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Towards Precision Models of Collider Physics

Towards Precision Models of Collider Physics. High Energy Physics Seminar, December 2008, Pittsburgh. Overview. Dec 2008. Introduction Calculating Collider Observables Colliders from the Ultraviolet to the Infrared VINCIA Hard jets Towards extremely high precision: a new proposal

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Towards Precision Models of Collider Physics

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  1. Towards Precision Modelsof Collider Physics High Energy Physics Seminar, December 2008, Pittsburgh

  2. Overview Dec 2008 • Introduction • Calculating Collider Observables • Colliders from the Ultraviolet to the Infrared • VINCIA • Hard jets • Towards extremely high precision: a new proposal • Infrared Collider Physics • What “structure”? What to do about it? • Hadronization and All That • Stringy uncertainties Disclaimer: discussion of hadron collisions in full, gory detail not possible in 1 hour  focus on central concepts and current uncertainties Precision Collider Physics - 2

  3. QuantumChromoDynamics • Main Tool: Matrix Elements calculated in fixed-order perturbative quantum field theory • Example: High transverse-momentum interaction Reality is more complicated Precision Collider Physics - 3

  4. Collider Energy Scales Hadron Decays Non-perturbative hadronisation, colour reconnections, beam remnants, non-perturbative fragmentation functions, pion/proton ratio, kaon/pion ratio, ... Soft Jets and Jet Structure Soft/collinear radiation (brems), underlying event (multiple perturbative 22 interactions + … ?), semi-hard brems jets, … Exclusive & Widths Resonance Masses… Hard Jet Tail High-pT jets at large angles Inclusive s • + Un-Physical Scales: • QF , QR : Factorization(s) & Renormalization(s) • QE : Evolution(s) Precision Collider Physics - 4

  5. Principal virtues Stochastic error O(N-1/2) independent of dimension Full (perturbative) quantum treatment at each order (KLN theorem: finite answer at each (complete) order) Monte Carlo at Fixed Order “Experimental” distribution of observable O in production of X: Fixed Order (all orders) {p} : momenta k : legs ℓ : loops “Monte Carlo”: N. Metropolis, first Monte Carlo calculation on ENIAC (1948), basic idea goes back to Enrico Fermi High-dimensional problem (phase space) d≥5  Monte Carlo integration Note 1: For k larger than a few, need to be quite clever in phase space sampling Note 2: For ℓ > 0, need to be careful in arranging for real-virtual cancellations Precision Collider Physics - 5

  6. Event Generators • Generator philosophy: • Improve Born-level perturbation theory, by including the ‘most significant’ corrections  complete events • Parton Showers • Matching • Hadronisation • The Underlying Event • Soft/Collinear Logarithms • Finite Terms, “K”-factors • Power Corrections • All of the above (+ more?) roughly (+ many other ingredients: resonance decays, beam remnants, Bose-Einstein, …) Asking for fully exclusive events is asking for quite a lot … Precision Collider Physics - 6

  7. 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) Precision Collider Physics - 7

  8. “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 Precision Collider Physics - 8

  9. Constructing LL Showers • 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 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) Variations  Comprehensive uncertainty estimates (showers with uncertainty bands) Matching  Reduced Dependence (systematic reduction of uncertainty) Precision Collider Physics - 9

  10. Colliders in the Ultraviolet – VINCIA In collaboration with W. Giele, D. Kosower

  11. Overview • Matching Fundamentals, Current recipes • Multiplicative • ~ reweighted/vetoed showers • Additive • ~ sliced and/or subtracted matrix elements • Matching à la Vincia • Properties of dipole-antenna showers • Additive Matching • VINCIA: Additive matching through second order •  Multi-leg 1-loop matching? •  Multiplicative Matching • VINCIA: Multiplicative matching through second orderand beyond •  positive-weight NLL showers? NNLO matching? Precision Collider Physics - 11

  12. Based on Dipole-Antennae Shower off color-connected pairs of partons Plug-in to PYTHIA 8 (C++) So far: 3 different shower evolution variables: pT-ordering (= ARIADNE ~ PYTHIA 8) Dipole-mass-ordering (~ but not = PYTHIA 6, SHERPA) Thrust-ordering (3-parton Thrust) For each: an infinite family of antenna functions Laurent series in branching invariants with arbitrary finite terms Shower cutoff contour: independent of evolution variable IR factorization “universal” Several different choices for αs (evolution scale, pT, mother antenna mass, 2-loop, …) Phase space mappings: 2 different choices implemented Antenna-like (ARIADNE angle) or Parton-shower-like: Emitter + longitudinal Recoiler 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 Precision Collider Physics - 12

  13. Example: Jet Rates • Splitting functions only defined up to non-singular terms (finite terms) • Finite terms generally process-dependent  impossible to “tune” • Uncertainty in hard region already at first order • Cascade down to produce uncontrolled tower of subleading logs Varying finite terms only with αs(MZ)=0.137, μR=pT, pThad = 0.5 GeV Precision Collider Physics - 13

