomes stable Take next particle from list if above pT seed threshold Take next particle from list if above pT seed threshold Repeat procedure and find next proto-jet Repeat procedure and find next proto-jet Note that this is done with all particles, including the ones found in previous cones Note that this is done with all particles, including the ones found in previous cones Continue until no more proto-jets above threshold can be constructed Continue until no more proto-jets above threshold can be constructed The same particle can be used by 2 or more jets The same particle can be used by 2 or more jets Check for overlap between proto-jets Check for overlap between proto-jets Add lower pT jet to higher pT jet if sum of particle pT in overlap is above a certain fraction of the lower pT jet (merge) Add lower pT jet to higher pT jet if sum of particle pT in overlap is above a certain fraction of the lower pT jet (merge) Else remove overlapping particles from higher pT jet and add to lower pT jet (split) Else remove overlapping particles from higher pT jet and add to lower pT jet (split) All surviving proto-jets are the final jets All surviving proto-jets are the final jets

12 P. Loch U of Arizona March 09, 2010 Iterative Seeded Fixed Cone Use following jet finder rules: Use following jet finder rules: Find particle with largest pT above a seed threshold Find particle with largest pT above a seed threshold Create an ordered list of particles descending in pT and pick first particle Create an ordered list of particles descending in pT and pick first particle Draw a cone of fixed size around this particle Draw a cone of fixed size around this particle Resolution parameter of algorithm Resolution parameter of algorithm Collect all other particles in cone and re-calculate cone directions from those Collect all other particles in cone and re-calculate cone directions from those Use four-momentum re-summation Use four-momentum re-summation Collect particles in new cone of same size and find new direction as above Collect particles in new cone of same size and find new direction as above Repeat until direction does not change → cone becomes stable Repeat until direction does not change → cone becomes stable Take next particle from list if above pT seed threshold Take next particle from list if above pT seed threshold Repeat procedure and find next proto-jet Repeat procedure and find next proto-jet Note that this is done with all particles, including the ones found in previous cones Note that this is done with all particles, including the ones found in previous cones Continue until no more proto-jets above threshold can be constructed Continue until no more proto-jets above threshold can be constructed The same particle can be used by 2 or more jets The same particle can be used by 2 or more jets Check for overlap between proto-jets Check for overlap between proto-jets Add lower pT jet to higher pT jet if sum of particle pT in overlap is above a certain fraction of the lower pT jet (merge) Add lower pT jet to higher pT jet if sum of particle pT in overlap is above a certain fraction of the lower pT jet (merge) Else remove overlapping particles from higher pT jet and add to lower pT jet (split) Else remove overlapping particles from higher pT jet and add to lower pT jet (split) All surviving proto-jets are the final jets All surviving proto-jets are the final jets

13 P. Loch U of Arizona March 09, 2010 Iterative Seeded Fixed Cone Use following jet finder rules: Use following jet finder rules: Find particle with largest pT above a seed threshold Find particle with largest pT above a seed threshold Create an ordered list of particles descending in pT and pick first particle Create an ordered list of particles descending in pT and pick first particle Draw a cone of fixed size around this particle Draw a cone of fixed size around this particle Resolution parameter of algorithm Resolution parameter of algorithm Collect all other particles in cone and re-calculate cone directions from those Collect all other particles in cone and re-calculate cone directions from those Use four-momentum re-summation Use four-momentum re-summation Collect particles in new cone of same size and find new direction as above Collect particles in new cone of same size and find new direction as above Repeat until direction does not change → cone becomes stable Repeat until direction does not change → cone becomes stable Take next particle from list if above pT seed threshold Take next particle from list if above pT seed threshold Repeat procedure and find next proto-jet Repeat procedure and find next proto-jet Note that this is done with all particles, including the ones found in previous cones Note that this is done with all particles, including the ones found in previous cones Continue until no more proto-jets above threshold can be constructed Continue until no more proto-jets above threshold can be constructed The same particle can be used by 2 or more jets The same particle can be used by 2 or more jets Check for overlap between proto-jets Check for overlap between proto-jets Add lower pT jet to higher pT jet if sum of particle pT in overlap is above a certain fraction of the lower pT jet (merge) Add lower pT jet to higher pT jet if sum of particle pT in overlap is above a certain fraction of the lower pT jet (merge) Else remove overlapping particles from higher pT jet and add to lower pT jet (split) Else remove overlapping particles from higher pT jet and add to lower pT jet (split) All surviving proto-jets are the final jets All surviving proto-jets are the final jets

