Physics at LHC lecture one Sven-Olaf Moch Sven-Olaf.Moch@desy.de DESY, Zeuthen in collaboration with Martin zur Nedden Humboldt-Universität, October 22, 2007, Berlin Sven-Olaf Moch Physics at LHC p.1
LHC LHC (the big picture) Sven-Olaf Moch Physics at LHC p.2
QCD primer Sven-Olaf Moch Physics at LHC p.3
Asymptotic freedom in QCD Effective couplung constant α s depends on resolution, momentum scale Q 0.6 0.5 α S ( Q 2 ) screening (like in QED) anti-screening (color charge of g) 0.4 0.3 0.2 0.1 0 cc α S (M 2 ) = 0.115 Z bb 4-loop 3-loop 2-loop 1-loop Z t t 1 10 10 2 10 3 10 4 Q 2 (GeV 2 ) At large scales: application of perturbation theory (but α s α QED ) Sven-Olaf Moch Physics at LHC p.4
Feynman rules (I) Propagators fermions, gluons, ghosts covariant gauge i p j δ ij i /p m a, µ p b, ν δ ab i g µν p 2 + (1 λ) pµ p ν (p 2 ) 2 a p b δ ab i p 2 Sven-Olaf Moch Physics at LHC p.5
Feynman rules (cont d) (II) Vertices a, µ i g (t a ) ji γ µ i j b, ν q a, µ p c, ρ r g f abc ((p q) ρ g µν + (q r) µ g νρ + (r p) ν g µρ ) a, µ b, ν c, ρ d, σ i g 2 f xac f xbd (g µν g ρσ g µσ g νρ ) i g 2 f xad f xbc (g µν g ρσ g µρ g νσ ) i g 2 f xab f xcd (g µρ g νσ g µσ g νρ ) a, µ b q c g f abc q µ Sven-Olaf Moch Physics at LHC p.6
Soft and collinear singularities e + e -annihilation (massless quarks) Born cross section σ (0) = 4πα2 3s e e + q q Sven-Olaf Moch Physics at LHC p.7
Soft and collinear singularities e + e -annihilation (massless quarks) Born cross section σ (0) = 4πα2 3s Study QCD corrections (real emissions) e e + q q e q e q g g e + q Cross section dimensional regularization D = 4 2ǫ (with f(ǫ) = 1 + O(ǫ 2 )) σ q qg = σ (0) 3 X q e 2 q f(ǫ) C F α s 2π scaled energies x 1 = 2 E q s and x 2 = 2 E q s Z e + dx 1 dx 2 x 2 1 + x 2 2 ǫ(2 x 1 x 2 ) (1 x 1 ) 1+ǫ (1 x 2 ) 1+ǫ q Sven-Olaf Moch Physics at LHC p.7
NLO epem Soft and collinear divergencies (0 x 1, x 2 1 and x 1 + x 2 1) p k 1 x 1 = x 2 E g s (1 cos θ 2g ) and p k 1 x 2 = x 1 E g s (1 cos θ 1g ) Integrate over phase space for real emission contributions σ q qg = σ (0) 3 X q e 2 q f(ǫ) C F α s 2π 2 ǫ 2 + 3 ǫ + 19 «2 + O(ǫ) Sven-Olaf Moch Physics at LHC p.8
NLO epem Soft and collinear divergencies (0 x 1, x 2 1 and x 1 + x 2 1) p k 1 x 1 = x 2 E g s (1 cos θ 2g ) and p k 1 x 2 = x 1 E g s (1 cos θ 1g ) Integrate over phase space for real emission contributions σ q qg = σ (0) 3 X q e 2 q f(ǫ) C F α s 2π Divergencies cancel against virtual contributions 2 ǫ 2 + 3 ǫ + 19 «2 + O(ǫ) e q e q 2 e + σ q q(g) = σ (0) 3 X q q e + e 2 q f(ǫ) C F α s 2π 2ǫ 2 3ǫ 8 + O(ǫ) «q Sven-Olaf Moch Physics at LHC p.8
Infrared safety Total cross section (R(s)) is directly calculable in perturbation theory (finite) R(s) = 3 X q e 2 q n 1 + α o s π + O(α2 s) Sven-Olaf Moch Physics at LHC p.9
Infrared safety Total cross section (R(s)) is directly calculable in perturbation theory (finite) R(s) = 3 X q e 2 q n 1 + α o s π + O(α2 s) e QCD factorization Collinear divergencies remain for hadronic observables factorization q q g µ e e e + q g q µ + q g q Left: single-hadron inclusive e + e -annihilation (time-like kinematics) Center: Drell-Yan process in pp-scattering (space-like kinematics) Right: Deep-inelastic e p-scattering (space-like kinematics) Sven-Olaf Moch Physics at LHC p.9
Perturbative QCD and factorization Sven-Olaf Moch Physics at LHC p.10
Perturbative QCD at colliders Hard hadron-hadron scattering constituent partons from each incoming hadron interact at short distance (large momentum transfer Q 2 ) p f i i Q µ µ QCD factorization separate sensitivity to dynamics from different scales j f j p σ pp X = X ijk f i (µ 2 ) f j (µ 2 ) ˆσ ij k α s (µ 2 ),Q 2, µ 2 D k X (µ 2 ) factorization scale µ, subprocess cross section ˆσ ij k for parton types i, j and hadronic final state X Sven-Olaf Moch Physics at LHC p.11
