Download slides:pptx - Experimental Elementary Particle Physics Group

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
2
Theoretical Requirements For Jet Finders
P. Loch
U of Arizona
March 09, 2010
Very important at LHC
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
E.g., jet cross-section shapes
infrared sensitivity
(soft gluon radiation merges jets)
Need to be able to compare
experiments and theory
Comparison at the level of distributions
ATLAS and CMS will unfold experimental effects
and limitations independently – different
detector systems
Theoretical guidelines
Infrared safety
Adding or removing soft particles should not
change the result of jet clustering
collinear sensitivity (1)
(sensitive to Et ordering of seeds)
Collinear safety
Splitting of large pT particle into two collinear
particles should not affect the jet finding
collinear sensitivity (2)
(signal split into two towers below threshold)
3
Iterative Seeded Fixed Cone
Use following jet finder rules:
Find particle with largest pT above a seed threshold
Create an ordered list of particles descending in pT
and pick first particle
Draw a cone of fixed size around this particle
Resolution parameter of algorithm
Collect all other particles in cone and re-calculate
cone directions from those
Use four-momentum re-summation
Collect particles in new cone of same size and find
new direction as above
Repeat until direction does not change → cone
becomes stable
Take next particle from list if above pT seed
threshold
Repeat procedure and find next proto-jet
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
The same particle can be used by 2 or more 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)
Else remove overlapping particles from higher pT
jet and add to lower pT jet (split)
All surviving proto-jets are the final jets
P. Loch
U of Arizona
March 09, 2010
4
Iterative Seeded Fixed Cone
Use following jet finder rules:
Find particle with largest pT above a seed threshold
Create an ordered list of particles descending in pT
and pick first particle
Draw a cone of fixed size around this particle
Resolution parameter of algorithm
Collect all other particles in cone and re-calculate
cone directions from those
Use four-momentum re-summation
Collect particles in new cone of same size and find
new direction as above
Repeat until direction does not change → cone
becomes stable
Take next particle from list if above pT seed
threshold
Repeat procedure and find next proto-jet
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
The same particle can be used by 2 or more 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)
Else remove overlapping particles from higher pT
jet and add to lower pT jet (split)
All surviving proto-jets are the final jets
P. Loch
U of Arizona
March 09, 2010
R   2   2  Rcone
5
Iterative Seeded Fixed Cone
Use following jet finder rules:
Find particle with largest pT above a seed threshold
Create an ordered list of particles descending in pT
and pick first particle
Draw a cone of fixed size around this particle
Resolution parameter of algorithm
Collect all other particles in cone and re-calculate
cone directions from those
Use four-momentum re-summation
Collect particles in new cone of same size and find
new direction as above
Repeat until direction does not change → cone
becomes stable
Take next particle from list if above pT seed
threshold
Repeat procedure and find next proto-jet
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
The same particle can be used by 2 or more 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)
Else remove overlapping particles from higher pT
jet and add to lower pT jet (split)
All surviving proto-jets are the final jets
P. Loch
U of Arizona
March 09, 2010
R   2   2  Rcone
(first protojet)
6
Iterative Seeded Fixed Cone
Use following jet finder rules:
Find particle with largest pT above a seed threshold
Create an ordered list of particles descending in pT
and pick first particle
Draw a cone of fixed size around this particle
Resolution parameter of algorithm
Collect all other particles in cone and re-calculate
cone directions from those
Use four-momentum re-summation
Collect particles in new cone of same size and find
new direction as above
Repeat until direction does not change → cone
becomes stable
Take next particle from list if above pT seed
threshold
Repeat procedure and find next proto-jet
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
The same particle can be used by 2 or more 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)
Else remove overlapping particles from higher pT
jet and add to lower pT jet (split)
All surviving proto-jets are the final jets
P. Loch
U of Arizona
March 09, 2010
R   2   2  Rcone
7
Iterative Seeded Fixed Cone
Use following jet finder rules:
Find particle with largest pT above a seed threshold
Create an ordered list of particles descending in pT
and pick first particle
Draw a cone of fixed size around this particle
Resolution parameter of algorithm
Collect all other particles in cone and re-calculate