14 P. Loch U of Arizona March 09, 2010 Iterative Seeded Fixed Cone Use following jet finder rules: Use following jet finder rules: Find particle with largest pT above a seed threshold Find particle with largest pT above a seed threshold Create an ordered list of particles descending in pT and pick first particle Create an ordered list of particles descending in pT and pick first particle Draw a cone of fixed size around this particle Draw a cone of fixed size around this particle Resolution parameter of algorithm Resolution parameter of algorithm Collect all other particles in cone and re-calculate cone directions from those Collect all other particles in cone and re-calculate cone directions from those Use four-momentum re-summation Use four-momentum re-summation Collect particles in new cone of same size and find new direction as above Collect particles in new cone of same size and find new direction as above Repeat until direction does not change → cone becomes stable Repeat until direction does not change → cone becomes stable Take next particle from list if above pT seed threshold Take next particle from list if above pT seed threshold Repeat procedure and find next proto-jet Repeat procedure and find next proto-jet Note that this is done with all particles, including the ones found in previous cones Note that this is done with all particles, including the ones found in previous cones Continue until no more proto-jets above threshold can be constructed Continue until no more proto-jets above threshold can be constructed The same particle can be used by 2 or more jets The same particle can be used by 2 or more jets Check for overlap between proto-jets Check for overlap between proto-jets Add lower pT jet to higher pT jet if sum of particle pT in overlap is above a certain fraction of the lower pT jet (merge) Add lower pT jet to higher pT jet if sum of particle pT in overlap is above a certain fraction of the lower pT jet (merge) Else remove overlapping particles from higher pT jet and add to lower pT jet (split) Else remove overlapping particles from higher pT jet and add to lower pT jet (split) All surviving proto-jets are the final jets All surviving proto-jets are the final jets

15 P. Loch U of Arizona March 09, 2010 Iterative Seeded Fixed Cone Use following jet finder rules: Use following jet finder rules: Find particle with largest pT above a seed threshold Find particle with largest pT above a seed threshold Create an ordered list of particles descending in pT and pick first particle Create an ordered list of particles descending in pT and pick first particle Draw a cone of fixed size around this particle Draw a cone of fixed size around this particle Resolution parameter of algorithm Resolution parameter of algorithm Collect all other particles in cone and re-calculate cone directions from those Collect all other particles in cone and re-calculate cone directions from those Use four-momentum re-summation Use four-momentum re-summation Collect particles in new cone of same size and find new direction as above Collect particles in new cone of same size and find new direction as above Repeat until direction does not change → cone becomes stable Repeat until direction does not change → cone becomes stable Take next particle from list if above pT seed threshold Take next particle from list if above pT seed threshold Repeat procedure and find next proto-jet Repeat procedure and find next proto-jet Note that this is done with all particles, including the ones found in previous cones Note that this is done with all particles, including the ones found in previous cones Continue until no more proto-jets above threshold can be constructed Continue until no more proto-jets above threshold can be constructed The same particle can be used by 2 or more jets The same particle can be used by 2 or more jets Check for overlap between proto-jets Check for overlap between proto-jets Add lower pT jet to higher pT jet if sum of particle pT in overlap is above a certain fraction of the lower pT jet (merge) Add lower pT jet to higher pT jet if sum of particle pT in overlap is above a certain fraction of the lower pT jet (merge) Else remove overlapping particles from higher pT jet and add to lower pT jet (split) Else remove overlapping particles from higher pT jet and add to lower pT jet (split) All surviving proto-jets are the final jets All surviving proto-jets are the final jets

