1. Peter Skands Theoretical Physics, Fermilab Harvard U, Mar 17 2009 Towards Precision Models of Collider Physics

2. Peter Skands Towards Precision Models of Collider Physics - 2 ►Main Tool: Matrix Elements calculated in fixed-order perturbative quantum field theory Example: Q uantum C hromo D ynamics Reality is more complicated High transverse- momentum interaction

3. Peter Skands Towards Precision Models of Collider Physics - 3 ►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 ► But hadrons are not elementary ► + QCD diverges at low p T  multiple perturbative parton-parton collisions e.g. 4  4, 3  3, 3  2 Q F >> Λ QCD QFQF QFQF … 2222 IS R FS R 2222 IS R FS R ► No factorization theorem  Herwig++, Pythia, Sherpa: MPI models Particle Production Underlying Event has perturbative part!

4. Peter Skands Towards Precision Models of Collider Physics - 4 Particle Production Need-to-know issues for IR sensitive quantities (e.g., N ch ) + Stuff at Q F ~ Λ QCD Q F >> Λ QCD ME+ISR/FSR + perturbative MPI QFQF QFQF … 2222 IS R FS R 2222 IS R FS R ►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?

5. Peter Skands Towards Precision Models of Collider Physics - 5 Factorization, Infrared Safety, and Unitarity ►Do we really need to calculate all of this? 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, … My Resonance Mass… Hard Jet Tail High-p T jets at large angles & Width s Inclusive Exclusive Hadron Decays + Un-Physical Scales: Q F, Q R : Factorization(s) & Renormalization(s) Q E : Evolution(s) 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, …)

6. Peter Skands Theoretical Physics, Fermilab Three Ways To High Precision

7. Peter Skands Towards Precision Models of Collider Physics - 7 The Way of the Chicken ►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 H1 MC Summary of Hera-LHC Workshop: Parton Distributions Ball et al; Feltesse, Glazov, Radescu; 0901.2504 [hep-ph]

8. Peter Skands Towards Precision Models of Collider Physics - 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, m 1, m 2, p Tjet1, p Tjet2, …)  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 Cacciari, Salam, Soyez: JHEP 0804(2008)063 Alwall, de Visscher, Maltoni: JHEP 0902(2009)017 Cone  “anti-kT” ~ IR safe cone FASTJET Plehn, Tait: 0810.2919 [hep-ph] Plehn, Rainwater, PS: PLB645(2007)217

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

10. Peter Skands Towards Precision Models of Collider Physics - 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 1.Parton Showers 2.Matching 3.Hadronisation 4.The Underlying Event 1.Soft/Collinear Logarithms 2.Finite Terms, “K”-factors 3.Power Corrections (more if not IR safe) 4.? roughly (+ many other ingredients: resonance decays, beam remnants, Bose-Einstein, …) Asking for complete events is a tall order …

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

12. Peter Skands Towards Precision Models of Collider Physics - 12 ►Naively, brems suppressed by α s ~ 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 (Bremsstrahlung Example: SUSY @ LHC) FIXED ORDER pQCD inclusive X + 1 “jet” inclusive X + 2 “jets” LHC - sps1a - m~600 GeV (Computed with SUSY-MadGraph) Cross section for 1 or more 50-GeV jets larger than total σ, obviously non- sensical Alwall, de Visscher, Maltoni: JHEP 0902(2009)017 Plehn, Tait: 0810.2919 [hep-ph] Plehn, Rainwater, PS: PLB645(2007)217

13. Peter Skands Towards Precision Models of Collider Physics - 13 Beyond Fixed Order 1 ►dσ X = … ►dσ X+1 ~ dσ X g 2 2 s ab /(s a1 s 1b ) ds a1 ds 1b ►dσ X+2 ~ dσ X+1 g 2 2 s ab /(s a2 s 2b ) ds a2 ds 2b ►dσ X+3 ~ dσ X+2 g 2 2 s ab /(s a3 s 3b ) ds a3 ds 3b dσXdσX α s ab s ai s ib dσ X+1 dσ X+2 This is an approximation of inifinite- order tree-level cross sections “DLA”

