Aktuelle Entwicklungen in der Theorie II Gitter-Eichtheorie

1. Aktuelle Entwicklungen in der Theorie II Gitter-Eichtheorie • Hartmut Wittig • Institut für Kernphysik und Helmholtz Institut Mainz • KHuK Jahrestagung • 30. November 2012 TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAAAAAAAAAAA

2. Overview Nucleon properties from lattice QCD Resonances and scattering Hadronic contributions to the muon QCD Thermodynamics Ab initio nuclear physics 2 | Overview

3. I. Nucleon Properties 3 | Nucleon Properties fromLattice QCD

4. Nucleon properties from lattice QCD • Nucleon form factors, charge radii and axial charge • Average momentum fraction • Nucleon mass and sigma term • Strangeness in the nucleon Achieve full control over systematic errors Provide stable lattice estimate 4 | Nucleonpropertiesfromlattice QCD

5. Nucleon form factors and axial charge • Experimental dependence and charge radii not reproduced • Lattice simulations underestimate axial charge • Systematic effects not fully controlled • Lattice artefacts • Chiral extrapolation to physical pion mass • Finite-volume effects • “Contamination” from excited states 5 | Nucleonpropertiesfromlattice QCD • Determine form factors from ratios of three- and two-point functions, • Source-sink separation fmdue to bad signal/noise ratio

6. Nucleon form factors and axial charge • Correlator ratio: • Summed insertion: 6 | Nucleonpropertiesfromlattice QCD

7. Nucleon form factors and axial charge [Capitani, Della Morte, von Hippel, Jäger, Jüttner, Knippschild, Meyer, H.W., Phys Rev D86 (2012) 074502] • flavours of improved Wilson fermions; • MeV, , fm 7 | Nucleonpropertiesfromlattice QCD

8. Nucleon form factors and axial charge [Capitani, Della Morte, von Hippel, Jäger, Knippschild, Meyer, Rae, H.W., arXiv:1211.1282] • flavours of improved Wilson fermions; • MeV, , fm 8 | Nucleonpropertiesfromlattice QCD

9. Moments of parton distribution functions • Average momentum of unpolarisediso-vector PDF: • Cannot reconcile lattice and phenomenological estimates for [Alekhin, Blümlein, Moch, Phys Rev D86 (2012) 054009] 9 | Nucleonpropertiesfromlattice QCD • Excited state contamination cannot explain discrepancy • Strong pion mass dependence?

10. Moments of parton distribution functions [QCDSF Collaboration, Bali et al., Phys Rev D86 (2012) 054504] • flavours of improved Wilson fermions; • MeV, 74, fm at 10 | Nucleonpropertiesfromlattice QCD

11. Strangeness contribution to the proton spin • Inconclusive results for • Lattice calculations of involve calculation of quark-disconnected diagrams 11 | Nucleonpropertiesfromlattice QCD • Stochastic methods: “stochastic” versus “gauge” noise

12. Strangeness contribution to the proton spin [QCDSF Collaboration, Bali et al., Phys Rev Lett 108 (2012) 222001] • flavours of improved Wilson fermions; • MeV, , fm • Non-singlet renormalisation factor: 12 | Nucleonpropertiesfromlattice QCD • Results: ( scheme, ) (No continuum limit, no chiral extrapolation, quenched strange quark)

13. II. Resonances and Scattering 13 | ResonancesandScattering

14. Resonances in Lattice QCD • Resonances mostly treated naïvely in lattice QCD: • Lüscher formalism: extract resonance parameters from finite-size scaling of multi-hadron states in a box • Signature for resonance: avoided level crossing, e.g. for 14 | Nucleonpropertiesfromlattice QCD • Mathematically exact formalism in the one-channel case

15. πK scattering and the κ(800) resonance [Döring and Meissner, JHEP 1201 (2012) 009] • broad resonance; avoided level crossing washed out • Two decay channels: and • Use infinite-volume methods to predict finite-volume energy levels, as a guide for future lattice simulations Perform global fit to meson-meson PW data pole and width of Use solution to generate pseudo (lattice) data Analyse data in terms of fit potential with LO chiral interaction constraints 15 | Nucleonpropertiesfromlattice QCD • Obtain scattering phases and pole position from extended Lüscher method

16. Scattering processes off charmed mesons [Liu, Orginos, Guo, Hanhart and Meissner, arXiv:1208.4535] • Compute scattering lengths of and in lattice QCD • Chiral fits based on unitarisedChPT: determine 5 LECs plus one parameter of UChPT • Values of LECs allow for predictions in other channels: • Results support interpretation of the as a molecule 16 | Nucleonpropertiesfromlattice QCD • Prediction for isospin breaking strong decay width:

17. III. Hadronic contributions to the muon 17 | Hadroniccontributionstothemuon

18. Hadronic vacuum polarisation contribution (combined data) 18 |Hadronic contributionstothemuon • Theory prediction uses experimental data as input • Ab initio estimate from Lattice QCD: total accuracy of required!

