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Towards Precision Models of Collider Physics

Explore the concepts and uncertainties in high-energy physics seminar. Topics include calculating collider observables, hard jets, resolutions, event generators, and LL showers.

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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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