Terascale Meeting, U of Oregon, Eugene, February 2009 Modeling the Underlying Event Modeling the Underlying Event Peter Skands Theoretical Physics, Fermilab
Models – – Classic Example Classic Example Models UA5 @ 540 GeV, single pp, charged multiplicity in minimum-bias events Simple physics More Physics: models ~ Poisson Multiple interactions + Can ‘tune’ to get impact-parameter average right, but dependence much too small fluctuations Moral (will return to the models later) : � inadequate 1) It is not possible to ‘tune’ anything better physics model than the underlying physics model allows 2) Failure of a physically motivated model usually points to more, interesting physics Underlying Event in Herwig and Pythia ‐ 2 Peter Skands
Monte Carlo Philosophy Monte Carlo Philosophy ► 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. Soft/Collinear Logarithms 2. Matching 2. Finite Terms, “K” ‐ factors roughly roughly 3. Hadronisation 3. Power Corrections (more if not IR safe) 4. The Underlying Event 4. ? (+ many other ingredients: resonance decays, beam remnants, Bose-Einstein, …) Asking for complete events is a tall order … Underlying Event in Herwig and Pythia ‐ 3 Peter Skands
Additional Sources of Particle Production Additional Sources of Particle Production ► Starting point: matrix element + parton shower • hard parton-parton scattering � (normally 2 � 2 in MC) Q F • + bremsstrahlung associated with it ISR � � 2 � n in (improved) LL approximation ISR FSR FSR … 2 � 2 2 � 2 FSR FSR ► But hadrons are not elementary ISR ISR ► + QCD diverges at low p T Q F � multiple perturbative parton-parton collisions Q F >> Λ QCD e.g. 4 � 4, 3 � 3, 3 � 2 ► No factorization theorem Underlying Event has perturbative part! � Herwig++, Pythia, Sherpa: MPI models Underlying Event in Herwig and Pythia ‐ 4 Peter Skands
Additional Sources of Particle Production Additional Sources of Particle Production Q F >> Λ QCD + ME+ISR/FSR Stuff at + perturbative MPI Q F ~ Λ QCD ► Hadronization Q F ► Remnants from the incoming beams ISR ISR ► Additional (non-perturbative / FSR FSR … collective) phenomena? 2 � 2 2 � 2 • Bose-Einstein Correlations FSR FSR • Non-perturbative gluon exchanges / ISR ISR color reconnections ? • String-string interactions / collective Q F multi-string effects ? • “Plasma” effects? Need-to-know issues for IR • Interactions with “background” sensitive quantities (e.g., N ch ) vacuum, remnants, or active medium? Underlying Event in Herwig and Pythia ‐ 5 Peter Skands
Naming Conventions Naming Conventions See also Tevatron-for-LHC Report of the QCD Working Group, hep-ph/0610012 Some freedom in how much particle ► Many nomenclatures being used. production is ascribed to each: “hard” vs “soft” models • Not without ambiguity. I use: Q cut … ISR ISR FSR FSR … 2 � 2 2 � 2 FSR FSR ISR ISR … Q cut Underlying Beam Primary Event Remnants Interaction Note: each is colored � Not possible to (~ trigger) separate clearly at hadron level Inelastic, non-diffractive Underlying Event in Herwig and Pythia ‐ 6 Peter Skands
Why Perturbative MPI? 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 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 = color-screening cutoff (E cm -dependent, but large uncert) Saturation? Current models need MPI IR cutoff > PS IR cutoff Underlying Event in Herwig and Pythia ‐ 7 Peter Skands
Why Perturbative MPI? Why Perturbative MPI? ► + Experimental investigations (AFS, CDF) • Jet #1 Direction Jet #1 Direction Find pairwise balanced minijets, Δφ Δφ • Evidence for “lumpy” components in “Toward” “Toward” “transverse” regions “TransMAX” “TransMIN” “TransMAX” “TransMIN” • But that overview should be given by an “Away” “Away” experimentalist Jet #2 Direction ► Here will focus on • Given that these are the models used by Tevatron and LHC experiments (and for pp at RHIC), what are their properties? • What are they missing? NB: Herwig: no MPI. ► Especially in low-x context Here will talk about • Jimmy/Herwig++ � discussion session Underlying Event in Herwig and Pythia ‐ 8 Peter Skands
