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Interactions of Light with Light Mesons Stefan Leupold Interactions of light with light mesons Interactions of light with light mesons Stefan Leupold Uppsala University Light Meson Dynamics, Mainz, Feb. 2014 1 Stefan Leupold Interactions of light with light mesons 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 with light mesons Table of Contents 1 What we are after 2 Transition form factors and two-gamma physics 3 Lagrangian approach 4 Dispersive approach to pion transition form factor 3 Stefan Leupold Interactions of light with light mesons Challenges of hadron (+nuclear) physics structure of matter understand masses of hadrons (also, e.g., mass ordering: mσ < mρ, 1440 < 1520) life times, branching ratios of hadron resonances form factors and intrinsic structure nature of hadrons (how much quark-antiquark? how much hadron-hadron? ...) (nuclei, neutron stars) new forms of matter high-precision frontier of standard model 4 Stefan Leupold Interactions of light with light mesons Challenges of hadron (+nuclear) physics structure of matter new forms of matter non-qq¯ mesons (exotic quantum numbers, exotic decomposition, X/Y/Z states, glueballs, meson molecules, ...) non-3q baryons, di-baryons (∆ ∆ by WASA?), ... − (quark-gluon plasma, color superconductors, early universe, core of neutron stars) high-precision frontier of standard model 5 Stefan Leupold Interactions of light with light mesons Challenges of hadron (+nuclear) physics structure of matter new forms of matter high-precision frontier of standard model determine parameters of standard model (light quark masses, CKM matrix, ...) traces of physics beyond standard model (rare decays, g 2 of muon, ...) − 6 Stefan Leupold Interactions of light with light mesons Challenges of hadron (+nuclear) theory structure of matter new forms of matter high-precision frontier of standard model from phenomenological models to real quantum field theories physical form factors instead of ad-hoc cutoff form factors do not neglect loops just because they are complicated assign degrees of importance to processes, diagrams (e.g. power counting, separation of relevant from irrelevant degrees of freedom) reliable uncertainty estimates treat unitarity/rescattering, analyticity serious We are not there yet! 7 background for physics beyond standard model e+ 0 + 0 rare pion decay π e e− π ! e− γ(k) kρ g 2 of muon had + 5 permutations of the qi q3λ q − q2ν 1µ µ(p) µ(p′) Stefan Leupold Interactions of light with light mesons 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? 8 e+ π0 e− γ(k) kρ had + 5 permutations of the qi q 3λ q2ν q1µ µ(p) µ(p′) Stefan Leupold Interactions of light with light mesons 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 0 + rare pion decay π e e− ! g 2 of muon − 8 γ(k) kρ had + 5 permutations of the qi q 3λ q2ν q1µ µ(p) µ(p′) Stefan Leupold Interactions of light with light mesons Hadronic contribution to g 2 of the muon − light-by-light scattering 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) ( ) ( ) 0 , γ ∗ γ ∗ π (you've seen this before for rare pion decay), ! ( ) ( ) $ γ ∗ γ ∗ 2π,... $ 9 Stefan Leupold Interactions of light with light mesons Shopping list for hadron theory and experiment ( ) ( ) transition form factors of pseudoscalars γ ∗ γ ∗ P 0 $ with P = π ; η; η0;::: , several interesting kinematical regions next slide (for pion) ! 10 Stefan Leupold Interactions of light with light mesons 0 2 2 π γ∗(q )γ∗(q ) transition form factor ! v s 2 qs 0 e− π e− e+ e+ 0 + + π e e−e e− ! 