14. Peter Skands Towards Precision Models of Collider Physics - 14 Beyond Fixed Order 2 ►dσ X = … ►dσ X+1 ~ dσ X g 2 2 s ab /(s a1 s 1b ) ds a1 ds 1b ►dσ X+2 ~ dσ X+1 g 2 2 s ab /(s a2 s 2b ) ds a2 ds 2b ►dσ X+3 ~ dσ X+2 g 2 2 s ab /(s a3 s 3b ) ds a3 ds 3b + Unitarisation: σ tot = int( dσ X )  σ X;excl = σ X - σ X+1 - σ X+2 - … ►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 = σ X+1 (Q) = σ X;incl – σ X;excl (Q) Later, some 3-jets migrate further, etc  σ X+n (Q) = σ X;incl – ∑σ X+m<n;excl (Q) This evolution takes place between two scales, Q in ~ s and Q end ~ Q had ►σ X;tot = Sum ( σ X+0,1,2,3,…;excl ) = int( dσ X ) dσXdσX α s ab s ai s ib dσ X+1 dσ X+2 Given a jet definition, an event has either 0, 1, 2, or … jets “DLA”

15. Peter Skands Towards Precision Models of Collider Physics - 15 LL Shower Monte Carlos ►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 ( σ LO, σ NLO, σ NNLO, σ exp, …)  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 Pure Shower (all orders) O: Observable {p} : momenta w X = |M X | 2 or K|M X | 2 S : Evolution operator Leading Order

16. Peter Skands Towards Precision Models of Collider Physics - 16 “S” (for Shower) ►Evolution Operator, S (as a function of “time” t=1/Q ) Defined in terms of Δ(t 1,t 2 ) (Sudakov)  The integrated probability the system does not change state between t 1 and t 2  NB: Will not focus on where Δ comes from here, just on how it expands = Generating function for parton shower Markov Chain “X + nothing” “X+something” A: splitting function

17. Peter Skands Towards Precision Models of Collider Physics - 17 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”, dΦ n+1 /dΦ n ) The renormalization scheme (vertex-by-vertex argument of α s ) The infrared cutoff contour (hadronization cutoff) + Matching prescription and “matching scales” Variations  Comprehensive uncertainty estimates (showers with uncertainty bands) Matching to MEs (& N n LL?)  Reduced Dependence (systematic reduction of uncertainty)

18. Peter Skands Towards Precision Models of Collider Physics - 18 “Matching” ? ►A (Complete Idiot’s) Solution – Combine 1. [X] ME + showering 2. [X + 1 jet] ME + showering 3. … ►Doesn’t work [X] + shower is inclusive [X+1] + shower is also inclusive X inclusive X+1 inclusive X+2 inclusive ≠ X exclusive X+1 exclusive X+2 inclusive Run generator for X (+ shower) Run generator for X+1 (+ shower) Run generator for … (+ shower) Combine everything into one sample What you get What you want Overlapping “bins”One sample

19. Peter Skands Towards Precision Models of Collider Physics - 19 The Matching Game ►[X] ME + shower already contains sing{ [X + n jet] ME } So we really just missed the non-LL bits, not the entire ME! Adding full [X + n jet] ME is 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 : w n = [X + n jet] ME – Shower{w n-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 P n = [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 …

20. Peter Skands Towards Precision Models of Collider Physics - 20 (NLO with Addition) ►First Order Shower expansion Unitarity of shower  3-parton real = ÷ 2-parton “virtual” ►3-parton real correction ( A 3 = |M 3 | 2 /|M 2 | 2 + finite terms; α, β ) ►2-parton virtual correction (same example) PS Finite terms cancel in 3-parton O Finite terms cancel in 2- parton O (normalization) Multiplication at this order  α, β = 0 (POWHEG )

21. Peter Skands Towards Precision Models of Collider Physics - 21 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 VINCIA ►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 + arbitrary finite terms (Taylor series) Phase space map  Antenna-like or Parton-shower-like Renormalization scheme ( μ R = {evolution scale, p T, s, 2-loop, …} ) Infrared cutoff contour (hadronization cutoff)  Same options as for evolution time, but independent of time  universal choice Dipoles (=Antennae, not CS) – a dual description of QCD a b r VIRTUAL NUMERICAL COLLIDER WITH INTERLEAVED ANTENNAE Giele, Kosower, PS: PRD78(2008)014026 + Les Houches ‘NLM’ 2007

