Erice Hadronic contribution. muon g 2 from a Dyson-Schwinger perspective. Tobias Göcke yo

Transcription

1 Erice Introduction Hadronic contribution to the muon g 2 from a Dyson-Schwinger perspective 4. Summary and Outlook Tobias Göcke yo 2. A Together with C. Functional S. Fischer (JLU) and R. Williams 3. (Complutense, Results Madrid) Approach yo [Fischer, TG, Williams, arxiv: ] yo [TG, Fischer, Williams, arxiv: ] yo [TG, Fischer, Williams, arxiv: ] JUSTUS-LIEBIG- UNIVERSITÄT GIESSEN Tobias Göcke (JLU Gießen) Hadr. contr. to a µ from a DSE perspective / 18

2 1. Introduction Hadronic contribution to the muon g 2 from a Dyson-Schwinger perspective 4. Summary and Outlook 2. A Functional Approach 3. Results

3 1. Introduction Hadronic contribution to the muon g 2 from a Dyson-Schwinger perspective 4. Summary and Outlook 2. A Functional Approach 3. Results

4 1. Introduction a µ is... Precisely determined by experiment and accurately predicted by Standard Model Precision test for the Standard Model More sensitive to contributions from high scales than a e since : m µ m e Sensitive to QCD and potential new physics contributions Deviation between experiment and theory? So one has to... get the SM predictions under control use non-perturbative methods for QCD-contributions. Tobias Göcke (JLU Gießen) Hadr. contr. to a µ from a DSE perspective / 18

5 1. Introduction Magnetic moment µ, g-factor µ = g e 2m S Dirac equation: g = 2 Schwinger: anomalous part a µ = g 2 2 α/2π Relativistic QFT a µ := F 2 (0) = gµ 2 2 ] = ( ie)ū(p ) [F 1 (q 2 )γ α + if 2 (q 2 ) σ αβq β 2m µ u(p) Tobias Göcke (JLU Gießen) Hadr. contr. to a µ from a DSE perspective / 18

6 1. Introduction Precision tests of the standard model contribution a µ [10 11 ] Experiment (63) SM (49) hadronic LO 6 949(43) hadronic LbL 105(26) exp. - th. 261(80) [B. L. Roberts, arxiv: (2010)] [Hagiwara, Liao, Martin, Nomura, Teubner, arxiv: (2011)] New Physics? 3.3σ effect Lattice? First results but needs time Tobias Göcke (JLU Gießen) Hadr. contr. to a µ from a DSE perspective / 18

7 1. Introduction Precision tests of the standard model contribution a µ [10 11 ] Experiment (63) SM (49) hadronic LO 6 949(43) hadronic LbL 105(26) exp. - th. 261(80) [B. L. Roberts, arxiv: (2010)] [Hagiwara, Liao, Martin, Nomura, Teubner, arxiv: (2011)] New Physics? 3.3σ effect Lattice? First results but needs time Tobias Göcke (JLU Gießen) Hadr. contr. to a µ from a DSE perspective / 18

8 1. Introduction Two Hadronic Contributions hadronic vacuum polarization hadr. light by light scattering one-scale problem known from dispersion relation leading contribution two-scale problem only accessible through theory systematic uncertainty? How to deal with these objects? calculate both from the same approach use the little brother as test case Tobias Göcke (JLU Gießen) Hadr. contr. to a µ from a DSE perspective / 18

9 1. Introduction Hadronic contribution to the muon g 2 from a Dyson-Schwinger perspective 4. Summary and Outlook 2. A Functional Approach 3. Results

10 2. A Functional Approach - Overview Diagrammatic representation = = q + Maris-Tandy model of quark-gluon interaction: [Maris and Tandy, arxiv:nucl-th/ ] both functions in one approach one description for high and low energy important for two-scale problem building blocks Tobias Göcke (JLU Gießen) Hadr. contr. to a µ from a DSE perspective / 18

11 1. Introduction Hadronic contribution to the muon g 2 from a Dyson-Schwinger perspective 4. Summary and Outlook 2. A Functional Approach 3. Results

12 3. Results - Hadronic Vacuum Polarization = Π µν (q) = ( δ µν q 2 q µ q ν ) Π(q 2 ) Adler function: D(q) = dπ/d ln q 2 two parameter sets, u and d quark masses fixed to the I:pion mass II: rho mass use u, d, s, c, b quarks (isospin-limit: m u = m d ) all parameters fixed by meson phenomenology model interaction ψψ m u/d m π or m ρ m s m K or m φ mc/b c c and b b vector states Tobias Göcke (JLU Gießen) Hadr. contr. to a µ from a DSE perspective / 18

13 3. Results - Hadronic Vacuum Polarization = Π µν (q) = ( δ µν q 2 q µ q ν ) Π(q 2 ) Adler function: D(q) = dπ/d ln q 2 two parameter sets, u and d quark masses fixed to the I:pion mass II: rho mass use u, d, s, c, b quarks (isospin-limit: m u = m d ) all parameters fixed by meson phenomenology model interaction ψψ m u/d m π or m ρ m s m K or m φ mc/b c c and b b vector states Tobias Göcke (JLU Gießen) Hadr. contr. to a µ from a DSE perspective / 18

14 3. Results - Hadronic Vacuum Polarization = Π µν (q) = ( δ µν q 2 q µ q ν ) Π(q 2 ) Adler function: D(q) = dπ/d ln q 2 two parameter sets, u and d quark masses fixed to the I:pion mass II: rho mass use u, d, s, c, b quarks (isospin-limit: m u = m d ) all parameters fixed by meson phenomenology model interaction ψψ m u/d m π or m ρ m s m K or m φ mc/b c c and b b vector states Tobias Göcke (JLU Gießen) Hadr. contr. to a µ from a DSE perspective / 18

