Jet Physics. Yazid Delenda. 1st Jijel Meeting on Theoretical Physics. Jijel, October 29-31, University Batna 1

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1 Jet Physics Yazid Delenda University Batna 1 1st Jijel Meeting on Theoretical Physics Quantum Mechanics, Gravitation and Particle Physics Jijel, October 29-31, ⵜ ⴰ ⵙ ⴷⴰ ⵡⵉ ⵜ ⵏ ⵜ ⴱⴰ ⵜ ⴻ ⵏ ⵜ U NIV ERSI T E BATN A

2 Introduction to jets What are jets? Definition: Jets are collimated sprays of hadrons A jet is the detector picture of the parton that initiated it (to a good approximation) (1 st Jijel Meeting on Theor. Phys.) Jet Physics Y. Delenda 2 / 32

3 Introduction to jets Jets play central role in new physics searches Papers by ATLAS collaboration (1 st Jijel Meeting on Theor. Phys.) Jet Physics Y. Delenda 3 / 32

4 Introduction to jets Jets play central role in new physics searches Papers by ATLAS collaboration which cite the anti-k t jet clustering algorithm, a widely used jet algorithm [22%] (1 st Jijel Meeting on Theor. Phys.) Jet Physics Y. Delenda 4 / 32

5 Introduction to jets Rapidity definition Is LHC a CoM frame? In hadron colliders, collisions are not symmetric (Lab frame CoM frame). Need to define boost-invariant momentum coordinates (1 st Jijel Meeting on Theor. Phys.) Jet Physics Y. Delenda 5 / 32

6 Introduction to jets Rapidity definition Rapidity Lorentz transformations for E & p z along z axis with speed β = tanh ϱ } E = E cosh ϱ + p z sinh ϱ p z = p z cosh ϱ + E E + p z = E + p z sinh ϱ E p z E p e 2ϱ z Define rapidity: y 1 2 ln E + p z E p z Then y y = y + ϱ, with ϱ constant. Rapidity differences y are boost-invariant. Then for all particles in an event, can shift rapidities by same constant, and consider rapidity as boost-invariant. (1 st Jijel Meeting on Theor. Phys.) Jet Physics Y. Delenda 6 / 32

7 Introduction to jets Rapidity definition Rapidity Lorentz transformations for E & p z along z axis with speed β = tanh ϱ } E = E cosh ϱ + p z sinh ϱ p z = p z cosh ϱ + E E + p z = E + p z sinh ϱ E p z E p e 2ϱ z Define rapidity: y 1 2 ln E + p z E p z Then y y = y + ϱ, with ϱ constant. Rapidity differences y are boost-invariant. Then for all particles in an event, can shift rapidities by same constant, and consider rapidity as boost-invariant. (1 st Jijel Meeting on Theor. Phys.) Jet Physics Y. Delenda 6 / 32

8 Introduction to jets Rapidity definition Pseudo rapidity For massless particles (or very energetic particles), we have p E Then Define pseudo-rapidity: y = 1 2 ln 1 + cos θ 1 cos θ = ln cot θ 2 η = ln cot θ 2 which equals rapidity in the massless (or high energy) limit. Useful quantity for experiment. (1 st Jijel Meeting on Theor. Phys.) Jet Physics Y. Delenda 7 / 32

9 Introduction to jets Rapidity definition Pseudo-rapidity vs θ (1 st Jijel Meeting on Theor. Phys.) Jet Physics Y. Delenda 8 / 32

10 Introduction to jets Rapidity definition Pseudo-rapidity vs θ η = 1 θ = 130 η =0 θ =90 η =1 θ =40 φ η =2, θ =15 η =3, θ =6 η =4, θ =2 Schwartz, 2017, ArXiv: (1 st Jijel Meeting on Theor. Phys.) Jet Physics Y. Delenda 9 / 32

11 Introduction to jets QCD running coupling Strong coupling running The renormalised coupling constant depends on diagrams like these: QCD renormalisation group equation α s µ 2 R µ 2 R = β(α s ) = b 0 α 2 s + b 1 α 3 s + b 2 α 4 s + with b 0 = (11C A 4 T R n f )/(12π) = (33 2n f )/(12π)> 0, b 1 = (153 19n f )/(24π 2 ),... Notice First term in β function is negative (as apposed to that in QED). Thus α s runs oppositely to α EM. (1 st Jijel Meeting on Theor. Phys.) Jet Physics Y. Delenda 10 / 32

12 Introduction to jets QCD running coupling Strong coupling running At one loop α s (Q 2 ) = α s (µ 2 ) 1 + α s (µ 2 )b 0 ln(q 2 /µ 2 ) α S (Q) CMS incl. jets : α S (M ) = Z CMS R D0 inclusive jets D0 angular correlation H1 ZEUS 2 10 CMS tt cross section CMS inclusive jets 3 10 Q (GeV) (1 st Jijel Meeting on Theor. Phys.) Jet Physics Y. Delenda 11 / 32

13 Introduction to jets QCD running coupling Asymptotic freedom 2004 Nobel Prize: David Gross, H. David Politzer and Frank Wilczek for discovery of asymptotic freedom in the theory of the strong interactions. At high energy, quarks behave as free particles (perturbation theory applicable) (1 st Jijel Meeting on Theor. Phys.) Jet Physics Y. Delenda 12 / 32

14 Introduction to jets QCD running coupling Confinement But quarks/gluons not observed in particle detectors When Q Λ QCD (large time scales), then α s PT breaks. Quarks undergo a hadronization: quarks and gluons are (eventually) confined into hadrons (confinement). Hadronization (MC) Models Lund String Model Flux tube model Cluster model Independent fragmentation model (1 st Jijel Meeting on Theor. Phys.) Jet Physics Y. Delenda 13 / 32