19. Hadronic vacuum polarisation contribution • Lattice approach: evaluate convolution integral over Euclidean momenta 19 | Hadronic contributionstothemuon • Convolution function peaked far below lowest Fourier momentum • Quark-disconnected diagrams contribute

20. Hadronic vacuum polarisation contribution • Current lattice estimates not competitive with dispersive approach: • Improve statistical accuracy • Simulate at the physical pion mass • Include quark-disconnected diagrams 20 | Hadronic contributionstothemuon

21. Hadronic vacuum polarisation contribution [Della Morte, Jäger, Jüttner, H.W., JHEP 1203 (2012) 055, and to appear] • Apply twisted boundary conditions to reach lower momenta • New ensembles: MeV, , fm 21 | Hadronic contributionstothemuon

22. Lattice calculations versus dispersion relations [Bernecker, Meyer, EPJA 47 (2011) 148, and in preparation] • Relation between vacuum polarisation and -ratio in the Euclidean domain: • Lattice calculations yield • Use parameterisation of measured and evaluate the integral 22 | Hadronic contributionstothemuon

23. IV. QCD Thermodynamics 23 | QCD Thermodynamics

24. Freeze-out conditions in heavy-ion collisions • RHIC energy scan: measure fluctuations of conserved charges: Net baryon number (B), electric charge (C), Strangeness (S) • Fluctuations provide information on hadronisation: Freeze-out curve: • Evaluate cumulants of net charge fluctuations as a function of and 24 | QCD Thermodynamics Initial condition: Can measure experimentally Can compute in Hadron Resonance Gas model and Lattice QCD

25. Freeze-out conditions in heavy-ion collisions [BNL-Bielefeld Collaboration, Bazavov et al., Phys Rev Lett 109 (2012) 192302] • flavours ofimproved staggered quarks (“HISQ”); • MeV, lattice sizes and • Compute charge densities and fluctuations via Taylor expansion • Lattice simulation yields prediction for -dependence of • STAR Collab. (preliminary) 25 | Nucleonpropertiesfromlattice QCD

26. V. Ab initio Nuclear Physics 26 | Ab initionuclearphysics

27. The Hoyle state from first principles • Hoyle state: excited state of 12above the84threshold • Important catalyst in the CNO nuclear cycle • Hoyle state decays electromagnetically into then into • Investigate spectrum and structure of triple-alpha systems via Monte Carlo simulations of chiral effective field theory 27 | Ab initionuclearphysics Include terms up to NNLO, i.e. [Epelbaum, Krebs, Lee, Meissner,… ]

28. The Hoyle state from first principles [Epelbaum, Krebs, Lee, Meissner, Phys Rev Lett 106 (2012) 192501] • Compute projection amplitude of quantum state on periodic lattice • Spectrum of 12 28 | Ab initionuclearphysics • Good agreement with experiment; consistent two- and three-body forces must be included • Anthropic test: how sensitive is the triple-α process against small modifications in QED and QCD?

29. The Hoyle state from first principles [Epelbaum, Krebs, Lähde, Lee, Meissner, arXiv:1208.1328 ] • Compute projection amplitude of quantum state on periodic lattice • Extract information on the structure by preparing different initial states: Successive creation of 4 nucleons Clusters of alpha-particle 29 | Ab initionuclearphysics “bent arm” configuration Preferred by Hoyle state

30. Cluster of Excellence: Precision Physics, Fundamental Interactions andStructureof Matter Spokespersons: Matthias Neubert Institute forPhysics Hartmut Wittig Institute forNuclearPhysics TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAAAAAAAAAAA

31. Mainz Institute for Theoretical Physics (MITP) Scientific Programmes, Workshops and Schools: • Approx. 3 programmesp.a., each lasting 3-8 weeks, combined with a topical workshop • Co-organisedby a team of external scientists and local researchers • Applications evaluated by International Advisory Board • Additional 2 schools over the 5-year funding period, lasting 2-3 weeks each MITP Programs in 2013: Low-energy precision physics external organisers: K. Kumar, M. Ramsey-Musolf local organisers: H. Meyer, H. Spiesberger The first three years of the LHC external organisers: M. Carena, T. Plehn local organisers: B. Jäger, M. Neubert 31 | The PRISMA Cluster of Excellence NimaArkani-Hamed Marcela Carena Michael Creutz GianGiudice William Marciano Neal Weiner Manfred Lindner Jan Louis Dirk Kreimer ChristofWetterich Martin Savage Dieter Zeppenfeld Call for Proposals for 2014