cone directions from those
Use four-momentum re-summation
Collect particles in new cone of same size and find
new direction as above
Repeat until direction does not change → cone
becomes stable
Take next particle from list if above pT seed
threshold
Repeat procedure and find next proto-jet
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
The same particle can be used by 2 or more 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)
Else remove overlapping particles from higher pT
jet and add to lower pT jet (split)
All surviving proto-jets are the final jets
P. Loch
U of Arizona
March 09, 2010
R   2   2  Rcone
(second protojet)
8
Iterative Seeded Fixed Cone
Use following jet finder rules:
Find particle with largest pT above a seed threshold
Create an ordered list of particles descending in pT
and pick first particle
Draw a cone of fixed size around this particle
Resolution parameter of algorithm
Collect all other particles in cone and re-calculate
cone directions from those
Use four-momentum re-summation
Collect particles in new cone of same size and find
new direction as above
Repeat until direction does not change → cone
becomes stable
Take next particle from list if above pT seed
threshold
Repeat procedure and find next proto-jet
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
The same particle can be used by 2 or more 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)
Else remove overlapping particles from higher pT
jet and add to lower pT jet (split)
All surviving proto-jets are the final jets
P. Loch
U of Arizona
March 09, 2010
R   2   2  Rcone
(two jets)
9
Iterative Seeded Fixed Cone
Use following jet finder rules:
Find particle with largest pT above a seed threshold
Create an ordered list of particles descending in pT
and pick first particle
Draw a cone of fixed size around this particle
Resolution parameter of algorithm
Collect all other particles in cone and re-calculate
cone directions from those
Use four-momentum re-summation
Collect particles in new cone of same size and find
new direction as above
Repeat until direction does not change → cone
becomes stable
Take next particle from list if above pT seed
threshold
Repeat procedure and find next proto-jet
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
The same particle can be used by 2 or more 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)
Else remove overlapping particles from higher pT
jet and add to lower pT jet (split)
All surviving proto-jets are the final jets
P. Loch
U of Arizona
March 09, 2010
R   2   2  Rcone
10
Iterative Seeded Fixed Cone
Use following jet finder rules:
Find particle with largest pT above a seed threshold
Create an ordered list of particles descending in pT
and pick first particle
Draw a cone of fixed size around this particle
Resolution parameter of algorithm
Collect all other particles in cone and re-calculate
cone directions from those
Use four-momentum re-summation
Collect particles in new cone of same size and find
new direction as above
Repeat until direction does not change → cone
becomes stable
Take next particle from list if above pT seed
threshold
Repeat procedure and find next proto-jet
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
The same particle can be used by 2 or more 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)
Else remove overlapping particles from higher pT
jet and add to lower pT jet (split)
All surviving proto-jets are the final jets
P. Loch
U of Arizona
March 09, 2010
R   2   2  Rcone
11
Iterative Seeded Fixed Cone
Use following jet finder rules:
Find particle with largest pT above a seed threshold
Create an ordered list of particles descending in pT
and pick first particle
Draw a cone of fixed size around this particle
Resolution parameter of algorithm
Collect all other particles in cone and re-calculate
cone directions from those
Use four-momentum re-summation
Collect particles in new cone of same size and find
new direction as above
Repeat until direction does not change → cone
becomes stable
Take next particle from list if above pT seed
threshold
Repeat procedure and find next proto-jet
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
The same particle can be used by 2 or more 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)
Else remove overlapping particles from higher pT
jet and add to lower pT jet (split)
All surviving proto-jets are the final jets
P. Loch
U of Arizona
March 09, 2010
R   2   2  Rcone
12
Iterative Seeded Fixed Cone
Use following jet finder rules:
Find particle with largest pT above a seed threshold
Create an ordered list of particles descending in pT
and pick first particle
Draw a cone of fixed size around this particle
Resolution parameter of algorithm
Collect all other particles in cone and re-calculate
cone directions from those
Use four-momentum re-summation
Collect particles in new cone of same size and find
new direction as above
Repeat until direction does not change → cone
becomes stable
Take next particle from list if above pT seed
threshold