15 3. Results - Hadronic Vacuum Polarization = Π µν (q) = ( δ µν q 2 q µ q ν ) Π(q 2 ) Adler function: D(q) = dπ/d ln q 2 two parameter sets, u and d quark masses fixed to the I:pion mass II: rho mass use u, d, s, c, b quarks (isospin-limit: m u = m d ) all parameters fixed by meson phenomenology model interaction ψψ m u/d m π or m ρ m s m K or m φ mc/b c c and b b vector states Tobias Göcke (JLU Gießen) Hadr. contr. to a µ from a DSE perspective / 18

16 3. Results - Hadronic Vacuum Polarisation Adler function D(Q) dispersion relation DSE Q [GeV] [Eidelman, Jegerlehner, Kataev, Veretin, hep-ph/ ] a HVP,DSE [TG, Fischer, Williams, arxiv: (2011)] [Jegerlehner and Nyffeler,arXiv: (2009)] µ = ( ) aµ HVP,disp.rel. = (52.6) Tobias Göcke (JLU Gießen) Hadr. contr. to a µ from a DSE perspective / 18

17 3. Results - Hadronic Vacuum Polarisation a HVP µ 10 11, s-mass invariant DSE N f =2 DSE N f =2+1 [1] N f =2 [2] N f = M ρ [GeV] [1]: [Feng, Jansen, Petschlies and Renner; arxiv: (2011)] [2]: [Boyle, Del Debbio, Kerrane and Zanotti; arxiv: (2011)] Tobias Göcke (JLU Gießen) Hadr. contr. to a µ from a DSE perspective / 18

18 3. Results - Hadronic Vacuum Polarisation Adler function: contribution of transverse vertex VMD D(Q) bare vertex BC vertex transverse vertex full vertex Q [GeV] Tobias Göcke (JLU Gießen) Hadr. contr. to a µ from a DSE perspective / 18

19 3. Results - rôle of the vertex pion form factor F π, influence of the ρ in the full vertex [Maris and Tandy, nucl-th/ v1 (2000)] Tobias Göcke (JLU Gießen) Hadr. contr. to a µ from a DSE perspective / 18

20 3. Results - LbL - π, η, η Pole pseudoscalar (PS) exchance π only a π pole µ = 58(7) π, η and η a PS pole µ = 80.7(12) [Fischer, TG, Williams, arxiv: ] [TG, Fischer, Williams, arxiv: ] good agreement with existing approaches Tobias Göcke (JLU Gießen) Hadr. contr. to a µ from a DSE perspective / 18

21 3. Results - LbL - Quark Loop quark loop bare vertex aµ LBL,QL = 61(2) vertex consistent with current conservation aµ LBL,QL = 176(4) full vertex from BSE including the ρ-pole (unpublished): aµ LBL,QL = 106(5) [Fischer, TG, Williams, arxiv: ] [TG, Fischer, Williams, arxiv: ] enhancement compared to existing approaches enhanced vertices due to current conservation (WTI) Tobias Göcke (JLU Gießen) Hadr. contr. to a µ from a DSE perspective / 18

22 1. Introduction Hadronic contribution to the muon g 2 from a Dyson-Schwinger perspective 4. Summary and Outlook 2. A Functional Approach 3. Results

23 5. Summary and Outlook summary DSE calculation of g 2 HVP a HVP,DSE µ = ( ) aµ HVP,disp.rel. = 6949(43) Adler function can be described reasonably LbL a LbL,DSE µ = 187(47) aµ LbL,EFT = 105(26) preliminary estimate (only LbL from DSE): a DSE µ = (71) DSE: a exp µ aµ theo = 228(95) σ [HLMNT]: aµ exp aµ theo = 261(80) σ [Hagiwara, Liao, Martin, Nomura, Teubner, arxiv: (2011)] [Prades, de Rafael, Vainshtein, arxiv: ] Tobias Göcke (JLU Gießen) Hadr. contr. to a µ from a DSE perspective / 18

24 5. Summary and Outlook outlook overcome resonance expansion (π 0, η, η ) pole dominance Thank You for the attention! supported by DFG under grant No. Fi 970/8-1 Helmholtz Young Investigator Grant No. VH-NG-332 Helmholtz International Center for FAIR within the LOEWE program of the State of Hesse Science Fund FWF under Project No. P20592-N16 Ministerio de Educación (Spain): Programa Nacional de Movilidad de Recursos Humanos del, Plan Nacional de I-D+i Tobias Göcke (JLU Gießen) Hadr. contr. to a µ from a DSE perspective / 18

25 5. Summary and Outlook outlook overcome resonance expansion (π 0, η, η ) pole dominance Thank You for the attention! supported by DFG under grant No. Fi 970/8-1 Helmholtz Young Investigator Grant No. VH-NG-332 Helmholtz International Center for FAIR within the LOEWE program of the State of Hesse Science Fund FWF under Project No. P20592-N16 Ministerio de Educación (Spain): Programa Nacional de Movilidad de Recursos Humanos del, Plan Nacional de I-D+i Tobias Göcke (JLU Gießen) Hadr. contr. to a µ from a DSE perspective / 18

26 5. Summary and Outlook outlook overcome resonance expansion (π 0, η, η ) pole dominance Thank You for the attention! supported by DFG under grant No. Fi 970/8-1 Helmholtz Young Investigator Grant No. VH-NG-332 Helmholtz International Center for FAIR within the LOEWE program of the State of Hesse Science Fund FWF under Project No. P20592-N16 Ministerio de Educación (Spain): Programa Nacional de Movilidad de Recursos Humanos del, Plan Nacional de I-D+i Tobias Göcke (JLU Gießen) Hadr. contr. to a µ from a DSE perspective / 18