Stefan Leupold Hyperon-photon physics Hyperon-photon physics Stefan Leupold Uppsala University NoSTAR 2017, Columbia, SC, August 2017 1 Stefan Leupold Hyperon-photon physics Table of Contents 1 Motivation: structure of matter 2 Theory for low-energy form factors 3 Summary and outlook 2 n p T q q T T Σ− Λ Σ0 T Σ+ T q T q q T T and from Ξ− Ξ0 Gell-Mann's multiplets q q − 0 + ++ containing strange hadrons ∆ ∆ ∆ ∆ T q T q q q T , expect valuable information T Σ∗− Σ∗0 Σ∗+ ! from combining T q T q q electromagnetism and T strangeness T Ξ∗− Ξ∗0 T , complements information q T q ! T from nucleon form factors TΩ− q Stefan Leupold Hyperon-photon physics Historical remark first hints for compositeness of proton came from non-trivial gyromagnetic ratio = 2 6 3 Stefan Leupold Hyperon-photon physics Historical remark n p T first hints for compositeness q q T of proton came from T Σ− Λ Σ0 T Σ+ non-trivial gyromagnetic T q T q q ratio = 2 T 6 T and from Ξ− Ξ0 Gell-Mann's multiplets q q − 0 + ++ containing strange hadrons ∆ ∆ ∆ ∆ T q T q q q T , expect valuable information T Σ∗− Σ∗0 Σ∗+ ! from combining T q T q q electromagnetism and T strangeness T Ξ∗− Ξ∗0 T , complements information q T q ! T from nucleon form factors TΩ− 3 q Stefan Leupold Hyperon-photon physics Electromagnetic form factors of hyperons to large extent terra incognita electron-hyperon scattering complicated instead: + − ¯ reactions e e hyperon anti-hyperon (Y1 Y2) BESIII , form factors and! transition form factors ! 2 2 for large time-like q > (mY1 + mY2 ) (time-like means q2 > 0, i.e. energy transfer > momentum transfer) + − decays Y1 Y2 e e HADES+PANDA ! 2 2 , transition form factors for small time-like q < (mY1 mY2 ) ! − 4 Stefan Leupold Hyperon-photon physics Theory for baryon low-energy form factors ideally as model independent as possible , use (if possible) effective field theories (EFTs) ! and general QFT principles (unitarity, analyticity, . ) existing (in EFT spirit): for octet: chiral perturbation theory (EFT), Kubis/Meißner, Eur. Phys. J. C 18, 747 (2001) , predictions for electric and magnetic radii ! (= slopes of form factors) , shortcomings: no explicit decuplet, no explicit vector mesons ,! for curvatures one already needs vector mesons ! for transitions decuplet-octet: chiral perturbation theory for ∆-N, Pascalutsa/Vanderhaeghen/Yang, Phys. Rept. 437, 125 (2007) , no vector mesons and not for hyperons ! 5 Stefan Leupold Hyperon-photon physics Theory for hyperon low-energy form factors new approach: hadronic chiral perturbation theory plus dispersion theory , easier to include decuplet ! , dispersion theory includes ρ meson as measured in π-π ! Σ0-Λ transition form factors: C. Granados, E. Perotti, SL, Eur.Phys.J. A53, 117 (2017) , some results on next slides ! decuplet-octet transitions: E. Perotti, O. Junker, SL, work in progress very similar in spirit: J.M. Alarc´on, A.N. Hiller Blin, M.J. Vicente Vacas, C. Weiss, Nucl.Phys. A964, 18 (2017) 6 Stefan Leupold Hyperon-photon physics ( ) Hyperon transition form factors Σ ∗ for Σ=Σ∗ Λ e+e− need transition form factors ! Λ dispersive framework: at low energies q2 dependence is governed by lightest intermediate states ( ) Σ ∗ π+ , obtain from ! π − Λ π+ , need pion vector form factor (measured) ! π− ( ) π