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Towards Precision Models of Collider Physics

Dive into precision modeling of collider physics with quantum chromodynamics (QCD). Explore fixed-order perturbative field theory matrix elements, parton showers, and more. Discover the importance of factorization, infrared safety, and unitarity in achieving high precision. Learn about hadronization, soft jets, jet structure, and exclusive resonance masses in this comprehensive guide. Uncover three key approaches to high precision in collider physics: the way of the Chicken, the way of the Fox, and the way of the Ox. Get insights into calculating everything in QCD, including parton showers and matching techniques.

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Towards Precision Models of Collider Physics

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  1. LBNL, Apr 9 2009 Towards Precision Models of Collider Physics

  2. QuantumChromoDynamics • Main Tool: Matrix Elements calculated in fixed-order perturbative quantum field theory • Example: High transverse-momentum interaction Reality is more complicated Towards Precision Models of Collider Physics - 2

  3. Particle Production QF FSR FSR 22 22 ISR ISR ISR Underlying Event has perturbative part! • Starting point: matrix element + parton shower • hard parton-parton scattering • (normally 22 in MC) • + bremsstrahlung associated with it •  2n in (improved) LL approximation ISR FSR … FSR • But hadrons are not elementary • + QCD diverges at low pT  multiple perturbative parton-parton collisions QF QF >> ΛQCD e.g. 44, 3 3, 32 • No factorization theorem • Herwig++, Pythia, Sherpa: MPI models Towards Precision Models of Collider Physics - 3

  4. Particle Production QF FSR FSR 22 22 ISR ISR ISR • Hadronization • Remnants from the incoming beams • Additional (non-perturbative / collective) phenomena? • Bose-Einstein Correlations • Non-perturbative gluon exchanges / color reconnections ? • String-string interactions / collective multi-string effects ? • “Plasma” effects? • Interactions with “background” vacuum, remnants, or active medium? QF >> ΛQCD ME+ISR/FSR + perturbative MPI + Stuff at QF ~ ΛQCD ISR FSR … FSR QF Need-to-know issues for IR sensitive quantities (e.g., Nch) Towards Precision Models of Collider Physics - 4

  5. Factorization, Infrared Safety, and Unitarity • These Things • Are Your Friends • IR Safety: guarantees non-perturbative (NP) corrections suppressed by powers of NP scale • Factorization: allows you to sum inclusively over junk you don’t know how to calculate • Unitarity:allows you to estimate things you don’t know from things you know (e.g., loop singularities = - tree ones; P(fragmentation) = 1, …) • Do we really need to calculate all of this? Hadron Decays Non-perturbative hadronisation, color reconnections, beam remnants, strings, non-perturbative fragmentation functions, charged/neutral ratio, baryons, strangeness... Soft Jets and Jet Structure Bremsstrahlung, underlying event (multiple perturbative parton interactions + more?), semi-hard brems jets, jet broadening, … Exclusive & Width My Resonance Mass… Hard Jet Tail High-pT jets at large angles Inclusive s • + Un-Physical Scales: • QF , QR : Factorization(s) & Renormalization(s) • QE : Evolution(s) Towards Precision Models of Collider Physics - 5

  6. Three Ways To High Precision

  7. The Way of the Chicken H1 MC Summary of Hera-LHC Workshop: Parton Distributions Ball et al; Feltesse, Glazov, Radescu; 0901.2504 [hep-ph] • Who needs QCD? I’ll use leptons • Sum inclusively over all QCD • Leptons almost IR safe by definition • WIMP-type DM, Z’, EWSB  may get some leptons • Beams = hadrons for next decade (RHIC / Tevatron / LHC) • At least need well-understood PDFs • High precision = higher orders enter QCD • Isolation  indirect sensitivity to dirt • Fakes  indirect sensitivity to dirt • Not everything gives leptons • Need to be a lucky chicken … • The unlucky chicken • Put all its eggs in one basket and didn’t solve QCD Towards Precision Models of Collider Physics - 7

