Hypernuclear Physics - electroproduction of hypernuclei Petr Bydžovský in collaboration with Miloslav Sotona Nuclear Physics Institute, Řež near Prague, Czech Republic Workshop on Electromagnetic Interactions, Bosen, Aug. 30 – Sept. 4, 2009

Outline: Introduction Electroproduction of hypernuclei Elementary process Results for p-shell hypernuclei Summary

What is hypernucleus? Bound system of nucleons and hyperon(s):  – hypernuclei  e.g. 3,4 H , 4,5,6,7,8 He , Li, Be, B, C, N, O, Al, Si, S, Ca, V, Fe, Y, La, Pb, Bi Long living system:  -hypernucleus lifetime is approx s - bound state (SI) can exist; electromagnetic transitions are possible Discovered in decay of a hypernucleus was observed in the emulsion by Marian Danysz and Jerzy Pniewski (Phil. Mag. 44 (1953) 348.) No Pauli blocking for the hyperon – transparent shell-structure

Hotchi et al, Phys. Rev. C 64 (2001)  hyperon occupies s, p, d, and f shell orbits in 89 Y  multiplets of states -   single particle states are well defined - description of the nucleus in terms of baryons is reasonable

Why to study hypernuclei? Energy spectra – information about effective YN interaction spin dependent parts (  N scattering data – only averaged s-state interaction,  well depths is reasonably fixed )  mixing (  N  0 + N)  charge symmetry breaking ( mirror nuclei, e.g. 4 He  – 4 H    16 N   –  16 O  ) Non mesonic weak decay of  :  N  nN (  n /  p, asymmetry ) Modifications of  hyperon properties in the nuclear medium (e.g. magnetic moment from precise measurement of M1 transitions)

How to produce hypernuclei? ( K -,  - ) – small momentum transfer (below 100 MeV/c) (stopped / inflight) – non spin-flip dominates (  S =  L = 0 ) – predominantly substitutional states populated (poor spectrum) –   mb/sr (strangeness exchange) (  , K + ) – larger momentum transfer than in ( K -,  - ) (300 MeV/c) –  S = 0,  L =  J = 1, 2 natural-parity states populated –    b/sr (associated production of strangeness) – rich series of  single-particle states –  -ray spectroscopy ( e,e’K + ) – momentum transfer as in (  , K + ) (350 MeV/c) – spin-flip dominates:  S = 1,  L = 1, 2,  J = 1, 2, 3 – wide variety of  single-particle states are populated –  nb/sr (production of strangeness in the electromagnetic process) – production on proton – other hypernuclei than in ( , K )

Momentum transfer to hyperon

Electroproduction of Hypernuclei Production of hypernuclei in excited states – spectrum of states Quasi-free production (e.g.  q.-f. threshold in 12 B  is MeV) H : 12 B  ,  16 N , 9 Li  … Final-state interaction  information about YN interaction

Kinematics Detection of e ’ and K + at very forward angles (  e : 0 – 6 o,  K : 6 o ) due to a steeply decreasing angular dependence of the virtual-photon flux and nucleus-hypernucleus transition form factors. Hypernuclear production cross section is measured as a function of hypernucleus excitation energy. pHpH

Calculation of the cross sections PWIA in multiple-scattering formalism (Hsiao&Cotanch, 1983); relativistic DWIA (Bennhold&Wright, 1989) – single-particle single- hole model, Fermi motion, kaon distortion, “simple” elementary operator  results are very sensitive to a form of the elementary operator Our calculations in DWIA (Sotona&Frullani, 1994) One-photon approximation – the electromagnetic and hadron parts can be separated The unpolarized cross section in lab frame:

Many-body matrix element in DWIA (incoming/outgoing particle momenta are high ~1 GeV): J  (i) – elementary hadron current in lab frame (frozen-nucleon approx.)    – virtual-photon wave function (one-photon approx., no Coulomb distortion)  K – distorted kaon wave f. (eikonal approx. with 1 st order optical potential, KN interaction is weak)  A (  H ) - target nucleus (hypernucleus) nonrelativistic wave functions

Shell model description of p-shell nuclei and hypernuclei  A - Cohen-Kurath NN in s 4 p A-4 model space    - phenomenological effective  interaction (John Millener) radial integrals are parameterized (  in s-shell): parameters , S , S N, and T fitted to  -ray spectra of 7 Li , 9 Be , and 16 O   0.33, S    S N  -0.35, T  all in MeV )  mixing (  N  N) is included (s N 4 p N A-5 s  + s N 4 p N A-5 s  )

 N is weaker than NN => hypernucleus states can be build up on the states of the core nucleus (weak coupling model) Example: doublet of states  in p-states (p 1/2 or p 3/2 )

6 channels : N = p, n; Y =  ; K = K +, K 0 Elementary process Electroproduction of hyperons on nucleons Separation of electromagnetic and hadron parts –  T,  L,  TT,  TL for the binary process

