Strong interactions for the precision frontier in particle and nuclear physics

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Theoretical Physics Universität Bonn, Germany Colloquium Indiana University, Bloomington,

1 Strong interactions for the precision frontier in particle and nuclear physics Bastian Kubis Helmholtz-Institut für Strahlen- und Kernphysik (Theorie) Bethe Center for Theoretical Physics Universität Bonn, Germany Colloquium Indiana University, Bloomington, March 10th 2014 B. Kubis, Strong interactions for the precision frontier in particle and nuclear physics p. 1

2 Outline Introduction: why the strong interactions are difficult Strong and weak interactions Spectroscopy, CP violation, and Dalitz plots Strong interactions and electromagnetism The anomalous magnetic moment of the muon Summary / Outlook B. Kubis, Strong interactions for the precision frontier in particle and nuclear physics p. 2

3 The Standard Model of particle physics mass charge spin name Quarks Leptons 2.4 MeV/c ⅔ u up Three generations of matter (fermions) I II III 1.27 GeV/c ⅔ c charm 4.8 MeV/c 104 MeV/c - - s ddown strange ν <2.2 ev/c electron neutrino ν μ <0.17 MeV/c GeV/c ⅔ t top GeV/c - b bottom muon neutrino ν τ <15.5 MeV/c tau neutrino γ photon g gluon GeV/c Z Z boson e MeV/c MeV/c GeV/c 80.4 GeV/c - - ± μ 2 τ2 2 ± W electron muon tau W boson *Yet to be confirmed Gauge bosons 2 ~125 GeV/c 0 H * Higgs boson matter particle: quarks and leptons force carriers: gauge bosons how did we find these? how to find something beyond? B. Kubis, Strong interactions for the precision frontier in particle and nuclear physics p. 3

4 The Standard Model of particle physics mass charge spin name Quarks Leptons 2.4 MeV/c u up Three generations of matter (fermions) I II III 1.27 GeV/c ⅔ c charm 4.8 MeV/c 104 MeV/c - - s ddown strange GeV/c ⅔ t top 4.2 GeV/c - b bottom <2.2 ev/c <0.17 MeV/c ν e ν μ ν τ electron neutrino <15.5 MeV/c muon neutrino tau neutrino MeV/c MeV/c GeV/c e μ τ electron muon tau γ photon g gluon GeV/c 0 1 Z 0 Z boson 80.4 GeV/c ±1 1W *Yet to be confirmed W boson ± Gauge bosons 2 ~125 GeV/c 0 0 H * Higgs boson matter particle: quarks and leptons force carriers: gauge bosons how did we find these? how to find something beyond? discoveries at high energies: production of new particles g g t t B. Kubis, Strong interactions for the precision frontier in particle and nuclear physics p. 3

5 The Standard Model of particle physics mass charge spin name Quarks Leptons 2.4 MeV/c ⅔ u up Three generations of matter (fermions) I II III 1.27 GeV/c ⅔ c charm 4.8 MeV/c 104 MeV/c - - s ddown strange GeV/c ⅔ t top 4.2 GeV/c - b bottom <2.2 ev/c <0.17 MeV/c ν e ν μ ν τ electron neutrino <15.5 MeV/c muon neutrino tau neutrino MeV/c MeV/c GeV/c e μ τ electron muon tau γ photon g gluon GeV/c 0 1 Z 0 Z boson 80.4 GeV/c ±1 1W *Yet to be confirmed W boson ± Gauge bosons 2 ~125 GeV/c 0 0 H * Higgs boson discoveries at high energies: production of new particles discoveries in precision experiments: effects of virtual particles matter particle: quarks and leptons force carriers: gauge bosons how did we find these? how to find something beyond? s d W u,c,t g d d B. Kubis, Strong interactions for the precision frontier in particle and nuclear physics p. 3

6 Why the strong interactions are difficult Perturbation theory and coupling constants expand amplitudes in powers of coupling constants α scattering amplitude α(...) B. Kubis, Strong interactions for the precision frontier in particle and nuclear physics p. 4