  8. The Way of the Fox • I’ll use semi-inclusive observables • Sum inclusively over the worst parts of QCD • Still need to be friends with IR safety  jet algs • FASTJET • Beams = hadrons for next decade (RHIC / Tevatron / LHC) • Still need well-understood PDFs • High precision = more higher orders more QCD • Large hierarchies (s, m1, m2, pTjet1, pTjet2, …)  Careful ! • Huge jet rate enhancements : perturbative series “blows up” •  cannot truncate at any fixed order • For 600 GeV particles, a 100 GeV jet can be “soft” • Use infinite-order approximations = parton showers • Only “LL”  not highly precise + only good when everything is hierarchical • Need to combine with explicit matrix elements matching (more later) • Still, non-factorizable + non-pert corrections set an ultimate limit FASTJET Cacciari, Salam, Soyez: JHEP 0804(2008)063 Cone  “anti-kT” ~ IR safe cone Plehn, Rainwater, PS: PLB645(2007)217 Plehn, Tait: 0810.2919 [hep-ph] Alwall, de Visscher, Maltoni: JHEP 0902(2009)017 Towards Precision Models of Collider Physics - 8

  9. Now Hadronize This hadronization bbar from tbar decay pbar beam remnant p beam remnant qbar from W q from W q from W b from t decay ? Triplet Anti-Triplet Simulation from D. B. Leinweber, hep-lat/0004025 gluon action density: 2.4 x 2.4 x 3.6 fm Towards Precision Models of Collider Physics - 9

  10. The Way of the Ox • Calculate Everything: solve QCD requires compromise • Improve Born-level perturbation theory, by including the ‘most significant’ corrections  complete events  any observable you want • Parton Showers • Matching • Hadronisation • The Underlying Event • Soft/Collinear Logarithms • Finite Terms, “K”-factors • Power Corrections (more if not IR safe) • ? roughly (+ many other ingredients: resonance decays, beam remnants, Bose-Einstein, …) Asking for complete events is a tall order … Towards Precision Models of Collider Physics - 10

  11. “Solving QCD” Part 1: Bremsstrahlung Towards Precision Models of Collider Physics - 11

  12. Beyond Fixed Order 1 dσX+2 “DLA” α sab saisib • dσX = … • dσX+1 ~ dσX g2 2 sab /(sa1s1b) dsa1ds1b • dσX+2 ~ dσX+1 g2 2 sab/(sa2s2b) dsa2ds2b • dσX+3 ~ dσX+2 g2 2 sab/(sa3s3b) dsa3ds3b dσX dσX+1 dσX+2 This is an approximation of inifinite-order tree-level cross sections Towards Precision Models of Collider Physics - 12

  13. Beyond Fixed Order 2 dσX+2 “DLA” α sab saisib • dσX = … • dσX+1 ~ dσX g2 2 sab /(sa1s1b) dsa1ds1b • dσX+2 ~ dσX+1 g2 2 sab/(sa2s2b) dsa2ds2b • dσX+3 ~ dσX+2 g22 sab/(sa3s3b) dsa3ds3b +Unitarisation:σtot = int(dσX)  σX;excl= σX - σX+1 - σX+2- … dσX dσX+1 dσX+2 Given a jet definition, an event has either 0, 1, 2, or … jets • Interpretation: the structure evolves! (example: X = 2-jets) • Take a jet algorithm, with resolution measure “Q”, apply it to your events • At a very crude resolution, you find that everything is 2-jets • At finer resolutions  some 2-jets migrate  3-jets =σX+1(Q) = σX;incl– σX;excl(Q) • Later, some 3-jets migrate further, etc  σX+n(Q) = σX;incl– ∑σX+m<n;excl(Q) • This evolution takes place between two scales, Qin ~ s and Qend ~ Qhad • σX;tot = Sum (σX+0,1,2,3,…;excl ) = int(dσX) Towards Precision Models of Collider Physics - 13

  14. Evolution Operator, S “Evolves” phase space point: X  … As a function of “time” t=1/Q Observable is evaluated on final configuration S unitary (as long as you never throw away or reweight an event)  normalization of total (inclusive)σ unchanged (σLO,σNLO, σNNLO, σexp, …) Only shapes are predicted (i.e., also σ after shape-dependent cuts) Can expand S to any fixed order (for given observable) Can check agreement with ME Can do something about it if agreement less than perfect: reweight or add/subtract Arbitrary Process: X LL Shower Monte Carlos O: Observable {p} : momenta wX = |MX|2 or K|MX|2 S : Evolution operator Leading Order Pure Shower (all orders) Towards Precision Models of Collider Physics - 14