Approaches: isobaric model multipole analysis Regge formalism quark models hybrid Regge-plus-resonance unitary approach (coupled channels) chiral perturbation theory chiral unitary framework (chiral Lagrangian and coupled channels)

Isobaric model for full t-matrix : T = V + V G t driving term N    KY or KY  KY coupled channels coupled-channel approaches : Pener, Feuster, Mosel ( K-matrix method ) Chiang, Tabakin, Lee, Saghai isobaric models – approximation: T = V => violation of unitarity - no experimental information about t(  K   K) - fitted coupling constants absorb a part of the re-scattering effects Meson-baryon final-state interaction

Driving term - effective hadron Lagrangian - perturbation theory on tree-level approximation gauge-invariant operators n = 6 for electro-production n = 4 for photo-production s, t, u- channel Feynman graphs - Born - contact (PV coupling) - resonances

s-channel e  N  NN* N  K N, N* PS coupling (N) g KN  g KN*  t-channel e g KK*  g KK1  gauge invariance K, K*, K 1 N  K g KN  g K*N  V,T g K1N  V,T u-channel NK   Y*       Y* g KN  g KN  g KNY* spin = 1/2, 3/2, 5/2, … m N* < 2 GeV well known SU(3) symmetry

 p   p (P.R.C78,035204(2008))  p  K +  S 11 (1535) P 33 (1232) P 11 (1710) D 13 (1895) no dominant resonance in K photoproduction

Many resonances (20-30) with a reasonable branching ratio to the K  channel are assumed => large number of models ( with a good  2 ) Constraints on the models: - SU(3) symmetry - violated by 20 % gives limits: - crossing symmetry: (tree level) - duality hypothesis: exchanges in s-channel t-channel N * (spin 1/2, 3/2, 5/2,…) (K *, K 1,…)

Form factors in vertexes: electromagnetic – phenomenological form (Lomon) hadron – violation of gauge invariance – a contact term is included to restore the invariance (Haberzettl) Examples of isobaric models: both models include: extended Born terms (p, , , K) t-channel resonances K*(890), K 1 (1270) Saclay-Lyon A: no hadronic f. f., SU(3), crossing, nucleon (spin 1/2 and 3/2) and hyperon resonances Kaon-MAID: hadronic f. f., SU(3), no hyperon, only nucleon (spin 1/2 and 3/2) resonances

Production at small kaon angles – large uncertainty in calculations of the cross sections for production of hypernuclei production of hypernuclei W = 1.82 GeV

Results of DWIA calculation of the cross section for the electroproduction (but very small Q 2 ) of 12 B  at 1.3 GeV uncertainty 20 – 30 %

Higher energies kinematics for electroproduction of hypernuclei in Hall A, JLab, experiment E p(e,e’K)  Kaon-MAID

Results for p-shell hypernuclei Excitation spectra of 12 B , 16 N , and 9 Li  (JLab Hall A experiment) Angular dependence of the cross sections

12 C  target - Hypernuclear Spectrum of 12 B  Theoretical prediction (dashed line): elementary operator – Saclay-Lyon A model  N interaction from 7 Li   -ray spectra (M. Iodice et al, Phys. Rev. Lett. 99 (2007) )    GeV  e =  K = 6 o Q 2 = GeV 2 s  p 1/2 , p 3/2    B    g. s.    B    11 B( 3/2 -, 5.02 ) 1 -, , 2 +, 3 + larger model space?

16 O target - Hypernuclear Spectrum of 16 N  Theoretical prediction : elementary operator – Saclay-Lyon A model  N interaction fitted to 16 O  and 15 N  spectra Data: the E experiment in JLab, Hall A (F. Cusanno et al) different splitting ss pp Larger model space? (1 h  calculations)

9 Be target - Hypernuclear Spectrum of 9 Li  Theoretical calculation : elementary operator – Saclay-Lyon A model, wave functions by John Millener (fitted to  -ray spectroscopy data) predictions for various energy resolutions (FWHM)

Angular dependence of the cross section for electroproduction of 16 N  at E  = 2.21 GeV and  e = 6 o Cross sections in lab frame for doublet J = 1 -, 2 - at E x 6.71 and 6.93 MeV  Ke is kaon lab angle with respect to beam - in general, steeply decreasing dependence (the momentum transfer changes rapidly); - the slope depends on the spin (J); - behaviour depends on the elementary amplitude (at small  K ) – information about the amplitude at small angles.

Summary Elementary process - data at very small  K are needed to fix the models at forward angles (necessary for reliable hypernuclear calculations); Hypernucleus electroproduction -predictions of the DWIA shell-model calculations agree well with the spectra of 12 B  and 16 N  for  in s-state  -in the p  region more elaborate calculations ( e.g. 1h  ) are needed to fully understand the data ; -the Saclay-Lyon model for the elementary process gives reasonable cross sections – good behaviour at small  K ?