Repeat procedure and find next proto-jet
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
The same particle can be used by 2 or more 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)
Else remove overlapping particles from higher pT
jet and add to lower pT jet (split)
All surviving proto-jets are the final jets
P. Loch
U of Arizona
March 09, 2010
R   2   2  Rcone
(first protojet)
13
Iterative Seeded Fixed Cone
Use following jet finder rules:
Find particle with largest pT above a seed threshold
Create an ordered list of particles descending in pT
and pick first particle
Draw a cone of fixed size around this particle
Resolution parameter of algorithm
Collect all other particles in cone and re-calculate
cone directions from those
Use four-momentum re-summation
Collect particles in new cone of same size and find
new direction as above
Repeat until direction does not change → cone
becomes stable
Take next particle from list if above pT seed
threshold
Repeat procedure and find next proto-jet
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
The same particle can be used by 2 or more 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)
Else remove overlapping particles from higher pT
jet and add to lower pT jet (split)
All surviving proto-jets are the final jets
P. Loch
U of Arizona
March 09, 2010
R   2   2  Rcone
14
Iterative Seeded Fixed Cone
Use following jet finder rules:
Find particle with largest pT above a seed threshold
Create an ordered list of particles descending in pT
and pick first particle
Draw a cone of fixed size around this particle
Resolution parameter of algorithm
Collect all other particles in cone and re-calculate
cone directions from those
Use four-momentum re-summation
Collect particles in new cone of same size and find
new direction as above
Repeat until direction does not change → cone
becomes stable
Take next particle from list if above pT seed
threshold
Repeat procedure and find next proto-jet
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
The same particle can be used by 2 or more 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)
Else remove overlapping particles from higher pT
jet and add to lower pT jet (split)
All surviving proto-jets are the final jets
P. Loch
U of Arizona
March 09, 2010
R   2   2  Rcone
15
Iterative Seeded Fixed Cone
Use following jet finder rules:
Find particle with largest pT above a seed threshold
Create an ordered list of particles descending in pT
and pick first particle
Draw a cone of fixed size around this particle
Resolution parameter of algorithm
Collect all other particles in cone and re-calculate
cone directions from those
Use four-momentum re-summation
Collect particles in new cone of same size and find
new direction as above
Repeat until direction does not change → cone
becomes stable
Take next particle from list if above pT seed
threshold
Repeat procedure and find next proto-jet
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
The same particle can be used by 2 or more 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)
Else remove overlapping particles from higher pT
jet and add to lower pT jet (split)
All surviving proto-jets are the final jets
P. Loch
U of Arizona
March 09, 2010
R   2   2  Rcone
16
Iterative Seeded Fixed Cone
Use following jet finder rules:
Find particle with largest pT above a seed threshold
Create an ordered list of particles descending in pT
and pick first particle
Draw a cone of fixed size around this particle
Resolution parameter of algorithm
Collect all other particles in cone and re-calculate
cone directions from those
Use four-momentum re-summation
Collect particles in new cone of same size and find
new direction as above
Repeat until direction does not change → cone
becomes stable
Take next particle from list if above pT seed
threshold
Repeat procedure and find next proto-jet
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
The same particle can be used by 2 or more 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)
Else remove overlapping particles from higher pT
jet and add to lower pT jet (split)
All surviving proto-jets are the final jets
P. Loch
U of Arizona
March 09, 2010
R   2   2  Rcone
17
Iterative Seeded Fixed Cone
Use following jet finder rules:
Find particle with largest pT above a seed threshold
Create an ordered list of particles descending in pT
and pick first particle
Draw a cone of fixed size around this particle
Resolution parameter of algorithm
Collect all other particles in cone and re-calculate
cone directions from those
Use four-momentum re-summation
Collect particles in new cone of same size and find
new direction as above
Repeat until direction does not change → cone
becomes stable
Take next particle from list if above pT seed
threshold
Repeat procedure and find next proto-jet
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
The same particle can be used by 2 or more 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)
Else remove overlapping particles from higher pT
jet and add to lower pT jet (split)