15 Introduction to jets Hadronization What happens when quarks hadronize? Consider for example simple process in LEP e + e qq. (1 st Jijel Meeting on Theor. Phys.) Jet Physics Y. Delenda 14 / 32

16 Introduction to jets Hadronization What happens when quarks hadronize? In flux tube model we have the following picture: We get streams of hadrons in the directions of the initial q q pair: We get two jets of hadrons (1 st Jijel Meeting on Theor. Phys.) Jet Physics Y. Delenda 15 / 32

17 2 Jet production at LEP (1 st Jijel Meeting on Theor. Phys.) Jet Physics Y. Delenda 16 / 32

18 2 Jet production at LEP (1 st Jijel Meeting on Theor. Phys.) Jet Physics Y. Delenda 17 / 32

19 3 Jet event? (1 st Jijel Meeting on Theor. Phys.) Jet Physics Y. Delenda 18 / 32

20 3 Jet event? (1 st Jijel Meeting on Theor. Phys.) Jet Physics Y. Delenda 19 / 32

21 Is it 3 or 4 Jet event? (1 st Jijel Meeting on Theor. Phys.) Jet Physics Y. Delenda 20 / 32

22 Jet algorithms Need concrete definition of a jet, several are available in the market: Sequencial recombination (all CIS) k t clustering algorithm anti-k t clustering algorithm (ATLAS & CMS) Cambridge/Aachen algorithm Cone algorithms (Mostly not CIS) Mid-point cone algorithm (CMS) Iterative cone Seed-less infrared-safe cone algorithm (LHC) [CIS] (1 st Jijel Meeting on Theor. Phys.) Jet Physics Y. Delenda 21 / 32

23 Sequential Recombination Jet algorithms hadron( pairs (i, j), define their distance d ij = min k p [(ηi ti tj), kp η j ) 2 + (φ i φ j ) 2] ; hadrons i, define its beam distance d ib = k p ti R2. Find smallest of all distances, d min. If d min = d ib, object i is a jet and is removed from list. If d min = d ij, objects i and j are merged with p µ = p µ i + pµ j (other schemes available) Iterate until all objects are removed. R: jet radius (specified by user). p = 2: anti-k t algorithm [arxiv: [hep-ph]] p = +2: k t algorithm [Nucl.Phys. B406 (1993) ] p = 0: Cambridge/Aachen algorithm [hep-ph/ ] (1 st Jijel Meeting on Theor. Phys.) Jet Physics Y. Delenda 22 / 32

24 Cone-type Jet algorithms Seedless infrared-safe Cone algorithm [arxiv: [hep-ph]] Search for all stable cones of radius R (in a seedless way) Definition: Stable cone: cone pointing in same direction as 4-momentum of contents Resolve jet overlaps with split/merge procedure with overlap parameter f. An online tool for visualising impact of jet choice on dijet mass distribution (generated with Pythia) ttp:// salam/jet-quality/ FastJet: a C++ lib for implementing k t, anti-k t, SISCone, and C/A algorithms in MC event generators (1 st Jijel Meeting on Theor. Phys.) Jet Physics Y. Delenda 23 / 32

25 What algorithm, and what jet radius R? ATLAS s choice: Anti-k t with R = 0.4, 0.6 Why? required for jet energy scale calibration. HCal data does not provide 4-momentum of individual hadrons. Energy of jet is calibrated (calibration only available for specific jet radii) Problematic for theorists: we need jet radius flexibility Solution: Particle flow at CMS with PID (and Topo-clusters at ATLAS?) CMS s choice: Mainly anti-k t with R = 0.5, 0.7 Particle flow can be used to construct jets with arbitrary radii (1 st Jijel Meeting on Theor. Phys.) Jet Physics Y. Delenda 24 / 32

26 Jets at ATLAS ATLAS dijet event (1st Jijel Meeting on Theor. Phys.) Jet Physics Y. Delenda 25 / 32

27 Jets at ATLAS ATLAS multi-jet event (1 st Jijel Meeting on Theor. Phys.) Jet Physics Y. Delenda 26 / 32

28 What choice of Jet algorithm & R (for us theorists)? Choice of algorithm Should project hard partonic structure of event, without much modification from QCD effects (parton shower, hadronization). Must be infrared and collinear-safe to be able to apply PT: soft/collinear gluons shouldn t modify final-state jets. We have shown that optimal jet radii should be small in order to minimise so called non-global effects (important for observables defined in limited region of phase space) (1 st Jijel Meeting on Theor. Phys.) Jet Physics Y. Delenda 27 / 32

29 What choice of Jet algorithm & R (for us theorists)? How about choice of jet radius vs. NP effects (1 st Jijel Meeting on Theor. Phys.) Jet Physics Y. Delenda 28 / 32

30 What choice of Jet algorithm & R (for us theorists)? How about choice of jet radius vs. NP effects Small-R jets have less contamination from pile up and underlying event [ R 2 ] (1 st Jijel Meeting on Theor. Phys.) Jet Physics Y. Delenda 29 / 32

31 What choice of Jet algorithm & R (for us theorists)? (1 st Jijel Meeting on Theor. Phys.) Jet Physics Y. Delenda 30 / 32

32 What choice of Jet algorithm & R (for us theorists)? How about choice of jet radius vs. NP effects However hadronization alters energy content of a small-r jet [hadronization effects 1/R] (1 st Jijel Meeting on Theor. Phys.) Jet Physics Y. Delenda 31 / 32

33 What choice of Jet algorithm & R (for us theorists)? Jet substructure Trimming Grooming Pruning MDT Filtering Tagging (1 st Jijel Meeting on Theor. Phys.) Jet Physics Y. Delenda 32 / 32