N ew D eve l o p m e n t s i n P a r t o n S h owe r s P. S k a n d s ( C E R N ) Goal: solve this (Request to experiments: solve this) Fields Hits Symmetries 0100110 Amplitudes Acceptance Theory Experiment Monte Carlo Feedback Loop GEANT Resummation B-Field Strings .... ... Theory worked out to Measurements corrected to Hadron Level Hadron Level with acceptance cuts with acceptance cuts (~ detector-independent) (~ model-independent) Wo r k i n c o l l a b o r a t i o n w i t h W. G i e l e , D. K o s o w e r, A . L a r k o s k i , J . L o p e z - V i l l a r e j o ( s e c t o r s h o w e r s , h e l i c i t y - d e p e n d e n c e ) , A . G e h r m a n n - d e - R i d d e r, M . R i t z m a n n ( m a s s e f f e c t s , i n i t i a l - s t a t e r a d i a t i o n ) , E . L a e n e n , L . H a r t g r i n g ( o n e - l o o p c o r r e c t i o n s )
THEORY q ψ qi − 1 q ( i γ µ )( D µ ) ij ψ j L = ¯ q − m q ¯ ψ i ψ i 4 F a µ ν F aµ ν + quark masses and value of α s 2
q ψ qi − 1 q ( i γ µ )( D µ ) ij ψ j L = ¯ q − m q ¯ ψ i ψ i 4 F a µ ν F aµ ν “Nothing” Gluon action density: 2.4x2.4x3.6 fm QCD Lattice simulation from D. B. Leinweber, hep-lat/0004025 3
Perturbation Theory High%transverse- momentum% interac2on% Reality is more complicated 4
Monte Carlo Generators 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)) 1. So?/Collinear)Logarithms) 2. Matching) 2. Finite)Terms,)“K”Ifactors) roughly 3. Hadronisa7on) 3. Power)Correc7ons) (more)if)not)IR)safe)) 4. The)Underlying)Event) 4. ?) (+ many other ingredients: resonance decays, beam remnants, Bose-Einstein, …) 5
Bremsstrahlung Charges Stopped I S R I S R Associated field The harder they stop, the harder the fluctations that continue to become strahlung (fluctuations) continues 6
Bremsstrahlung dσ X+1 & dσ X+2& d d σ X$ σ X+2 & This gives an approximation to infinite-order tree-level cross sections (here “DLA”) But something is not right … Total cross section would be infinite … 7
Loops and Legs Summation The Virtual corrections X (2) X+1 (2) … are missing s p o X+1 (1) X+2 (1) X+3 (1) X (1) … o L Universality (scaling) Jet-within-a-jet-within-a-jet-... X+1 (0) X+2 (0) X+3 (0) Born … L e g s 8
Resummation dσ X+1 & dσ X+2& d d σ X$ σ X+2 & Unitarity Imposed by Event evolution : KLN: When (X) branches to (X+1): Virt = - Int(Tree) + F Gain one (X+1). Loose one (X). σ X+1 (Q) = σ X;incl – σ X;excl (Q) In LL showers : neglect F → includes both real and virtual corrections (in LL approx) 9
Bootstrapped pQCD Resummation Born + Shower X (2) X+1 (2) … Unitarity s p o X+1 (1) X+2 (1) X+3 (1) X (1) … o L Exponentiation Universality (scaling) X+1 (0) X+2 (0) X+3 (0) Born … Jet-within-a-jet-within-a-jet-... L e g s 10
Matching ► A (Complete Idiot’s) Solution – Combine 1. [X] ME + showering Run generator for X (+ shower) 2. [X + 1 jet] ME + showering Run generator for X+1 (+ shower) 3. … Run generator for … (+ shower) Combine everything into one sample ► Doesn’t work • [X] + shower is inclusive • [X+1] + shower is also inclusive ≠ What you What you want get Overlapping “bins” One sample 11
The Matching Game Shower off X Adding back full ME for X+n would be already contains LL part of all X+n overkill • Solution 1: “Additive” (most widespread) Seymour (Herwig), CPC 90 (1995) 95 CKKW (Sherpa), JHEP 0111 (2001) 063 Lönnblad (Ariadne), JHEP 0205 (2002) 046 Frixione-Webber (MC@NLO), JHEP 0206 (2002) 029 Add event samples, with modified weights + many more recent ... w X = |M X | 2 + Shower w X+1 = |M X+1 | 2 – Shower{w X } + Shower w X+n = |M X+n | 2 – Shower{w X ,w X+1 ,...,w X+n-1 } + Shower Only CKKW and MLM HERWIG: for X+1 @ LO (Shower = 0 in dead zone of angular-ordered shower) MC@NLO: for X+1 @ LO and X @ NLO (note: correction can be negative) CKKW & MLM : for all X+n @ LO (force Shower = 0 above “matching scale” and add ME there) SHERPA (CKKW), ALPGEN (MLM + HW/PY), MADGRAPH (MLM + HW/PY), PYTHIA8 (CKKW-L from LHE files), … 12
