Stefan Leupold Interactions of light mesons with photons Interactions of light mesons with photons Stefan Leupold Uppsala University Meson 2014, Cracow, May/June 2014 1
Stefan Leupold Interactions of light mesons with photons Collaborators Uppsala: Per Engstr¨ om, Bruno Strandberg (now Glasgow) , Hazhar Ghaderi, Carla Terschl¨ usen GSI: Igor Danilkin (now JLAB) , Matthias Lutz Bonn: Franz Niecknig, Martin Hoferichter (now Bern) , Sebastian Schneider, Bastian Kubis 2
Stefan Leupold Interactions of light mesons with photons Table of Contents Transition form factors and two-gamma physics 1 Lagrangian approach 2 Dispersive approach to pion transition form factor 3 3
Stefan Leupold Interactions of light mesons with photons Reactions of hadrons with (virtual) photons Why is it interesting? explore intrinsic structure of hadrons � form factors � to which extent does vector meson dominance hold? 4
Stefan Leupold Interactions of light mesons with photons Reactions of hadrons with (virtual) photons Why is it interesting? explore intrinsic structure of hadrons � form factors � to which extent does vector meson dominance hold? background for physics beyond standard model e + � rare pion decay π 0 → e + e − π 0 e − γ ( k ) k ρ � g − 2 of muon had + 5 permutations of the q i q 3 λ q 2 ν q 1 µ µ ( p ) µ ( p ′ ) 4
Stefan Leupold Interactions of light mesons with photons Hadronic contribution to g − 2 of the muon γ ( k ) k ρ light-by-light scattering had + 5 permutations of the q i q 3 λ q 2 ν q 1 µ µ ( p ) µ ( p ′ ) γ ∗ γ ∗ ↔ hadron(s) is not directly accessible by experiment ֒ → need good theory with reasonable estimate of uncertainty (ideally an effective field theory) ֒ → need experiments to constrain such hadronic theories true for all hadronic contributions: the lighter the hadronic system, the more important (though high-energy contributions not unimportant for light-by-light) → γ ( ∗ ) γ ( ∗ ) ↔ π 0 (you’ve seen this before for rare pion decay) , ֒ γ ( ∗ ) γ ( ∗ ) ↔ 2 π , . . . 5
Stefan Leupold Interactions of light mesons with photons Shopping list for hadron theory and experiment transition form factors of pseudoscalars γ ( ∗ ) γ ( ∗ ) ↔ P with P = π 0 , η, η ′ , . . . ֒ → several interesting kinematical regions � next slide (for pion) 6
Stefan Leupold Interactions of light mesons with photons π 0 → γ ∗ ( q 2 v ) γ ∗ ( q 2 s ) transition form factor 2 q s e − π 0 e − e + e + π 0 → e + e − e + e − 2 q v π 0 → γγ e − π 0 e + (figures from Bastian Kubis) 7
Stefan Leupold Interactions of light mesons with photons Shopping list for hadron theory and experiment transition form factors of pseudoscalars γ ( ∗ ) γ ( ∗ ) ↔ P with P = π 0 , η, η ′ , . . . if invariant mass of dilepton around mass of a vector meson: � relation to transition form factors of vector to pseudoscalar mesons V ↔ P γ ( ∗ ) with V = ρ 0 , ω, φ, . . . 8
Stefan Leupold Interactions of light mesons with photons Shopping list for hadron theory and experiment transition form factors of pseudoscalars γ ( ∗ ) γ ( ∗ ) ↔ P with P = π 0 , η, η ′ , . . . if invariant mass of dilepton around mass of a vector meson: � relation to transition form factors of vector to pseudoscalar mesons V ↔ P γ ( ∗ ) with V = ρ 0 , ω, φ, . . . “two-gamma physics” γγ → π + π − , π 0 π 0 , π 0 η, K ¯ K , . . . (cross relation to polarizability of the pion) ֒ → has triggered a lot of experimental activity, in particular MesonNet (WASA, KLOE, MAMI, HADES, . . . ) 8
Stefan Leupold Interactions of light mesons with photons Two complementary approaches Lagrangian approach use only hadrons which are definitely needed (here: lowest nonets of pseudoscalar and vector mesons) sort interaction terms concerning importance, essentially based on large- N c include causal rescattering/unitarization for reactions (I. Danilkin, L. Gil, M. Lutz, Phys.Lett. B703, 504 (2011)) long-term goal: obtain sensible estimates of uncertainties dispersive approach include most important hadronic inelasticities use measured (and dispersively improved) phase shifts (2-body) use Breit-Wigner plus background for narrow resonances ( n -body, n > 2) error estimates from more vs. less subtracted dispersion relations 9
Stefan Leupold Interactions of light mesons with photons Table of Contents Transition form factors and two-gamma physics 1 Lagrangian approach 2 Dispersive approach to pion transition form factor 3 10
