Emergent Phenomena in High-Energy Particle Collisions Peter Skands (Monash University) Image Credits: blepfo Physics Colloquium, UNSW VINCIA VINCIA November, 2019
Emergence G. H. Lewes (1875): "the emergent is unlike its components insofar as … it cannot be reduced to their sum or their difference." In Quantum Field Theory: Components = Elementary interactions encoded in the Lagrangian Perturbative expansions ~ elementary interactions to n th power What else is there? Structure beyond (fixed-order) perturbative expansions (in Quantum Chromodynamics) : Fractal scaling, of jets within jets within jets … (can actually be guessed) Confinement, of coloured partons within hadrons ($1M for proof) Image Credits: mrwallpaper.com Image Credits: Yeimaya
Quantum Chromodynamics (QCD) ๏ T HE THEORY OF QUARKS AND GLUONS ; THE STRONG NUCLEAR FORCE Elementary interactions encoded in the Lagrangian 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 m q : Quark Mass Terms Gluon-Field Kinetic Terms (Higgs + QCD condensates) and Self-Interactions Gauge Covariant Derivative: makes L invariant under SU(3) C rotations of ψ q Perturbative expansions ➜ Feynman diagrams (g s2 = 4 πα s ) A µ ψ 1 g s ψ qL ψ qR ψ j g s g s2 q = ψ 2 m q ψ 3 ¯ ψ q ψ q Would anything interesting happen if we put lots of these together? 3 � P E T ER S K A ND S
Proton-Proton Collision at E CM = 7 TeV ATL-2011-030 � 4 P E T ER S K A ND S
More than just a (fixed-order perturbative) expansion in α s ๏ Multi-parton structures beyond fixed-order perturbation theory • Jets (the fractal of perturbative QCD) ⟷ Infinite-order perturbative structures of indefinite particle number most of my research ⟷ universal amplitude structures in QFT Strings (strong gluon fields) ⟷ Dynamics of confinement ⟷ Hadronization phase transition ⟷ quantum-classical correspondence. Non- perturbative dynamics. String physics. String breaks. Hadrons ⟷ Spectroscopy (incl excited and exotic states) , lattice QCD, (rare) decays, mixing, light nuclei. Hadron beams → multiparton interactions, diffraction, … 5 � P E T ER S K A ND S
(Ulterior Motives for Studying QCD) There are more things in heaven and earth, Horatio, than are dreamt of in your philosophy The Standard Model Hamlet + … … … ? LHC Run 1+2: no “low-hanging” new physics 90% of data still to come ➜ higher sensitivity to smaller signals. High-statistics data ↔ high-accuracy theory � 6 P E T ER S K A ND S
1) Perturbative QCD ๏ asdasdasd Q 2 ∂α s ๏ The “running” of α s : ) = − α 2 s ( b 0 + b 1 α s + b 2 α 2 s + . . . ) , ∂ Q 2 = • sdfsdf 0.5 b 0 = 11 C A − 2 n f April 2012 2 ssdfsdf C A =3 for SU(3) n 5 f 2 ๏ 3 � s (Q) 12 π + � decays (N 3 LO) SDFGSFG n f 3 3 Lattice QCD (NNLO) 0 = 153 − 19 n f ๏ 5 b 3 = known 3 ๏ QSDFSD − A − 5 C A n f − 3 C F n f 7 8 π DIS jets (NLO) 5 2 8 0.4 1 24 π 2 2 b 1 = 17 C 2 Heavy Quarkonia (NLO) 24 π 2 = e + e – jets & shapes (res. NNLO) C b 2 Z pole fit (N 3 LO) pp –> jets (NLO) ๏ At high scales Q >> 1 GeV 0.3 • Coupling α s (Q) << 1 • Perturbation theory in α s should 0.2 be reliable : LO, NLO, NNLO, … From S. Bethke, Nucl.Phys.Proc.Suppl. E.g., in event shown on previous slide: 234 (2013) 229 0.1 E.g., in the event shown a few slides !•! 1st!jet:!! p T !=!520!GeV! ! ! QCD � ( � ) = 0.1184 ± 0.0007 s Z ago, each of the six “jets” had !•! 2nd!jet:!! p T !=!460!GeV! ! ! 1 10 100 !•! 3rd!jet:!! p T !=!130!GeV! ! ! Q [GeV] Q ~ E T = 84 - 203 GeV !•! 4th!jet:!! p T !=!!50!GeV ! ! Full symbols are results based on N3LO QCD, open circles are based on NNLO, open triangles and squares on NLO QCD. The cross-filled square is based on lattice QCD. 7 � P E T ER S K A ND S
The Infrared Strikes Back ๏ Naively, QCD radiation suppressed by α s ≈ 0.1 • Truncate at fixed order = LO, NLO, … • E.g., σ (X+jet)/ σ (X) ∝ α s Example: Pair production of SUSY particles at LHC 14 , with M SUSY ≈ 600 GeV Example: SUSY pair production at 14 TeV, with MSU LHC - sps1a - m~600 GeV Plehn, Rainwater, PS PLB645(2007)217 FIXED ORDER pQCD σ for X + jets much larger than inclusive X + 1 “jet” naive estimate inclusive X + 2 “jets” σ 50 ~ σ tot tells us that there will “always” be a ~ 50-GeV jet “inside” a 600-GeV process (Computed with SUSY-MadGraph) All the scales are high, Q >> 1 GeV, so perturbation theory should be OK … 8 � P E T ER S K A ND S
This is just the physics of Bremsstrahlung Radiation Radiation Accelerated a.k.a. Charges Bremsstrahlung Synchrotron Radiation Associated field The harder they get kicked, the harder the fluctations that continue to become strahlung (fluctuations) continues � 9 P E T ER S K A ND S
