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What is a Jet?

Stephen Ellis UW . Where I come from, Seattle, WA the answer is simple !. What is a Jet?. Summer Student Lecture Programme 2010. Here want to discuss - What is a jet at the LHC?. Again the answer is “qualitatively” simple to see -

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What is a Jet?

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  1. Stephen Ellis UW Where I come from, Seattle, WA the answer is simple ! What is a Jet? Summer Student Lecture Programme 2010

  2. Here want to discuss - What is a jet at the LHC? • Again the answer is “qualitatively” simple to see - • JET = collimated spray of hadronic “stuff” in the detector CERN S.D. Ellis 09.07.10

  3. ASIDE: Kinematics language – hadron colliders  • transverse momentum where  is polar angle wrt the beam direction (z axis), invariant under boosts along beam scalar transverse energyfor a single particle or narrow jet (M << E), • pseudorapidity (just geometry)or true rapidity a boost along beam is where •  is azimuthal angle around the beam beam  beam  CERN S.D. Ellis 09.07.10

  4. Generic Detector at Tevatron or LHC CERN S.D. Ellis 09.07.10

  5. “Unroll”  and plot energy in - plane –“Lego plot” • Again the answer is “qualitatively” simple to see - • JET = collimated spray of hadronic “stuff” in the detector But, as usual, the devil is in the DETAILS, e.g., When do we see jets? Why do we see Jets? What is a careful definition of a jet? CERN S.D. Ellis 09.07.10

  6. Q: When do we see large pT jets?A: Rarely! But they are VERY interesting! • Most (so-called Minimum Bias) events contain many SMALL pT particles and rarely large pT jets – (curl in the magnetic field) CERN S.D. Ellis 09.07.10

  7. Why do we see large pT jets? • This is a really good question! • The short answer is because of QCD • Here give only an introduction to the answer (mostly in images) • See the Lectures over the next weeks (they will answer the hard questions), especially John Terning CERN S.D. Ellis 09.07.10

  8. (Incomplete) References: (I’ll focus on concepts/images) • QCD Summary on the Web at the Particle Data Group site: http://pdg.lbl.gov/2009/reviews/rpp2009-rev-qcd.pdf • The CTEQ Handbook in Rev. Mod. Phys. Volume 67, Number 1, January 1995, (pp. 157-248) and on the Web (Version 1.1): http://www.phys.psu.edu/~cteq/#Handbook • QCD and Collider Physics, R.K. Ellis, W.J. Stirling and B.R. Webber, Camb.Monogr. Part. Phys. Nucl. Phys. Cosmol. 81 (1996) • Hard Interactions of Quarks and Gluons: A Primer for LHC Physics, J. Campbell, J. Huston and W.J. Stirling, Rept.Prog.Phys.70:89,2007, http://arxiv.org/PS_cache/hep-ph/pdf/0611/0611148v1.pdf • Jets in Hadron-Hadron Collisions , S.D. Ellis, J. Huston, K. Hatakeyama, P. Loch, M. Toennesmann, Prog. Part. Nucl. Phys. 60:484-551, 2008 , arXiv:0712.2447 CERN S.D. Ellis 09.07.10

  9. So here we go – the Fundamental Truths of the Strong Interactions! • Hadrons with strong interactions (protons, neutrons, pions,…) are composite states of “smaller” objects – the partons = quarks and gluons • Hadrons have “size” of about a fermi (fm) = 10-15 mwhich is an energy scale of order 200 MeVRecall distance ~ 1/Energy or • For interactions of this energy scale (or smaller) – nuclear physics – degrees of freedom are the hadrons CERN S.D. Ellis 09.07.10

  10. More basics: • For interactions exchanging energy >> 200 MeV – particle physics – resolve the partons inside the hadrons ( << 1 fermi) • Partons interact with each other due to “color” charge: quark = color 3 (3 colors), also 6 flavors (u,d,s,c,b,t), gluon = color 8 (8 kinds of gluons, no flavor) Quantum ChromoDynamics - QCD • Hadrons themselves are color singlets (zero color charge!) 333 = 1 (baryons) 33 = 1 (meson) CERN S.D. Ellis 09.07.10

  11. The (Classical) QCD Lagrangian Gluons couple to gluons Acting on the triplet and octet, respectively, the covariant derivative is The matrices for the fundamental (tabB) and adjoint (TCDB) representations carry the information about the Lie algebra (fBCD is the structure constant of the group) CERN S.D. Ellis 09.07.10

  12. Essential properties 1: UV • In quantum world – no bare quarks or gluons, always surrounded by “cloud” of qq pairs and gluons  effective or “running” color charge depends on color charge inside a volume determined by resolving wave length or momentum of the (coherent) interactionscolor coupling (S) is large at large distances, small energies – IR slavery - partons confined in hadronsColor coupling small at small distances, large energies – Asymptotic (UV) freedom – perturbation theory works for large pT jets CERN S.D. Ellis 09.07.10

