Soft Physics Models q qi 1 q ( i )( D ) ij j L = i q m q i - PowerPoint PPT Presentation

S t a n d a r d M o d e l P h y s i c s , C o p e n h a g e n , A p r i l 2 0 1 2 Soft Physics Models q ψ qi − 1 q ( i γ µ )( D µ ) ij ψ j L = ¯ ψ i q − m q ¯ ψ i 4 F a µ ν F aµ ν P e t e r S k a n d s ( C E R N ) Many plots from mcplots.cern.ch - with A. Karneyeu, D. Konstantinov, S. Prestel, A. Pytel (+ funding from LPCC)

From Partons to Pions General-Purpose Monte Carlo models Start from pQCD (still mostly LO) . Extend towards Infrared. HERWIG/JIMMY, PYTHIA, SHERPA, EPOS Hard Physics Elastic & Diffractive Direction of this talk Elastic Min-Bias Jets/W/Z/H/Top/… ∞ 0 Λ QCD 5 GeV Elastic & Diffractive Unitarity Color Screening Hard Process Treated as separate class Showers (ISR+FSR) Regularization of pQCD Perturbative 2 → 2 (ME) Little predictivity Multiple 2 → 2 (MPI) Hadronization Resonance Decays PYTHIA uses string fragmentation , (N)LO Matching (N)LL HERWIG, SHERPA use cluster fragmentation (Also possible to start from non-perturbative QCD (via optical theorem) and extend towards UV) E.g., PHOJET, DPMJET, QGSJET, SIBYLL, … (But will not cover here) P . Skands 2

Factorization + Infrared Safety High%transverse- momentum% interac2on% Reality is more complicated 3

Perturbative Tools Factorization: Subdivide Calculation Multiple Parton Interactions go beyond existing theorems → perturbative short- Q F Q 2 distance physics in Underlying Event → Generalize factorization to MPI Q 2 Infrared * Safety IR fe Corrections ∝ Q 2 * Soft and Collinear UV … in minimum-bias, we typically do not have a hard scale (Q UV ~ Q IR ), wherefore all observables depend significantly on IR physics … Combining IR safe + IR sensitive observables → stereo vision : IR safe → overall energy flow/correlations IR sensitive → spectra and correlations of individual particles/tracks. P . Skands 4

Multiple Interactions = Allow several parton-parton interactions per hadron-hadron collision. Requires extended factorization ansatz. Earliest MC model (“old” PYTHIA 6 model) Sjöstrand, van Zijl PRD36 (1987) 2019 Bahr, Butterworth, Seymour: arXiv:0806.2949 [hep-ph] d σ 2 → 2 / dp 2 ⇠ dp 2 ⊥ ⊥ f Q F Q 2 Leading-Order pQCD × f o p 4 p 4 t ) n u ⊥ ⊥ o C Z d σ Dijet s i dp 2 r r e a w ⊥ p dp 2 h n i > 1 m o p 2 h ⊥ o S ⊥ , min c n r o o f t ( r a P Lesson from bremsstrahlung in pQCD: divergences → fixed-order breaks down Perturbation theory still ok, with resummation (unitarity) h n i < 1 → Resum dijets? Yes → MPI! σ 2 → 2 ( p ⊥ min ) = ⌥ n � ( p ⊥ min ) σ tot Parton-Parton Cross Section Hadron-Hadron Cross Section P . Skands 5

1: A Simple Model The minimal model incorporating single-parton factorization, perturbative unitarity, and energy-and-momentum conservation σ 2 → 2 ( p ⊥ min ) = ⌥ n � ( p ⊥ min ) σ tot Parton-Parton Cross Section Hadron-Hadron Cross Section 1. Choose p T min cutoff = main tuning parameter 2. Interpret <n>(p T min ) as mean of Poisson distribution Equivalent to assuming all parton-parton interactions equivalent and independent ~ each take an instantaneous “snapshot” of the proton 3. Generate n parton-parton interactions (pQCD 2 → 2) Veto if total beam momentum exceeded → overall (E,p) cons Ordinary CTEQ, MSTW, NNPDF, … 4. Add impact-parameter dependence → <n> = <n>(b) Assume factorization of transverse and longitudinal d.o.f., → PDFs : f(x,b) = f(x)g(b) b distribution ∝ EM form factor → JIMMY model Butterworth, Forshaw, Seymour Z.Phys. C72 (1996) 637 Constant of proportionality = second main tuning parameter 5. Add separate class of “soft” (zero-p T ) interactions representing interactions with p T < p T min and require σ soft + σ hard = σ tot → Herwig++ model Bähr et al, arXiv:0905.4671 P . Skands 6

2: Interleaved Evolution Equivalent to 1 at lowest order, but can include correlated evolution + generalizes “perturbative resolution” to higher twist Sjöstrand, P .S., JHEP 0403 (2004) 053; EPJ C39 (2005) 129 “New” Pythia model Fixed order (B)SM matrix elements 2 → 2 Parton Showers (matched to further Matrix Elements)  Underlying Event multiparton PDFs derived (note: interactions correllated in colour: from sum rules hadronization not independent) perturbative “intertwining”? Beam remnants Fermi motion / primordial k T + (x,b) correlations Corke, Sjöstrand JHEP 1105 (2011) 009 + KMR model (see talk by K. Zapp) P . Skands 7