The Matching Game Shower off X Adding back full ME for X+n would be already contains LL part of all X+n overkill • Solution 2: “Multiplicative” Bengtsson-Sjöstrand (Pythia), PLB 185 (1987) 435 + more Bauer-Tackmann-Thaler (GenEva), JHEP 0812 (2008) 011 Giele-Kosower-Skands (Vincia), PRD84 (2011) 054003 One event sample w X = |M X | 2 + Shower Make a “course correction” to the shower at each order R X+1 = |M X+1 | 2 /Shower{w X } + Shower R X+n = |M X+n | 2 /Shower{w X+n-1 } + Shower Only VINCIA PYTHIA: for X+1 @ LO (for color-singlet production and ~ all SM and BSM decay processes) POWHEG Box POWHEG: for X+1 @ LO and X @ NLO (note: positive weights) HERWIG++ … VINCIA: for all X+n @ LO and X @ NLO (only worked out for decay processes so far) 13
Markov pQCD Start at Born level Loops | M F | 2 Generate “shower” emission +2 Work in Progress The VINCIA Code | M F +1 | 2 LL X a i | M F | 2 ∼ +1 i ∈ ant X ~ PYTHIA + POWHEG Correct to Matrix Element GKS, PRD78(2008)014026 ∈ This Talk +0 GKS, PRD84(2011)054003 | M F +1 | 2 PYTHIA trick P a i | M F | 2 a i → a i → +0 +1 +2 +3 Legs t a e p P | | e Unitarity of Shower R Z MC@NLO & POWHEG MLM & CKKW Virtual = − Real Z Correct to Matrix Element Z | M F | 2 → | M F | 2 + 2Re[ M 1 F M 0 F ] + Real POWHEG trick LO for 1 st emission “Matching Scale” LL for 2 nd emission and beyond → hierarchies not matched P . Skands - New Developments in Parton Showers 14
X ∈ The Denominator v | M F +1 | 2 P a i | M F | 2 a i → In a traditional parton shower, you would face the following problem: Existing parton showers are not really Markov Chains Further evolution (restart scale) depends on which branching happened last → proliferation of terms Number of histories contributing to n th branching ∝ 2 n n! ~ + + + j = 2 → 4 terms Parton- (or Catani-Seymour) Shower: ( ) + ~ j = 1 After 2 branchings: 8 terms After 3 branchings: 48 terms → 2 terms After 4 branchings: 384 terms (+ parton showers have complicated and/or frame-dependent phase-space mappings, especially at the multi-parton level) P . Skands - New Developments in Parton Showers 15
Matched Markovian Antenna Showers Antenna showers: one term per parton pair 2 n n! → n! Giele, Kosower, Skands, PRD 84 (2011) 054003 + Change “shower restart” to Markov criterion: Given an n -parton configuration, “ordering” scale is Q ord = min(Q E1 ,Q E2 ,...,Q En ) Unique restart scale, independently of how it was produced + Matching: n! → n Given an n -parton configuration, its phase space weight is: (+ generic Lorentz- |M n | 2 : Unique weight, independently of how it was produced invariant and on-shell phase-space factorization) Matched Markovian Antenna Shower: Parton- (or Catani-Seymour) Shower: After 2 branchings: 2 terms After 2 branchings: 8 terms After 3 branchings: 3 terms After 3 branchings: 48 terms After 4 branchings: 4 terms After 4 branchings: 384 terms + Sector antennae Larkosi, Peskin,Phys.Rev. D81 (2010) 054010 → 1 term at any order Lopez-Villarejo, Skands, JHEP 1111 (2011) 150 P . Skands - New Developments in Parton Showers 16
Approximations Q: How well do showers do? Exp : Compare to data. Difficult to interpret; all-orders cocktail including hadronization, tuning, uncertainties, etc Th : Compare products of splitting functions to full tree-level matrix elements Plot distribution of Log 10 (PS/ME) (fourth order) (second order) (third order) 1 1 1 Fraction of Phase Space Z 4 Z 5 Z 6 → → → Vincia 1.025 + MadGraph 4.426 Vincia 1.025 + MadGraph 4.426 Vincia 1.025 + MadGraph 4.426 -1 -1 -1 10 10 10 Matched to Z 3 Matched to Z 3 Matched to Z 3 → → → Strong Ordering Strong Ordering Strong Ordering S T RO N G O R D E R I N G GGG -2 -2 -2 10 10 ψ PS m -ord D -3 -3 -3 ARI 10 10 -4 -4 -4 10 10 -2 -1.5 -1 -0.5 0 0.5 -2 -1.5 -1 -0.5 0 0.5 -2 -1.5 -1 -0.5 0 0.5 log (PS/ME) log (PS/ME) log (PS/ME) 10 10 10 Dead Zone: 1-2% of phase space have no strongly ordered paths leading there * * fine from strict LL point of view: those points correspond to “unordered” non-log-enhanced configurations P . Skands - New Developments in Parton Showers 17
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