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Extrapolations to LHC: theory

Fermilab, 2009. Extrapolations to LHC: theory. Overview. Best-guess predictions for the LHC A bit more about bremsstrahlung and showers Larger phase space at LHC  “soft” becomes harder … Matching becomes more important A preview of “LHC-era” matching approaches (still science fiction).

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Extrapolations to LHC: theory

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  1. Fermilab, 2009 Extrapolations to LHC: theory

  2. Overview • Best-guess predictions for the LHC • A bit more about bremsstrahlung and showers • Larger phase space at LHC  “soft” becomes harder … • Matching becomes more important • A preview of “LHC-era” matching approaches (still science fiction)

  3. Tracks (pre-Perugia) UA5 200 GeV

  4. Tracks (post-Perugia) UA5 200 GeV CDF 630 GeV UA5 900 GeV CDF 1800 GeV LHC 10 TeV

  5. PS, Proceedings of the Perugia MPI Workshop 2008

  6. Perugia Variations

  7. Predictions PS, Proceedings of the Perugia MPI Workshop 2008

  8. Drell-Yan (matched) CDF CDF Perugia variations LHC LHC Perugia variations

  9. Top (not matched) CDF Perugia variations CDF LHC Perugia variations LHC

  10. Top (matched) 1st jet No matching 1st jet Matched 2nd jet No matching 2nd jet Matched Alwall, de Visscher, Maltoni (Madgraph), JHEP 02(2009)017

  11. More about Bremsstrahlung

  12. 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

  13. 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)

  14. 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)

  15. 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)

  16. “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

  17. 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)

  18. 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

  19. 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

  20. 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”

  21. 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

  22. 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)

  23. 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

  24. 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

  25. 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

  26. 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?

  27. Conclusions • I hope you enjoyed this workshop as much as I did • I hope you learnt as much as I did • Let’s keep in touch!

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