  13. Some arithmetic yields an effective (renormalized at “1-loop”) coupling** in terms of 2 scales,M and  Measure this From quarks Resolution scale Recall 1/(1+x) = 1 – x + x2 -… (summed the logarithms!) This result is more compactly specified by the renormalization group equation, which can be evaluated order-by-order in perturbation From gluons, CA = 3 **Masses and wave functions also exhibit renormalization. CERN S.D. Ellis 09.07.10

  14. Note: Must Sum Large Logarithms The “running” coupling illustrates typical features of QCD – • expanding to a fixed power of s is often not enough* • large logarithms (the remnants of the infinities) must be resumed to all orders by some technique – QCD only tells us how s varies with , not its value at a given  • By measuring s at some scale 0 , e.g., MZ, can define a dimensionful parameter QCD – at 1-loop Dimensional transmutation !!at  = QCD, S is REALLY BIG! * In any case is an asymptotic expansion, not convergent CERN S.D. Ellis 09.07.10

  15. Asymptotic Freedom/Infrared Slavery in data Our knowledge of the behavior in the UV is now encoded in QCD. Note that the precise value of QCD will to depend on the order of the  function used (1-loop, 2-loop, etc.) and the scheme. The data does not change, only the internal theoretical parameters. • The running of the coupling is clear in the data, as is the precision of our knowledge of s, e.g., s(mZ) = 0.1184  0.0007 (2009 world average). Means QCD ~ 220 MeV, which agrees with size of hadrons where coupling gets large Note: in QED the running is the other direction! Only fermions, no gluons, β < 0 CERN S.D. Ellis 09.07.10

  16. Essential properties 2: IR • Matrix elements in QCD are also enhanced for the emission of soft and/or collinear gluons (similar to QED); logarithmically large contributions – formally singular for massless partons (in QCD the gluons are massless and the 3 light quarks [u,d,s] are light compared to of QCD) Quarks and gluons are “dressed” by other quarks and gluons – how momentum is shared depends on resolution scale set by photon’s momentum q CERN S.D. Ellis 09.07.10

  17. As with the coupling we must sum the large logarithms! (hide the infinities) • Think of a function q(x, ) that defines the probability to find a quark of momentum fraction x and resolution scale  in a (dressed) quark • QCD does not tell us the size of q(x, ) but rather how it depends on  ,i.e., how the “dressing” happens • Look more carefully (increase ) find more soft stuff and less hard stuff (like peeling an onion) CERN S.D. Ellis 09.07.10

  18. The probability to find quark in a quark with momentum fraction x depends on resolution scale  • The splitting function P (like the  function) is what is calculable in pQCD. • The splitting function can be interpreted as the probability to find a parton of type a in a parton of type b with a fraction z of its longitudinal momentum and transverse momentum < , per unit log kT(= momentum transverse) CERN S.D. Ellis 09.07.10

  19. Since hadrons are built from partons – probability to find a quark i in a proton p with momentum faction x depends on resolution scale  in the same way  Parton Distribution Functions (PDFs), fi/p(x,) – we have “factored” all the long-distance (including non-perturbative) physics, scales < , into this function • Measure the PDFs at some scale 0, e.g., by bouncing electrons off a proton (Deep Inelastic Scattering = DIS) with q = 0, and then QCD tells us the PDFs at other (typically larger) scales • Today the PDFs are found with “global” fits to lots of data, including jet data CERN S.D. Ellis 09.07.10

  20. Virtual or “sea” stuff Partons move to smaller x as Q increases Valence quarksp = uud CERN S.D. Ellis 09.07.10

  21. That was for “incoming” partons (in hadrons) • Same structure for “outgoing partons” scattered or created in the “hard” (large energy transfer) process at hard scale  = Q: these accelerated color charges “shower” (perturbatively) into many (collinear/soft) partons (at lower scales) and eventually organize themselves (non-perturbatively) into color singlet hadrons (hadronization) • Described by a “Fragmentation” function D/i(z,) describing the probability to find a pion of momentum faction z in the shower initiated by parton i starting at scale  you can see the jets coming now!! CERN S.D. Ellis 09.07.10

  22. Essential properties 2a: Hadronization • Since the 3 light quarks (u, d, s) are light compared to QCD, quark-antiquark pairs are “easy” to make in typical strong interactions – “shake” a proton at the 1 GeV scale and some pions out fall • Partons are confined (in hadrons) but the hadrons are “fragile”, easily split into more hadrons proton (confined quarks) 0 (confined quarks) CERN S.D. Ellis 09.07.10 From Carlos