16 P. Loch U of Arizona March 09, 2010 Iterative Seeded Fixed Cone Use following jet finder rules: Use following jet finder rules: Find particle with largest pT above a seed threshold Find particle with largest pT above a seed threshold Create an ordered list of particles descending in pT and pick first particle Create an ordered list of particles descending in pT and pick first particle Draw a cone of fixed size around this particle Draw a cone of fixed size around this particle Resolution parameter of algorithm Resolution parameter of algorithm Collect all other particles in cone and re-calculate cone directions from those Collect all other particles in cone and re-calculate cone directions from those Use four-momentum re-summation Use four-momentum re-summation Collect particles in new cone of same size and find new direction as above Collect particles in new cone of same size and find new direction as above Repeat until direction does not change → cone becomes stable Repeat until direction does not change → cone becomes stable Take next particle from list if above pT seed threshold Take next particle from list if above pT seed threshold Repeat procedure and find next proto-jet Repeat procedure and find next proto-jet Note that this is done with all particles, including the ones found in previous cones Note that this is done with all particles, including the ones found in previous cones Continue until no more proto-jets above threshold can be constructed Continue until no more proto-jets above threshold can be constructed The same particle can be used by 2 or more jets The same particle can be used by 2 or more jets Check for overlap between proto-jets Check for overlap between proto-jets Add lower pT jet to higher pT jet if sum of particle pT in overlap is above a certain fraction of the lower pT jet (merge) Add lower pT jet to higher pT jet if sum of particle pT in overlap is above a certain fraction of the lower pT jet (merge) Else remove overlapping particles from higher pT jet and add to lower pT jet (split) Else remove overlapping particles from higher pT jet and add to lower pT jet (split) All surviving proto-jets are the final jets All surviving proto-jets are the final jets

17 P. Loch U of Arizona March 09, 2010 Iterative Seeded Fixed Cone Use following jet finder rules: Use following jet finder rules: Find particle with largest pT above a seed threshold Find particle with largest pT above a seed threshold Create an ordered list of particles descending in pT and pick first particle Create an ordered list of particles descending in pT and pick first particle Draw a cone of fixed size around this particle Draw a cone of fixed size around this particle Resolution parameter of algorithm Resolution parameter of algorithm Collect all other particles in cone and re-calculate cone directions from those Collect all other particles in cone and re-calculate cone directions from those Use four-momentum re-summation Use four-momentum re-summation Collect particles in new cone of same size and find new direction as above Collect particles in new cone of same size and find new direction as above Repeat until direction does not change → cone becomes stable Repeat until direction does not change → cone becomes stable Take next particle from list if above pT seed threshold Take next particle from list if above pT seed threshold Repeat procedure and find next proto-jet Repeat procedure and find next proto-jet Note that this is done with all particles, including the ones found in previous cones Note that this is done with all particles, including the ones found in previous cones Continue until no more proto-jets above threshold can be constructed Continue until no more proto-jets above threshold can be constructed The same particle can be used by 2 or more jets The same particle can be used by 2 or more jets Check for overlap between proto-jets Check for overlap between proto-jets Add lower pT jet to higher pT jet if sum of particle pT in overlap is above a certain fraction of the lower pT jet (merge) Add lower pT jet to higher pT jet if sum of particle pT in overlap is above a certain fraction of the lower pT jet (merge) Else remove overlapping particles from higher pT jet and add to lower pT jet (split) Else remove overlapping particles from higher pT jet and add to lower pT jet (split) All surviving proto-jets are the final jets All surviving proto-jets are the final jets

