Aktuelle Entwicklungen in der Theorie II

Gitter-Eichtheorie

Hartmut WittigInstitut für Kernphysik und Helmholtz Institut Mainz

KHuK Jahrestagung30. November 2012

2 | Overview

Overview

I. Nucleon properties from lattice QCD

II. Resonances and scattering

III. Hadronic contributions to the muon

IV. QCD Thermodynamics

V. Ab initio nuclear physics

3 | Nucleon Properties from Lattice QCD

I. Nucleon Properties

4 | Nucleon properties from lattice QCD

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 fullcontrol oversystematicerrors

Provide stablelattice estimate

5 | Nucleon properties from lattice QCD

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

Determine form factors from ratios of three- and two-point functions,

Source-sink separation fm due to bad signal/noise ratio

6 | Nucleon properties from lattice QCD

Nucleon form factors and axial charge

Correlator ratio:

Summed insertion:

𝑆 ( 𝑡 𝑠 )≡∑𝑡=0

𝑡 𝑠

𝑅𝐴 (𝑡 , 𝑡 𝑠 )=𝑐+𝑡𝑠 {𝑔 Abare+𝑂 (𝑒−Δ 𝑡 𝑠 )}

7 | Nucleon properties from lattice QCD

Nucleon form factors and axial charge

flavours of improved Wilson fermions;

MeV, , fm

[Capitani, Della Morte, von Hippel, Jäger, Jüttner, Knippschild, Meyer, H.W., Phys Rev D86 (2012) 074502]

𝑔 A=1.223±0.063stat❑ ¿¿

flavours of improved Wilson fermions;

MeV, , fm

8 | Nucleon properties from lattice QCD

Nucleon form factors and axial charge[Capitani, Della Morte, von Hippel, Jäger, Knippschild, Meyer, Rae, H.W., arXiv:1211.1282]

9 | Nucleon properties from lattice QCD

Moments of parton distribution functions

Average momentum of unpolarised iso-vector PDF:

⟨𝑥 ⟩𝑢−𝑑=∫0

1

𝑑𝑥 𝑥 {𝑢 (𝑥 )+𝑢 (𝑥 )−𝑑 (𝑥 )−𝑑 (𝑥 ) }

Cannot reconcile lattice and phenomenological estimates for [Alekhin, Blümlein, Moch, Phys Rev D86 (2012) 054009]

Excited state contamination cannot explain discrepancy

Strong pion mass dependence?

10 | Nucleon properties from lattice QCD

Moments of parton distribution functions[QCDSF Collaboration, Bali et al., Phys Rev D86 (2012) 054504]

flavours of improved Wilson fermions;

MeV, 74, fm

at

11 | Nucleon properties from lattice QCD

Strangeness contribution to the proton spin12ΔΣ+𝐿𝑞+Δ𝐺=

12, ΔΣ=Δ𝑢+Δ𝑑+Δ 𝑠+…

Inconclusive results for

Lattice calculations of involve calculation of quark-disconnected diagrams

Stochastic methods: “stochastic” versus “gauge” noise

12 | Nucleon properties from lattice QCD

[QCDSF Collaboration, Bali et al., Phys Rev Lett 108 (2012) 222001]

flavours of improved Wilson fermions;

MeV, , fm

Strangeness contribution to the proton spin

Non-singlet renormalisation factor:

Δ𝑞MS (𝜇)=𝑍 Ans (1+𝑏 A𝑎𝑚q ) Δ𝑞bare+ 1

2z (𝜇 ) (Δ𝑢+Δ𝑑)bare

Results:

( scheme, )

(No continuum limit, no chiral extrapolation, quenched strange quark)

13 | Resonances and Scattering

II. Resonances and Scattering

14 | Nucleon properties from lattice QCD

Mathematically exact formalism in the one-channel case

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

15 | Nucleon properties from lattice QCD

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

1. Perform global fit to meson-meson PW data pole and width of 2. Use solution to generate pseudo (lattice) data3. Analyse data in terms of fit potential with LO chiral interaction constraints

Obtain scattering phases and pole position from extended Lüscher method

16 | Nucleon properties from lattice QCD

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 unitarised ChPT: 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

Prediction for isospin breaking strong decay width:

17 | Hadronic contributions to the muon

III. Hadronic contributions tothe muon

18 |Hadronic contributions to the muon

Hadronic vacuum polarisation contribution

𝑎𝜇VP;had=(690.75±4.75) ∙10−10

(combined data)

Theory prediction uses experimental data as input Ab initio estimate from Lattice QCD: total accuracy of required!

19 | Hadronic contributions to the muon

Hadronic vacuum polarisation contribution

Convolution function peaked far below lowest Fourier momentum Quark-disconnected diagrams contribute

Lattice approach: evaluate convolution integral over Euclidean momenta

20 | Hadronic contributions to the muon

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

21 | Hadronic contributions to the muon

Hadronic vacuum polarisation contribution

Apply twisted boundary conditions to reach lower momenta

New ensembles: MeV, , fm

[Della Morte, Jäger, Jüttner, H.W., JHEP 1203 (2012) 055, and to appear]

22 | Hadronic contributions to the muon

Lattice calculations versus dispersion relations

Relation between vacuum polarisation and -ratio in the Euclidean domain:

[Bernecker, Meyer, EPJA 47 (2011) 148, and in preparation]

Lattice calculations yield Use parameterisation of measured and evaluate the integral

23 | QCD Thermodynamics

IV. QCD Thermodynamics

24 | QCD Thermodynamics

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

𝑅𝑚 ,𝑛𝑋 ≡

𝜒𝑚 ,𝜇𝑋

𝜒𝑛 ,𝜇𝑋 , 𝑋=𝐵 ,𝑄

Initial condition:

Can measure experimentally

Can compute in Hadron Resonance Gas model and Lattice QCD

25 | Nucleon properties from lattice QCD

Freeze-out conditions in heavy-ion collisions

flavours of improved staggered quarks (“HISQ”);

MeV, lattice sizes and

Compute charge densities and fluctuations via Taylor expansion

[BNL-Bielefeld Collaboration, Bazavov et al., Phys Rev Lett 109 (2012) 192302]

Lattice simulation yields prediction for -dependence of

STAR Collab. (preliminary)

26 | Ab initio nuclear physics

V. Ab initio Nuclear Physics

27 | Ab initio nuclear physics

The Hoyle state from first principles

Hoyle state: excited state of 12 above the 8 4 threshold

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

Include terms up to NNLO, i.e.

[Epelbaum, Krebs, Lee, Meissner,… ]

28 | Ab initio nuclear physics

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

Theory (NNLO)

Experiment

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 | Ab initio nuclear physics

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

“bent arm” configurationPreferred by Hoyle state

Precision Physics, Fundamental Interactionsand Structure of Matter

Cluster of Excellence:

Hartmut WittigInstitute for Nuclear Physics

Matthias NeubertInstitute for Physics

Spokespersons:

31 | The PRISMA Cluster of Excellence

Approx. 3 programmes p.a., each lasting 3-8 weeks, combined with a topical workshop

Co-organised by 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

Scientific Programmes, Workshops and Schools:

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. Plehnlocal organisers: B. Jäger, M. Neubert

Mainz Institute for Theoretical Physics (MITP)

Call for Proposals for 2014

Nima Arkani-Hamed Marcela CarenaMichael CreutzGian GiudiceWilliam MarcianoNeal Weiner

Manfred LindnerJan LouisDirk KreimerChristof WetterichMartin SavageDieter Zeppenfeld