Introduction Hadron spectrum Quark masses etc. Summary Physical predictions from lattice QCD Christian Hoelbling Bergische Universität Wuppertal Budapest: S. Katz Marseille: L. Lellouch, A. Portelli, A. Sastre Wuppertal: Sz. Borsanyi, S. Durr, Z. Fodor, S. Krieg, T. Kurth, T. Lippert, K. Szabo, B. Toth FFP 14, Marseille July 17, 2014 1/39 Christian Hoelbling (Wuppertal) Physical predictions from lattice QCD
Introduction Hadron spectrum Quark masses etc. Summary How to stay clean in the brown muck Purpose of lattice QCD QCD fundamental objects: quarks and gluons QCD observed objects: protons, neutrons ( π , K, . . . ) ! Huge discrepancy: not even the same particles observed as in the Lagrangean ➛ Perturbation theory has no chance Need to solve low energy QCD to: Compute hadronic and nuclear properties “people who love QCD” Masses, decay widths, scattering lengths, thermodynamic properties, . . . Compute hadronic background “people who hate QCD” Non-leptonic weak MEs, quark masses, g-2, . . . 2/39 Christian Hoelbling (Wuppertal) Physical predictions from lattice QCD
Introduction Hadron spectrum Quark masses etc. Summary How to stay clean in the brown muck LATTICE DISCRETIZATION ν UV cutoff: space-time lattice μ Hypercubic, spacing a Momentum cutoff p µ < 2 π/ a IR cutoff on finite lattice a U (x+e ) Ψ (x) μ μ ☞ anti-commuting quark fields ψ ( x ) live on the sites � x +ˆ µ dz µ A µ ( z ) ∈ SU ( 3 ) live on links ☞ gluon fields U µ ( x ) = e ig x Essential: QCD perturbative on cutoff scale 1 / a ≫ Λ QCD (asymptotic freedom) Perform Euclidean path integral stochastically 3/39 Christian Hoelbling (Wuppertal) Physical predictions from lattice QCD
Introduction Hadron spectrum Quark masses etc. Summary How to stay clean in the brown muck Lattice Lattice QCD = QCD when Cutoff removed (continuum limit) Infinite volume limit taken At physical hadron masses (Especially π ) Numerically challenging to reach light quark masses Statistical error from stochastic estimate of the path integral 4/39 Christian Hoelbling (Wuppertal) Physical predictions from lattice QCD
Introduction Hadron spectrum Quark masses etc. Summary Lattice setup Landscape M π vs. a ETMC '09 (2) ETMC '10 (2+1+1) 600 MILC '10 MILC '12 QCDSF '10 (2) QCDSF-UKQCD '10 BMWc '10 M π [MeV] BMWc'08 400 PACS-CS '09 RBC/UKQCD '10 JLQCD/TWQCD '09 HSC '08 BGR '10 200 CLS '10 (2) 0 0 0.05 0.1 0.15 a[fm] 5/39 Christian Hoelbling (Wuppertal) Physical predictions from lattice QCD
Introduction Hadron spectrum Quark masses etc. Summary Lattice setup Landscape L vs. M π ETMC '09 (2) 6 ETMC '10 (2+1+1) MILC '10 MILC '12 5 0.1% QCDSF '10 (2) QCDSF-UKQCD '10 BMWc '10 4 BMWc'08 0.3% L[fm] PACS-CS '09 RBC/UKQCD '10 3 JLQCD/TWQCD '09 1% HSC '08 BGR '10 (2) 2 CLS '10(2) 1 100 200 300 400 500 600 700 M π [MeV] 6/39 Christian Hoelbling (Wuppertal) Physical predictions from lattice QCD
Introduction Hadron spectrum Quark masses etc. Summary Lattice setup Landscape M K vs. M π ETMC '10 (2+1+1) MILC '10 800 QCDSF-UKQCD '10 BMWc'10 PACS-CS '09 1/2 [MeV] JLQCD/TWQCD '09 RBC-UKQCD '10 600 HSC '08 2 ) 2 -M π (2M K 400 200 0 200 400 600 M π [MeV] 7/39 Christian Hoelbling (Wuppertal) Physical predictions from lattice QCD
Introduction Hadron spectrum Quark masses etc. Summary Lattice setup Skeleton of a lattice calculation 600 Compute target observable M π [MeV] 400 Extrapolate to physical point 200 Renormalize if necessary 0 0 0.05 0.1 0.15 a[fm] 6 800 5 0.1% 1/2 [MeV] 4 600 0.3% L[fm] 2 ) 2 -M π 3 1% (2M K 400 2 1 200 0 200 400 600 100 200 300 400 600 700 500 M π [MeV] M π [MeV] 8/39 Christian Hoelbling (Wuppertal) Physical predictions from lattice QCD
Introduction Hadron spectrum Quark masses etc. Summary We have done our homework Ground state mass extraction With operators that couple to the ground state (e.g.to the π + ) � Ψ d γ µ γ 5 Ψ u � � ¯ ( � A µ ( t ) = x , t ) x � one can obtain asymptotically the ground state mass → |� π | A 0 | 0 �| 2 C ( t ) 0 ( t ) A 0 ( 0 ) � t →∞ t →∞ C ( t ) = � A † e − M π t → M eff − ln − π 2 M π C ( t + 1 ) u t 0 A 0 A 0 d 9/39 Christian Hoelbling (Wuppertal) Physical predictions from lattice QCD
Introduction Hadron spectrum Quark masses etc. Summary We have done our homework Effective masses and correlated fits 0.9 0.8 0.7 0.6 a M 0.5 N 0.4 0.3 K 0.2 0.1 0 4 8 12 t/a 10/39 Christian Hoelbling (Wuppertal) Physical predictions from lattice QCD