7 Why the strong interactions are difficult Perturbation theory and coupling constants expand amplitudes in powers of coupling constants α scattering amplitude α(...) + α 2 (...) works well for electromagnetic and weak interactions: α 10 2 B. Kubis, Strong interactions for the precision frontier in particle and nuclear physics p. 4

8 Why the strong interactions are difficult The running coupling constant in Quantum Chromodynamics 0.5 α s (Q) Data Theory Deep Inelastic Scattering e + e - Annihilation Hadron Collisions Heavy Quarkonia Λ(5) MS NLO NNLO Lattice α s(μ Z) { 245 MeV QCD O(α MeV s) 181 MeV asymptotic freedom at high energies ("weak QCD") confinement at low energies ("strong QCD"): no quarks + gluons, only (colour-neutral) hadrons baryons (rgb) + mesons (r r) Q [GeV] B. Kubis, Strong interactions for the precision frontier in particle and nuclear physics p. 5

9 Why the strong interactions are difficult The running coupling constant in Quantum Chromodynamics 0.5 α s (Q) Data Theory Deep Inelastic Scattering e + e - Annihilation Hadron Collisions Heavy Quarkonia Λ(5) MS NLO NNLO Lattice α s(μ Z) { 245 MeV QCD O(α MeV s) 181 MeV asymptotic freedom at high energies ("weak QCD") confinement at low energies ("strong QCD"): no quarks + gluons, only (colour-neutral) hadrons baryons (rgb) + mesons (r r) Q [GeV] Perturbative QCD not applicable for hadron spectroscopy hadron scattering, decays nuclear physics B. Kubis, Strong interactions for the precision frontier in particle and nuclear physics p. 5

10 Why the strong interactions are difficult Alternative methods Effective field theories symmetries, scale separation Λ χ π,k,η B. Kubis, Strong interactions for the precision frontier in particle and nuclear physics p. 6

11 Why the strong interactions are difficult Alternative methods Effective field theories symmetries, scale separation Λ χ π,k,η Dispersion relations analyticity, unitarity, crossing symmetry B. Kubis, Strong interactions for the precision frontier in particle and nuclear physics p. 6

12 Why the strong interactions are difficult Alternative methods Effective field theories symmetries, scale separation Λ χ π,k,η Dispersion relations analyticity, unitarity, crossing symmetry Lattice QCD solve discretized version of QCD numerically B. Kubis, Strong interactions for the precision frontier in particle and nuclear physics p. 6

13 Part I: Strong and weak interactions: Spectroscopy, CP violation, and Dalitz plots B. Kubis, Strong interactions for the precision frontier in particle and nuclear physics p. 7

14 Modern spectroscopy mesons in the quark model: q q states certain quantum numbers J PC not allowed: q L q 0 +, 0, 1 +, 2 +,... exotics lattice QCD: 1 + state 1.3 GeV above the ρ Dudek et al B. Kubis, Strong interactions for the precision frontier in particle and nuclear physics p. 8

15 Modern spectroscopy mesons in the quark model: q q states certain quantum numbers J PC not allowed: q L q 0 +, 0, 1 +, 2 +,... exotics lattice QCD: 1 + state 1.3 GeV above the ρ Dudek et al experiments: π γ???? p p COMPASS@CERN CLAS, GlueX@JLab B. Kubis, Strong interactions for the precision frontier in particle and nuclear physics p. 8

16 Modern spectroscopy mesons in the quark model: q q states certain quantum numbers J PC not allowed: q L q 0 +, 0, 1 +, 2 +,... exotics lattice QCD: 1 + state 1.3 GeV above the ρ Dudek et al experiments: π γ???? p p COMPASS@CERN CLAS, GlueX@JLab Things to control using dispersion relations: (exotic) phases interfere with known reference phases effects of three-/many-body final-state interactions? resonances ˆ= poles in the complex scattering-energy plane B. Kubis, Strong interactions for the precision frontier in particle and nuclear physics p. 8

17 CP violation in weak interactions CP violation: one of the prerequisites for matter antimatter asymmetry in the universe B. Kubis, Strong interactions for the precision frontier in particle and nuclear physics p. 9

