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Angular Correlations in High Energy Collisions Andrew Larkoski SLAC with Martin Jankowiak 1104.1646, ???? GGI Interpreting LHC Discoveries, November 7, 2011 What Defines QCD? Approximately scale-invariant non-Abelian gauge theory

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SLIDE 1

Angular Correlations in High Energy Collisions

Andrew Larkoski SLAC with Martin Jankowiak 1104.1646, ????

GGI “Interpreting LHC Discoveries”, November 7, 2011

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SLIDE 2

What Defines QCD?

  • Approximately scale-invariant non-Abelian

gauge theory at high energies

2

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SLIDE 3

What Defines QCD?

  • Approximately scale-invariant non-Abelian

gauge theory at high energies

  • Consequences:
  • Soft & Collinear singularities

3

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SLIDE 4

What Defines QCD?

  • Approximately scale-invariant non-Abelian

gauge theory at high energies

  • Consequences:
  • Collimated, high energy jets

4

Jet

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SLIDE 5

What Defines QCD?

  • Approximately scale-invariant non-Abelian

gauge theory at high energies

  • Consequences:
  • Anomalous dimensions
  • “T

extbook”:

  • “Fractal Phase Space”

5

  • G. Gustafson, A. Nilsson / QCD cascades

107

L

(b)

  • y

I

1[
  • Fig. 1. (a) The phase space available for a gluon emitted by a high energy Cl~ system is a triangular

region in the (y, K)-plane (K = in k ~//12; L = In s/A 2). (b) If one gluon is emitted at (y i, K~) the phase space for a second (softer) gluon is represented by the area of this folded surface. (c) Each emitted gluon increases the phase space for the softer gluons. The total gluonic phase space can be described by this multi-faceted surface. The length of the baseline corresponds to the quantity A(L), the length of the dashed line to A(L, K).

To study the hard perturbative phase we use two important tools, which we shortly describe below: (i) The dipole formulation of QCD cascades [3]; (ii) An infrared stable measure on parton states related to the hadronic multiplicity [4].

(i) Dipole

  • formulation. A high-energy q~-system radiates gluons according to

the dipole formula 3a~ dk 2 dn = 4rr2 k2 dyd~,. (1)

..k

Here the phase space available is given by the relation

lln(s/k~)

[Yl-<3

(2)

which corresponds to the triangular region in a y - In k 2 diagram as shown in fig.

  • la. The rapidity range available, Ay, is given by ln(s/k~).

if two gluons are emitted, then the distribution of the hardest gluon is described by eq. (1), while the distribution of the second, softer, gluon corresponds to two dipoles, one stretched between the quark and the first gluon, and the second between this gluon and the antiquark [5].

Gustafson, Nilsson 1991; Bjorken 1992

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SLIDE 6

What Defines QCD?

  • Our Goal: Define an observable that can

distinguish between approximately scale invariant objects and objects that have an intrinsic, high energy scale

  • This observable will be a function which

quantifies the scaling properties of the system

  • The argument of the function is a

resolution parameter

6

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SLIDE 7

Defining an Observable

  • Requirements from theory:
  • Infrared and Collinear safety
  • Want to compute in pert. theory

7

+ + = finite

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SLIDE 8

Defining an Observable

  • Requirements from theory:
  • Scale invariant ~ constant
  • Want to extract a dimension
  • Can do this by defining an angular

correlation between constituents

8

Increasing resolution

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SLIDE 9

Defining an Observable

  • Requirements from theory:
  • Correlation should be z-boost invariant
  • Jet mass!
  • Angular Correlation Function (ACF)