22. Peter Skands Towards Precision Models of Collider Physics - 22 ►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 VINCIA in Action Giele, Kosower, PS : PRD78(2008)014026 + Les Houches ‘NLM’ 2007 VIRTUAL NUMERICAL COLLIDER WITH INTERLEAVED ANTENNAE Parton-level Hadron-level

23. Peter Skands Towards Precision Models of Collider Physics - 23 ►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 VINCIA in Action Giele, Kosower, PS : PRD78(2008)014026 + Les Houches ‘NLM’ 2007 VIRTUAL NUMERICAL COLLIDER WITH INTERLEAVED ANTENNAE Parton-level Hadron-level

24. Peter Skands Towards Precision Models of Collider Physics - 24 ►Can vary evolution variable, kinematics maps, radiation functions, renormalization choice, matching strategy (here just varying splitting functions) ►After 2 nd order matching  Non-pert part can be precisely constrained. (will need 2 nd order logs as well for full variation) VINCIA in Action Giele, Kosower, PS : PRD78(2008)014026 + Les Houches ‘NLM’ 2007 VIRTUAL NUMERICAL COLLIDER WITH INTERLEAVED ANTENNAE Coming soon to a pythia-8 near you Parton-level Hadron-level

25. Peter Skands Towards Precision Models of Collider Physics - 25 “Solving QCD” Part 2: Underlying Event

26. Peter Skands Towards Precision Models of Collider Physics - 26 Naming Conventions ►Many nomenclatures being used. Not without ambiguity. I use: Q cut 2222 IS R FS R 2222 IS R FS R Primary Interaction (~ trigger) Underlying Event (UE) Beam Remnants Note: each is colored  Not possible to separate clearly at hadron level Some freedom in how much particle production is ascribed to each: “hard” vs “soft” models … … … See also Tevatron-for-LHC Report of the QCD Working Group, hep-ph/0610012 Inelastic, non-diffractive Multiple Parton Interactions (MPI)

27. Peter Skands Towards Precision Models of Collider Physics - 27 (Why Perturbative MPI?) ►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 ►(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 = color-screening cutoff (E cm -dependent, but large uncert) Bahr, Butterworth, Seymour: arXiv:0806.2949 [hep-ph]

28. Peter Skands Towards Precision Models of Collider Physics - 28  Underlying Event (note: interactions correllated in colour: hadronization not independent) Sjöstrand & PS : JHEP03(2004)053, EPJC39(2005)129 multiparton PDFs derived from sum rules Beam remnants Fermi motion / primordial k T Fixed order matrix elements Parton Showers (matched to further Matrix Elements) perturbative “intertwining”? The Interleaved Idea “New” Pythia model

29. Peter Skands Towards Precision Models of Collider Physics - 29 Underlying Event and Color ►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? Tevatron Run II Pythia 6.2 Min-bias (N ch ) Tune A old default Central Large UE Peripheral Small UE Non-perturbative component in string fragmentation (LEP value) Not only more (charged particles), but each one is harder Diffractive? Successful models: string interactions (area law) PS & D. Wicke : EPJC52(2007)133 ; J. Rathsman : PLB452(1999)364 Solving QCD Part 3: Hadronization

30. Peter Skands Towards Precision Models of Collider Physics - 30 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)

31. Peter Skands Towards Precision Models of Collider Physics - 31 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)

32. Peter Skands Towards Precision Models of Collider Physics - 32 Perugia Models |η| < 2.5 p T > 0.5 GeV LHC 10 TeV (min-bias) = 12.5 ± 1.5 LHC 14 TeV (min-bias) = 13.5 ± 1.5 1.8 < η < 4.9 pT > 0.5 GeV LHC 10 TeV (min-bias) = 6.0 ± 1.0 LHC 14 TeV (min-bias) = 6.5 ± 1.0  Aspen Predictions: (stable particle definition: cτ ≥ 10mm)

33. Peter Skands Towards Precision Models of Collider Physics - 33Conclusions ►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

34. Peter Skands Towards Precision Models of Collider Physics - 34 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) : 1)It is not possible to ‘tune’ anything better than the underlying physics model allows 2)Failure of a physically motivated model usually points to more physics (interesting) 3)Failure of a fit not as interesting

35. Peter Skands Towards Precision Models of Collider Physics - 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

36. Peter Skands Towards Precision Models of Collider Physics - 36 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