18 P. Loch U of Arizona March 09, 2010 Iterative Seeded Fixed Cone Use following jet finder rules: Use following jet finder rules: Find particle with largest pT above a seed threshold Find particle with largest pT above a seed threshold Create an ordered list of particles descending in pT and pick first particle Create an ordered list of particles descending in pT and pick first particle Draw a cone of fixed size around this particle Draw a cone of fixed size around this particle Resolution parameter of algorithm Resolution parameter of algorithm Collect all other particles in cone and re-calculate cone directions from those Collect all other particles in cone and re-calculate cone directions from those Use four-momentum re-summation Use four-momentum re-summation Collect particles in new cone of same size and find new direction as above Collect particles in new cone of same size and find new direction as above Repeat until direction does not change → cone becomes stable Repeat until direction does not change → cone becomes stable Take next particle from list if above pT seed threshold Take next particle from list if above pT seed threshold Repeat procedure and find next proto-jet Repeat procedure and find next proto-jet Note that this is done with all particles, including the ones found in previous cones Note that this is done with all particles, including the ones found in previous cones Continue until no more proto-jets above threshold can be constructed Continue until no more proto-jets above threshold can be constructed The same particle can be used by 2 or more jets The same particle can be used by 2 or more jets Check for overlap between proto-jets Check for overlap between proto-jets Add lower pT jet to higher pT jet if sum of particle pT in overlap is above a certain fraction of the lower pT jet (merge) Add lower pT jet to higher pT jet if sum of particle pT in overlap is above a certain fraction of the lower pT jet (merge) Else remove overlapping particles from higher pT jet and add to lower pT jet (split) Else remove overlapping particles from higher pT jet and add to lower pT jet (split) All surviving proto-jets are the final jets All surviving proto-jets are the final jets

19 P. Loch U of Arizona March 09, 2010 Iterative Seeded Fixed Cone Use following jet finder rules: Use following jet finder rules: Find particle with largest pT above a seed threshold Find particle with largest pT above a seed threshold Create an ordered list of particles descending in pT and pick first particle Create an ordered list of particles descending in pT and pick first particle Draw a cone of fixed size around this particle Draw a cone of fixed size around this particle Resolution parameter of algorithm Resolution parameter of algorithm Collect all other particles in cone and re-calculate cone directions from those Collect all other particles in cone and re-calculate cone directions from those Use four-momentum re-summation Use four-momentum re-summation Collect particles in new cone of same size and find new direction as above Collect particles in new cone of same size and find new direction as above Repeat until direction does not change → cone becomes stable Repeat until direction does not change → cone becomes stable Take next particle from list if above pT seed threshold Take next particle from list if above pT seed threshold Repeat procedure and find next proto-jet Repeat procedure and find next proto-jet Note that this is done with all particles, including the ones found in previous cones Note that this is done with all particles, including the ones found in previous cones Continue until no more proto-jets above threshold can be constructed Continue until no more proto-jets above threshold can be constructed The same particle can be used by 2 or more jets The same particle can be used by 2 or more jets Check for overlap between proto-jets Check for overlap between proto-jets Add lower pT jet to higher pT jet if sum of particle pT in overlap is above a certain fraction of the lower pT jet (merge) Add lower pT jet to higher pT jet if sum of particle pT in overlap is above a certain fraction of the lower pT jet (merge) Else remove overlapping particles from higher pT jet and add to lower pT jet (split) Else remove overlapping particles from higher pT jet and add to lower pT jet (split) All surviving proto-jets are the final jets All surviving proto-jets are the final jets

