The angular dependence of the 16O(e,e’K+)16LN and H(e,e’K+)L

F. Garibaldi – Jlab December 12-2012

The WATERFALL target: reactions on 16O and 1H nuclei

1H (e,e’K)L

16O(e,e’K)16NL

1H (e,e’K)L,S

L

S

Energy Calibration Run

Results on the WATERFALL target - 16O and 1H

Water thickness from elastic cross section on H Precise determination of the particle momenta and beam energy using the Lambda and Sigma peak reconstruction (energy scale calibration)

10/13/09

p(e,e'K+)L on WaterfallProduction run

Expected data from E07-012, study the angular dependence of

p(e,e’K)L and 16O(e,e’K)16NL at low Q2

Results on H target – The p(e,e’K)L Cross Section

p(e,e'K+)L on LH2 Cryo Target Calibration run

•None of the models is able to describe the data over the entire range•New data is electroproduction – could longitudinal amplitudes dominate?

W=2.2 GeV

The Proposal: studying, using waterfall target, different processes

The elementary process on the proton

Electroproduction of as function of Kaon angle

- Systematic study of reaction as function of A and neutron rich nuclei (E05-015)

- Understanding of the elementary reaction

- Angular distribution (momentum transfer)

what is missing ?

How?

The interpretation of the hypernuclear spectra is difficult because of the lack of relevant information about the elementary process.

Contains direct information on the target and hypernuclear structure, production mechanisms

Hall A experimental setup (septum magnets, waterfall target, excellent energy resolution AND Particle Identification ) give unique opportunity to measure, simultaneously, hypernuclear process AND elementary process

In this kinematical region models for the K+- L electromagnetic production on protons differ drastically

The ratio of the hypernuclear and elementary cross section measured at the same kinematics is almost model independent at very forward kaon scattering angles

Why?

The cross section of (e,e’K) on a nuclear target and its angular dependence determined by:

- Transition operator, which is given by the model used to describe the elem. prod. on protons

- Structure (that is the many particle wave function) of the target nucleus and hypernuclear state

- Momentum transferred to the nucleus, q = p - pK

- Angular dependence determined mainly by the momentum transferred to the nucleus (q) via the nucleus - hypernucleus transition form factor (q is a rapidly increasing function of the kaon scattering angle)

- The ratio of the hypernuclear and elementary cross section doesn’t depend strongly on the electroproducion model and contains direct information on hypercnulear structure and production mechanism

Electroproduction on 16O - angular distribution

- The slope depends on the spin of hypernuclear state - Excitation of hypernuclear states brings in a different combinations of the elementary amplitudes for different final states - The nuclear structure for a specific final state can emphasize either spin-flip or non-spin flip amplitudes, as well as combinations of them with different phases. - Deviations from an exponential decreases of cross sections with q could be caused by interference between the different amplitudes

Simultaneously measuring the electroproduction cross section on oxygen and hydrogen at a few kaon scattering angles will shed new light on problems of hypernuclear physics AND discriminate between groups of elementary models

The elementary process: The p(e,e’K+)L electromagnetic X-section

qeqk

Fe

e’k

pL

Scattering plane(leptonic) Reaction plane

(hadronic)

d5dE 'dedK

d *

dK

* p k L

d *

dK

dT

dK

d L

dK

cos2F dT

dK

2 1 cosF d LT

dK

JHadr K L ˆ J

Hadr p u pL Ai s, t,Q2 Mi

i1

6

u P

ep

K+

e’L

*LeptJ

The appropriate set of propagators (particles) and coupling constants has to be established from the data and from theoretical guidelines (SU3 broken symmetry)

At CEBAF energies non-perturbative QCD degrees of freedom have to be taken into account.- IN PRINCIPLE: the amplitude can be calculated in QCD. IN PRACTICE: semi-phenomenological description Quantum HadronDynamics(QHD), degrees of freedom, nucleon, kaon, resonances.A diagrammatic semi-phenomenological approach based on hadronic field theories (effective hadronic Lagrangian - QHD) is likely well applicable in the description of the process

L,S(L*,…) *

K+ L

p =K+ L

p *

P(N*,D*,…)p

*

K+ L

K(K1,…)

L K+

* p

s-channel t-channel u-channel

+ +

two groups of models differing by the treatment of hadronic vertices

show LARGE DIFFERENCES Assumption for the hadronic form factor :- KMAID, Jansen, H2 : with h.f.f.- Saclay-Lyon, WiJiCo : without h.f.f.

The theoretical description is poor in the kinematical region

relevant for hypernuclear calculations

No dominant resonance contributes to the kaon electro and photo-production (like Delta for pion). a large number of possible resonances can contribute many free parameters, the coupling constants must be fixed by experiment. …many models on the market which differ just in the choice of the resonances.

The elementary process: The p(e,e’K+)L electromagnetic X-section

A phenomenon which can be addressed by the expected data:The sharp damping of the cross section at very small kaon angles which is connected to the fundamental ingredients of the models, accounting for the hadronic form factors. This is also very important in the hypernuclear calculations.

Photo-production existing data and model predictions

The elementary process: The p(e,e’K+)L electromagnetic X-section

K+-L electro-production cross section will be measured in an unexplored kinematical region typical of HYPERNUCLEAR experiments.In the angular range proposed(QCM

k=5.4-18 deg) the electro-magnetic production models show a strong angular dependence. Measuring the elementary cross section in such an angular range will provide a set of data very important to constrain models and provide information on the use of hadronic form factors.

Q2=0.06 (GeV/c)2

THIS EXPERIMENTPROJECTED DATA

Electro-production model predictions

From electro-production to photo-production on hydrogen• Selection of a model• Eventually new fit on model parameters including these new data• Model dependent evaluation of interference terms w.r.t. the dominant transverse term (kinematics very close to the photon point)

kinematics and counting ratesWaterfall Target thicknes = 130 mg/cm2

Beam current = 100 Abeam time request

SNR ≥ 6

beam time request

With new setup in Hall A if 3 angles in one shot, a factor 3 in the yield (?)

~ 5 days

16O(e,e’K)16NL 16O(p,K+)16OL16O(K-, p- ) 16OL

~ 800 KeV

similar discrepancy for elementary reaction

this has to be understood !