Σ ∗ and hyperon-pion scattering amplitudes π Λ 7 Stefan Leupold Hyperon-photon physics Hyperon-pion scattering amplitudes contain π Σ( ) \right-hand cuts" (pion rescattering) π ∗ , straightforward from ! unitarity and analyticity π (and experimental pion phase shift) π Λ ( ) and rest: π Σ ∗ ( ) left-hand cuts, polynomial terms π Σ ∗ , not straightforward = ? ,! use three-flavor baryon chiral ! perturbation theory π Λ π Λ 8 Stefan Leupold Hyperon-photon physics Input for hyperon-pion scattering amplitudes ideally use data , available for pion-nucleon, but not for pion-hyperon ! , instead: three-flavor baryon chiral perturbation theory (χPT) ! at leading and next-to-leading order (NLO) including decuplet states (optional for Σ0 Λ transition, but turns out to be important!) ! ( ) ( )π Σ ∗ π Σ ∗ ( ) π Σ ∗ Σ/Σ∗ + ≈ π π Λ Λ π Λ 9 Stefan Leupold Hyperon-photon physics χPT input for hyperon-pion scattering amplitudes three-point couplings fairly well known, but how to determine NLO four-point coupling constants? only one parameter (b10) for Σ-Λ transition , but not very well known ! \resonance saturation" estimates Meißner/Steininger/Kubis, Nucl.Phys. B499, 349 (1997); Eur.Phys.J. C18, 747 (2001) or from fit to πN and KN scattering data with coupled-channel Bethe-Salpeter approach ( ) π Σ ∗ Lutz/Kolomeitsev, Nucl.Phys. A700, 193 (2002) maybe in the future: π Λ cross-check from lattice QCD parameter is directly related to magnetic transition radius of Σ-Λ 10 Stefan Leupold Hyperon-photon physics Transition form factors Σ-Λ 0.01 2.5 small hA, cutoff la. hA, sm. b10, sm. cut. 0.005 radius adjust. sm. hA, sm. b10, la. cut. large hA, cutoff 2 la. hA, av. b10, sm. cut. 0 sm. hA, av. b10, la. cut. la. hA, la. b10, sm. cut. -0.005 1.5 sm. hA, la. b10, la. cut. -0.01 1 E -0.015 M G G 0.5 -0.02 -0.025 0 -0.03 -0.5 -0.035 -0.04 -1 -1 -0.8 -0.6 -0.4 -0.2 0 -1 -0.8 -0.6 -0.4 -0.2 0 q2 [GeV2] q2 [GeV2] electric transition form factor very small over large range , what one might measure at low energies is ! magnetic transition form factor , data integrated over Λ-e− angle, but differential in q2 might be ! sufficient 2 2 2 note: Dalitz decay region 4me < q < (mΣ mΛ) hardly visible here − 11 Stefan Leupold Hyperon-photon physics Magnetic transition form factor Σ-Λ 2.5 la. hA, sm. b10, sm. cut. sm. hA, sm. b10, la. cut. 2 la. hA, av. b10, sm. cut. sm. hA, av. b10, la. cut. la. hA, la. b10, sm. cut. 1.5 sm. hA, la. b10, la. cut. 1 M G 0.5 0 -0.5 -1 -1 -0.8 -0.6 -0.4 -0.2 0 q2 [GeV2] large uncertainty , directly related to uncertainty in NLO low-energy constant b10 ! , can be determined from measuring magnetic transition radius ! 12 Stefan Leupold Hyperon-photon physics Summary exploring structure of hadrons learned a lot about hadrons from electromagnetic probes . from strangeness , high time to combine these lines of research ! electromagnetic (transition) form factors of hyperons + − at low energies: Dalitz decays YA YB e e ! complementary theory program: combining dispersion theory with baryon octet+decuplet chiral perturbation theory , first results: ! electric form factor of Σ-Λ transition very small (also found in recent quark{Dyson-Schwinger calculations, Sanchis-Alepuz/Alkofer/Fischer, arXiv:1707.08463 [hep-ph]) magnetic form factor