All surviving proto-jets are the final jets
P. Loch
U of Arizona
March 09, 2010
R   2   2  Rcone
(second protojet)
18
Iterative Seeded Fixed Cone
Use following jet finder rules:
Find particle with largest pT above a seed threshold
Create an ordered list of particles descending in pT
and pick first particle
Draw a cone of fixed size around this particle
Resolution parameter of algorithm
Collect all other particles in cone and re-calculate
cone directions from those
Use four-momentum re-summation
Collect particles in new cone of same size and find
new direction as above
Repeat until direction does not change → cone
becomes stable
Take next particle from list if above pT seed
threshold
Repeat procedure and find next proto-jet
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
The same particle can be used by 2 or more 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)
Else remove overlapping particles from higher pT
jet and add to lower pT jet (split)
All surviving proto-jets are the final jets
P. Loch
U of Arizona
March 09, 2010
R   2   2  Rcone
(second protojet)
19
Iterative Seeded Fixed Cone
Use following jet finder rules:
Find particle with largest pT above a seed threshold
Create an ordered list of particles descending in pT
and pick first particle
Draw a cone of fixed size around this particle
Resolution parameter of algorithm
Collect all other particles in cone and re-calculate
cone directions from those
Use four-momentum re-summation
Collect particles in new cone of same size and find
new direction as above
Repeat until direction does not change → cone
becomes stable
Take next particle from list if above pT seed
threshold
Repeat procedure and find next proto-jet
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
The same particle can be used by 2 or more 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)
Else remove overlapping particles from higher pT
jet and add to lower pT jet (split)
All surviving proto-jets are the final jets
P. Loch
U of Arizona
March 09, 2010
R   2   2  Rcone
(one jet)
20
Iterative Seeded Fixed Cone
Use following jet finder rules:
Find particle with largest pT above a seed threshold
Create an ordered list of particles descending in pT
and pick first particle
Draw a cone of fixed size around this particle
Resolution parameter of algorithm
Collect all other particles in cone and re-calculate
cone directions from those
Use four-momentum re-summation
Collect particles in new cone of same size and find
new direction as above
Repeat until direction does not change → cone
becomes stable
Take next particle from list if above pT seed
threshold
Repeat procedure and find next proto-jet
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
The same particle can be used by 2 or more 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)
Else remove overlapping particles from higher pT
jet and add to lower pT jet (split)
All surviving proto-jets are the final jets
P. Loch
U of Arizona
March 09, 2010
R   2   2  Rcone
(one jet)
Iterative Seeded Fixed Cone
21
P. Loch
U of Arizona
March 09, 2010
Other problems with iterative cone finders:
“Dark” tower problem
Original seed moves out of cone
Significant energy lost for jets
initial cone
1st cone
(not stable)
original seed lost for jets!
2nd cone
(not stable)
3rd cone
(stable)
22
Iterative Seeded Fixed Cone
Other problems with iterative cone finders:
“Dark” tower problem
Original seed moves out of cone
Significant energy lost for jets
P. Loch
U of Arizona
March 09, 2010
Iterative Seeded Fixed Cone
23
P. Loch
U of Arizona
March 09, 2010
Advantages
Simple geometry based algorithm
Easy to implement
Fast algorithm
Ideal for online application in experiment
Disadvantages
Not infrared safe
Can partially be recovered by splitting & merging
Introduces split/merge pT fraction f (typically 0.50 - 0.75)
Kills “trace” of pertubative infinities in experiment
Hard to confirm higher order calculations in “real life” without infinities!
Not collinear safe
Used pT seeds (thresholds)
Jets not cone shaped
Splitting and merging potentially makes jets bigger than original cone size
and changes jet boundaries
P. Loch
U of Arizona
March 09, 2010
Recursive Recombination
24
Motivated by gluon splitting
function
QCD branching happens all the
time
Attempt to undo parton
fragmentation
Pair with strongest divergence
likely belongs together
kT/Durham, first used in e+eCatani, Dokshitzer, Olsson,
Turnock & Webber 1991
dk j  M
2
g gi g j
(E j
Ei , ij
(k j )
2 sC A

dE j
d ij
min(Ei , E j )  ij
1)
Distance between all particles i and j
yij 
2min(Ei2 , E 2j )(1  cos ij )
Q2
yij  ycut  combine i and j , else stop
Drop normalization to Q2 (not fixed in pp)
yij  dij  min(di , d j )Rij2 , di , j  pT2i , j
Longitudinal invariant version
for hadron colliders
Rij2  (yi  y j )2  (i   j )2
Transverse momentum instead d  d  combine i and j , else stop
ij
cut
of energy
Catani, Dokshitzer, Seymour & (exclusive kT)
Webber 1993
Inclusive longitudinal invariant clustering
S.D. Ellis & D. Soper 1993
Valid at all orders!