Color Space

Color Flow in MC Models *) except as reflected by “Planar Limit” the implementation of QCD coherence effects in Equivalent to N C →∞ : no color interference * the Monte Carlos via angular or dipole ordering Rules for color flow: For an entire cascade: Illustrations from: P .Nason & P .S., PDG Review on MC Event Generators , 2012 Example: Z 0 → qq String #1 String #2 String #3 Coherence of pQCD cascades → not much “overlap” between strings → planar approx pretty good LEP measurements in WW confirm this (at least to order 10% ~ 1/N c2 ) P . Skands 9

Color Connections Each MPI (or cut Pomeron) exchanges color between the beams ► The colour flow determines the hadronizing string topology • Each MPI, even when soft, is a color spark Different models • Final distributions crucially depend on color space make different ansätze 1 FWD 2 3 CTRL 4 FWD 2 # of Sjöstrand & PS, JHEP 03(2004)053 strings P . Skands 10

Color Connections Each MPI (or cut Pomeron) exchanges color between the beams ► The colour flow determines the hadronizing string topology • Each MPI, even when soft, is a color spark Different models • Final distributions crucially depend on color space make different ansätze 1 FWD 2 3 CTRL 5 FWD 3 # of Sjöstrand & PS, JHEP 03(2004)053 strings Forward region (and forward-backward + forward-central correlations ) sensitive to beam-remnant break-up! P . Skands 11

Color Connections Better theory models needed N C → ∞ Rapidity Some ideas: Hydro? (EPOS) E-dependent string parameters? (DPMJET) Multiplicity ∝ N MPI “Color Ropes”? P . Skands 12

Color Reconnections? E.g., … Generalized Area Law (Rathsman: Phys. Lett. B452 (1999) 364) Better theory models needed Color Annealing (P .S., Wicke: Eur. Phys. J. C52 (2007) 133) … Do the systems really form and hadronize independently? Can Gaps be Created? Higgs → bb Should escape (low m H → small Γ ), but at least my CR models don’t yet respect that Rapidity Watch out for spurious effects My view: More ideas: Universality is ok (a string is a string) Coherent string formation? Problem is 3 ≠ ∞ < Color reconnections? Multiplicity ∝ N MPI Use String Area Law to govern String dynamics? collapse of color wavefunction P . Skands 13

D a t a http://lhcathome2.cern.ch/ S o f t P h y s i c s M o d e l s a n d L H C D a t a

Apples to Apples σ tot ≈ EXPERIMENT THEORY MODELS pp → pp ( * QED = ∞ ) ELASTIC QED+QCD ~ SINGLE DIFFRACTION pp → p+gap+X ≠ Small gaps suppressed but not zero Gap = observable pp → X+gap+X ≠ Small gaps suppressed but not zero DOUBLE DIFFRACTION Gap = observable pp → X (no gap) ≠ Large gaps suppressed but not zero INELASTIC NON-DIFFRACTIVE Gap = observable (+ multi-gap diffraction) Amplitudes Hits Monte Carlo Trigger Parton Showers B-Field Multiple Interactions Theory Experiment GEANT Feedback Loop Strings 0100110 Diffraction Acceptance Collective Effects Cuts Hadron Decays .... ... Theory worked out to Measurements corrected to Hadron Level Hadron Level with acceptance cuts with acceptance cuts 15 (~ detector-independent) (~ model-independent)

FSR: Jet Shapes Integrated Jet Shape Integrated Jet Shape as function of R as function of R Central Region |y| < 0.3 Forward 2.1 < |y| < 2.8 80 < p T < 110 80 < p T < 110 Core Tail Core Tail Central region OK Forward region less good Also ok for smaller p T values (Also larger UE uncertainties) only if UE is well tuned Issue for WBF? P . Skands Plots from mcplots.cern.ch 16

ISR * : Drell-Yan p T ATLAS: arXiv:1107.2381 CMS: arXiv:1110.4973 *From Quarks, at Q=M Z ISR X p ⊥ ( Z ) ∼ p ⊥ ( j ) ~ ~ j ∈ jets Drell-Yan p T Spectrum (at Q=M Z ) ISR ISR Particularly sensitive to 1. α s renormalization scale choice 2. Recoil strategy (color dipoles vs global vs …) 3. FSR off ISR (ISR jet broadening) Non-trivial result that modern GPMC shower models all reproduce it ~ correctly Note: old PYTHIA 6 model (Tune A) did not give correct distribution, except with extreme μ R choice (DW, D6, Pro-Q2O) P . Skands Plots from mcplots.cern.ch 17

ISR: Dijet Decorrelation ATLAS Phys.Rev.Lett. 106 (2011) 172002 (210 < p T < 260) ~ 1 in units of 180 degrees Dijet Azimuthal Decorrelation ~ ½ IR Safe Summary (ISR/FSR) : LO + showers generally in good O(20%) agreement with LHC (modulo bad tunes, pathological cases ) Room for improvement: Quantification of uncertainties is still more art than science. Cutting Edge : multi-jet matching at NLO and systematic NLL showering Bottom Line: perturbation theory is solvable. Expect progress. P . Skands Plots from mcplots.cern.ch 18