Can we build a simple theoretical model of this? cf. equivalent-photon approximation Weiszäcker, Williams ~ 1934 Radiation Radiation Accelerated a.k.a. Charges Bremsstrahlung Synchrotron Radiation ๏ The Lagrangian of QCD is scale invariant (neglecting small quark masses) • Characteristic of point-like constituents ➤ Observables depend on dimensionless quantities , like angles and energy ratios � 10 P E T ER S K A ND S
The rules of bremsstrahlung see e.g PS, Introduction to QCD , TASI 2012, arXiv:1207.2389 Most bremsstrahlung is driven by divergent 1 i propagators → simple structure a ∝ 2( p a · p b ) j b Gauge amplitudes factorize k in singular limits ( → universal “conformal” or “fractal” structure) Partons ab P(z) = Altarelli-Parisi splitting kernels, with z = E a /(E a +E b ) → collinear: P ( z ) |M F +1 ( . . . , a, b, . . . ) | 2 a || b → g 2 2( p a · p b ) |M F ( . . . , a + b, . . . ) | 2 s C Coherence → Parton j really emitted by (i,k) “antenna” Gluon j → soft: ( p i · p k ) |M F +1 ( . . . , i, j, k. . . ) | 2 j g → 0 → g 2 ( p i · p j )( p j · p k ) |M F ( . . . , i, k, . . . ) | 2 s C + scaling violation: g s 2 → 4 πα s (Q 2 ) 11 � P E T ER S K A ND S
Iterating the structure ๏ Repeated application of bremsstrahlung rules → nested factorizations • More and more partons resolved at increasingly smaller scales • Can be cast as a differential evolution : • d P /dQ 2 : differential probability to resolve more structure as function of a “resolution scale”, Q 2 ~ virtuality • It’s a quantum fractal : P is probability to resolve another parton as we decrease Q 2 : gluon → two gluons, quark → quark + gluon, gluon → quark-antiquark pair. • As we continue to “zoom”, the integrated probability for resolving another “jet” can naively exceed 100% • That’s what the X+jet cross sections were trying to tell us earlier: σ (X+jet) > σ (X) 12 � P E T ER S K A ND S
(From Legs to Loops) see e.g PS, Introduction to QCD , TASI 2012, arXiv:1207.2389 Unitarity : sum(probability) = 1 Kinoshita-Lee-Nauenberg: → → q k q k q k q k (sum over degenerate quantum states = finite: infinities must cancel!) q i q i q i Z g ik g jk g ik a a a ! q i Loop = Tree + F 2 q k − q i q i � � � M (0) 2Re[ M (1) M (0) ∗ ] � � q k +1 � Neglect non-singular piece, F → “Leading-Logarithmic” (LL) Approximation → Can also include loops-within-loops-within-loops … → Bootstrap for All-Orders Quantum Corrections! ๏ Parton Showers: reformulation of pQCD corrections as gain-loss diff eq. • Iterative (Markov-Chain) evolution algorithm, based on universality and unitarity |M n +1 | 2 • With evolution kernel ~ (or soft/collinear approx thereof) |M n | 2 • Generate explicit fractal structure across all scales (via Monte Carlo Simulation) • Evolve in some measure of resolution ~ hardness, virtuality, 1/time … ~ fractal scale 2 → 4 π α s (Q 2 ) • + account for scaling violation via quark masses and g s � 13 P E T ER S K A ND S
<latexit sha1_base64="5908dNHyEDP1woOqzatAGLOe9XI=">ACKXiclVBNSwMxEM36WevXqkcvwSJ4KrtV0GPRi8cK9gPapWT2TY0myxJVihL/Tle/CteFBT16h8xbfegrRcfDzem2FmXphwpo3nfThLyura+uFjeLm1vbOru39AyVRTqVHKpWiHRwJmAumGQytRQOKQzMcXk385h0ozaS4NaMEgpj0BYsYJcZKXbeKO9L6oSIUsv/YpyNu27JK3tT4EXi56SEctS67kunJ2kagzCUE63bvpeYICPKMphXOykGhJCh6QPbUsFiUEH2fTMT62Sg9HUtkSBk/VnxMZibUexaHtjIkZ6HlvIv7ltVMTXQZE0lqQNDZoijl2Eg8iQ3mAJq+MgSQhWzt2I6IDY1Y8Mt2hD8+ZcXSaNS9k/LlZuzUvUyj6OADtEROkE+OkdVdI1qI4oekBP6BW9OY/Os/PufM5al5x85gD9gvP1DUwHrXI=</latexit> Divide and Conquer ๏ Iterated/Nested Factorizations → Split the problem into many ~ simple pieces P event = P hard ⊗ P dec ⊗ P ISR ⊗ P FSR ⊗ P MPI ⊗ P Had ⊗ . . . z }| { Quantum mechanics → Probabilities → Make Random Choices (as in nature) ➜ Method of Choice: Markov-Chain Monte Carlo ➜ “Event Generators” Hard Process & Decays: Use process-specific (N)LO matrix elements → Sets “hard” resolution scale for process: Q MAX ISR & FSR (Initial & Final-State Radiation): Universal DGLAP equations → differential evolution, dP/dQ 2 , as function of resolution scale; run from Q MAX to Q Confinement ~ 1 GeV MPI (Multi-Parton Interactions) Additional (soft) parton-parton interactions: LO matrix elements → Additional (soft) “Underlying-Event” activity (Not the topic for today) Hadronization Non-perturbative model of color-singlet parton systems → hadrons 14 � P E T ER S K A ND S
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