Emergent Phenomena in High-Energy Particle Collisions Peter Skands (Monash University) Image Credits: blepfo January, 2020 VINCIA VINCIA Universitetet i Stavanger
Monash University Named for General Sir John Monash (Australian WWI military commander) Founded in 1958 70,000 students (Australia’ s largest uni) ~ 20km SE of Melbourne City Centre Melbourne School of Physics & Astronomy ; 4 HEP theorists 2 HEP experimentalists (LHCb, CMS, COMET) + post docs & students Physics Lab (Also: LIGO, SKA, …) 2 � P E T ER S K A ND S
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? 4 � P E T ER S K A ND S
Proton-Proton Collision at E CM = 7 TeV ATL-2011-030 � 5 P E T ER S K A ND S
More than just a (fixed-order perturbative) expansion ๏ 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, … 6 � 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 � 7 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. 8 � 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 … 9 � P E T ER S K A ND S
This is just the physics of Bremsstrahlung cf. equivalent-photon approximation Weiszäcker, Williams ~ 1934 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 � 10 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 � 11 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) P ( z ) Partons ab |M F +1 ( . . . , a, b, . . . ) | 2 a || b → g 2 2( p a · p b ) |M F ( . . . , a + b, . . . ) | 2 s C → collinear: P(z) = “Dokshitzer-Gribov-Lipatov-Altarelli-Parisi splitting kernels ”, with z = E a /(E a +E b ) ( p i · p k ) Gluon j |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 → soft: Coherence → Parton j really emitted by (i,k) “dipole” or “antenna” + scaling violation: g s 2 → 4 πα s (Q 2 ) 12 � 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 • � 13 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) � 14 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 � 15 P E T ER S K A ND S
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