Collider physics II: Jets 1 Tuesday, September 11, 12
Two aspects of new developments • Better QCD jet. - Smarter jet algorithm. - Noise suppression with jet grooming. • Jet substructure. - Boosted top. - Higgs. Boston Jet Workshop: http://jets.physics.harvard.edu/workshop/Main.html Northwest Terascale workshop http://www.physics.uoregon.edu/~soper/Jets2011/talks.html Boost 2011, May, 23-27, Princeton. http://boost2011.org Boost 2012, July, 23-27, Valencia, Spain. http://ific.uv.es/boost2012/ 2 Tuesday, September 11, 12
Want to play with it? - Parton level Signal and background: Madgraph, Alpgen, ... - ME+PS matching, UE, Pileup: Pythia, Herwig, Sherpa, ... - Some detector effect, in particular, granularity 0.1x0.1 PGS, Delphes, “by hand”. - Jet tools. Fastjet. http://www.lpthe.jussieu.fr/~salam/fastjet/ SpartyJet http://projects.hepforge.org/spartyjet/ 3 Tuesday, September 11, 12
The importance of jets: - “Everywhere” at hadron colliders. - Present in (almost) all new physics signals. Many of them only have hadronic channels. jet jet jet ¯ q q ¯ q q ∗ ˜ ˜ g q ∗ ˜ .... ... ˜ q .... ... ˜ g ˜ q q jet ¯ q q jet jet 4 Tuesday, September 11, 12
Jet look likes - When produced at TeV-scale energies, they have a large boost. q, ... b q ... Z W ± top q ... W ± q, ... ¯ q � ... q � ... boost q, ... b q, ... q, ... ¯ q ... q � q � , ... Z W ± top Jets with substructure. Challenge: distinguishing them from QCD jets (q and g). 5 Tuesday, September 11, 12
Need new jet tools for the LHC. - More energetic, bigger, jet at the LHC. LHC jet: 50 GeV - several TeV Tevatron jet: 50 - 100s GeV • Much higher “noise” level at the LHC. - LHC: 10-100 GeV / rapidity - Tevatron: 2-10 GeV / rapidity 6 Tuesday, September 11, 12
Hadron collision Sketch of an event Drawing: F. Krauss 7 Tuesday, September 11, 12
Why can we calculate at all? - Perturbatively, we can only calculate with quark and gluon in hard collisions. - Factorization. - IRC safety, need proper choice of observable. Soft or collinear radiation should not be able to induce “large” changes in the observable. Otherwise, we cannot compare calculation with observables. 8 Tuesday, September 11, 12
Factorization: intuition proton 9 Tuesday, September 11, 12
Factorization: intuition Hard interaction time (distance) scale Q -1 proton 9 Tuesday, September 11, 12
Factorization: intuition Hard interaction time (distance) scale Q -1 proton “talking” to the rest of the proton time(distance) scale m proton-1 9 Tuesday, September 11, 12
Factorization: intuition Hard interaction time (distance) scale Q -1 proton If Q -1 ≪ m proton-1 (hard interaction) Two processes should not affect each other → Factorization! “talking” to the rest of the proton time(distance) scale m proton-1 9 Tuesday, September 11, 12
Factorization: intuition Hard interaction time (distance) scale Q -1 proton If Q -1 ≪ m proton-1 (hard interaction) Two processes should not affect each other → Factorization! A similar story for final states fragmentation, q,g ⇒ hadrons (pion, K...) “talking” to the rest of the proton time(distance) scale m proton-1 9 Tuesday, September 11, 12
Factorization - Schematics of production at hadron colliders. 2 ? × phase-space matrix elements Threshold Parton densities Partonic cross section 10 Tuesday, September 11, 12
Hadron collision. Sketch of an event Hard interaction, gg ⇒ g h t tbar ⇒ h t tbar decay PDF PDF 11 Tuesday, September 11, 12
Hadron collision Sketch of an event Clusters of hadronic energy final state object: jet p jet = Σ p of constituents Inclusive: independent of final states, just energy PDF PDF 12 Tuesday, September 11, 12
Hadron collision Sketch of an event Clusters of hadronic energy final state object: jet p jet = Σ p of constituents Inclusive: independent of final states, just energy Very important: need p jet ≈ p parton Can use parton level calculation to predict jet properties PDF PDF 12 Tuesday, September 11, 12
Hadron collision Sketch of an event soft, long distance interactions Fragmentation (q,g ⇒ hadrons) ... PDF PDF Initial state radiation 13 Tuesday, September 11, 12
Factorization σ = B 1 ⊗ B 2 ⊗ H ⊗ J 1 ⊗ J 2 ⊗ S S J 1 B 1 = dx 1 f(x 1 ), B 2 = dx 2 f(x 2 ). H = H ⊗ J 1 ⊗ J 2 ⊗ S B 2 B 1 J 2 14 Tuesday, September 11, 12