18 CP violation in weak interactions CP violation: one of the prerequisites for matter antimatter asymmetry in the universe in the Standard Model: embedded in the weak interactions, Cabibbo Kobayashi Maskawa matrix V CKM = V ud V us V ub V cd V cs V cb V td V ts V tb CP-violation given by a complex phase in V B. Kubis, Strong interactions for the precision frontier in particle and nuclear physics p. 9

19 CP violation in weak interactions CP violation: one of the prerequisites for matter antimatter asymmetry in the universe in the Standard Model: embedded in the weak interactions, Cabibbo Kobayashi Maskawa matrix V CKM = V ud V us V ub V cd V cs V cb V td V ts V tb CP-violation given by a complex phase in V Standard-Model CP violation too small search for new/unconventional sources of CP violation charm D / beauty B decays electric dipole moments (proton/neutron/deuteron... ) B. Kubis, Strong interactions for the precision frontier in particle and nuclear physics p. 9

20 CP violation in weak interactions CP violation in partial widths Γ(P f) Γ( P f) at least two interfering decay amplitudes different weak (CKM) phases different strong (final-state-interaction) phases B. Kubis, Strong interactions for the precision frontier in particle and nuclear physics p. 10

21 CP violation in weak interactions CP violation in partial widths at least two interfering decay amplitudes different weak (CKM) phases Γ(P f) Γ( P f) different strong (final-state-interaction) phases two-body decays: D ππ, K K decay at fixed total energy fixed strong phase B. Kubis, Strong interactions for the precision frontier in particle and nuclear physics p. 10

CP violation in weak interactions CP violation in partial widths at least two interfering decay amplitudes different weak (CKM) phases Γ(P f) Γ( P f) different strong (final-state-interaction) phases

22 CP violation in weak interactions CP violation in partial widths at least two interfering decay amplitudes different weak (CKM) phases Γ(P f) Γ( P f) different strong (final-state-interaction) phases two-body decays: D ππ, K K decay at fixed total energy fixed strong phase three-body decays: D 3π, ππk Dalitz plot ˆ= density distribution in two kinematical variables resonances rapid phase variation enhances CP-violation in parts of the decay region B. Kubis, Strong interactions for the precision frontier in particle and nuclear physics p. 10

23 Amplitude analyses in Dalitz plots The traditional picture: isobar model / Breit Wigner resonances π f 0, ρ... B, D π modulus K π B, D π κ, K... K phase [ o ] s [GeV 2 ] s [GeV 2 ] B. Kubis, Strong interactions for the precision frontier in particle and nuclear physics p. 11

24 Amplitude analyses in Dalitz plots The traditional picture: isobar model / Breit Wigner resonances B, D f 0, ρ so what s not to like? some resonances don t look like Breit Wigners at all! π π K use exact scattering phase shifts instead B, D δ 0 (0) κ, K... CFD Old K decay data Na48/2 K->2 π decay Kaminski et al. Grayer et al. Sol.B Grayer et al. Sol. C Grayer et al. Sol. D Hyams et al. 73 π π K "σ" f s 1/2 (MeV) B. Kubis, Strong interactions for the precision frontier in particle and nuclear physics p. 11

25 Amplitude analyses in Dalitz plots The traditional picture: isobar model / Breit Wigner resonances B, D f 0, ρ so what s not to like? some resonances don t look like Breit Wigners at all! π π K use exact scattering phase shifts instead B, D κ, K particle rescattering s 1/2 (MeV) δ 0 (0) CFD Old K decay data Na48/2 K->2 π decay Kaminski et al. Grayer et al. Sol.B Grayer et al. Sol. C Grayer et al. Sol. D Hyams et al. 73 π π K "σ" f B. Kubis, Strong interactions for the precision frontier in particle and nuclear physics p. 11

26 A simple Dalitz plot: φ 3π events in 1834 bins KLOE 2003 analyzed in terms of: sum of 3 Breit Wigners (ρ ±, ρ 0 ) + constant background term π ρ φ π π + crossed + Problem: unitarity fixes Im/Re parts adding a contact term destroys this relation φ π π π B. Kubis, Strong interactions for the precision frontier in particle and nuclear physics p. 12