Stefan Leupold Interactions of light mesons with photons Transition form factor ω → π 0 + dilepton 100 (P1) (P2) data and our Lagrangian approach stand. VMD NA60 show strong deviations from vector-meson dominance (VMD) our approach describes data fairly 10 |F ωπ 0 | 2 well except for large invariant masses close to phase-space limit (log plot!) 1 second experimental confirmation desirable 0 0.2 0.4 0.6 m l + l − [GeV] C. Terschl¨ usen, S.L., Phys. Lett. B691, 191 (2010) 11
Stefan Leupold Interactions of light mesons with photons Transition form factor φ → η + dilepton 10 |F φη | 2 θ = − 2 ° θ = + 2 ° VMD VEPP-2M 5 our Lagrangian approach deviates from VMD new data from KLOE will come 0 soon -5 0.0 0.2 0.4 q [GeV] C. Terschl¨ usen, S.L., M.F.M. Lutz, Eur.Phys.J. A48, 190 (2012) 12
Stefan Leupold Interactions of light mesons with photons γγ → π + π − , π 0 π 0 300 60 Mark II Crystal Ball γγ → π + π - γγ → π 0 π 0 Belle Belle CELLO Belle syst. error Belle syst. error 200 40 σ [nb] σ [nb] 100 20 0 0 0.3 0.7 1.1 0.3 0.7 1.1 s 1/2 [GeV] s 1/2 [GeV] dashed black lines: tree level, blue lines: with coupled-channel rescattering of two pseudoscalar mesons overall good description, room for improvement concerning f 0 (980) at high energies spin-2 mesons are missing I.V. Danilkin, M.F.M. Lutz, S.L., C. Terschl¨ usen, Eur.Phys.J. C73, 2358 (2013) 13
Stefan Leupold Interactions of light mesons with photons γγ → π 0 η 60 60 Crystal Ball Crystal Ball γγ → π 0 η γγ → π 0 η Belle Belle Belle syst. error Belle syst. error 40 40 σ [nb] σ [nb] 20 20 0 0 0.7 0.95 1.2 0.7 0.95 1.2 s 1/2 [GeV] s 1/2 [GeV] dashed black line: tree level, blue line: with coupled-channel rescattering of two pseudoscalar mesons a 0 (980) dynamically generated I.V. Danilkin, M.F.M. Lutz, S.L., C. Terschl¨ usen, Eur.Phys.J. C73, 2358 (2013) 14
Stefan Leupold Interactions of light mesons with photons γγ → K + K − , K 0 ¯ K 0 , ηη (pure predictions) 45 30 ARGUS γγ → K + K - T ASSO γγ → K 0 K 0 CELLO 30 20 σ [nb] σ [nb] 15 10 0 0 1 1.1 1.2 1 1.1 1.2 s 1/2 [GeV] s 1/2 [GeV] 4.5 Belle γγ → ηη 3 σ [nb] 1.5 0 1.1 1.15 1.2 s 1/2 [GeV] 15
Stefan Leupold Interactions of light mesons with photons Table of Contents Transition form factors and two-gamma physics 1 Lagrangian approach 2 Dispersive approach to pion transition form factor 3 16
Stefan Leupold Interactions of light mesons with photons π 0 → γ ∗ ( q 2 v ) γ ∗ ( q 2 s ) transition form factor 2 q s e − π 0 e − e + e + π 0 → e + e − e + e − 2 q v π 0 → γγ e − π 0 e + (figures from Bastian Kubis) 17
Stefan Leupold Interactions of light mesons with photons π 0 → γ ∗ ( q 2 v ) γ transition form factor 2 q s e − π 0 e − e + e + π 0 → e + e − e + e − 2 q v π 0 → γγ e − π + π 0 e − π 0 e + π − e + γ (figures from Bastian Kubis) 18
Stefan Leupold Interactions of light mesons with photons π 0 → γγ ∗ ( q 2 s ) transition form factor 2 q s e − π 0 ω ( φ ) e + γ e − π 0 e − e + e + π 0 → e + e − e + e − 2 q v π 0 → γγ e − π 0 e + (figures from Bastian Kubis) 19
Stefan Leupold Interactions of light mesons with photons Pion transition form factor — dispersive approach want prediction for e + e − → π 0 γ (up to ≈ 1 GeV) ֒ → dominant inelasticities: I = 1: e + e − → π + π − → π 0 γ I = 0: e + e − → π 0 π + π − → π 0 γ required input for I = 1: pion phase shift and pion form factor � measured strength of amplitude π + π − → π 0 γ � chiral anomaly (M. Hoferichter, B. Kubis, D. Sakkas, Phys.Rev. D86 (2012) 116009) input for I = 0 (three-body!): dominated by narrow resonances ω , φ → use Breit-Wigners plus background for amplitude ֒ → fit to e + e − → π + π − π 0 ֒ 20
Stefan Leupold Interactions of light mesons with photons Pion transition form factor ( e + e − → π 0 γ ) unsubtracted dispersion relation uncertainty estimate from 2 10 quality of ω/φ → π 0 γ σ ( q ) e + e − → π 0 γ [nb] 1 10 Schneider et al., PRD86, 054013 0 can be extended to decay 10 region π 0 → γ e + e − and to -1 10 VEPP-2M spacelike region CMD-2 -2 10 final aim: double virtual transition form factor -3 10 0.5 0.6 0.7 0.8 0.9 1 1.1 q [GeV] ֒ → relevant for g − 2 and π 0 → e + e − M. Hoferichter, B. Kubis, S.L., F. Niecknig and S. P. Schneider, in preparation 21
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