2 qv π0 γγ e− ! π0 e+ (figures from Bastian Kubis) 11 + 0 0 0 \two-gamma physics" γγ π π−; π π ; π η; KK¯ ;::: (cross relation to polarizability! of the pion) , has triggered a lot of experimental activity, ! in particular MesonNet (WASA, KLOE, MAMI, HADES, . ) Stefan Leupold Interactions of light with light mesons Shopping list for hadron theory and experiment ( ) ( ) transition form factors of pseudoscalars γ ∗ γ ∗ P 0 $ with P = π ; η; η0;::: if invariant mass of dilepton around mass of a vector meson: relation to transition form factors of vector to pseudoscalar mesons ( ) 0 V Pγ ∗ with V = ρ ; !; φ, : : : $ 12 Stefan Leupold Interactions of light with light mesons Shopping list for hadron theory and experiment ( ) ( ) transition form factors of pseudoscalars γ ∗ γ ∗ P 0 $ with P = π ; η; η0;::: if invariant mass of dilepton around mass of a vector meson: relation to transition form factors of vector to pseudoscalar mesons ( ) 0 V Pγ ∗ with V = ρ ; !; φ, : : : $ + 0 0 0 \two-gamma physics" γγ π π−; π π ; π η; KK¯ ;::: (cross relation to polarizability! of the pion) , has triggered a lot of experimental activity, ! in particular MesonNet (WASA, KLOE, MAMI, HADES, . ) 12 Stefan Leupold Interactions of light with light mesons 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-Nc 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 13 Stefan Leupold Interactions of light with light mesons Table of Contents 1 What we are after 2 Transition form factors and two-gamma physics 3 Lagrangian approach 4 Dispersive approach to pion transition form factor 14 Stefan Leupold Interactions of light with light mesons Transition form factor ! π0+ dilepton ! 100 (P1) (P2) data and our Lagrangian approach stand. VMD NA60 show strong deviations from vector-meson dominance (VMD) 2 | 0 10 our approach describes data fairly ωπ |F well except for large invariant masses close to phase-space limit (log plot!) 1 second experimental confirmation 0 0.2 0.4 0.6 desirable − ml+l [GeV] C. Terschl¨usen,S.L., Phys. Lett. B691, 191 (2010) 15 Stefan Leupold Interactions of light with light mesons Transition form factor φ η+ dilepton ! 10 2 |Fφη| 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) 16 Stefan Leupold Interactions of light with light mesons + 0 0 γγ π π−; π π ! 300 60 Mark II + - Crystal Ball 0 0 Belle γγ → π π Belle γγ → π π CELLO Belle syst. error Belle syst. error 200 40 ] ] b b n n [ [ σ 100 σ 20 0 0 0.3 0.7 1.1 0.3 0.7 1.1 s1/2 [GeV] s1/2 [GeV] dashed black lines: tree level, blue lines: with coupled-channel rescattering of two pseudoscalar mesons overall good description, room for improvement concerning f0(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) 17 Stefan Leupold Interactions of light with light mesons γγ to other meson pairs , stay tuned for Matthias' talk ! 18 Stefan Leupold Interactions of light with light mesons Table of Contents 1 What we are after 2 Transition form factors and two-gamma physics 3 Lagrangian approach 4 Dispersive approach to pion transition form factor 19 Stefan Leupold Interactions of light with light mesons 0 2 2 π γ∗(q )γ∗(q ) transition form factor ! v s 2 qs 0 e− π e− e+ e+ 0 + + π e e−e e− ! 2 qv π0 γγ e− ! π0 e+ (figures from Bastian Kubis) 20 Stefan Leupold Interactions of light with light mesons 0 2 π γ∗(q )γ transition form factor ! v 2 qs 0 e− π e− e+ e+ 0 + + π e e−e e− ! 2 qv 0 + 0 π γγ e− π π e− ! π0 e+ e+ π− γ (figures from Bastian Kubis) 21 Stefan Leupold Interactions of light with light mesons 0 2 π γγ ∗(q ) transition form factor ! s 2 qs 0 e− π ω(φ) e+ γ 0 e− π e− e+ e+ 0 + + π e e−e e− ! 2 qv π0 γγ e− ! π0 e+ (figures from Bastian Kubis) 22 Stefan Leupold Interactions of light with light mesons Pion transition form factor | dispersive approach + 0 want prediction for e e− π γ (up to 1 GeV) ! ≈ , dominant inelasticities: ! I = 1: e+e π+π π0γ − ! − ! I = 0: e+e π0π+π π0γ − ! − ! required input for I = 1: pion phase shift and pion form factor measured strength of amplitude π+π π0γ chiral anomaly − ! (M. Hoferichter, B. Kubis, D. Sakkas, Phys.Rev. D86 (2012) 116009) input for I = 0 (three-body!): dominated by narrow resonances !, φ , use Breit-Wigners plus background for amplitude ! , fit to e+e π+π π0 and decay widths !/φ π0γ ! − ! − ! 23 Stefan Leupold Interactions of light with light mesons + 0 Pion transition form factor (e e− π γ) ! height between peaks is not 2 10 a fit! 101 [nb] can be extended to decay γ 0 π 0 + → 0 − region π γ e e− and to e 10 + e ) ! q spacelike region ( σ 10-1 VEPP-2M CMD-2 final aim: double virtual 10-2 transition form factor -3 , relevant for g 2 and 10 0.5 0.6 0.7 0.8 0.9 1 1.1 ! 0 + − q[GeV] π e e− ! M.
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