A simple Dalitz plot: φ 3π 2 10 6 events in 1834 bins KLOE 2003 analyzed in terms of: sum of 3 Breit Wigners (ρ ±, ρ 0 ) + constant background term π ρ φ π π + crossed + Problem: unitarity fixes

27 A simple Dalitz plot: φ 3π events in 1834 bins KLOE 2003 analyzed in terms of: sum of 3 Breit Wigners (ρ ±, ρ 0 ) + constant background term π ρ φ π π + crossed + Problem: unitarity fixes Im/Re parts adding a contact term destroys this relation φ π π π reconcile data with dispersion relations? Niecknig, BK, Schneider 2012 B. Kubis, Strong interactions for the precision frontier in particle and nuclear physics p. 12

28 Experimental comparison to φ 3π successive slices through Dalitz plot: Niecknig, BK, Schneider bin number χ 2 /ndof pairwise interaction only (with correct ππ scattering phase) B. Kubis, Strong interactions for the precision frontier in particle and nuclear physics p. 13

29 Experimental comparison to φ 3π successive slices through Dalitz plot: Niecknig, BK, Schneider bin number χ 2 /ndof full 3-particle rescattering, only overall normalization adjustable B. Kubis, Strong interactions for the precision frontier in particle and nuclear physics p. 13

30 Experimental comparison to φ 3π successive slices through Dalitz plot: Niecknig, BK, Schneider bin number χ 2 /ndof full 3-particle rescattering, 2 adjustable parameters (additional "subtraction constant" to suppress inelastic effects) B. Kubis, Strong interactions for the precision frontier in particle and nuclear physics p. 13

31 Experimental comparison to φ 3π successive slices through Dalitz plot: Niecknig, BK, Schneider bin number χ 2 /ndof perfect fit respecting analyticity and unitarity possible contact term emulates neglected rescattering effects no need for "background" inseparable from "resonance" B. Kubis, Strong interactions for the precision frontier in particle and nuclear physics p. 13

32 Heavier decays: D+ π+π+k d 3 π+ 2.5 t [GeV2 ] u d 2 u K D+ 1.5 c s W+ 1 d π+ 0.5 u s [GeV 2 2] CLEO 2008 B. Kubis, Strong interactions for the precision frontier in particle and nuclear physics p. 14

33 Heavier decays: D+ π+π+k d 3 π+ 2.5 d 2 u K D+ 1.5 c s W+ 1 d π+ 0.5 u s [GeV ] K0 (1950) CLEO pion kaon 2 Sππ 1 Pππ SπK 1/2 PπK 3/2 PπK SπK 1/2 1/2 pion pion Ω0 t [GeV2 ] u K0 (1430) 100 "κ" 50 3/ s [GeV] B. Kubis, Strong interactions for the precision frontier in particle and nuclear physics p. 14

34 Heavier decays: D+ π+π+k d 3 π+ 2.5 d 2 u K D+ 1.5 c s W+ 1 d π+ 0.5 u s [GeV ] CLEO pion kaon 2 Sππ 1/2 1 Pππ 1/2 SπK PπK 3/2 PπK SπK 3/ /2 pion pion K (892) Ω1 t [GeV2 ] u s [GeV] B. Kubis, Strong interactions for the precision frontier in particle and nuclear physics p. 14

35 Heavier decays: D+ π+π+k d 3 π+ t [GeV2 ] 2.5 u d 2 u K D+ 1.5 c s W+ 1 d π+ u s [GeV 2 2] CLEO 2008 Fit in the elastic region: "improved isobar model" χ2 /ndof 1.4 full three-body rescattering χ2 /ndof 1.1 visible improvement similar to φ 3π Niecknig, BK in progress B. Kubis, Strong interactions for the precision frontier in particle and nuclear physics p. 14

36 Part II: Strong interactions and electromagnetism: The anomalous magnetic moment of the muon B. Kubis, Strong interactions for the precision frontier in particle and nuclear physics p. 15

37 The anomalous magnetic moment of the muon gyromagnetic ratio: magnetic moment spin µ = g e 2m S Dirac theory for spin-1/2 fermions: g µ = 2 rad. corr.: g µ = 2(1+a µ ), a µ anomalous magnetic moment one of the most precisely measured quantities in particle physics a µ = ( ±63) BNL E B. Kubis, Strong interactions for the precision frontier in particle and nuclear physics p. 16