dij  min(di , d j ) Rij2 R 2
P. Loch
U of Arizona
March 09, 2010
Recursive Recombination
25
Motivated by gluon splitting
function
QCD branching happens all the
time
Attempt to undo parton
fragmentation
Pair with strongest divergence
likely belongs together
kT/Durham, first used in e+eCatani, Dokshitzer, Olsson,
Turnock & Webber 1991
dk j  M
2
g gi g j
(E j
Ei , ij
(k j )
2 sC A

dE j
d ij
min(Ei , E j )  ij
1)
Distance between all particles i and j
yij 
2min(Ei2 , E 2j )(1  cos ij )
Q2
yij  ycut  combine i and j , else stop
Drop normalization to Q2 (not fixed in pp)
yij  dij  min(di , d j )Rij2 , di , j  pT2i , j
Longitudinal invariant version
for hadron colliders
Rij2  (yi  y j )2  (i   j )2
Transverse momentum instead d  d  combine i and j , else stop
ij
cut
of energy
Catani, Dokshitzer, Seymour & (exclusive kT)
Webber 1993
Inclusive longitudinal invariant clustering
S.D. Ellis & D. Soper 1993
Valid at all orders!
dij  min(di , d j ) Rij2 R 2
P. Loch
U of Arizona
March 09, 2010
Recursive Recombination
26
Motivated by gluon splitting
function
QCD branching happens all the
time
Attempt to undo parton
fragmentation
Pair with strongest divergence
likely belongs together
kT/Durham, first used in e+eCatani, Dokshitzer, Olsson,
Turnock & Webber 1991
dk j  M
2
g gi g j
(E j
Ei , ij
(k j )
2 sC A

dE j
d ij
min(Ei , E j )  ij
1)
Distance between all particles i and j
yij 
2min(Ei2 , E 2j )(1  cos ij )
Q2
yij  ycut  combine i and j , else stop
Drop normalization to Q2 (not fixed in pp)
yij  dij  min(di , d j )Rij2 , di , j  pT2i , j
Longitudinal invariant version
for hadron colliders
Rij2  (yi  y j )2  (i   j )2
Transverse momentum instead d  d  combine i and j , else stop
ij
cut
of energy
Catani, Dokshitzer, Seymour & (exclusive kT)
Webber 1993
Inclusive longitudinal invariant clustering
S.D. Ellis & D. Soper 1993
Valid at all orders!
dij  min(di , d j ) Rij2 R 2
P. Loch
U of Arizona
March 09, 2010
Recursive Recombination
27
Motivated by gluon splitting
function
QCD branching happens all the
time
Attempt to undo parton
fragmentation
Pair with strongest divergence
likely belongs together
kT/Durham, first used in e+eCatani, Dokshitzer, Olsson,
Turnock & Webber 1991
dk j  M
2
g gi g j
(E j
Ei , ij
(k j )
2 sC A

dE j
d ij
min(Ei , E j )  ij
1)
Distance between all particles i and j
yij 
2min(Ei2 , E 2j )(1  cos ij )
Q2
yij  ycut  combine i and j , else stop
Drop normalization to Q2 (not fixed in pp)
yij  dij  min(di , d j )Rij2 , di , j  pT2i , j
Longitudinal invariant version
for hadron colliders
Rij2  (yi  y j )2  (i   j )2
Transverse momentum instead d  d  combine i and j , else stop
ij
cut
of energy
Catani, Dokshitzer, Seymour & (exclusive kT)
Webber 1993
Inclusive longitudinal invariant clustering
S.D. Ellis & D. Soper 1993
Valid at all orders!
