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Antenna Showers and Color Annealing

Workshop on collider physics, Argonne, May 2006. Antenna Showers and Color Annealing. with W. Giele, D. Kosower, M. Sandhoff, T. Sj ö strand, D. Wicke. Peter Skands Theoretical Physics Dept. Fermi National Accelerator Laboratory. Overview. Quest for unification.

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Antenna Showers and Color Annealing

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  1. Workshop on collider physics, Argonne, May 2006 Antenna Showers and Color Annealing with W. Giele, D. Kosower, M. Sandhoff, T. Sjöstrand, D. Wicke Peter Skands Theoretical Physics Dept Fermi National Accelerator Laboratory

  2. Overview • Quest for unification High Precision at Hadron Colliders:  • QCD at high energy colliders •  Road to High Precision: Solve more of QCD, control it more exactly • Large pT: Matching with QCD antennae. The VINCIA code • Medium pT: Three new infinite families of parton showers • Small pT:Colour Annealing in PYTHIA 6.4. First results

  3. QCD at High-Energy Colliders

  4. Collider Energy Scales Hadron Decays Non-Perturbative hadronisation, colour reconnections, beam remnants, non-perturbative fragmentation functions, pion/proton, kaon/pion, ... Soft Jets + Jet Structure Multiple collinear/soft emissions (initial and final state brems radiation), Underlying Event (multiple perturbative 22 interactions + … ?), semi-hard separate brems jets Exclusive & Widths Resonance Masses … This has an S matrix expressible as a series in gi, ln(Q1/Q2), ln(x), m-1, fπ-1, … To do precision physics: Need to compute and/or control all large terms  EVENT GENERATORS Hard Jet Tail High-pT wide-angle jets Inclusive s + “UNPHYSICAL” SCALES: • QF , QR : Factorisation & Renormalisation

  5. e.g. talk by Lillie 1 pb 1 fb High-pT phenomenology • The signal • Large cross sections for coloured BSM resonances • E.g. monojet signature for ED relies on hard QCD radiation • Cascade decays  Many-body final states • Backgrounds • Also large cross sections for top, nZ/W, other resonances (?), … • With jets • Theory: • Fixed-order perturbation theory • Asymptotic freedom  improved convergence at high pT • Phase space increases Resonances & Hard Jets: SM and BSM Resonance Production, Hard Jet Tail (esp. ISR), Successive (cascade) resonance decays Problem 1: Many legs is hard  E.g. successive factorization of res. decays Problem 2: Many loops is hard  Get a personal physician for Frank Problem 3: Only good for inclusive observables  Match to resummation

  6. LHC - sps1a - m~600 GeV Plehn, Rainwater, PS (2005) FIXED ORDER pQCD e.g. talk by Gupta e.g. talk by Sullivan inclusiveX + 1 “jet” inclusiveX + 2 “jets” e.g. talk by Lecomte Medium-pT phenomenology Minijets & Jet Structure: Semi-hard separate brems jets (esp. ISR), jet broadening (FSR), gcc/bb, multiple perturbative 22 interactions (underlying event), … ? • Extra Jets • In signal • = extra noise / confusion • Combinatorics, vetos • In backgrounds • Irreducible backgrounds • Some fraction  fakes! • Heavy flavour • Jet energy scale • Jet broadening • Underlying activity • Theory • Fixed Order with explicit jets • Parton Showers / Resummation • Models of Underlying Event Problem 1: Need to get both soft and hard emissions “right”  ME/PS Matching Problem 2: Underlying Event not well understood  what does it look like at LHC?

  7. Color Reconnection (example) “normal” ttbar Non-Perturbative: hadronisation, beam remnants, fragmentation functions, intrinsic kT, colour reconnections, pion/proton ratios, kaon/pion ratios, Bose-Einstein, diffraction, elastic, … Soft Vacuum Fields? String interactions? Size of effect < 1 GeV? Low-pT phenomenology • Measurements at LEP  • Fragmentation models (HERWIG, PYTHIA) “tuned” • Strangeness and baryon production rates well measured • Colour reconnections ruled out in WW (to ~ 10%) • Measurements at hadron colliders • Different vacuum, colour in initial state  “colour promiscuity”? • Underlying Event and Beam Remnants • Intrinsic kT • Lots of min-bias. Fragmentation tails  fakes! Example Problem: What is the non-perturbative uncertainty on the top mass?