38 The anomalous magnetic moment of the muon gyromagnetic ratio: magnetic moment spin µ = g e 2m S Dirac theory for spin-1/2 fermions: g µ = 2 rad. corr.: g µ = 2(1+a µ ), a µ anomalous magnetic moment one of the most precisely measured quantities in particle physics a µ = ( ±63) BNL E HMNT 07 (e + e -based) 285 ± 51 JN 09 (e + e ) 299 ± 65 Davier et al. 09/1 (τ-based) 157 ± 52 Davier et al. 09/1 (e + e ) 312 ± 51 Davier et al. 09/2 (e + e w/ BABAR) 255 ± 49 HLMNT 10 (e + e w/ BABAR) 259 ± 48 DHMZ 10 (τ newest) 195 ± 54 DHMZ 10 (e + e newest) 287 ± 49 BNL-E821 (world average) 0 ± 63 BNL-E a µ a µ exp and one with a significant (??) deviation from the Standard Model: a exp µ a SM µ = (27.6±8.6) Davier et al new g 2 experiment at Fermilab: reduce experimental error by factor 4 B. Kubis, Strong interactions for the precision frontier in particle and nuclear physics p. 16

39 The Standard Model prediction fora µ a µ [10 11 ] a µ [10 11 ] experiment QED O(α) QED O(α 2 ) QED O(α 3 ) QED O(α 4 ) QED O(α 5 ) QED total electroweak had. VP (LO) had. VP (NLO) had. LbL total B. Kubis, Strong interactions for the precision frontier in particle and nuclear physics p. 17

40 The Standard Model prediction fora µ a µ [10 11 ] a µ [10 11 ] experiment QED O(α) QED O(α 2 ) QED O(α 3 ) QED O(α 4 ) QED O(α 5 ) QED total electroweak had. VP (LO) had. VP (NLO) had. LbL µ µ γ Schwinger 1948 total B. Kubis, Strong interactions for the precision frontier in particle and nuclear physics p. 17

41 The Standard Model prediction fora µ a µ [10 11 ] a µ [10 11 ] experiment QED O(α) QED O(α 2 ) QED O(α 3 ) QED O(α 4 ) QED O(α 5 ) QED total electroweak had. VP (LO) had. VP (NLO) had. LbL total µ µ µ µ e, µ, τ Petermann 1957 Sommerfield 1957 B. Kubis, Strong interactions for the precision frontier in particle and nuclear physics p. 17

42 The Standard Model prediction fora µ a µ [10 11 ] a µ [10 11 ] experiment QED O(α) QED O(α 2 ) QED O(α 3 ) QED O(α 4 ) QED O(α 5 ) QED total electroweak had. VP (LO) had. VP (NLO) had. LbL I(a) I(b) I(c) I(d) I(e) I(f) I(g) I(h) I(i) I(j) II(a) II(b) II(c) II(d) II(e) II(f) III(a) III(b) III(c) IV V VI(a) VI(b) VI(c) VI(d) VI(e) VI(f) VI(g) VI(h) VI(i) VI(j) VI(k) Kinoshita et al total B. Kubis, Strong interactions for the precision frontier in particle and nuclear physics p. 17

43 The Standard Model prediction fora µ a µ [10 11 ] a µ [10 11 ] experiment QED O(α) QED O(α 2 ) QED O(α 3 ) QED O(α 4 ) QED O(α 5 ) QED total µ µ Z 0, H electroweak had. VP (LO) had. VP (NLO) had. LbL total W ν W B. Kubis, Strong interactions for the precision frontier in particle and nuclear physics p. 17

44 The Standard Model prediction fora µ a µ [10 11 ] a µ [10 11 ] experiment QED O(α) QED O(α 2 ) QED O(α 3 ) QED O(α 4 ) QED O(α 5 ) QED total electroweak had. VP (LO) had. VP (NLO) had. LbL µ µ hadrons total B. Kubis, Strong interactions for the precision frontier in particle and nuclear physics p. 17