  15. “S” (for Shower) “X + nothing” “X+something” • Evolution Operator, S (as a function of “time” t=1/Q) • Defined in terms of Δ(t1,t2)(Sudakov) • The integrated probability the system does not change state between t1 and t2 • NB: Will not focus on where Δ comes from here, just on how it expands • = Generating function for parton shower Markov Chain A: splitting function Towards Precision Models of Collider Physics - 15

  16. Controlling the Calculation • In the previous slide, you saw many dependencies on things not traditionally found in matrix-element calculations: • The final answer will depend on: • The choice of shower evolution “time” • The splitting functions (finite terms not fixed) • The phase space map (“recoils”, dΦn+1/dΦn ) • The renormalization scheme (vertex-by-vertex argument of αs) • The infrared cutoff contour (hadronization cutoff) • + Matching prescription and “matching scales” Variations  Comprehensive uncertainty estimates (showers with uncertainty bands) Matching to MEs (& NnLL?) Reduced Dependence (systematic reduction of uncertainty) Towards Precision Models of Collider Physics - 16

  17. “Matching” ? X inclusive X exclusive ≠ X+1 inclusive X+1 exclusive X+2 inclusive X+2 inclusive • A (Complete Idiot’s) Solution – Combine • [X]ME+ showering • [X + 1 jet]ME+ showering • … • Doesn’t work • [X] + shower is inclusive • [X+1] + shower is also inclusive Run generator for X (+ shower) Run generator for X+1 (+ shower) Run generator for … (+ shower) Combine everything into one sample What you want What you get Overlapping “bins” One sample Towards Precision Models of Collider Physics - 17

  18. The Matching Game • [X]ME+ showeralready containssing{[X + n jet]ME} • So we really just missed the non-LL bits, not the entire ME! • Adding full [X + n jet]MEis overkill LL singular terms are double-counted • Solution 1: work out the difference and correct by that amount •  add “shower-subtracted” matrix elements • Correction events with weights : wn = [X + n jet]ME – Shower{wn-1,2,3,..} • I call these matching approaches “additive” • Herwig, CKKW, MLM, ARIADNE + MC@NLO • Solution 2: work out the ratio between PS and ME •  multiply shower kernels by that ratio (< 1 if shower is an overestimate) • Correction factor on n’th emission Pn = [X + n jet]ME / Shower{[X+n-1 jet]ME} • I call these matching approaches “multiplicative” • Pythia, POWHEG, VINCIA Seymour, CPC90(1995)95 + many more recent … Sjöstrand, Bengtsson : NPB289(1987)810; PLB185(1987)435 + one or two more recent … Towards Precision Models of Collider Physics - 18

  19. NLO with Addition Multiplication at this order  α, β = 0 (POWHEG ) • First Order Shower expansion PS Unitarity of shower  3-parton real = ÷ 2-parton “virtual” • 3-parton real correction (A3 = |M3|2/|M2|2 + finite terms; α, β) Finite terms cancel in 3-parton O • 2-parton virtual correction (same example) Finite terms cancel in 2-parton O (normalization) Towards Precision Models of Collider Physics - 19

  20. Based on Dipole-Antennae Shower off color-connected pairs of partons Plug-in to PYTHIA 8 (C++) So far: Choice of evolution time: pT-ordering Dipole-mass-ordering Thrust-ordering Splitting functions QCD singular terms + arbitrary finite terms (Taylor series) Phase space map Antenna-like or Parton-shower-like Renormalization scheme (μR = {evolution scale, pT, s, 2-loop, …} ) Infrared cutoff contour (hadronization cutoff) Same options as for evolution time, but independent of time  universal choice VINCIA VIRTUAL NUMERICAL COLLIDER WITH INTERLEAVED ANTENNAE Gustafson, PLB175(1986)453; Lönnblad (ARIADNE), CPC71(1992)15. Azimov, Dokshitzer, Khoze, Troyan, PLB165B(1985)147 Kosower PRD57(1998)5410; Campbell,Cullen,Glover EPJC9(1999)245 Dipoles (=Antennae, not CS) – a dual description of QCD a Giele, Kosower, PS : hep-ph/0707.3652 + Les Houches 2007 r b Towards Precision Models of Collider Physics - 20

  21. Ordering Phase Space for 23 kT m2 collinear Partitioned-Dipole Eg Angle soft pT (Ariadne) mant 1-T Dipole-Antenna Towards Precision Models of Collider Physics - 21