  8. Large pT: Matching with QCD antennae. The VINCIA code

  9. Fixed Order + Resummation X=Anything (e.g. ttbar) PS=Parton Shower [ + FEHiP: NNLO (no PS) for pp hhγγ + jets ]

  10. New Approaches – Why Bother? • MC@NLO: • Used to think it was impossible! Giant step towards precision QCD  • But complicated  tough to implement new processes  (just ask Carlo) • “Only” gets first jet right (rest is PS)  • Hardwired to HERWIG  • CKKW & MLM: • Best approach when multiple hard jets important. • Retains LO normalization  • Dependence on matching scale  • CKKW@NLO: Nagy & Soper … • MC with SCET: Bauer & Schwartz … Not easy to control theoretical error on exponentiated part (also goes for ARIADNE, HERWIG, PYTHIA, …) 

  11. VINCIA – Basic Sketch • Perturbative expansion for some observableJ, ds = Sm=0dsm ; dsm= dPm|M|2d(J-J(k1,k2,…,km)) • Assume • We calculate some Matrix Elementsds0 , ds1 , … dsn (w or w/o loops) • And we have some approximationdsn+1 ~ Tn n+1 dsn(~ parton shower) • A ‘best guess’ cross section for J is then: ds ~ ds0 + ds1 + … + dsn (1 + Tn n+1 + Tn n+1Tn+1n+2+ … )  ds ~ ds0 + ds1 + … + dsn Sn; Sn= 1 + Tn n+1 Sn+1 • For this to make sense, the Tn n+1 have to at least contain the correct singularities (in order to correctly sum up all logarithmically enhanced terms), but they are otherwise arbitrary. • Now reorder this series in a useful way …

  12. Reordering Example: “H” gluons • Assume we know Hgg and Hggg. Then reorder: • ds ~ dsgg + dsggg Sggg = Sggdsgg + Sggg (dsggg – Tgggggdsgg) = Sggdsgg + Sggg dcggg(generalises to n gluons) • I.e shower off gg and subtracted ggg matrix element. • Double countingavoidedsince singularities (shower) subtracted indcggg . • The shower kernels, Tgg, are precisely the singular subtraction terms used in HO perturbative calculations. As a basis we use Gehrman-Glover antennae: Use 1=Sn-Tnn+1Sn+1 Gehrmann-De Ridder, Gehrmann, Glover PLB612(2005)49

  13. What is the Difference? CKKW (& friends) in a nutshell: • Generate a n-jet Final State from n-jet (singular) ME • Construct a “fake” PS history • Apply Sudakov weights on each “line” in history  from inclusive n-jet ME to exclusive n-jet (i.e. probability that n-jet remains n-jet above cutoff)  gets rid of double counting when mixed with other ME’s. • Apply PS with no emissions above cutoff VINCIA in a nutshell: • Subtract PS singularities from n-jet ME (antenna subtraction) • Generate a n-jet Final State from the subtracted (finite) ME. • Apply PS with same antenna function  Leading Logs resummed + full NLO: divergent part already there  just include extra finite contribution in ds = ds0(0)+ ds1(0) + sing[ds0(1)] + F(1) + … + NNLO/NLL possible? + Easy to vary shower assumption  first parton shower with ‘error band’!(novelty in itself) Gehrmann-De Ridder, Gehrmann, Glover JHEP09(2005)056

  14. Medium pT: Three new infinite families of parton showers

  15. parton shower: ¹ ¹ q q q q g q g q ! ! o r ¹ ¹ q q g ! • Basic Formalism: Sudakov Exponentiation: • “Evolution” in X =measure of hardness (p2, pT2, … ) • z:energy-sharing • n partons  n+1.Cut off at some low scale  natural match to hadronisation models dipole shower: Sudakov Form Factor = ‘no- branching’ probability Parton Showers: the basicsEssentially: a simple approximation  infinite perturbative orders • Today, basically 2 (dual) approaches: • Parton Showers (12, e.g. HERWIG, PYTHIA) • and Dipole Showers (23, e.g. ARIADNE, VINCIA) • Formally correct in collinear limit pT(i) << pT(i-1),but (very) approximate for hard emissions (we return to this) • Depends on various phenomenological params(color screening cutoff, renorm. scale choice, ...) compare to data ‘best’ choice ~ `tune'

  16. The VINCIA code Illustration with quarks, sorry 1 VIrtual Numerical Collider with Interfering Antennae 2 • C++ code running: gluon cascade • Dipole shower with 3 different ordering variables: RI(m12,m23) = 4 s12s23/s = p2T;ARIADNE 3 RII(m12,m23) = 2 min(s12,s23) ~ m2PYTHIA m12 PS RIII(m12,m23) = 27 s12s23s31/s2 ~ p2T;PYTHIA m23

  17. = y s s = i j i j µ ¶ 1 y y X 1 2 2 3 ( ) ( ) n m C 1 1 ¡ ¡ + + + + a y y y y y y = 1 2 2 3 1 2 2 3 1 2 2 3 m n ; 2 2 y y y y 1 2 2 3 2 3 1 2 0 m n = ; The VINCIA code Illustration with quarks, sorry 1 VIrtual Numerical Collider with Interfering Antennae • For each evolution variable: • an infinite family of antenna functions, all with correct collinear and soft behaviour: • Using rescaled invariants: • Our antenna function (a.k.a. radiation function, a.k.a. subtraction function) is: 2 3 • Changes to Gehrman-Glover: •  ordinary DGLAP limit •  First parton shower with systematic possibility for variation (+ note: variation absorbed by matching!)

