QCD and Event Generators Lecture 1 of 3 Peter Skands Monash - PowerPoint PPT Presentation

QCD and Event Generators Lecture 1 of 3 Peter Skands Monash University (Melbourne, Australia) VINCIA VINCIA

Disclaimer ๏ This course covers: i.e., fixed perturbative order in : LO, NLO, … α s ๏ Lecture 1: QCD at Fixed Order ๏ Lecture 2: Beyond Fixed Order — Showers and Merging ๏ Lecture 3: Beyond Perturbations — Hadronization and Underlying Event ๏ Supporting Lecture Notes (~80 pages) : “Introduction to QCD” , arXiv:1207.2389 + MCnet Review: “General-Purpose Event Generators” , Phys.Rept.504(2011)145 ๏ It does not cover: Jet Physics → Lectures by A. Larkoski Plenty more could be said about QCD. ๏ Resummation techniques other than showers ๏ Focus here is on “users of QCD” Simulation of BSM physics ๏ Event Generator Tuning ๏ Monte Carlo (sampling) techniques ๏ Heavy Ions and Cosmic Rays ๏ + many other (more specialised) topics such as: heavy quarks, hadron and τ decays, exotic hadrons, lattice ๏ QCD, loop amplitude calculations, spin/polarisation, non-global logs, subleading colour, factorisation caveats, PDF uncertainties, DIS, low-x, low-energy, higher twist, pomerons, rescattering, coalescence, neutrino beams, … 2 QCD and Event Generators P. Skands Monash U.

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: fundamental-rep SU(3) colour indices i , j ∈ [1,3] α − 1 α ( i γ μ ) αβ ( D μ ) ij βδ q j q i q i α q i 4 F a μν F a μν : adjoint-rep SU(3) colour index ℒ = ¯ δ − m q ¯ a ∈ [1,8] : Dirac spinor indices α , β , . . . ∈ [1,4] Gluon Gauge Fields & Covariant Derivative ๏ Quark fields ( D μ ) ij = δ ij ∂ μ − ig s t a ij A a   ψ 1 μ ψ j L invariant under ψ 2 q = a a ∈ [1,8] ψ → U ψ   ⇒ Feynman rules ψ 3 SU(3) i , j ∈ [1,3] Local Gauge Symmetry j i with the Gell-Mann Matrices (t a = ½λ a ) (Traceless and Hermitian) 0 1 0 1 0 1 0 1 0 1 0 0 − i 0 1 0 0 0 0 1 λ 1 = A , λ 2 = A , λ 3 = A , λ 4 = 1 0 0 i 0 0 0 − 1 0 0 0 0 @ @ @ @ A 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 0 0 0 1 0 1 0 1 0 0 − i 0 0 0 0 0 0 √ 3 λ 5 = A , λ 6 = A , λ 7 = A , λ 8 = 1 0 0 0 0 0 0 0 1 0 0 − i B C √ @ @ @ 3 @ A − 2 i 0 0 0 1 0 0 i 0 0 0 √ 3 4 QCD and Event Generators P. Skands Monash U.

Interactions in Colour Space ℒ : q ( i γ µ )( D µ ) ij ψ j ¯ ๏ A quark-gluon interaction ψ i q − • (= one term in sum over colours) ( D μ ) ij = δ ij ∂ μ − ig s t a ij A a μ A 1 µ ¯ − i λ 1 2 g s ψ qR ψ qG ∝ 0 1 0 1 0 1 0 0 − i � � = 1 0 0 1 0 0 1 2 g s @ A @ A 0 0 0 0 ψ qG ψ qR Gluon (adjoint) colour index ∈ [1,8] Gluon Lorentz-vector index ∈ [0,3] ij γ µ ij γ µ − i g s t 1 αβ A 1 − i g s t 2 αβ A 2 µ − . . . µ Fermion spinor indices ∈ [1,4] Quark colour indices ∈ [1,3] Amplitudes Squared summed over colours → traces over t matrices → Colour Factors (see literature) 5 QCD and Event Generators P. Skands Monash U.