20 P. Loch U of Arizona March 09, 2010 Iterative Seeded Fixed Cone Use following jet finder rules: Use following jet finder rules: Find particle with largest pT above a seed threshold Find particle with largest pT above a seed threshold Create an ordered list of particles descending in pT and pick first particle Create an ordered list of particles descending in pT and pick first particle Draw a cone of fixed size around this particle Draw a cone of fixed size around this particle Resolution parameter of algorithm Resolution parameter of algorithm Collect all other particles in cone and re-calculate cone directions from those Collect all other particles in cone and re-calculate cone directions from those Use four-momentum re-summation Use four-momentum re-summation Collect particles in new cone of same size and find new direction as above Collect particles in new cone of same size and find new direction as above Repeat until direction does not change → cone becomes stable Repeat until direction does not change → cone becomes stable Take next particle from list if above pT seed threshold Take next particle from list if above pT seed threshold Repeat procedure and find next proto-jet Repeat procedure and find next proto-jet Note that this is done with all particles, including the ones found in previous cones Note that this is done with all particles, including the ones found in previous cones Continue until no more proto-jets above threshold can be constructed Continue until no more proto-jets above threshold can be constructed The same particle can be used by 2 or more jets The same particle can be used by 2 or more jets Check for overlap between proto-jets Check for overlap between proto-jets Add lower pT jet to higher pT jet if sum of particle pT in overlap is above a certain fraction of the lower pT jet (merge) Add lower pT jet to higher pT jet if sum of particle pT in overlap is above a certain fraction of the lower pT jet (merge) Else remove overlapping particles from higher pT jet and add to lower pT jet (split) Else remove overlapping particles from higher pT jet and add to lower pT jet (split) All surviving proto-jets are the final jets All surviving proto-jets are the final jets

21 P. Loch U of Arizona March 09, 2010 Iterative Seeded Fixed Cone Other problems with iterative cone finders: Other problems with iterative cone finders: “Dark” tower problem “Dark” tower problem Original seed moves out of cone Original seed moves out of cone Significant energy lost for jets Significant energy lost for jets initial cone1 st cone (not stable) 2 nd cone (not stable) 3 rd cone (stable) original seed lost for jets!

22 P. Loch U of Arizona March 09, 2010 Iterative Seeded Fixed Cone Other problems with iterative cone finders: Other problems with iterative cone finders: “Dark” tower problem “Dark” tower problem Original seed moves out of cone Original seed moves out of cone Significant energy lost for jets Significant energy lost for jets

23 P. Loch U of Arizona March 09, 2010 Iterative Seeded Fixed Cone Advantages Advantages Simple geometry based algorithm Simple geometry based algorithm Easy to implement Easy to implement Fast algorithm Fast algorithm Ideal for online application in experiment Ideal for online application in experiment Disadvantages Disadvantages Not infrared safe Not infrared safe Can partially be recovered by splitting & merging Can partially be recovered by splitting & merging Introduces split/merge pT fraction f (typically ) Kills “trace” of pertubative infinities in experiment Kills “trace” of pertubative infinities in experiment Hard to confirm higher order calculations in “real life” without infinities! Not collinear safe Not collinear safe Used pT seeds (thresholds) Used pT seeds (thresholds) Jets not cone shaped Jets not cone shaped Splitting and merging potentially makes jets bigger than original cone size and changes jet boundaries Splitting and merging potentially makes jets bigger than original cone size and changes jet boundaries

24 P. Loch U of Arizona March 09, 2010 Recursive Recombination Motivated by gluon splitting function Motivated by gluon splitting function QCD branching happens all the time QCD branching happens all the time Attempt to undo parton fragmentation Attempt to undo parton fragmentation Pair with strongest divergence likely belongs together Pair with strongest divergence likely belongs together kT/Durham, first used in e + e - kT/Durham, first used in e + e - Catani, Dokshitzer, Olsson, Turnock & Webber 1991 Catani, Dokshitzer, Olsson, Turnock & Webber 1991 Longitudinal invariant version for hadron colliders Longitudinal invariant version for hadron colliders Transverse momentum instead of energy Transverse momentum instead of energy Catani, Dokshitzer, Seymour & Webber 1993 Catani, Dokshitzer, Seymour & Webber 1993 S.D. Ellis & D. Soper 1993 S.D. Ellis & D. Soper 1993 Valid at all orders! Valid at all orders!