45 The Standard Model prediction fora µ a µ [10 11 ] a µ [10 11 ] experiment QED O(α) QED O(α 2 ) QED O(α 3 ) QED O(α 4 ) QED O(α 5 ) QED total µ µ electroweak had. VP (LO) had. VP (NLO) had. LbL µ µ total B. Kubis, Strong interactions for the precision frontier in particle and nuclear physics p. 17

46 The Standard Model prediction fora µ a µ [10 11 ] a µ [10 11 ] experiment QED O(α) QED O(α 2 ) QED O(α 3 ) QED O(α 4 ) QED O(α 5 ) QED total hadrons electroweak had. VP (LO) had. VP (NLO) had. LbL µ total B. Kubis, Strong interactions for the precision frontier in particle and nuclear physics p. 17

47 The Standard Model prediction fora µ a µ [10 11 ] a µ [10 11 ] experiment QED O(α) QED O(α 2 ) QED O(α 3 ) QED O(α 4 ) QED O(α 5 ) QED total electroweak had. VP (LO) had. VP (NLO) had. LbL total hadronic part dominates the uncertainty by far! Jegerlehner, Nyffeler 2009 Davier et al and references therein B. Kubis, Strong interactions for the precision frontier in particle and nuclear physics p. 17

48 Hadronic vacuum polarization how to control hadronic vacuum polarization? characteristic scale set by muon mass this is not a perturbative QCD problem! dispersion relations to the rescue: use the optical theorem! µ µ hadrons B. Kubis, Strong interactions for the precision frontier in particle and nuclear physics p. 18

49 Hadronic vacuum polarization how to control hadronic vacuum polarization? characteristic scale set by muon mass this is not a perturbative QCD problem! dispersion relations to the rescue: use the optical theorem! Im γ γ γ hadrons hadrons 2 µ µ hadrons σ tot (e + e hadrons) B. Kubis, Strong interactions for the precision frontier in particle and nuclear physics p. 18

50 Hadronic vacuum polarization how to control hadronic vacuum polarization? characteristic scale set by muon mass this is not a perturbative QCD problem! dispersion relations to the rescue: use the optical theorem! had VP aµ 4M 2 π K(s)σ tot (e + e hadrons) µ µ hadrons K(s): kinematical function, for large s: σ tot (e + e hadrons) 1/s K(s) 1/s, B. Kubis, Strong interactions for the precision frontier in particle and nuclear physics p. 18

51 Hadronic vacuum polarization how to control hadronic vacuum polarization? characteristic scale set by muon mass this is not a perturbative QCD problem! dispersion relations to the rescue: use the optical theorem! had VP aµ 4M 2 π K(s)σ tot (e + e hadrons) µ µ hadrons K(s): kinematical function, for large s: σ tot (e + e hadrons) 1/s K(s) 1/s, had VP more than 75% of aµ given by energies s 1 GeV 2 Jegerlehner, Nyffeler 2009 dominated by e + e π + π pion electromagnetic form factor well constrained by data KLOE, BABAR... ρ, ω 0.0 GeV, Υ ψ 9.5 GeV 3.1 GeV φ, GeV 1.0 GeV B. Kubis, Strong interactions for the precision frontier in particle and nuclear physics p. 18

52 Hadronic light-by-light scattering hadronic light-by-light soon to dominate Standard Model uncertainty hadrons µ B. Kubis, Strong interactions for the precision frontier in particle and nuclear physics p. 19

53 Hadronic light-by-light scattering hadronic light-by-light soon to dominate Standard Model uncertainty hadrons different contributions estimated (in ): µ π 0, η, η π ±, K ± scalars axials, quarks µ µ µ µ 99±16 19±13 15±7 21±3 hadronic modelling at its worst... Jegerlehner, Nyffeler 2009 B. Kubis, Strong interactions for the precision frontier in particle and nuclear physics p. 19