  22. Second Order 0 1 2 3 AR pT + AR recoil max # of paths DZ min # of paths • Second Order Shower expansion for 4 partons (assuming first already matched) • Problem 1: dependence on evolution variable • Shower is ordered  t4 integration only up to t3 •  2, 1, or 0 allowed “paths” • 0 = Dead Zone : not good for reweighting QE = pT(i,j,k) = mijmjk/mijk Towards Precision Models of Collider Physics - 22

  23. Second OrderEXTREMA of Over/Under-counting 0 1 2 3 • Second Order Shower expansion for 4 partons (assuming first already matched) Define over/under-counting ratio: PStree / MEtree NB: EXTREMA of R4 distribution (100M points) Towards Precision Models of Collider Physics - 23

  24. The Right Choice • Current Vincia without matching, but with “improved” antenna functions (including suppressed unordered branchings) PS ME • Removes dead zone + still better approx than virt-ordered • (Good initial guess  better reweighting efficiency) • Problem 2: leftover Subleading Logs after matching • There are still unsubtractred subleading divergences in the ME Towards Precision Models of Collider Physics - 24

  25. VINCIA in Action – LEP Event Shapes • At Pure LL, • Can definitely see a non-perturbative correction, but hard to precisely constrain it • Can see ‘hard corrections’ too, which are not under control Parton-level Hadron-level Giele, Kosower, PS : PRD78(2008)014026 + Les Houches ‘NLM’ 2007 Towards Precision Models of Collider Physics - 25

  26. VINCIA in Action – LEP Event Shapes • After 1st Order Matching • ~ MC@NLO Parton-level Hadron-level Giele, Kosower, PS : PRD78(2008)014026 + Les Houches ‘NLM’ 2007 Towards Precision Models of Collider Physics - 26

  27. VINCIA in Action – LEP Event Shapes Coming soon to a pythia-8 near you • After 2nd order matching • 2nd order Logs (NLL):  Non-perturbative part can be precisely constrained • 2nd order ME:  Hard rad can be precisely constrained Parton-level Hadron-level Giele, Kosower, PS : PRD78(2008)014026 + Les Houches ‘NLM’ 2007 Towards Precision Models of Collider Physics - 27

  28. “Solving QCD” Part 2: Underlying Event Towards Precision Models of Collider Physics - 28

  29. Naming Conventions FSR FSR 22 22 ISR ISR ISR See also Tevatron-for-LHC Report of the QCD Working Group, hep-ph/0610012 Some freedom in how much particle production is ascribed to each: “hard” vs “soft” models • Many nomenclatures being used. • Not without ambiguity. I use: Qcut … ISR FSR … FSR … Qcut Multiple Parton Interactions (MPI) Beam Remnants Primary Interaction (~ trigger) Underlying Event (UE) Note: each is colored  Not possible to separate clearly at hadron level Inelastic, non-diffractive Towards Precision Models of Collider Physics - 29

  30. (Why Perturbative MPI?) = color-screening cutoff (Ecm-dependent, but large uncert) • Analogue: Resummation of multiple bremsstrahlung emissions • Divergent σ for one emission (X + jet, fixed-order) • Finite σ for divergent number of jets (X + jets, infinite-order) • N(jets) rendered finite by finite perturbative resolution = parton shower cutoff Bahr, Butterworth, Seymour: arXiv:0806.2949 [hep-ph] • (Resummation of) Multiple Perturbative Interactions • Divergent σ for one interaction (fixed-order) • Finite σ for divergent number of interactions (infinite-order) • N(jets) rendered finite by finite perturbative resolution Towards Precision Models of Collider Physics - 30

  31. The Interleaved Idea “New” Pythia model Fixed order matrix elements Parton Showers (matched to further Matrix Elements) • Underlying Event (note: interactions correllated in colour: hadronization not independent) multiparton PDFs derived from sum rules perturbative “intertwining”? Beam remnants Fermi motion / primordial kT Sjöstrand & PS : JHEP03(2004)053, EPJC39(2005)129 Towards Precision Models of Collider Physics - 31