dij  min(di , d j ) Rij2 R 2
kT –like Algorithms
28
Classic procedure
Calculate all distances dji for
list of particles
Uses distance parameter
P. Loch
U of Arizona
March 09, 2010
Inclusive longitudinal invariant clustering
dij  min(di , d j ) Rij2 R 2
di  pT2i
Calculate di for all particles
Uses pT
If minimum of both lists is a
dij, combine i and j and add
to list
Remove i and j, of course
If minimum is a di, call i a
jet and remove from list
Alternatives
Recalculate all distances and
Cambridge/Aachen clustering
continue all particles are
Uses angular distances only
removed or called a jet
Clustering sequence follows jet
Features
Clustering sequence is
ordered in kT
Follows jet structure
structure
Anti-kT clustering
No particular ordering,
sequence not meaningful
kT –like Algorithms
29
Classic procedure
Calculate all distances dji for
list of particles
Uses distance parameter
Calculate di for all particles
Uses pT
If minimum of both lists is a
dij, combine i and j and add
to list
P. Loch
U of Arizona
March 09, 2010
Inclusive longitudinal invariant clustering
dij  min(di , d j ) Rij2 R 2
di  pT2in
Cambridge/Aachen (n  0)
cluster smallest dij first until dij >1
Remove i and j, of course
If minimum is a di, call i a
jet and remove from list
Alternatives
Recalculate all distances and
Cambridge/Aachen clustering
continue all particles are
Uses angular distances only
removed or called a jet
Clustering sequence follows jet
Features
Clustering sequence is
ordered in kT
Follows jet structure
structure
Anti-kT clustering
No particular ordering,
sequence not meaningful
kT –like Algorithms
30
Classic procedure
Calculate all distances dji for
list of particles
Uses distance parameter
Calculate di for all particles
Uses pT
If minimum of both lists is a
dij, combine i and j and add
to list
P. Loch
U of Arizona
March 09, 2010
Inclusive longitudinal invariant clustering
dij  min(di , d j ) Rij2 R 2
di  pT2in
Cambridge/Aachen (n  0)
cluster smallest dij first until dij >1
Anti-kT (n  1)
follow classic algorithm
Remove i and j, of course
If minimum is a di, call i a
jet and remove from list
Alternatives
Recalculate all distances and
Cambridge/Aachen clustering
continue all particles are
Uses angular distances only
removed or called a jet
Clustering sequence follows jet
Features
Clustering sequence is
ordered in kT
Follows jet structure
structure
Anti-kT clustering
No particular ordering,
sequence not meaningful
kT Examples
31
kT, n=1
Anti-kT, n=-1
P. Loch
U of Arizona
March 09, 2010
Cambridge/Aachen, n=0
kT Examples
32
kT, n=1
Anti-kT, n=-1
P. Loch
U of Arizona
March 09, 2010
Cambridge/Aachen, n=0
kT Examples
33
kT, n=1
Anti-kT, n=-1
P. Loch
U of Arizona
March 09, 2010
Cambridge/Aachen, n=0
kT Examples
34
kT, n=1
Anti-kT, n=-1
P. Loch
U of Arizona
March 09, 2010
Cambridge/Aachen, n=0
kT Examples
35
kT, n=1
Anti-kT, n=-1
P. Loch
U of Arizona
March 09, 2010
Cambridge/Aachen, n=0
kT Examples
36
kT, n=1
Anti-kT, n=-1
P. Loch
U of Arizona
March 09, 2010
Cambridge/Aachen, n=0
37
Recursive Recombination Algorithms
P. Loch
U of Arizona
March 09, 2010
38
Recursive Recombination Algorithms
P. Loch
U of Arizona
March 09, 2010
39
Recursive Recombination Algortihms
P. Loch
U of Arizona
March 09, 2010
40
Recursive Recombination Algortihms
P. Loch
U of Arizona
March 09, 2010
41
Recursive Recombination Algorithms
P. Loch
U of Arizona
March 09, 2010
42
Recursive Recombination Algorithms
P. Loch
U of Arizona
March 09, 2010
43
Recursive Recombination Algorithms
P. Loch
U of Arizona
March 09, 2010
44
Recursive Recombination Algorithms
P. Loch
U of Arizona
March 09, 2010
45
Recursive Recombination Algorithms
P. Loch
U of Arizona
March 09, 2010
46
Recursive Recombination Algorithms
P. Loch
U of Arizona
March 09, 2010