9

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SLIDE 10

Angular Correlation Function

  • Expectations
  • ACF in QCD ~ R2

10

R

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SLIDE 11

Angular Correlation Function

  • Expectations
  • ACF in QCD ~ R2

11

R

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SLIDE 12

Angular Correlation Function

  • Expectations
  • ACF in QCD ~ R2

12

R

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SLIDE 13

Angular Correlation Function

  • Expectations
  • ACF for heavy particle jet will have “cliffs”

at characteristic values of R

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R

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SLIDE 14

Angular Correlation Function

  • Expectations
  • ACF for heavy particle jet will have “cliffs”

at characteristic values of R

14

R = R*

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SLIDE 15

Angular Correlation Function

  • Expectations
  • ACF for heavy particle jet will have “cliffs”

at characteristic values of R

15

R

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SLIDE 16

Angular Structure Function

  • How to extract a dimension:
  • “Standard way”:
  • Problems: limiting procedure, only

defined in unphysical/unreachable limit

  • No simple way to see structure

16

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SLIDE 17

Angular Structure Function

  • How to extract a dimension:
  • Better: take a derivative
  • Benefits: Defined for all R, cliffs in ACF

manifest themselves as peaks in derivative

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SLIDE 18

Angular Structure Function

  • Define angular structure function (ASF):
  • Structure in ASF is ~uniform in R for QCD

18

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SLIDE 19

Angular Structure Function

  • Delta-function is noisy in finite data
  • Smooth ASF by replacing:
  • K is taken to be a smooth gaussian kernel:

19

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SLIDE 20

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Top Tagging

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SLIDE 21

Jet Substructure

  • Problem: Boosted stuff at LHC doesn’t

necessarily lead to distinct jets as it did in lower energy experiments

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SLIDE 22

Jet Substructure

  • Problem: Boosted stuff at LHC doesn’t

necessarily lead to distinct jets as it did in lower energy experiments

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4 well-separated jets

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SLIDE 23

Jet Substructure

  • Problem: Boosted stuff at LHC doesn’t

necessarily lead to distinct jets as it did in lower energy experiments

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Combinatoric problem: how to pair them?

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SLIDE 24

Jet Substructure

  • Problem: Boosted stuff at LHC doesn’t

necessarily lead to distinct jets as it did in lower energy experiments

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Combinatoric problem: how to pair them?

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SLIDE 25

Jet Substructure

  • Problem: Boosted stuff at LHC doesn’t

necessarily lead to distinct jets as it did in lower energy experiments

25

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SLIDE 26

Jet Substructure

  • Problem: Boosted stuff at LHC doesn’t

necessarily lead to distinct jets as it did in lower energy experiments

26

  • Boost removes

combinatoric problem

  • Jets are no longer

widely separated

  • Study inside of “fat” jets
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SLIDE 27

Jet Substructure

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SLIDE 28

Jet Substructure

  • Declustering
  • Define a branching tree with a sequential

jet algorithm

  • kT-type sequential jet algorithm
  • 1) Compute
  • n = 1: kT
  • n = 0: Cambridge-Aachen
  • n = -1: anti-kT

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Ellis, Soper Catani, et al.

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SLIDE 29
  • kT-type sequential jet algorithm
  • 2) Merge closest pair of particles

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Jet Substructure

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SLIDE 30
  • kT-type sequential jet algorithm
  • 2) Merge closest pair of particles

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Jet Substructure

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SLIDE 31
  • kT-type sequential jet algorithm
  • 2) Merge closest pair of particles

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Jet Substructure

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SLIDE 32
  • kT-type sequential jet algorithm
  • 2) Merge closest pair of particles

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Jet Substructure

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SLIDE 33
  • kT-type sequential jet algorithm
  • 2) Merge closest pair of particles

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Jet Substructure

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SLIDE 34
  • kT-type sequential jet algorithm
  • 3) Continue until no pair of particles is

close

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Jet

Jet Substructure

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SLIDE 35
  • Idea: Clustering procedure defines a

branching tree!

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Jet Substructure

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SLIDE 36
  • Idea: Clustering procedure defines a

branching tree!

36

  • QCD: branches of small

mass, small angle, low energy

  • Heavy particle: some

branches with large mass, large energy

  • Isolate/remove QCD

branches

Courtesy Jon Walsh

Jet Substructure

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SLIDE 37

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“Jet Substructure Without Trees”

  • Use ACF and ASF to extract angular and

mass scales directly from constituents without reference to any clustering tree

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SLIDE 38
  • Cliffs in = separation of hard subjets
  • for a top quark jet

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G(R) G(R)

0.0 0.5 1.0 1.5 2.0 2.5 3.0 0.0 0.2 0.4 0.6 0.8 1.0 R R

Why the ASF?

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SLIDE 39
  • Cliffs in = separation of hard subjets
  • Which correspond to something physical?