25 P. Loch U of Arizona March 09, 2010 Recursive Recombination Motivated by gluon splitting function Motivated by gluon splitting function QCD branching happens all the time QCD branching happens all the time Attempt to undo parton fragmentation Attempt to undo parton fragmentation Pair with strongest divergence likely belongs together Pair with strongest divergence likely belongs together kT/Durham, first used in e + e - kT/Durham, first used in e + e - Catani, Dokshitzer, Olsson, Turnock & Webber 1991 Catani, Dokshitzer, Olsson, Turnock & Webber 1991 Longitudinal invariant version for hadron colliders Longitudinal invariant version for hadron colliders Transverse momentum instead of energy Transverse momentum instead of energy Catani, Dokshitzer, Seymour & Webber 1993 Catani, Dokshitzer, Seymour & Webber 1993 S.D. Ellis & D. Soper 1993 S.D. Ellis & D. Soper 1993 Valid at all orders! Valid at all orders!

26 P. Loch U of Arizona March 09, 2010 Recursive Recombination Motivated by gluon splitting function Motivated by gluon splitting function QCD branching happens all the time QCD branching happens all the time Attempt to undo parton fragmentation Attempt to undo parton fragmentation Pair with strongest divergence likely belongs together Pair with strongest divergence likely belongs together kT/Durham, first used in e + e - kT/Durham, first used in e + e - Catani, Dokshitzer, Olsson, Turnock & Webber 1991 Catani, Dokshitzer, Olsson, Turnock & Webber 1991 Longitudinal invariant version for hadron colliders Longitudinal invariant version for hadron colliders Transverse momentum instead of energy Transverse momentum instead of energy Catani, Dokshitzer, Seymour & Webber 1993 Catani, Dokshitzer, Seymour & Webber 1993 S.D. Ellis & D. Soper 1993 S.D. Ellis & D. Soper 1993 Valid at all orders! Valid at all orders!

27 P. Loch U of Arizona March 09, 2010 Recursive Recombination Motivated by gluon splitting function Motivated by gluon splitting function QCD branching happens all the time QCD branching happens all the time Attempt to undo parton fragmentation Attempt to undo parton fragmentation Pair with strongest divergence likely belongs together Pair with strongest divergence likely belongs together kT/Durham, first used in e + e - kT/Durham, first used in e + e - Catani, Dokshitzer, Olsson, Turnock & Webber 1991 Catani, Dokshitzer, Olsson, Turnock & Webber 1991 Longitudinal invariant version for hadron colliders Longitudinal invariant version for hadron colliders Transverse momentum instead of energy Transverse momentum instead of energy Catani, Dokshitzer, Seymour & Webber 1993 Catani, Dokshitzer, Seymour & Webber 1993 S.D. Ellis & D. Soper 1993 S.D. Ellis & D. Soper 1993 Valid at all orders! Valid at all orders!

28 P. Loch U of Arizona March 09, 2010 kT –like Algorithms Classic procedure Classic procedure Calculate all distances d ji for list of particles Calculate all distances d ji for list of particles Uses distance parameter Uses distance parameter Calculate d i for all particles Calculate d i for all particles Uses pT Uses pT If minimum of both lists is a d ij, combine i and j and add to list If minimum of both lists is a d ij, combine i and j and add to list Remove i and j, of course Remove i and j, of course If minimum is a d i, call i a jet and remove from list If minimum is a d i, call i a jet and remove from list Recalculate all distances and continue all particles are removed or called a jet Recalculate all distances and continue all particles are removed or called a jet Features Features Clustering sequence is ordered in kT Clustering sequence is ordered in kT Follows jet structure Follows jet structure Alternatives Alternatives Cambridge/Aachen clustering Cambridge/Aachen clustering Uses angular distances only Uses angular distances only Clustering sequence follows jet structure Clustering sequence follows jet structure Anti-kT clustering Anti-kT clustering No particular ordering, sequence not meaningful No particular ordering, sequence not meaningful

