Fractals, Strings, and Particle Collisions P e t e r S k a n d s ( M o n a s h U n i v e r s i t y ) Physics Colloquium, Adelaide University May 6, 2016
Quantum Chromodynamics (QCD) ๏ T HE THEORY OF QUARKS AND GLUONS ; THE STRONG NUCLEAR FORCE The elementary interactions are encoded in the Lagrangian QFT → Feynman Diagrams → Perturbative Expansions (in α s ) ๏ g s2 = 4 π α s THE BASIC ELEMENTS OF QCD: QUARKS AND GLUONS 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 q ψ qi − 1 q ( i γ µ )( D µ ) ij ψ j L = ¯ q − m q ¯ µ ν F aµ ν ψ i ψ i 4 F a Gluon-Field Kinetic Terms m q : Quark Mass Terms and Self-Interactions (Higgs + QCD condensates) Gauge Covariant Derivative: makes L invariant under SU(3) C rotations of ψ q 2 P e t e r S k a n d s M o n a s h U n i v e r s i t y
More than just a (fixed-order perturbative) expansion in α s ๏ Two sources of fascinating multi-particle structures • Scale Invariance (apparent from the massless Lagrangian) • Confinement (win $1,000,000 if you can prove) Jets (the fractal of perturbative QCD) ⟷ amplitude structures most of my research in quantum field theory ⟷ factorisation & unitarity. Precision jet (structure) studies. Strings (strong gluon fields) ⟷ quantum-classical correspondence. String physics. String breaks. Dynamics of hadronization phase transition. Hadrons ⟷ Spectroscopy (incl excited and exotic states) , lattice QCD, (rare) decays, mixing, light nuclei. Hadron beams → multiparton interactions, diffraction, … 3 P e t e r S k a n d s M o n a s h U n i v e r s i t y
Ulterior Motives for Studying QCD There are more things in heaven and earth, Horatio, than are dreamt of in your philosophy Shakespeare, Hamlet. Run 2 now underway … The Standard Model Almost twice the energy (13 TeV vs 8 TeV) Higher intensities … (at least until last Friday) + … … … ? LHC Run 1: still no explicit “new physics” → we’re still looking for deviations from SM Accurate modelling of QCD improve searches & precision 4 P e t e r S k a n d s M o n a s h U n i v e r s i t y
Ulterior Motives for Studying QCD There are more things in heaven and earth, Horatio, than are dreamt of in your philosophy Shakespeare, Hamlet. Run 2 now underway … The Standard Model Almost twice the energy (13 TeV vs 8 Tev) Higher intensities … (at least until last Friday) + … … … ? LHC Run 1: still no explicit “new physics” → we’re still looking for deviations from SM Accurate modelling of QCD improve searches & precision 5 P e t e r S k a n d s M o n a s h U n i v e r s i t y
1: JETS • 1st jet: p T = 520 GeV, η = -1.4, φ = -2.0 • 2nd jet: p T = 460 GeV, η = 2.2, φ = 1.0 • 3rd jet: p T = 130 GeV, η = -0.3, φ = 1.2 6 • 4th jet: p T = 50 GeV, η = -1.0, φ = -2.9
QCD in the Ultraviolet 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 = 0.5 b 0 = 11 C A − 2 n f April 2012 2 C A =3 for SU(3) n 5 f 2 3 � s (Q) 12 π + � decays (N 3 LO) n f 3 3 Lattice QCD (NNLO) 0 = 153 − 19 n f 5 b 3 = known 3 − 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 !•! 1st!jet:!! p T !=!520!GeV! ! ! QCD � ( � ) = 0.1184 ± 0.0007 s Z !•! 2nd!jet:!! p T !=!460!GeV! ! ! 1 10 100 !•! 3rd!jet:!! p T !=!130!GeV! ! ! Q [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 e r S k a n d s M o n a s h U n i v e r s i t y
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 e r S k a n d s M o n a s h U n i v e r s i t y
Jets have fractal substructure see PS, Introduction to QCD , TASI 2012, arXiv:1207.2389 Most bremsstrahlung is 1 i driven by divergent propagators a ∝ 2( p a · p b ) → simple structure 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 s2 → 4 πα s (Q 2 ) 9 P e t e r S k a n d s M o n a s h U n i v e r s i t y
Jets have fractal substructure ๏ Can apply this many times → nested factorizations → iteratively build up fractal structure • Can be cast as a differential evolution in the resolution scale, dProb/dQ 2 • It’s a quantum fractal: P is probability to resolve another jet as we decrease the scale • Eventually, it becomes more unlikely not to resolve a jet, than to resolve one • That’s what the X+jet cross sections were trying to tell us earlier: σ (X+jet) > σ (X) 10 P e t e r S k a n d s M o n a s h U n i v e r s i t y
Monte Carlo Event Generators: Divide and Conquer ๏ Factorization → Split the problem into many (nested) pieces + Quantum mechanics → Probabilities → Random Numbers P event = P hard ⊗ P dec ⊗ P ISR ⊗ P FSR ⊗ P MPI ⊗ P Had ⊗ . . . 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 (More later) 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 11 P e t e r S k a n d s M o n a s h U n i v e r s i t y
This is just the physics of Bremsstrahlung Radiation Radiation Accelerated Charges Associated field The harder they get kicked, the harder the fluctations that continue to become strahlung (fluctuations) continues 12 P e t e r S k a n d s M o n a s h U n i v e r s i t y
From Legs to Loops see 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 approximate 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 e r S k a n d s M o n a s h U n i v e r s i t y
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