  23. Essential properties 3: Factorization • It is possible to prove* in perturbation theory that (sufficiently inclusive) hard processes in QCD (& EW) can be factored into a convolution of functions describing 1) long distance behavior before (PDF)2) long distance after (Fragmentation functions) 3) the hard/short distance scattering cross section of the partons  This is the basis of collider theory/phenomenology * up to corrections that are power suppressed, ~ QCD /pTjet CERN S.D. Ellis 09.07.10

  24. Hadron – Hadron scattering • The jet cross section receives contributions from a vast number of channels (even at LO = Lowest Order) • For inclusive single hadron production, e.g., pp →  + X, we obtain a triple (factorized) convolution (both initial state and final state collinear issues). Typically choose the 2 scales, R(UV) and F (IR) to be equal, =  CERN S.D. Ellis 09.07.10

  25. Hadron – Hadron scattering - Why Jets • Single hadron rates are small and really want to focus on the underlying parton dynamics. • So we sum over the contents of the “collinear” shower and attempt to reconstruct the kinematics of the scattered parton (momentum is conserved) – that’s our jet • With an appropriately infrared safe jet definition, to be discussed below, the Next-to-LO (NLO) inclusive jet cross section exhibits the required regularization of all singularities – initial state are factored into the PDFs and final state cancel remarkably good agreement with data jet substructure the expected reduced dependence on the factorization scale and the renormalization scale (typically set equal) CERN S.D. Ellis 09.07.10

  26. Jets at NLO Q in jet Q in jet • sample real emission graphs G in jet Q+G in jet CERN S.D. Ellis 09.07.10

  27. Warning I • The experimentalists and their data know nothing about the factorization and renormalization scales - just the residue of a theorist’s trick to hidden infinities!! • If we could really evaluate QCD and not just approximate it in perturbation theory, the scale dependence would go away!! • A measure of the “goodness” of our approximation, is the “smallness” of the scale dependence – is reduced at higher orders (in perturbation theory) • For data CERN S.D. Ellis 09.07.10

  28. LO - monotonic NLO – has extrema • NLO Improved accuracy (smaller  dependence) and gives structure to the jet. For ET > 100 GeV there is a region where  variation is small, ~ ET/2 NLO becomes monotonic again at small ET /ET CERN S.D. Ellis 09.07.10 ET

  29. This big picture works very well – QCD is the correct theory! • Old cone jet data - CDF – compared to NLO, note the HUGE dynamic range 8 orders of magnitudeOf course, here cannot see 10% differences (come back to this) CERN S.D. Ellis 09.07.10

  30. Warning II – Underlying Event • In a typical hadron-hadron collision (minimum bias event) final state particles are approximately uniformly distributed in  (an original motivation for the “wee partons” with a dx/x ~ d distribution). • Even in an event with a “hard” interaction the soft interactions of the spectator partons  Underlying Event ~ Min-Bias event, which can contribute to a jet – not included in perturbative QCD CERN S.D. Ellis 09.07.10

  31. Warning III – Pile-Up • Jets can also receive contributions from completely uncorrelated pp collisions that happen to occur at (approximately) the same time – called “Pile-Up” CERN S.D. Ellis 09.07.10

  32. Put it together in the LHC! CERN S.D. Ellis 09.07.10

  33. Evolution In Words: • Initial long distance – color singlet coherent eigenstates – described by factored PDF • Short distance ( 1 fermi) – QCD parton scattering • Intermediate distances - “Bare” color charges shower (~collinear, final state radiation) Remnant colored charges also radiate (~ collinear with beam direction, initial state radiation)Remnant partons interaction softly to give Underlying Event • “long” distance (~ 1 fermi) - associate color singlet sets of partons into hadrons (hadronization) CERN S.D. Ellis 09.07.10

  34. Dictionary of Hadron Collider Terminology From Peter Skands

  35. The Goal at the LHC is a 1% (Precision) Description of Strong Interaction Physics (where Tevatron Run I is ~ 10%) To this end we want to precisely map • physics at 1 meter, i.e., all that stuff in the detector, e.g., E(,) On To • physics  1 fermi, i.e., what we can calculate with small numbers of partons, leptons and gauge bosons as functions of E, ,  We “understand” what happens at the level of short distance partons and leptons, i.e., perturbation theory is simple, can reconstruct masses, etc. CERN S.D. Ellis 09.07.10

  36. “SOLUTION”: associate “nearby” hadrons or partons into JETS via ALGORITHMS, i.e., rules that can be applied to data and theory • Cone Algorithms, based on being “nearby” in angular geometry • Recombination or kT Algorithm, based on pairwisemerging with nearness measured by a specific metric, essentially the relative momentum Turns a list of particles into a list of JETS Render PertThy IR & Collinear Safe (the infinities cancel) But mapping of hadrons to partons can never be 1 to 1, event-by-event! Colored states ≠ singlet states! NO UNIQUE BEST ALGORITHM!! CERN S.D. Ellis 09.07.10