29 P. Loch U of Arizona March 09, 2010 kT –like Algorithms Classic procedure Classic procedure Calculate all distances d ji for list of particles Calculate all distances d ji for list of particles Uses distance parameter Uses distance parameter Calculate d i for all particles Calculate d i for all particles Uses pT Uses pT If minimum of both lists is a d ij, combine i and j and add to list If minimum of both lists is a d ij, combine i and j and add to list Remove i and j, of course Remove i and j, of course If minimum is a d i, call i a jet and remove from list If minimum is a d i, call i a jet and remove from list Recalculate all distances and continue all particles are removed or called a jet Recalculate all distances and continue all particles are removed or called a jet Features Features Clustering sequence is ordered in kT Clustering sequence is ordered in kT Follows jet structure Follows jet structure Alternatives Alternatives Cambridge/Aachen clustering Cambridge/Aachen clustering Uses angular distances only Uses angular distances only Clustering sequence follows jet structure Clustering sequence follows jet structure Anti-kT clustering Anti-kT clustering No particular ordering, sequence not meaningful No particular ordering, sequence not meaningful

30 P. Loch U of Arizona March 09, 2010 kT –like Algorithms Classic procedure Classic procedure Calculate all distances d ji for list of particles Calculate all distances d ji for list of particles Uses distance parameter Uses distance parameter Calculate d i for all particles Calculate d i for all particles Uses pT Uses pT If minimum of both lists is a d ij, combine i and j and add to list If minimum of both lists is a d ij, combine i and j and add to list Remove i and j, of course Remove i and j, of course If minimum is a d i, call i a jet and remove from list If minimum is a d i, call i a jet and remove from list Recalculate all distances and continue all particles are removed or called a jet Recalculate all distances and continue all particles are removed or called a jet Features Features Clustering sequence is ordered in kT Clustering sequence is ordered in kT Follows jet structure Follows jet structure Alternatives Alternatives Cambridge/Aachen clustering Cambridge/Aachen clustering Uses angular distances only Uses angular distances only Clustering sequence follows jet structure Clustering sequence follows jet structure Anti-kT clustering Anti-kT clustering No particular ordering, sequence not meaningful No particular ordering, sequence not meaningful

31 P. Loch U of Arizona March 09, 2010 kT Examples kT, n=1Anti-kT, n=-1Cambridge/Aachen, n=0

32 P. Loch U of Arizona March 09, 2010 kT Examples kT, n=1Anti-kT, n=-1Cambridge/Aachen, n=0

33 P. Loch U of Arizona March 09, 2010 kT Examples kT, n=1Anti-kT, n=-1Cambridge/Aachen, n=0

34 P. Loch U of Arizona March 09, 2010 kT Examples kT, n=1Anti-kT, n=-1Cambridge/Aachen, n=0

35 P. Loch U of Arizona March 09, 2010 kT Examples kT, n=1Anti-kT, n=-1Cambridge/Aachen, n=0

36 P. Loch U of Arizona March 09, 2010 kT Examples kT, n=1Anti-kT, n=-1Cambridge/Aachen, n=0

37 P. Loch U of Arizona March 09, 2010 Recursive Recombination Algorithms

38 P. Loch U of Arizona March 09, 2010 Recursive Recombination Algorithms

39 P. Loch U of Arizona March 09, 2010 Recursive Recombination Algortihms

40 P. Loch U of Arizona March 09, 2010 Recursive Recombination Algortihms

41 P. Loch U of Arizona March 09, 2010 Recursive Recombination Algorithms

42 P. Loch U of Arizona March 09, 2010 Recursive Recombination Algorithms

43 P. Loch U of Arizona March 09, 2010 Recursive Recombination Algorithms

44 P. Loch U of Arizona March 09, 2010 Recursive Recombination Algorithms

45 P. Loch U of Arizona March 09, 2010 Recursive Recombination Algorithms

46 P. Loch U of Arizona March 09, 2010 Recursive Recombination Algorithms