in spacelike region can be predicted if radius is measured in timelike region (Dalitz decay) 13 Stefan Leupold Hyperon-photon physics backup slides 14 Stefan Leupold Hyperon-photon physics 0 + Σ Λ e e− ! basic: branching ratio (QED prediction 5 10−3) · advanced: differential distribution; resolve effect from non-trivial transition form factors GE , GM 2 d Γ n 2 2 2 2 2 2 2 2 o GE (q ) (mΛ+mΣ) (1 z )+ GM (q ) q (1+z ) dq2 dz ∼ j j − j j as compared to (leading-order) QED prediction d 2Γ QED µ2 q2 (1 + z 2) dq2 dz ∼ ΣΛ 0 with transition magnetic moment µΣΛ (known from Σ Λ γ) ! note: proportionality factor is function of q := pe+ + pe− , but not of z :=cos(angle(e−; Λ) in dilepton rest frame) 15 Stefan Leupold Hyperon-photon physics Challenge to extract form factors Σ0 Λ e+e− does not produce large e− invariant! masses for the lepton pair, 2 2 q < (77 MeV) 0 Σ e+ , transition form factor is close to unity ! (normalization at photon point) Λ , need high precision in experiment and ! theory to deduce transition form factor , expect effects on 1-2% level ! e− , effects from form factor compete with 0 Σ + ! QED corrections e , tedious but calculable ! Λ (T. Husek and SL, in preparation) 16 Stefan Leupold Hyperon-photon physics Full formulae for differential distribution double differential decay width Σ0 Λ e+e−: ! 2 2 1=2 d Γ 1 1=2 2 2 4me 2 = 3 3 λ (mΣ; s; mΛ) 1 ds dz (2π) 64mΣ − s jMj 4 2 e 2 = 2((mΣ mΛ) s) jMj s2 − − 2 n 2 2 4me 2 GE (s) (mΛ + mΣ) 1 1 z j j − − s 2 2 2 2 o + GM (s) (s (1 + z ) + 4m (1 z )) : j j e − note: electron mass neglected in main presentation independent kinematical variables defined on next slide 17 Stefan Leupold Hyperon-photon physics Full formulae for differential distribution, cont. independent kinematical variables: 2 2 s := (pe+ + pe− ) = q z is cos of angle between e− and Λ in rest frame of dilepton ∆m2 z := 2 (∆m )max 2 2 2 with ∆m := (pe+ + pΛ) (p − + pΛ) and − e r 4m2 ∆m2 := λ1=2(m2 ; s; m2 ) 1 e : max Σ Λ − s kinematical variables cover the ranges 2 2 z [ 1; 1] and 4m s (mΣ mΛ) 2 − e ≤ ≤ − K¨all´enfunction λ(a; b; c) := a2 + b2 + c2 2(ab + bc + ac) − 18 effective theories are systematic phenom. models are not $ \systematic" means that one can estimate the theory uncertainty/precision dispersion theory uses data instead of phenomenological models , (improvable) data uncertainties instead of ! (not improvable) model uncertainties but: not for every problem there exists an effective theory; dispersion theory not of practical use if one has to deal with too many channels, too many particles Stefan Leupold Hyperon-photon physics Theory for low-energy form factors Confessions of a theorist: every theorist has favorite toys mine are at the moment effective field theories (EFT) and dispersion theory , some arguments in favor of this choice: ! 19 but: not for every problem there exists an effective theory; dispersion theory not of practical use if one has to deal with too many channels, too many particles Stefan Leupold Hyperon-photon physics Theory for low-energy form factors Confessions of a theorist: every theorist has favorite toys mine are at the moment effective field theories (EFT) and dispersion theory , some arguments in favor of this choice: ! effective theories are systematic phenom.