  18. 1 R 1 ¡ p ¢ ; w R = 1 1 § ¡ ; w 2 = § 2 ( ) [ ] ¢ Q U U 0 0 1 ¡ 2 ; = R ; Type III solved numerically (+ num. options for I and II as well) Splines, so only need to evaluate once. Hopefully  fast. Scale of next branching: numerically solve The VINCIA code VIrtual Numerical Collider with Interfering Antennae • Sudakov Factor contains integral over PS: Compact analytical solutions for types I and II (here without Cmn pieces)

  19. VINCIA – First Branching • Starting scale Q = 20 GeV • Stopping scale Qhad = 1 GeV • ~ 1st order expansion in perturbation theory • Axes: yab = m2ab / m2dipole Type I ~ pT2 More collinear Type II ~ m2 More soft

  20. µ ¶ 1 y y X 1 2 2 3 ( ) ( ) n m C 1 1 ¡ ¡ + + + + a y y y y y y = 1 2 2 3 1 2 2 3 1 2 2 3 m n ; 2 2 y y y y 1 2 2 3 2 3 1 2 0 m n = ; VINCIA – Matching – kT jet rates • Type ISudakov (~ pT evolution) withC00 = -1,0,1 2-jet only – no matching ~ standard Parton Shower Matched: 2-jet + 3-jet ME + PS ~ matched Parton Shower

  21. Outlook – VINCIA writeup in progress… • Construction of VINCIA shower MC • gluon shower MC • based on LO,done! • based on NLO, done! (but ‘trivial’ so far) • ‘They’re just fooling around with it’ [T. Becher] • Including initial-state radiation … • Including quarks … •  Hadron collider shower MC • Higher orders: NNLO, NLL ?

  22. Small pT: Colour Annealing in PYTHIA 6.4. First results

  23. h i ( ) N p ? h c Motivation • Min-bias collisions at the Tevatron • Well described by Rick Field’s “Tune A” of PYTHIA • Theoretical framework is from 1987. I made some improvements. • Wanted to use “Tune A” as initial reference target • But it kept on being different … Multiplicity distribution OK (plus a lot of other things), but <pT>(Nch) never came out right  something must be wrong or missing?

  24. Underlying Event and Color • Multiplicity in string fragmentation ~ log(mstring) • More strings  more hadrons, but average pT stays same • Flat <pT>(Nch) spectrum ~ ‘uncorrellated’ underlying event • But if MPI interactions correlated in colour • each scattering does not produce an independent string, • average pT not flat • Central point: multiplicity vs pT correllation probes color correllations! • What’s so special about Tune A? • It and all other realistic ‘tunes’ made turn out to have to go to the very most extreme end of the parameter range, with 100% correllation in final state. Sjöstrand & v Zijl : Phys.Rev.D36:2019,1987  “Old” Pythia model

  25. W W Normal W W Reconnected Color Reconnection (example) Soft Vacuum Fields? String interactions? Size of effect < 1 GeV? Sjöstrand, Khoze, Phys.Rev.Lett.72(1994)28 & Z. Phys.C62(1994)281 + more … Color Reconnections • Searched for at LEP • Major source of W mass uncertainty • Most aggressive scenarios excluded • But effect still largely uncertain ~ 10% • Prompted by CDF data and Rick Field’s ‘Tune A’ to reconsider. What do we know? • More prominent in hadron-hadron collisions? • What is <pT>(Nch) telling us? • Top mass? • Implications for LHC? • Problem: existing models only for e+e-WW OPAL, Phys.Lett.B453(1999)153 & OPAL, hep-ex0508062

  26. ³ h S t t t : r e n g p a r a m e e r b f N i i t t t t n : u m e r o p a r o n - p a r o n n e r a c o n s i t n ( ) ³ P n 1 1 i t n - - = t r e c o n n e c Color Reconnection (example) Soft Vacuum Fields? String interactions? Size of effect < 1 GeV? Color Annealing Sandhoff + PS, in Les Houches ’05 SMH Proceedings, hep-ph/0604120 • Toy model of (non-perturbative) color reconnections, applicable to any final state • At hadronisation time, each string piece has a probability to interact with the vacuum / other strings: • String formation for interacting string pieces determined by annealing-like minimization of ‘Lambda measure’ (~string length~log(m)~N) •  good enough for order-of-magnitude

  27. First Results • Improved Description of Min-Bias • Effect Still largely uncertain • Worthwhile to look at top etc Investigating effect on DØ top mass with D. Wicke (U. Wuppertal)

  28. Conclusions – Underlying Event • Ever-present yet poorly understood part of QCD. How ‘good’ are current physical models? • What’s the relation between min-bias and underlying events? Are there color reconnections? Are they more prolific in hadron collisions? Are there other collective phenomena?Does this influence top mass etc? • New generation of models address more detailed questions: correllations, baryon flow, … more? • Energy Extrapolation largest uncertainty for LHC! RHIC pp collisions vital?  energy scaling • Increasing interest, both among theorists and experimenters.

  29. Coming Soon! Recommended Reading: “Les Houches Guidebook to Monte Carlo Generators for hadron collider physics”: hep-ph/0403045 “QCD (&) Event Generators” (DIS’05 minireview): hep-ph/0507129 “QCD radiation in the production of high s-hat final states”: hep-ph/0511306 “Colour Annealing – A Toy Model of Colour Reconnections”: in Les Houches ‘05 SMH proceedings

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