Hard scattering cross (I) section Standard approach to uncertainties in theoretical predictions d variation of factorization scale µ: dln µ 2 σ pp X = O(α l+1 s ) σ pp X = X ijk f i (µ 2 ) f j (µ 2 ) ˆσ ij k α s (µ 2 ), Q 2, µ 2 D k X (µ 2 ) Parton cross section ˆσ ij k calculable pertubatively in powers of α s constituent partons from incoming protons interact at short distances of order O(1/Q) Parton luminosity f i f j proton: very complicated multi-particle bound state colliders: wide-band beams of quarks and gluons Final state X: hadrons, mesons, jets,... fragmentation function D k X (µ 2 ) or jet algorithm interface with showering algorithms (Monte Carlo) Sven-Olaf Moch Physics at LHC p.12
Parton luminosity Feynman diagrams in leading order Proton in resolution 1/Q sensitive to lower momentum partons Sven-Olaf Moch Physics at LHC p.13
Parton luminosity Feynman diagrams in leading order Proton in resolution 1/Q sensitive to lower momentum partons Evolution equations for parton distributions f i predictions from fits to reference processes (universality) d d ln µ 2 f i(x, µ 2 ) = X h i P ik (α s (µ 2 )) f k (µ 2 ) (x) k Splitting functions P P = α s P (0) + α 2 s P (1) {z } + α3 s P (2) +... NLO: standard approximation (large uncertainties) Sven-Olaf Moch Physics at LHC p.13
Parton distributions evolution in proton Valence q q (additive quantum numbers) sea (part with q + q) 6 5 x f(x,q 2 ) at Q 2 = 15 GeV 4 gluon 3 2 sea 1 valence 0 10-2 10-1 1 x Parameterization (bulk of data from deep-inelastic scattering) structure function F 2 quark distribution scale evolution (perturbative QCD) gluon distribution Sven-Olaf Moch Physics at LHC p.14
Parton distributions evolution in proton Valence q q (additive quantum numbers) sea (part with q + q) 6 5 x f(x,q 2 ) at Q 2 = 10 4 GeV 4 gluon 3 2 sea 1 valence 0 10-2 10-1 1 x Parameterization (bulk of data from deep-inelastic scattering) structure function F 2 quark distribution scale evolution (perturbative QCD) gluon distribution Sven-Olaf Moch Physics at LHC p.14
PDFs from HERA to LHC to LHC HERA F 2 em F 2 -log10 (x) 5 x=6.32e-5 x=0.000102 x=0.000161 x=0.000253 x=0.0004 x=0.0005 x=0.000632 x=0.0008 x=0.0013 ZEUS NLO QCD fit H1 PDF 2000 fit H1 94-00 H1 (prel.) 99/00 ZEUS 96/97 4 x=0.0021 x=0.0032 BCDMS E665 NMC x=0.005 3 x=0.008 x=0.013 x=0.021 2 x=0.032 x=0.05 x=0.08 x=0.13 1 x=0.18 x=0.25 x=0.4 x=0.65 0 1 10 10 2 10 3 10 4 10 5 Q 2 (GeV 2 ) Precision HERA data on F 2 Scale evolution of PDFs in Q over two to three orders Sven-Olaf Moch Physics at LHC p.15
Vector boson production Kinematical variables (inclusive) energy (cms) s = Q 2 (space-like) scaling variable x = M 2 W ± /Z /s Sven-Olaf Moch Physics at LHC p.16
Vector boson production Kinematical variables (inclusive) energy (cms) s = Q 2 (space-like) scaling variable x = M 2 W ± /Z /s σ Br (nb) 1 σ Br(W lν) NNLO theory curves: Martin, Roberts, Stirling, Thorne σ Br(Z l + l - ) 20 years of measurements of W ± and Z cross sections at hadron colliders 10-1 CDF (630) D0 II (e) D0 II (µ) CDF II (e,1.2< η <2.8),223 pb -1 CDF II (e+µ),72pb -1 UA1 (µ) CDF I (e) CDF II Z(µ), 337pb -1 UA2 (e) DO I (e) CDF II Z(τ), 349pb -1 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5 E cm (TeV) Sven-Olaf Moch Physics at LHC p.16
Differential distributions Invariant mass distribution dσ dm 2 of lepton pair for Z-production in p p-collisions CDF data at s = 1.8 TeV and NLO QCD prediction Sven-Olaf Moch Physics at LHC p.17
Differential distributions Invariant mass distribution dσ dm 2 of lepton pair for Z-production in p p-collisions CDF data at s = 1.8 TeV and NLO QCD prediction M 4 dσ dm 2 = σ (0) 1 N M 2 s Z 1 0 dx 1 dx 2 δ x 1 x 2 M2 s «X e 2 q {f q (x 1 ) f q (x 2 ) + f q (x 1 ) f q (x 2 )} q dσ Double-differential cross section dm 2 local in PDFs dy y = 1 «2 ln x1 lepton-pair rapidity x 2 Sven-Olaf Moch Physics at LHC p.17
PDFs at attevatron and and LHC LHC Large overlap with HERA region Scale evolution of PDFs in Q over two to three orders from HERA region Sven-Olaf Moch Physics at LHC p.18
WImpact andon Z precision of LHC predictions W ±, Z-boson rapidity distribution (scale variation m W,Z 2 Anastasiou, Petriello, Melnikov 05 µ 2m W,Z ) NNLO QCD theoretical uncertainties (renormalization / factorization scale) at level of 1% Dissertori et al. 05 one of the few cross sections known to NNLO in pqcd we do believe to know it very well "Standard candle" process for parton luminosity Sven-Olaf Moch Physics at LHC p.19