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0.0 0.5 1.0 1.5 2.0 2.5 3.0 0.0 0.2 0.4 0.6 0.8 1.0 R R

G(R)

Why the ASF?

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SLIDE 40

40

1.5 1.0 0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 Η Φ R3 1.5 R1 0.67 R2

  • .

9 2 0.0 0.5 1.0 1.5 2.0 2.5 3.0 5 10 15 R R

Top Jet

Why the ASF?

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SLIDE 41

41

QCD Jet

1.5 1.0 0.5 0.0 0.5 0.0 0.5 1.0 1.5 2.0 Η Φ R1 1.12 0.0 0.5 1.0 1.5 2.0 1 2 3 4 R R

Why the ASF?

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SLIDE 42

Prominence

  • picks out physical peaks beautifully!
  • How do we define interesting peaks?
  • By height? Why?

42

∆G(R)

Is the little bump interesting?

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SLIDE 43

Prominence

  • Disclaimer: The following slides were made

for an audience in the US. I haven’t been able to find an analogy for Europeans.

43

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SLIDE 44

Prominence

44

  • Quiz: What is the highest mountain in the

contiguous US?

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SLIDE 45

Prominence

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  • Quiz: What is the highest mountain in the

contiguous US?

  • Mt. Whitney, CA
  • What is the most prominent mountain in

the contiguous US?

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SLIDE 46

Prominence

46

  • Quiz: What is the highest mountain in the

contiguous US?

  • Mt. Whitney, CA
  • What is the most prominent mountain in

the contiguous US?

  • Mt. Rainier, WA
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SLIDE 47

Prominence

  • Proposition: Define peaks by their

prominence

  • Prominence = amount peak sticks out

above ambient background

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Prominence

  • f little bump

is tiny!

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SLIDE 48

Prominence

  • Possible double counting of angular scales
  • Defining interesting peaks by prominence

removes double counting ambiguity

48

R

R

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SLIDE 49

Defining Observables

  • IRC safe observables from :

49

Η 0.0 0.5 1.0 1.5 2.0 2.5 3.0 5 10 15 R

∆G(R)

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SLIDE 50

50

  • Entire curve is IRC safe
  • Location of peaks in R

Η 0.0 0.5 1.0 1.5 2.0 2.5 3.0 5 10 15 R

R1 R2 R3

  • IRC safe observables from :

∆G(R)

Defining Observables

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SLIDE 51

Η 0.0 0.5 1.0 1.5 2.0 2.5 3.0 5 10 15 R

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R1 R2 R3

  • Location of peaks in R
  • Height of peaks

P1 P2 P3

  • IRC safe observables from :

∆G(R)

Defining Observables

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SLIDE 52

52

  • Location of peaks in R
  • Height of peaks
  • Number of peaks

Η 0.0 0.5 1.0 1.5 2.0 2.5 3.0 5 10 15 R

R1 R2 R3 P1 P2 P3

  • IRC safe observables from :

∆G(R)

Defining Observables

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SLIDE 53
  • Observables for dR = 0.06, min prom =

4.0, npeaks = 3

53 0.4 0.8 1.2 R1 0.05 0.10 0.15 0.20 0.25 0.30 0.5 1 1.5 R2 0.05 0.10 0.15 0.20 0.25 0.30 0.5 1 1.5 2 R3 0.02 0.04 0.06 0.08 0.10 0.12 0.14 25 50 75 100 m1 0.05 0.10 0.15 0.20 50 100 150 m2 0.05 0.10 0.15 0.20 80 160 240 m3 0.05 0.10 0.15

Top QCD

Top Tagger

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SLIDE 54

Top Tagger

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  • Correlation of

separation of subjets and their invariant mass

  • Top: m ~ R
  • QCD: m, R

uncorrelated Top QCD

0.0 0.5 1.0 1.5 2.0 50 100 150 200 R2 m2

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SLIDE 55
  • Comparison to other top taggers

55

0.1 1.0 10 100 10 20 30 40 50 60 70

ΕS ΕB

  • 1

1

Hopkins CMS Pruning ATLAS Thaler/Wang

Our Tagger Τ!Τ"

Top Tagger