Introduction Hadron spectrum Quark masses etc. Summary We have done our homework Chiral fit 2 O 1.5 N M [GeV] 1 ~0.125 fm a~ 0.5 a~ ~0.085 fm a~ ~0.065 fm physical M p 0 0.1 0.2 0.3 0.4 0.5 2 [GeV 2 ] M p 11/39 Christian Hoelbling (Wuppertal) Physical predictions from lattice QCD
Introduction Hadron spectrum Quark masses etc. Summary We have done our homework Finite volume effects The easy part: Virtual pion finite V effects Hadrons see mirror charges Exponential in lightest particle (pion) mass = cM 1 / 2 Leading effects M X ( L ) − M X L − 3 / 2 e M π L π (Colangelo et. al., 2005) M X 0.8 Nucleon M p L=4 Pion M p L=4 0.225 -M p L -3/2 fit -M p L -3/2 fit c 1 + c 2 e L c 1 + c 2 e L Colangelo et. al. 2005 Colangelo et. al. 2005 0.22 0.75 aM N aM p 0.215 0.7 0.21 12 16 20 24 28 32 36 12 16 20 24 28 32 36 L/a L/a More severe (if present): FV correction in resonances QED: 1 / L terms from photons (Davoudi, Savage 2014; BMWc 2014) 12/39 Christian Hoelbling (Wuppertal) Physical predictions from lattice QCD
Introduction Hadron spectrum Quark masses etc. Summary We have done our homework Systematic uncertainties Method: Large number of analyses including“all reasonable” choices Construct (weighted) distribution of results Median of this distribution ➛ final result Central 68 % ➛ systematic error Statistical error from bootstrap of the medians median median Omega 0.25 Nucleon 0.3 0.2 0.2 0.15 0.1 0.1 0.05 1640 1660 1680 1700 1720 900 920 940 960 980 M N [MeV] M Ω [MeV] 13/39 Christian Hoelbling (Wuppertal) Physical predictions from lattice QCD
Introduction Hadron spectrum Quark masses etc. Summary We have done our homework The light hadron spectrum 2000 Budapest-Marseille-Wuppertal collaboration O X * 1500 S * X M[MeV] D S L 1000 N r K* experiment 500 K width input p QCD 0 (BMWc, 2008) 14/39 Christian Hoelbling (Wuppertal) Physical predictions from lattice QCD
Introduction Hadron spectrum Quark masses etc. Summary We have done our homework Excited states Extracting excited states is much tougher: ☞ Extraction of energy levels is harder: Die out at large t need to use small t correlators ➠ ☞ Once extracted, relation to V → ∞ is nontrivial: Disentangle resonances and scattering states at finite volume Finite volume energy levels Spectral density E L 15/39 Christian Hoelbling (Wuppertal) Physical predictions from lattice QCD
Introduction Hadron spectrum Quark masses etc. Summary Relevance of fine structure Is the fine structure relevant? 1000 QED quark mass Proton, neutron: 800 2 ] mass [MeV/c 3 quarks 600 QCD Proton: uud 400 Neutron: udd 200 0 m u < m d : M p < M n m u = m d : M p > M n Proton decays M p + M e − � M n No hydrogen Proton Neutron 16/39 Christian Hoelbling (Wuppertal) Physical predictions from lattice QCD
Introduction Hadron spectrum Quark masses etc. Summary Relevance of fine structure Is the fine structure relevant? 940 QED quark mass Proton, neutron: 939 2 ] mass [MeV/c 3 quarks 938 QCD Proton: uud 937 Neutron: udd 936 935 m u < m d : M p < M n m u = m d : M p > M n Proton decays M p + M e − � M n No hydrogen Proton Neutron 16/39 Christian Hoelbling (Wuppertal) Physical predictions from lattice QCD
Introduction Hadron spectrum Quark masses etc. Summary Relevance of fine structure Is the fine structure relevant? 940 QED quark mass Proton, neutron: 939 2 ] mass [MeV/c 3 quarks 938 QCD Proton: uud 937 Neutron: udd 936 935 m u < m d : M p < M n m u = m d : M p > M n Proton decays M p + M e − � M n No hydrogen Proton Neutron 16/39 Christian Hoelbling (Wuppertal) Physical predictions from lattice QCD
Introduction Hadron spectrum Quark masses etc. Summary Relevance of fine structure Is the fine structure relevant? 940 Proton, neutron: 939 electron mass 2 ] mass [MeV/c 3 quarks 938 QED Proton: uud 937 quark mass Neutron: udd 936 935 m u < m d : M p < M n m u = m d : M p > M n Proton decays M p + M e − � M n No hydrogen Proton Neutron 16/39 Christian Hoelbling (Wuppertal) Physical predictions from lattice QCD
Introduction Hadron spectrum Quark masses etc. Summary Relevance of fine structure Anthropic puzzle? The light up quark 1 st generation: m u < m d Why? 2 nd generation: m c > m s 3 rd generation: m t > m b 17/39 Christian Hoelbling (Wuppertal) Physical predictions from lattice QCD
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