Well tested. ATLAS-CONF-2011-043, 7 TeV, 2.43 pb -1 5 5 [pb] [pb] 10 10 6 6 [pb/GeV] [pb/GeV] 10 10 ATLAS Preliminary ATLAS Preliminary 4 4 ! ! 10 10 5 5 " -1 R=0.4, L dt=2.43 pb 10 10 Data ( s =7 TeV)+syst. 3 3 10 10 4 4 T T ALPGEN+HERWIG AUET1 × 1.11 10 10 /d p /d p PYTHIA AMBT1 × 0.65 2 2 10 10 ALPGEN+PYTHIA MC09’ × 1.22 ! ! 3 3 10 10 N 2 # d d jets " -1 10 10 R=0.4, L dt=2.43 pb 2 2 Data ( s =7 TeV)+syst. 10 10 1 1 ATLAS-CONF-2011-043 ALPGEN+HERWIG AUET1 1.11 × 10 10 PYTHIA AMBT1 0.65 -1 -1 × 10 10 ALPGEN+PYTHIA MC09’ 1.22 × 1.5 1.5 MC/Data MC/Data 1.5 1.5 MC/Data MC/Data 100 100 200 200 300 300 400 400 500 500 600 600 700 700 800 800 2 2 3 3 4 4 5 5 6 6 1 1 1 1 0.5 0.5 0.5 0.5 100 200 300 400 500 600 700 800 100 200 300 400 500 600 700 800 2 2 3 3 4 4 5 5 6 6 p p (leading jet) [GeV] (leading jet) [GeV] Inclusive Jet Multiplicity Inclusive Jet Multiplicity T T 15 Tuesday, September 11, 12
Why is it hard? Tuesday, September 11, 12
Why is it hard? Tuesday, September 11, 12
Why is it hard? Tuesday, September 11, 12
Why is it hard? jet jet jet jet Tuesday, September 11, 12
Why is it hard? jet jet “beam” Multiple interaction, underlying events, pile-up jet jet Tuesday, September 11, 12
Why is it hard? jet jet “beam” Multiple interaction, underlying events, pile-up jet jet a. Overlapping jets. Tuesday, September 11, 12
Why is it hard? jet jet “beam” Multiple interaction, ISR (beam) clustered underlying events, pile-up jet jet a. Overlapping jets. Tuesday, September 11, 12
Why is it hard? jet jet Part of the beam? “beam” Multiple interaction, ISR (beam) clustered underlying events, pile-up jet jet a. Overlapping jets. Tuesday, September 11, 12
Why is it hard? Proper choice of cone size? jet jet Part of the beam? “beam” Multiple interaction, ISR (beam) clustered underlying events, pile-up jet jet a. Overlapping jets. Tuesday, September 11, 12
Why is it hard? Proper choice of cone size? jet jet Part of the beam? “beam” Multiple interaction, ISR (beam) clustered underlying events, pile-up jet jet a. Overlapping jets. • To best preserve we would like to: • Use “smart” jet shapes. • Reduce “noise”. Tuesday, September 11, 12
What do jets look like? 17 Tuesday, September 11, 12
Parton splitting, collinear limit Relevant kinematical variables t = p 2 M = ( p A + p B ) 2 p A z = E A θ p M E M p B φ The main feature of radiation can be seen by considering the Collinear limit: 휃 ⇒ 0, t ≪ E M2 Tuesday, September 11, 12
Collinear factorization n − 2 n − 2 collinear limit n − 1 n − 1 A A A M M B B B 1 1 2 2 |M n +1 | 2 = |M ( p 1 , ...p A , p B ) | 2 |M n ( p 1 , ...p M ) | 2 |M ( p M → p A p B ) | 2 × dt α S |M n +1 | 2 d Π n +1 ' |M n | 2 d Π n 2 π P ( z ) dzd φ t Tuesday, September 11, 12
Collinear factorization n − 2 n − 2 collinear limit n − 1 n − 1 A A A M M B B B 1 1 2 2 |M n +1 | 2 = |M ( p 1 , ...p A , p B ) | 2 |M n ( p 1 , ...p M ) | 2 |M ( p M → p A p B ) | 2 × dt α S |M n +1 | 2 d Π n +1 ' |M n | 2 d Π n 2 π P ( z ) dzd φ t collinear singularity: t ⇒ 0 Tuesday, September 11, 12
Collinear factorization n − 2 n − 2 collinear limit n − 1 n − 1 A A A M M B B B 1 1 2 2 |M n +1 | 2 = |M ( p 1 , ...p A , p B ) | 2 |M n ( p 1 , ...p M ) | 2 |M ( p M → p A p B ) | 2 × dt α S |M n +1 | 2 d Π n +1 ' |M n | 2 d Π n 2 π P ( z ) dzd φ t P ( z ) ∝ |M ( p M → p A p B ) | 2 collinear singularity: t ⇒ 0 Splitting function IR singularity: z ⇒ 0, 1 Tuesday, September 11, 12
Splitting function, IR singular as z ⇒ 0, 1 1 + z 2 P q → qg ( z ) = C F 1 − z , � 1 − z � z P g → gg ( z ) = C A + 1 − z + z (1 − z ) , z z 2 + (1 − z ) 2 � � P g → q ¯ q ( z ) = T R , Combining with dt α S |M n +1 | 2 d Π n +1 ' |M n | 2 d Π n 2 π P ( z ) dzd φ t Radiation wants to be collinear and soft Tuesday, September 11, 12
Shape of a jet: parton shower • From the initial parton, a jet is built up by many radiations (splittings). Q M2 = t Prefers collinear radiation P ~ ( z) -1 prefers soft radiation QCD jet: a cluster of radiation a) relatively soft b) close to the direction of P M c) approximately symmetrical around P M 21 Tuesday, September 11, 12
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