  37. Goals of IDEAL ALGORITHM • Fully Specified: including defining in detail how to map particle list onto jet list • Theoretically Well Behaved: the algorithm should be infrared and collinear safe (and insensitive) • Detector Independence: there should be no dependence on cell type, numbers, or size • Order Independence: The algorithms should behave equally at the parton, particle, and detector levels. • Uniformity: everyone uses the samealgorithms CERN S.D. Ellis 09.07.10

  38. Ideal Algorithm reveals the hidden truth - Never that good in real life! CERN S.D. Ellis 09.07.10

  39. Cone Algorithm – focus on the core of jet (non-local) • Jet = “stable cone”  4-vector of cone contents || cone direction • Well studied – but several issues • Cone Algorithm – particles, calorimeter towers, partons in cone of size R, defined in angular space, e.g., (y,), • CONE center - • CONE i C iff • Cone Contents  4-vector • 4-vector direction • Jet = stable coneFind by iteration, i.e., put next trial cone at CERN S.D. Ellis 09.07.10

  40. Example Lego & Flow CERN S.D. Ellis 09.07.10

  41. (Some) Cone Issues 1) Stable Cones can and do Overlap: need rules for merging and splitting, split/merge algorithm has new parameter fmergebut not the same for D0 and CDF 2)Seeds – experiments only look for jets around active regions (save computer time)  problem for theory, IR sensitive (Unsafe?) at NNLO  Don’t find “possible” central jet between two well separated proto-jets (partons) This is a BIG deal philosophically – but not a big deal numerically  Use SEEDLESS version (SISCone) at the LHC CERN S.D. Ellis 09.07.10

  42. Recombination Algorithm– focus on undoing the shower pairwise,  Natural definition of substructure Merge partons, particles or towers pairwise based on “closeness” defined by minimum value ofkT, i.e. make list of metric values(rapidity y and azimuth , pTtransverse to beam) If kT,(ij)is the minimum, merge pair (add 4-vectors), replace pair with sum in list and redo list; IfkT,iis the minimum →i is a jet! (no more merging for i, it is isolated by D), 1 angular size parameterD , plus = 1, ordinary kT, recombinesoft stuff first = 0, Cambridge/Aachen (CA),controlled by angles only  = -1, Anti-kT, justrecombinestuff around hard guys – cone-like (with hard seeds) CERN S.D. Ellis 09.07.10

  43. Recombination Algorithm – in action, here CA algorithm Think of starting with calorimeter cells, recombine “closest” pair at each step leading to larger pT For CA close in quantity (0.05 x 0.05) Cells with E > 1 GeV low pTtohigh pT CERN S.D. Ellis 09.07.10 Animation from the studio of J. Walsh

  44. Recombination Algorithm – the good and bad news • Jet identification is unique – no merge/split stage as in Cone • Everything in a jet, no Dark Towers as in Cone • Resulting jets can be amorphous, energy calibration difficult (need area for subtraction for UE?), Impact of UE and pile-up not so well understood, especially at LHC – but not an issue for Anti-kT • Analysis can be very computer intensive (naïvely time grows like N3, recalculate list after each merge) • New versions go like N ln N (only recalculate nearest neighbors) • They have been used and understood at the Tevatron • Using Anti-kT at LHC CERN S.D. Ellis 09.07.10

  45. Tevatron Both algorithms work and yield similar results CERN S.D. Ellis 09.07.10

  46. Latest Cone Data – being included in PDF fits PDF uncertainty tends to dominate, ~ 10%, especially at large pT Note: CDF uses  = pT/2 Note: D0 uses  = pT CERN S.D. Ellis 09.07.10

  47. Summary: • Jets are a natural component of events at hadron colliders (the LHC!) due to QCD • Not uniquely defined but understood at the 10% level (mostly PDFs), but this will improve with new Tevatron and LHC data • 1 % precision jet physics at the LHC is plausible, and likely necessary to find new physicsbut will take a lot of effort (yours?) CERN S.D. Ellis 09.07.10

  48. New feature at the LHC will be the study of jet substructure – eventually to distinguish QCD jets from the boosted decay products of W/Zs, top quarks, Higgs bosons, SUSY sparticles, …. • E.g., compare but problem is - improvements being studied! ttbar QCD dijet shaped by the jet algorithm falling, no intrinsic large mass scale σttbar≈ 10-3σjj CERN S.D. Ellis 09.07.10

  49. Extra Detail Slides CERN S.D. Ellis 09.07.10

  50. We really have a matrix problem (2nf+1 dimensional) • Luckily, symmetries come to our rescue (charge conjugation, SU(nf),…) – • QCD is flavor blind and, at leading order, is flavor diagonal CERN S.D. Ellis 09.07.10

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