Introduction to Hadronic Final State Reconstruction in Collider Experiments (Part VI)

Introduction to Hadronic Final State Reconstruction in Collider Experiments

(Part VI)

Peter LochUniversity of Arizona

Tucson, ArizonaUSA

2P. Loch

U of ArizonaMarch 09, 2010

Theoretical Requirements For Jet Finders

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 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 safety 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 Et ordering of seeds)

3P. Loch

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

4P. Loch

2 2coneR R

5P. Loch

2 2cone

(first protojet)R R

6P. Loch

2 2coneR R

7P. Loch

2 2cone

(second protojet)R R

8P. Loch

2 2cone

(two jets)R R

9P. Loch

2 2coneR R

10P. Loch

2 2coneR R

11P. Loch

2 2coneR R

12P. Loch

2 2cone

(first protojet)R R

13P. Loch

2 2coneR R

14P. Loch

2 2coneR R

15P. Loch

2 2coneR R

16P. Loch

2 2coneR R

17P. Loch

2 2cone

18P. Loch

2 2cone

19P. Loch

2 2cone

(one jet)R R

20P. Loch

2 2cone

(one jet)R R not an infrared safe algorithm!

21P. Loch

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)

2nd cone(not stable)

3rd cone(stable)

original seed lost for jets!

22P. Loch

Other problems with iterative cone finders: “Dark” tower problem

Original seed moves out of cone Significant energy lost for jets

23P. Loch

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

24P. Loch

Recursive Recombination

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+e-

Catani, Dokshitzer, Olsson, Turnock & Webber 1991

Longitudinal invariant version for hadron colliders Transverse momentum instead of

energy Catani, Dokshitzer, Seymour &

Webber 1993 S.D. Ellis & D. Soper 1993

Valid at all orders!

( ), )

( , 1)

ijs Aj g g g j

dE dCE E

dk M k

2 2, T ,

combine and , else st

Distance between all particles and

Drop normalization to (not fixed in pp)

2min( , )(1 cos )

min( , ) ,

i j ijij

ij ij i j ij i j i j

ij i j i

y d d d R d p

Inclusive longitu

combine and , else stop

di(exclusive

nal invari kT)

ij i j ij

ijd d i

d d d R R

25P. Loch

( ), )

( , 1)

ijs Aj g g g j

dE dCE E

dk M k

2 2, T ,

2min( , )(1 cos )

min( , ) ,

i j ijij

ij i j i

y d d d R d p

Inclusive longitu

di(exclusive

nal invari kT)

ij i j ij

ijd d i

d d d R R

26P. Loch

( ), )

( , 1)

ijs Aj g g g j

dE dCE E

dk M k

2 2, T ,

2min( , )(1 cos )

min( , ) ,

i j ijij

ij i j i

y d d d R d p

Inclusive longitu

di(exclusive

nal invari kT)

ij i j ij

ijd d i

d d d R R

27P. Loch

( ), )

( , 1)

ijs Aj g g g j

dE dCE E

dk M k

2 2, T ,

2min( , )(1 cos )

min( , ) ,

i j ijij

ij i j i

y d d d R d p

Inclusive longitu

di(exclusive

nal invari kT)

ij i j ij

ijd d i

d d d R R

28P. Loch

kT –like Algorithms

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 Remove i and j, of course

If minimum is a di, call i a jet and remove from list

Recalculate all distances and continue all particles are removed or called a jet

Features Clustering sequence is ordered in

kT Follows jet structure

Alternatives Cambridge/Aachen clustering

Uses angular distances only Clustering sequence follows jet

structure Anti-kT clustering

No particular ordering, sequence not meaningful

Inclusive longitudinal invariant clu

stering

( , )ij i j ij

d d d R R

29P. Loch

min( , )

Inclusive longitudinal invariant clustering

Cambridge/Aachen (cluster smallest first until >1

ij i j ij

d d d R

30P. Loch

Inclusive longitudinal invariant clustering

Cambridge/Aachcluster smallest first until >1

en ( 0)

Anti-kfollow classic algorith

min( ,

ij i j ij

ij ijd d

31P. Loch

kT Examples

kT, n=1 Anti-kT, n=-1 Cambridge/Aachen, n=0

32P. Loch

kT Examples

33P. Loch

kT Examples

34P. Loch

kT Examples

35P. Loch

kT Examples

36P. Loch

kT Examples

37P. Loch

Recursive Recombination Algorithms

38P. Loch

39P. Loch

Recursive Recombination Algortihms

40P. Loch

Recursive Recombination Algortihms

41P. Loch

42P. Loch

43P. Loch

44P. Loch

45P. Loch

46P. Loch

Introduction to Hadronic Final State Reconstruction in Collider Experiments (Part VI)

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