54 Hadronic light-by-light scattering hadronic light-by-light soon to dominate Standard Model uncertainty hadrons different contributions estimated (in ): µ π 0, η, η π ±, K ± scalars axials, quarks µ µ 99±16 19±13 15±7 21±3 hadronic modelling at its worst... Jegerlehner, Nyffeler 2009 largest (and unambiguous!) individual contribution: π 0 pole term depends on π 0 γ γ form factor (doubly virtual in general!) µ µ B. Kubis, Strong interactions for the precision frontier in particle and nuclear physics p. 19

55 On the road to a dispersive analysis ofπ 0 γ γ The Wess Zumino Witten (chiral) anomaly π 0 γγ fixed by the chiral anomaly: F π0 γγ = e2 4π 2 F π F π : pion decay constant measured at % level PrimEx 2011 B. Kubis, Strong interactions for the precision frontier in particle and nuclear physics p. 20

56 On the road to a dispersive analysis ofπ 0 γ γ The Wess Zumino Witten (chiral) anomaly π 0 γγ fixed by the chiral anomaly: F π0 γγ = e2 4π 2 F π F π : pion decay constant measured at % level PrimEx 2011 analyze the leading hadronic intermediate states: see also Gorchtein, Guo, Szczepaniak 2012 γ v π + γ ( ) s γ s π + π 0 γ ( ) v π π 0 π π 0 B. Kubis, Strong interactions for the precision frontier in particle and nuclear physics p. 20

57 On the road to a dispersive analysis ofπ 0 γ γ The Wess Zumino Witten (chiral) anomaly π 0 γγ fixed by the chiral anomaly: F π0 γγ = e2 4π 2 F π F π : pion decay constant measured at % level PrimEx 2011 analyze the leading hadronic intermediate states: see also Gorchtein, Guo, Szczepaniak 2012 γ v π + γ ( ) s γ s ω, φ γ ( ) v π π 0 π 0 B. Kubis, Strong interactions for the precision frontier in particle and nuclear physics p. 20

58 On the road to a dispersive analysis ofπ 0 γ γ The Wess Zumino Witten (chiral) anomaly π 0 γγ fixed by the chiral anomaly: F π0 γγ = e2 4π 2 F π F π : pion decay constant measured at % level PrimEx 2011 analyze the leading hadronic intermediate states: see also Gorchtein, Guo, Szczepaniak 2012 γ v π + γ ( ) s γ s ω, φ γ ( ) v π π 0 π 0 important ingredients: anomalous process γπ ππ vector-meson radiative decays ω/φ π 0 γ transition form factors ω/φ π 0 l + l analyze these in turn, using dispersion relations B. Kubis, Strong interactions for the precision frontier in particle and nuclear physics p. 20

59 The anomalous processγπ ππ e γπ ππ at zero energy: F 3π = 4π 2 Fπ 3 = (9.78±0.05) GeV 3 how well can we test this low-energy theorem? B. Kubis, Strong interactions for the precision frontier in particle and nuclear physics p. 21

60 The anomalous processγπ ππ e γπ ππ at zero energy: F 3π = 4π 2 Fπ 3 = (9.78±0.05) GeV 3 how well can we test this low-energy theorem? Primakoff reaction: π γ Z π π 0 counts beam K - ρ preliminary COMPASS 2004 hadron data m π [GeV] - π 0 COMPASS, work in progress B. Kubis, Strong interactions for the precision frontier in particle and nuclear physics p. 21

61 The anomalous processγπ ππ e γπ ππ at zero energy: F 3π = 4π 2 Fπ 3 = (9.78±0.05) GeV 3 how well can we test this low-energy theorem? Primakoff reaction: π γ Z π π 0 counts beam K - ρ preliminary COMPASS 2004 hadron data same quantum numbers as φ 3π: m π [GeV] - π 0 COMPASS, work in progress Truong 2002, Hoferichter, BK, Sakkas 2012 B. Kubis, Strong interactions for the precision frontier in particle and nuclear physics p. 21

62 The anomalous processγπ ππ e γπ ππ at zero energy: F 3π = 4π 2 Fπ 3 = (9.78±0.05) GeV 3 how well can we test this low-energy theorem? Primakoff reaction: π γ Z π π 0 counts beam K - ρ preliminary COMPASS 2004 hadron data same quantum numbers as φ 3π: extract F 3π from the complete spectrum m π [GeV] - π 0 COMPASS, work in progress model-independently, using ππ phase shift! Hoferichter, BK, Sakkas 2012 B. Kubis, Strong interactions for the precision frontier in particle and nuclear physics p. 21

