Towards LHC Phenomenology beyond Leading Order Gudrun Heinrich University of Durham Institute for Particle Physics Phenomenology 3 I P Birmingham, 25.11.09 Towards LHC Phenomenologybeyond Leading Order – p.1
The LHC . . . . . . has been planned long time ago . . . Towards LHC Phenomenologybeyond Leading Order – p.2
Linear Colliders also seem to have been supported . . . Towards LHC Phenomenologybeyond Leading Order – p.3
. . . so why do we say we are entering a New Era in Particle Physics? Towards LHC Phenomenologybeyond Leading Order – p.4
. . . so why do we say we are entering a New Era in Particle Physics? . . . because instead of hunting buffaloes, we are now hunting Higgs bosons . . . Towards LHC Phenomenologybeyond Leading Order – p.4
The Large Hadron Collider will shed light on the origin of mass ("Higgs mechanism") may discover supersymmetry or extra dimensions provide information about dark matter Towards LHC Phenomenologybeyond Leading Order – p.5
The Large Hadron Collider will shed light on the origin of mass ("Higgs mechanism") may discover supersymmetry or extra dimensions provide information about dark matter ∼ 1000 hadronic tracks in detector per event proton remnants or high energy interactions between quarks/gluons (QCD) ⇒ strong interactions play key role: enormous backgrounds ! Towards LHC Phenomenologybeyond Leading Order – p.5
The Large Hadron Collider will shed light on the origin of mass ("Higgs mechanism") may discover supersymmetry or extra dimensions provide information about dark matter ∼ 1000 hadronic tracks in detector per event proton remnants or high energy interactions between quarks/gluons (QCD) ⇒ strong interactions play key role: enormous backgrounds ! process events/sec QCD jets E T > 150 GeV 100 background 15 W → eν background t ¯ 1 t background Higgs, m H ∼ 130 GeV 0.02 signal gluinos, m ∼ 1 TeV 0.001 signal Towards LHC Phenomenologybeyond Leading Order – p.5
strong interactions basic principles of Quantum Chromo-Dynamics (QCD): asymptotic freedom: coupling α s ( Q 2 ) → 0 for Q 2 → ∞ 0.5 July 2009 α s (Q) Deep Inelastic Scattering constituents of hadrons (quarks and gluons) e + e – 0.4 Annihilation Heavy Quarkonia can be considered as freely interacting at high energies (i.e. short distances) 0.3 S. Bethke 0.2 0.1 α (Μ ) = 0.1184 ± 0.0007 QCD s Z 1 10 100 Q [GeV] factorisation: systematic separation of long-distance effects (non-perturbative) and short-distance cross sections (“hard scattering”) Towards LHC Phenomenologybeyond Leading Order – p.6
factorisation P 1 f a D c x 1 P 1 σ c ˆ ab x 2 P 2 f b P 2 σ ab ( p 1 , p 2 , Q 2 , Q 2 � f a ( x 1 , µ 2 f ) f b ( x 2 , µ 2 , α s ( µ 2 σ pp → X = f ) ⊗ ˆ r )) µ 2 µ 2 r f a,b,c ⊗ D c → X ( z, µ 2 f ) + O (1 /Q 2 ) f a , f b : parton distribution functions (universal), model proton structure ˆ σ ab : partonic hard scattering cross section, calculable order by order in perturbation theory D c → X ( z, µ 2 f ) : describing the final state e.g. fragmentation function, jet observable, etc. Towards LHC Phenomenologybeyond Leading Order – p.7
shortcomings of leading order predictions σ LO + α s ( µ ) ˆ σ = α k σ NLO ( µ ) + α 2 σ NNLO ( µ ) + . . . ˆ ˜ ˆ s ( µ ) ˆ s ( µ ) ˆ σ ( n ) /d ln( µ 2 ) = O ( α n +1 calculation at n -th order: d ˆ ) s truncation of perturbative series at LO ⇒ large renormalisation/factorisation scale dependence Towards LHC Phenomenologybeyond Leading Order – p.8
shortcomings of leading order predictions σ LO + α s ( µ ) ˆ σ = α k σ NLO ( µ ) + α 2 σ NNLO ( µ ) + . . . ˆ ˜ ˆ s ( µ ) ˆ s ( µ ) ˆ σ ( n ) /d ln( µ 2 ) = O ( α n +1 calculation at n -th order: d ˆ ) s truncation of perturbative series at LO ⇒ large renormalisation/factorisation scale dependence example: 3-jet observable in e + e − annihilation [A. Gehrmann-De Ridder, T. Gehrmann, N. Glover, GH ’09] uncertainty bands: M Z / 2 < µ < 2 M Z Towards LHC Phenomenologybeyond Leading Order – p.8
shortcomings of leading order predictions poor jet modelling Towards LHC Phenomenologybeyond Leading Order – p.9
shortcomings of leading order predictions poor jet modelling cases where shapes of distributions are not well predicted by LO (new partonic processes become possible beyond LO) Towards LHC Phenomenologybeyond Leading Order – p.9