How many? How many? ► The interaction cross section • With constant α s , … is an inclusive number. neglecting x integrals ► … so an event with n interactions … • … counts n times in σ 2j but only once in σ tot • Poisson only exact if the individual interactions are completely independent, so will be modified in real life � Her wig starts directly from Poisson � n , but includes vetos if (E,p) violated. � Pythia uses a transverse-momentum ordered Sudakov formalism, interleaved with the shower evolution ~ resummation. (E,p) explicitly conserved at each step. Underlying Event in Herwig and Pythia ‐ 9 Peter Skands
How many? How many? ► Different Cocktails � Probability distribution of N MPI Not necessary to believe in these particular Note: This is min- bias; <N int > larger numbers. for UE. But good to know this is what is obtained with out- of-the-box MC models <N int > new ~ 3.5 <N int > old ~ 6.0 Important Difference: Old model had no showers off MPI Buttar et al., Les Houches SMH Proceedings (2007) arXiv:0803.0678 [hep-ph] More plots collected at http://home.fnal.gov/~skands/leshouches-plots/ Underlying Event in Herwig and Pythia ‐ 10 Peter Skands
Different Cocktails? Different Cocktails? ► Observed charged particle multiplicity Moral: vastly different cocktails can give similar answers (stable particle definition: c τ ≥ 10mm) Buttar et al., Les Houches SMH Proceedings (2007) arXiv:0803.0678 [hep-ph] More plots collected at http://home.fnal.gov/~skands/leshouches-plots/ Underlying Event in Herwig and Pythia ‐ 11 Peter Skands
Impact Parameter Impact Parameter ► Impact parameter: central vs. peripheral collisions All models currently assume f(x,b) = f(x) g(b) � Obviously not the final word. Large difference between ► Large fluctuations � g(b) needs to be “lumpy” peripheral and central “No” UE in peripheral “Saturated” UE in “Jet pedestal” effect collisions (low central collisions multiplicity) (high multiplicity) Pythia: default: double gaussian: “hard core” (valence lumps?) Core size a 2 /a 1 = 0.5 Contains fraction β = 0.4 Herwig: EM form factor, but width rescaled to smaller radius μ ep = 0.7 GeV 2 � μ = 1.5 GeV 2 Underlying Event in Herwig and Pythia ‐ 12 Peter Skands
Multi- -parton pdfs parton pdfs Multi Snapshot of proton: re-use 1-parton inclusive f(x) Herwig Subsequently impose (E,p) cons by vetoing events that violate it. 1-parton inclusive f(x) = pdf for “trigger” scattering Pythia Multi-parton pdfs explicitly constructed, respecting flavour and momentum sum rules quarks gluons Underlying Event in Herwig and Pythia ‐ 13 Peter Skands
Interleaved Evolution Interleaved Evolution Pythia “New” Pythia model Fixed order Matrix elements parton shower (matched to further matrix elements) � Underlying Event multiparton (interactions correllated in colour: PDFs derived hadronization not independent) from sum rules perturbative “intertwining”? Beam remnants Fermi motion / primordial k T Sjöstrand, PS; JHEP03(2004)053, EPJC39(2005)129 Underlying Event in Herwig and Pythia ‐ 14 Peter Skands
Underlying Event and Color 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 re-connections too Underlying Event in Herwig and Pythia ‐ 15 Peter Skands
Underlying Event and Color 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 re-connections too Underlying Event in Herwig and Pythia ‐ 16 Peter Skands
Color Connections Color Connections ► ‘Old’ Model Pythia • Set up color flow for hard interaction + shower as usual • Treat MPI as separate color singlet systems – alternatively attach gluons where they would cause the smallest ‘kinks’ ► ‘New’ Model • ‘Random’ • Rapidity-ordered (connect systems along rapidity chain) • Lambda-optimized (cheating) ► ‘Random’ Herwig Underlying Event in Herwig and Pythia ‐ 17 Peter Skands
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