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A (complete idiot’s) Guide to Hadron Collisions

Cornell U, Jan 28 2009. A (complete idiot’s) Guide to Hadron Collisions. Overview. 2009. Introduction Calculating Collider Observables The LHC from the Ultraviolet to the Infrared Bremsstrahlung Hard jets Soft jets and jet substructure Towards extremely high precision: a new proposal

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A (complete idiot’s) Guide to Hadron Collisions

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  1. Cornell U, Jan 28 2009 A (complete idiot’s) Guide to Hadron Collisions

  2. Overview 2009 • Introduction • Calculating Collider Observables • The LHC from the Ultraviolet to the Infrared • Bremsstrahlung • Hard jets • Soft jets and jet substructure • Towards extremely high precision: a new proposal • The structure of the Underlying Event • 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 A Guide to Hadron Collisions - 2

  3. QuantumChromoDynamics • Main Tool: Matrix Elements calculated in fixed-order perturbative quantum field theory • Example: High transverse-momentum interaction Reality is more complicated A Guide to Hadron Collisions - 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) A Guide to Hadron Collisions - 4

  5. 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 • ? roughly (+ many other ingredients: resonance decays, beam remnants, Bose-Einstein, …) Asking for complete events is a tall order … A Guide to Hadron Collisions - 5

  6. 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 A Guide to Hadron Collisions - 6

  7. 1. Bremsstrahlung e+e- 3 jets Problem 1: bremsstrahlung corrections are singular for soft/collinear configurations  spoils fixed-order truncation A Guide to Hadron Collisions - 7

  8. Bremsstrahlung Example: SUSY @ LHC LHC - sps1a - m~600 GeV Plehn, Rainwater, PS PLB645(2007)217 FIXED ORDER pQCD inclusiveX + 1 “jet” inclusiveX + 2 “jets” Cross section for 1 or more 50-GeV jets larger than total σ, obviously non-sensical (Computed with SUSY-MadGraph) • Naively, brems suppressed byαs ~ 0.1 • Truncate at fixed order = LO, NLO, … • However, if ME >> 1 can’t truncate! • Example: SUSY pair production at 14 TeV, with MSUSY ~ 600 GeV • Conclusion: 100 GeV can be “soft” at the LHC • Matrix Element (fixed order) expansion breaks completely down at 50 GeV • With decay jets of order 50 GeV, this is important to understand and control A Guide to Hadron Collisions - 8

  9. 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 • But it’s not a parton shower, not yet an “evolution” • What’s the total cross section we would calculate from this? • σX;tot = int(dσX) + int(dσX+1) + int(dσX+2) + ... Just an approximation of a sum of trees  no real-virtual cancellations But wait, what happened to the virtual corrections? KLN? KLN guarantees that sing{int(real)} = ÷ sing{virtual} approximate virtual = int(real) A Guide to Hadron Collisions - 9

  10. 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;excl = int(dσX) - int(dσX+1,2,3,…;excl) = int(dσX) EXP[ - int(dσX+1 / dσX) ] • σX;tot = Sum (σX+0,1,2,3,…;excl ) = int(dσX) A Guide to Hadron Collisions - 10

  11. 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) A Guide to Hadron Collisions - 11

  12. “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 A Guide to Hadron Collisions - 12

  13. 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 to MEs (& NnLL?) Reduced Dependence (systematic reduction of uncertainty) A Guide to Hadron Collisions - 13

  14. 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 A Guide to Hadron Collisions - 14

  15. Example: LEP Event Shapes • Can vary • evolution variable, kinematics maps, radiation functions, renormalization choice, matching strategy (here just varying splitting functions) • At Pure LL, • can definitely see a non-perturbative correction, but hard to precisely constrain it Great, now even an “idiot” would know the uncertainty, how to improve? Giele, Kosower, PS : PRD78(2008)014026 + Les Houches ‘NLM’ 2007 A Guide to Hadron Collisions - 15

  16. The Matching Problem • [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” • 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” A Guide to Hadron Collisions - 16

  17. Matching in a nutshell • There are two fundamental approaches • Additive • Multiplicative • Most current approaches based onaddition, in one form or another • Herwig(Seymour, 1995), but also CKKW, MLM, MC@NLO, ... • 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 bymultiplication • 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 A Guide to Hadron Collisions - 17

  18. 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) A Guide to Hadron Collisions - 18

  19. VINCIA in Action • Can vary • evolution variable, kinematics maps, radiation functions, renormalization choice, matching strategy (here just varying splitting 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 A Guide to Hadron Collisions - 19

  20. VINCIA in Action • Can vary • evolution variable, kinematics maps, radiation functions, renormalization choice, matching strategy (here just varying splitting 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 A Guide to Hadron Collisions - 20

  21. VINCIA in Action • Can vary • evolution variable, kinematics maps, radiation functions, renormalization choice, matching strategy (here just varying splitting 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 A Guide to Hadron Collisions - 21

  22. 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 • Then… • Initial state, masses, polarization, subleading color, unstable particles, … • Also interesting that we can take more differentials than just δμR • Something to be learned here even for estimating fixed-order uncertainties? A Guide to Hadron Collisions - 22

  23. The Structure of the Underlying Event A Guide to Hadron Collisions - 23

  24. 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 A Guide to Hadron Collisions - 24

  25. Multiple Interactions  Balancing Minijets • Look for additional balancing jet pairs “under” the hard interaction. • Several studies performed, most recently by Rick Field at CDF  jets in the underlying event: 5-7 GeV should be perturbative! angle between 2 ‘best-balancing’ pairs (Run I) CDF, PRD 56 (1997) 3811 A Guide to Hadron Collisions - 25

  26. (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 A Guide to Hadron Collisions - 26

  27. 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 A Guide to Hadron Collisions - 27

  28. 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) A Guide to Hadron Collisions - 28

  29. 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 A Guide to Hadron Collisions - 29

  30. 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 A Guide to Hadron Collisions - 30

  31. 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 A Guide to Hadron Collisions - 31

  32. Not much was known about the colour correlations, so some “theoretically sensible” default values were chosen Rick Field (CDF) noted that the default model produced too soft charged-particle spectra. (The same is seen at RHIC) For his ‘Tune A’, Rick noted that <pT> increased when he increased the colour correlation parameters But needed ~ 100% correlation. So far not explained Virtually all ‘tunes’ now used by the Tevatron and LHC experiments employ these more ‘extreme’ correlations What is their origin? Why are they needed? Underlying Event and Colour 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) PS & D. Wicke : EPJC52(2007)133 ; J. Rathsman : PLB452(1999)364 A Guide to Hadron Collisions - 32

  33. 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 A Guide to Hadron Collisions - 33

  34. 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 k+ℓ > 0, need to be careful in arranging for real-virtual cancellations A Guide to Hadron Collisions - 34

  35. Z4 Matching by multiplication • 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 A Guide to Hadron Collisions - 35

  36. 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 A Guide to Hadron Collisions - 36

  37. What’s the problem? • How are the initiators and remnant partons correllated? • in impact parameter? • in flavour? • in x (longitudinal momentum)? • in kT (transverse momentum)? • in colour ( string topologies!) • What does the beam remnant look like? • (How) are the showers correlated / intertwined? A Guide to Hadron Collisions - 37

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