63 Transition form factorsω(φ) π 0 l + l π 0 γ γ form factor linked to ω(φ) π 0 γ transition: e e + π 0 e e + B. Kubis, Strong interactions for the precision frontier in particle and nuclear physics p. 22

64 Transition form factorsω(φ) π 0 l + l π 0 γ γ form factor linked to ω(φ) π 0 γ transition: e e + ω(φ) π 0 e e + B. Kubis, Strong interactions for the precision frontier in particle and nuclear physics p. 22

65 Transition form factorsω(φ) π 0 l + l π 0 γ γ form factor linked to ω(φ) π 0 γ transition: ω π + ω Im = π 0 π 0 π ω transition form factor related to pion vector form factor ω 3π decay amplitude }{{} calculate like φ 3π form factor normalization yields rate Γ(ω π 0 γ) (2nd most important ω decay channel) works at 95% accuracy Schneider, BK, Niecknig 2012 B. Kubis, Strong interactions for the precision frontier in particle and nuclear physics p. 22

66 Numerical results: ω π 0 µ + µ 9 F ωπ 0(s) NA60 09 NA60 11 Lepton-G VMD Terschlüsen et al. f 1 (s) = aω(s) full dispersive dγ ω π 0 µ + µ /ds [10 6 GeV 1 ] s [GeV] s [GeV] unable to account for steep rise in data (from heavy-ion collisions) NA , 2011 more "exclusive" data?! CLAS? ω 3π Dalitz plot? CLAS? B. Kubis, Strong interactions for the precision frontier in particle and nuclear physics p. 23

67 Towards a dispersive analysis ofe + e π 0 γ e + γ e π 0 e + γ γ e + γ e π 0 e π 0 combine isoscalar and isovector contribution to e + e π 0 γ: parameterise e + e 3π e.g. in terms of (dispersively improved) ω + φ Breit Wigner propagators with good analytic properties Lomon, Pacetti 2012; Moussallam 2013 prediction for e + e π 0 γ B. Kubis, Strong interactions for the precision frontier in particle and nuclear physics p. 24

68 Fit toe + e 3π data 10 3 σ(q)e + e 3π [nb] dispersive Fit SND q [GeV] Hoferichter, BK, Leupold, Niecknig, Schneider preliminary one subtraction/normalisation at q 2 = 0 fixed by γ 3π fitted: ω, φ residues, one additional (linear) subtraction B. Kubis, Strong interactions for the precision frontier in particle and nuclear physics p. 25

69 Comparison toe + e π 0 γ data 10 2 σ(q) e + e π 0 γ [nb] VEPP-2M CMD q[gev] Hoferichter, BK, Leupold, Niecknig, Schneider preliminary "prediction" no further parameters adjusted data well reproduced B. Kubis, Strong interactions for the precision frontier in particle and nuclear physics p. 26

70 Summary 2 pieces of modern strong-interaction physics using dispersion relations: Dalitz plot analyses rigorous using modern phase shift input allow to understand ad-hoc "background" methods applicable for many kinds of "amplitude analyses": CP violation, spectroscopy issues B. Kubis, Strong interactions for the precision frontier in particle and nuclear physics p. 27

71 Summary 2 pieces of modern strong-interaction physics using dispersion relations: Dalitz plot analyses rigorous using modern phase shift input allow to understand ad-hoc "background" methods applicable for many kinds of "amplitude analyses": CP violation, spectroscopy issues The muon anomalous magnetic moment hadronic physics needs to be constrained well before claiming "new physics" interrelate as much experimental information as possible B. Kubis, Strong interactions for the precision frontier in particle and nuclear physics p. 27

Towards a data-driven analysis of hadronic light-by-light scattering

Towards a data-driven analysis of hadronic light-by-light scattering Bastian Kubis Helmholtz-Institut für Strahlen- und Kernphysik (Theorie) Bethe Center for Theoretical Physics Universität Bonn, Germany