shortcomings of leading order predictions poor jet modelling cases where shapes of distributions are not well predicted by LO (new partonic processes become possible beyond LO) Minimal Supersymmetric Standard Model (MSSM): would be ruled out already without radiative corrections: mass of lightest Higgs boson at LO: M h ≤ min ( M A , M Z ) · | cos 2 β | . . . Towards LHC Phenomenologybeyond Leading Order – p.9
identifying New Physics at hadron colliders peak: easy, backgrounds can be measured Towards LHC Phenomenologybeyond Leading Order – p.10
identifying New Physics at hadron colliders peak: easy, backgrounds can be measured shape: hard need signal/background shapes from theory shape in general well described by Monte Carlo tools combining (LO) matrix elements and parton shower (Sherpa, Alpgen, Helac, . . . ) Towards LHC Phenomenologybeyond Leading Order – p.10
identifying New Physics at hadron colliders peak: easy, backgrounds can be measured shape: hard need signal/background shapes from theory shape in general well described by Monte Carlo tools combining (LO) matrix elements and parton shower (Sherpa, Alpgen, Helac, . . . ) rate (e.g. H → W + W − ) : very hard need both shape and normalisation from theory ⇒ leading order (LO) is not sufficient ! Towards LHC Phenomenologybeyond Leading Order – p.10
identifying New Physics at hadron colliders peak: easy, backgrounds can be measured shape: hard need signal/background shapes from theory shape in general well described by Monte Carlo tools combining (LO) matrix elements and parton shower (Sherpa, Alpgen, Helac, . . . ) rate (e.g. H → W + W − ) : very hard need both shape and normalisation from theory ⇒ leading order (LO) is not sufficient ! problem: typically multi-particle final states ⇒ calculations of higher orders increasingly difficult until recently: LO tools highly automated, whereas NLO calculations tedious case-by case exercises Towards LHC Phenomenologybeyond Leading Order – p.10
identifying New Physics at hadron colliders peak: easy, backgrounds can be measured shape: hard need signal/background shapes from theory shape in general well described by Monte Carlo tools combining (LO) matrix elements and parton shower (Sherpa, Alpgen, Helac, . . . ) rate (e.g. H → W + W − ) : very hard need both shape and normalisation from theory ⇒ leading order (LO) is not sufficient ! problem: typically multi-particle final states ⇒ calculations of higher orders increasingly difficult until recently: LO tools highly automated, whereas NLO calculations tedious case-by case exercises now paradigm change: we are moving towards automated NLO tools Towards LHC Phenomenologybeyond Leading Order – p.10
(heavy) SUSY particles: decay through cascades emitting quarks and leptons signatures: energetic jets and leptons, missing E T QCD radiation generates additional hard jets ¯ q q ¯ b ¯ q ˜ q χ 0 ˜ g 1 q t ˜ g l + ˜ g χ 0 ˜ l ˜ χ 0 2 b 1 l − b ¯ b b l − l + Towards LHC Phenomenologybeyond Leading Order – p.11
����������������������������������� ���������������������������� ������������������� �� Towards LHC Phenomenologybeyond Leading Order – p.12
ingredients for m -particle observable at NLO virtual part (one-loop integrals): NLO = A 2 /ǫ 2 + A 1 /ǫ + A 0 A V � � dσ V ∼ Re A † LO A V NLO real radiation part: soft/collinear emission of massless particles ⇒ need subtraction terms � sing dσ S = − A 2 /ǫ 2 − A 1 /ǫ + B 0 ⇒ � � � � dσ R − dσ S � σ NLO = dσ V dσ S + + ���� ǫ =0 m +1 s m cancel poles � �� � � �� � analytically numerically ǫ =0 � �� � numerically Towards LHC Phenomenologybeyond Leading Order – p.13
Modular structure Tree Modules One-Loop Module IR Modules � 2 Re ( A LO † A NLO,V ) � |A LO | 2 ⊕ ⊕ j S j j ✻ � |A NLO,R | 2 ⊖ j S j has been bottleneck so far Towards LHC Phenomenologybeyond Leading Order – p.14
NLO complexity calculations increasingly difficult for more particles in final state example for time scale to add one parton: pp → 2 jets at NLO (4-point process): Ellis/Sexton 1986 pp → 3 jets at NLO (5-point process): Bern et al, Kunszt et al. 1993-95 pp → 4 jets at NLO (6-point process): not yet available Towards LHC Phenomenologybeyond Leading Order – p.15
progress more efficient techniques to calculate loop amplitudes unitarity-based methods e.g. BlackHat, Rocket, CutTools, analytic, . . . improved methods based on Feynman diagrams e.g. GOLEM, Denner et. al, . . . Towards LHC Phenomenologybeyond Leading Order – p.16
Recommend
More recommend