  14. Constructing LL Showers • The final answer will depend on: • The choice of evolution “time” • The splitting functions (finite terms not fixed) • The phase space map (“recoils”, dΦn+1/dΦn ) • The renormalization scheme (argument of αs) • The infrared cutoff contour (hadronization cutoff) • They are all “unphysical”, in the same sense as QFactorizaton, etc. • At strict LL, any choice is equally good • Some NLL effects can be (approximately) absorbed by judicious choices • E.g., (E,p) cons., coherence, using pT as scale in αs, with ΛMSΛMC, … • Effectively, precision is better than strict LL, but still not formally NLL Variations  Comprehensive uncertainty estimates (showers with uncertainty bands) •  Clever choices fine (for process-independent things), can we do better? … + matching Precision Collider Physics - 14

  15. Matching in a nutshell • There are two fundamental approaches • Additive • Multiplicative • Most current approaches based on addition, in one form or another • Herwig (Seymour, 1995), but also CKKW, MLM, MC@NLO, ... • In these approaches, you add event samples with different multiplicities • Need separate ME samples for each multiplicity. Relative weights a priori unknown. • The job is to construct weights for them, and modify/veto the showers off them, to avoid double counting of both logs and finite terms • But you can also do it by multiplication • Pythia (Sjöstrand, 1987): modify only the shower • All events start as Born + reweight at each step. • Using the shower as a weighted phase space generator •  only works for showers with NO DEAD ZONES • The job is to construct reweighting coefficients • Complicated shower expansions  only first order so far • Generalized to include 1-loop first-order  POWHEG Seymour, Comput.Phys.Commun.90(1995)95 Sjöstrand, Bengtsson : Nucl.Phys.B289(1987)810; Phys.Lett.B185(1987)435 Norrbin, Sjöstrand : Nucl.Phys.B603(2001)297 Massive Quarks All combinations of colors and Lorentz structures Precision Collider Physics - 15

  16. 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) Precision Collider Physics - 16

  17. Matching to X+1: Tree-level • Herwig • In dead zone: Ai = 0 add events corresponding to unsubtracted |MX+1| • Outside dead zone: reweighted à la Pythia  Ai = |MX+1| •  no additive correction necessary • CKKW and L-CKKW • At this order identical to Herwig, with “dead zone” for kT > kTcut introduced by hand • MC@NLO • In dead zone: identical to Herwig • Outside dead zone: AHerwig >|MX+1| wX+1 negative  negative weights • Pythia • Ai = |MX+1| over all of phase space  no additive correction necessary • Powheg • At this order identical to Pythia •  no negative weights HERWIG TYPE PYTHIA TYPE Precision Collider Physics - 17

  18. Matching in Vincia • We are pursuing three strategies in parallel • Addition (aka subtraction) • Simplest & guaranteed to fill all of phase space (unsubtracted ME in dead regions) • But has generic negative weights and hard to exponentiate corrections • Multiplication (aka reweighting) • Guaranteed positive weights & “automatically” exponentiates  path to NLL • Complicated, so 1-loop matching difficult beyond first order. • Only fills phase space populated by shower: dead zones problematic • Hybrid • Combine: simple expansions, full phase space, positive weights, and exponentiation? • Goal • Multi-leg “plug-and-play” NLO + “improved”-LL shower Monte Carlo • Including uncertainty bands (exploring uncontrolled terms) • Extension to NNLO + NLL ? Precision Collider Physics - 18

  19. 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 Everyone’s usual nightmare of a parton shower QE = pT QE = pT Vincia MAX GGG AVG Vincia MIN Vincia AVG Precision Collider Physics - 19

  20. Second Order with Unordered Showers • For reweighting: allow power-suppressed “unordered” branchings GGG Uord AVG Vincia Uord MAX Vincia Uord AVG Vincia Uord MIN • Removes dead zone + better approx than fully unordered • (Good initial guess  better reweighting efficiency) • Problem 2: leftover Subleading Logs • There are still unsubtractred subleading divergences in the ME Precision Collider Physics - 20

  21. Leftover Subleading Logs • Subtraction in Dead Zone • ME completely unsubtracted in Dead Zone  leftovers • But also true in general: the shower is still formally LL everywhere • NLL leftovers are unavoidable • Additional sources: Subleading color, Polarization • Beat them or join them? • Beat them: not resummed •  brute force regulate with Theta (or smooth) function ~ CKKW “matching scale” • Join them: absorb leftovers systematically in shower resummation • But looks like we would need polarized NLL-NLC showers … ! • Could take some time … • In the meantime … do it by exponentiated matching Note: more legs  more logs, so ultimately will still need regulator. But try to postpone to NNLL level. Precision Collider Physics - 21