  32. Min-bias data at Tevatron showed a surprise Charged particle pT spectra were highly correlated with event multiplicity: not expected For his ‘Tune A’, Rick Field noted that a high correlation in color space between the different MPI partons could account for the behavior But needed ~ 100% correlation. So far not explained Virtually all ‘tunes’ now employ these more ‘extreme’ correlations But existing models too crude to access detailed physics What is their origin? Why are they needed? Underlying Event and Color Not only more (charged particles), but each one is harder Tevatron Run II Pythia 6.2 Min-bias <pT>(Nch) Tune A Diffractive? old default Non-perturbative <pT> component in string fragmentation (LEP value) Peripheral Small UE Central Large UE Successful models: string interactions (area law) Solving QCD Part 3: Hadronization PS & D. Wicke : EPJC52(2007)133 ; J. Rathsman : PLB452(1999)364 Towards Precision Models of Collider Physics - 32

  33. Perugia Models • Huge model building and tuning efforts by many groups (Herwig, Professor, Pythia, Sherpa, … ) • Summarized at a recent workshop on MPI in Perugia (Oct 2008) • For Pythia (PYTUNE), 6.4.20 now out  “Perugia” and “Professor” tunes • Scaling to LHC much better constrained, HARD/SOFT, + CTEQ6, LO* • TeV-1960, TeV-1800, TeV-630, (UA5-900, UA5-546, UA5-200) (stable particle definition: cτ ≥ 10mm) Towards Precision Models of Collider Physics - 33

  34. Perugia Models • Huge model building and tuning efforts by many groups (Herwig, Professor, Pythia, Sherpa, … ) • Summarized at a recent workshop on MPI in Perugia (Oct 2008) • For Pythia (PYTUNE), 6.4.20 now out  “Perugia” and “Professor” tunes • Scaling to LHC much better constrained, HARD/SOFT, + CTEQ6, LO* • TeV-1960, TeV-1800, TeV-630, (UA5-900, UA5-546, UA5-200) (stable particle definition: cτ ≥ 10mm) Towards Precision Models of Collider Physics - 34

  35. Perugia Models  Aspen Predictions: |η| < 2.5 pT > 0.5 GeV LHC 10 TeV (min-bias) <Ntracks> = 12.5 ± 1.5 LHC 14 TeV (min-bias) <Ntracks> = 13.5 ± 1.5 1.8 < η < 4.9 pT > 0.5 GeV LHC 10 TeV (min-bias) <Ntracks> = 6.0 ± 1.0 LHC 14 TeV (min-bias) <Ntracks> = 6.5 ± 1.0 (stable particle definition: cτ ≥ 10mm) + Bet! Towards Precision Models of Collider Physics - 35

  36. Conclusions • QCD Phenomenology is in a state of impressive activity • Increasing move from educated guesses to precision science • Better matrix element calculators+integrators (+ more user-friendly) • Improved parton showers and improved matching to matrix elements • Improved models for underlying events / minimum bias • Upgrades of hadronization and decays • Clearly motivated by dominance of LHC in the next decade(s) of HEP • Early LHC Physics: theory • At 14 TeV, everything is interesting • Even if not a dinner Chez Maxim, rediscovering the Standard Model is much more than bread and butter • Real possibilities for real surprises • It is both essential, and I hope possible, to ensure timely discussions on “non-classified” data, such as min-bias, dijets, Drell-Yan, etc  allow rapid improvements in QCD modeling (beyond simple retunes) after startup Towards Precision Models of Collider Physics - 36

  37. Classic Example: Number of tracks UA5 @ 540 GeV, single pp, charged multiplicity in minimum-bias events Simple physics models ~ Poisson Can ‘tune’ to get average right, but much too small fluctuations  inadequate physics model More Physics: Multiple interactions + impact-parameter dependence • Moral (will return to the models later): • It is not possible to ‘tune’ anything better than the underlying physics model allows • Failure of a physically motivated model usually points to more physics (interesting) • Failure of a fit not as interesting Towards Precision Models of Collider Physics - 37

  38. The Underlying Event and Color • The colour flow determines the hadronizing string topology • Each MPI, even when soft, is a color spark • Final distributions crucially depend on color space Note: this just color connections, then there may be color reconnections too Towards Precision Models of Collider Physics - 38

  39. The Underlying Event and Color • The colour flow determines the hadronizing string topology • Each MPI, even when soft, is a color spark • Final distributions crucially depend on color space Note: this just color connections, then there may be color reconnections too Towards Precision Models of Collider Physics - 39

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