  22. 24 Matching by reweighting • Starting point: • LL shower w/ large coupling and large finite terms to generate “trial” branchings (“sufficiently” large to over-estimate the full ME). • Accept branching [i] with a probability • Each point in 4-parton phase space then receives a contribution Sjöstrand-Bengtsson term 2nd order matching term (with 1st order subtracted out) (If you think this looks deceptively easy, you are right) Note: to maintain positivity for subleading colour, need to match across 4 events, 2 representing one color ordering, and 2 for the other ordering Precision Collider Physics - 22

  23. General 2nd Order (& NLL Matching) • Include unitary shower (S) and non-unitary “K-factor” (K) corrections • K: event weight modification (special case: add/subtract events) • Non-unitary  changes normalization (“K” factors) • Non-unitary  does not modify Sudakov  not resummed • Finite corrections can go here ( + regulated logs) • Only needs to be evaluated once per event • S: branching probability modification • Unitary  does not modify normalization • Unitary  modifies Sudakov  resummed • All logs should be here • Needs to be evaluated once for every nested 24 branching (if NLL) • Addition/Subtraction: S = 1, K ≠ 1 • Multiplication/Reweighting: S≠ 1 K = 1 • Hybrid: S = logs K = the rest Precision Collider Physics - 23

  24. The Z3 1-loop term • Second order matching term for 3 partons • Additive (S=1)  Ordinary NLO subtraction + shower leftovers • Shower off w2(V) • “Coherence” term: difference between 2- and 3-parton (power-suppressed) evolution above QE3. Explicit QE-dependence cancellation. • δα: Difference between alpha used in shower (μ = pT) and alpha used for matching  Explicit scale choice cancellation • Integral over w4(R) in IR region still contains NLL divergences  regulate • Logs not resummed, so remaining (NLL) logs in w3(R)also need to be regulated • Multiplicative : S = (1+…)  Modified NLO subtraction + shower leftovers • A*S contains all logs from tree-level  w4(R) finite. • Any remaining logs in w3(V) cancel against NNLO  NLL resummation if put back in S Precision Collider Physics - 24

  25. VINCIA in Action: Jet Rates • Splitting functions only defined up to non-singular terms (finite terms) • Finite terms generally process-dependent  impossible to “tune” • Uncertainty in hard region already at first order • Cascade down to produce uncontrolled tower of subleading logs Varying finite terms only with αs(MZ)=0.137, μR=pT, pThad = 0.5 GeV Precision Collider Physics - 25

  26. VINCIA in Action • Can vary • evolution variable, kinematics maps, radiation functions, renormalization choice, matching strategy (here just showing radiation functions) • At Pure LL, • can definitely see a non-perturbative correction, but hard to precisely constrain it Giele, Kosower, PS : PRD78(2008)014026 + Les Houches ‘NLM’ 2007 Precision Collider Physics - 26

  27. VINCIA in Action • Can vary • evolution variable, kinematics maps, radiation functions, renormalization choice, matching strategy (here just showing radiation functions) • At Pure LL, • can definitely see a non-perturbative correction, but hard to precisely constrain it Giele, Kosower, PS : PRD78(2008)014026 + Les Houches ‘NLM’ 2007 Precision Collider Physics - 27

  28. VINCIA in Action • Can vary • evolution variable, kinematics maps, radiation functions, renormalization choice, matching strategy (here just showing radiation functions) • After 2nd order matching • Non-pert part can be precisely constrained. (will need 2nd order logs as well for full variation) Giele, Kosower, PS : PRD78(2008)014026 + Les Houches ‘NLM’ 2007 Precision Collider Physics - 28

  29. The next big steps • Z3 at one loop • Opens multi-parton matching at 1 loop • Required piece for NNLO matching • If matching can be exponentiated, opens NLL showers • Work in progress • Write up complete framework for additive matching •  NLO Z3 and NNLO matching within reach • Finish complete framework multiplicative matching … • Complete NLL showers slightly further down the road • Turn to the initial state, massive particles, other NLL effects (polarization, subleading color, unstable particles, …) Precision Collider Physics - 29

  30. Colliders in the Infrared – PYTHIA In collaboration with T. Sjostrand, S. Mrenna

  31. Particle Production QF FSR FSR 22 22 ISR ISR ISR • 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 • Normally omitted in ME/PS expansions ( ~ higher twists / powers / low-x) But still perturbative, divergent QF Note: Can take QF >> ΛQCD e.g. 44, 3 3, 32 Precision Collider Physics - 31

  32. Additional Sources of 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) Precision Collider Physics - 32

  33. 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 Precision Collider Physics - 33

  34. 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 Precision Collider Physics - 34

  35. 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 Precision Collider Physics - 35

  36. Future Directions • Monte Carlo problem • Uncertainty on fixed orders and logs obscures clear view on hadronization and the underlying event • So we just need … • An NNLO + NLO multileg + NLL Monte Carlo (incl small-x logs), with uncertainty bands, please • Then … • We could see hadronization and UE clearly  solid constraints   Energy Frontier Intensity Frontier The Astro Guys Precision Frontier Anno 2018 The Tevatron and LHC data will be all the energy frontier data we’ll have for a long while Precision Collider Physics - 36

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