The Angular Dependence of 16O(e, e K) 16N and H(e,e K+)

- motivation

- angular distribution

- the elementary reaction

-kinematics and counting rates

- beam time request

- the apparatus

- summary and conclusion

(F. Garibaldi – Hall A – Hall C joint meeting - Jefferson Lab – May 15 2008

- hypernuclear physics

- the electromagnetic approach

- recent results

16O(e,e’K)16ΛN

I : 100 A Targ. thick: ~100 mg/cm2

Counting Rates: 0.1 – 10 Counting Rates: 0.1 – 10 counts/peak/hrcounts/peak/hr

ee = = KK = 6° = 6°

QQ22 = 0.079 (GeV/c) = 0.079 (GeV/c)22

EEbeambeam = 4.016 GeV = 4.016 GeV PPkk = 1.96 GeV/c = 1.96 GeV/c

PPee = 1.8 GeV/c = 1.8 GeV/c

ωω = = EE γγ = 2.2 GeV = 2.2 GeV

- energy resolution ~ 635 KeV, the best achieved in hypernuclear production experiments

- work is in progress to further improve the resolution

- first clear evidence of excited core states at ~2.5 and 6.5 MeV with high statistical significance

- the width of the strong ppeak and the distribution of strength within several MeV on either side of this peak can put constraints on the hypernuclear structure calculations

- hint for a peak at 9.65 MeV excitation energy (admixture)

1/2

1-

3/2

2-

(3+,2+)

2+admixture

sp= 4.47 nb/(GeV sr2

th= 4.68 nb/(GeV sr2 )

good agreement with theory

1/2

1-

3/2

2-admixture

(3+,2+)

2+

Red line: Fit to the dataBlue line: Theoretical curve: Saghai Saclay-Lyon (SLA) used for the elementary K- electroproduction on proton.Hypernuclear wave function obtained by M.Sotona and J.Millener

Red line: Fit to the dataBlue line: Theoretical curve: Saghai Saclay-Lyon (SLA) used for the elementary K- electroproduction on proton.Hypernuclear wave function obtained by M.Sotona and J.Millener

E94-107 12C(e,e’K)11B

1H (e,e’K)1H (e,e’K)

16O(e,e’K)16N

16O(e,e’K)16N

1H (e,e’K)1H (e,e’K)

Energy Calibration Run

Preliminary Results on the WATERFALL target - 16O and H spectra

Excitation Energy (MeV)

Nb/

sr2

Ge

V M

eV

Water thickness from elastic cross section on H Fine determination of the particle momenta and beam energy

using the Lambda peak reconstruction (resolution vs position)

Fit to the data (red line): Fit 4 regions with 4 Voigt functions 2

/ndf = 1.19 Theoretical model (blu line) superimposed curve

based on :i) SLA p(e,e’K+) (elementary process)ii) N interaction fixed parameters from KEK and

BNL 16O spectra

Results on 16O target – Hypernuclear Spectrum of 16N

- Peak Search :Identified 4 regions with excess counts above background

Binding Energy B=13.68 ± 0.16 (stat) ± 0.05 (sys) MeVMeasured for the first time with this level of accuracy (ambiguous interpretation from emulsion data; interaction involving production on n more difficult to normalize)

Binding Energy (MeV)

Cro

ss S

ecti

on [

nb

/(sr

2 MeV

GeV

)]

Results on 16O target – Hypernuclear Spectrum of 16N

11

11.5

12

12.5

13

13.5

14

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5

Serie1

E94-107

(+,K+)

(K-,-) (Kstop,-)

[2] O. Hashimoto, H. Tamura,Part Nucl Phys 57, 564 (2006)

[3] private communication from D. H. Davis, D. N. Dovee, fit of data from Phys Lett B 79, 157 (1978) [4] private communication from H. Tamura, erratum on Prog Theor Phys Suppl 117, 1 (1994)

[2] [3] [4]

Comparison with the mirror nucleus 16O

Difference expected with

respect to mirror nucleus:

400 – 500 keV (M. Sotona)

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

p(e,e'K+) on LH2 Cryo TargetCalibration run

Work on normalizations, acceptances, efficiencies still underway

Expected data from theExperiment E07-012 to study the angular dependence of p(e,e’K) and 16O(e,e’K)16N at Low Q2

(approved January, 2007)

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

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 AHall A experimental setupsetup (septum magnetsmagnets, waterfall targettarget, excellent energy resolutionenergy resolution ANDAND Particle IdentificationParticle Identification ) give unique opportunityunique opportunity to measure, simultaneously,

hypernuclear processhypernuclear process ANDAND elementary processelementary process

In this kinematical region models for the K+- 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 The cross section of (e,e’K) on a nuclear target and its angular dependence determined by: its angular dependence determined by:

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

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

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

- Angular dependenceAngular dependence determined mainlymainly by the momentum transferredmomentum transferred to the nucleus (q) via via the nucleus - hypernucleus transition form factortransition form factor (q is a q is a rapidly increasingrapidly increasing function function ofof the the kaon kaon scattering angle)scattering angle)

- - The The ratioratio of the of the hypernuclearhypernuclear and and elementaryelementary cross cross section doesn’t depend strongly section doesn’t depend strongly on on the the electroproducionelectroproducion model model and contains and contains direct informationdirect information on on hypercnulear structurehypercnulear structure and and production mechanismproduction 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 physicshypernuclear physics ANDAND discriminatediscriminate between groups of elementary models

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

ek

e

e’k

p

Scattering plane(leptonic) Reaction plane

(hadronic)

d5dE 'dedK

d *

dK

* p k )

d *

dK

dT

dK

d L

dK

cos2dT

dK

2 1 )cosd LT

dK

JHadr K ˆ J

Hadr p u p ) Ai s,t,Q2 )Mi

i1

6

u P )

e

p

K+

e’

*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

,(*,…)*

K+

p=

K+

p*

P(N*,*,…)

p*

K+

K(K1,…)

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+) 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+) electromagnetic X-section

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

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

Waterfall Target thicknes = 130 mg/cm2

Beam current = 100 A

beam time request

SNR ≥ 6

• Measurement and Feasibility: This measurement is a larger-angle version of E94-107, which has already run successfully in Hall A. If the cross sections drop rapidly with angle, the signal might become difficult to see, but given the range of models this appears to still provide a sufficient result.

 • Issues: The PAC was convinced that the

measurement of the elementary p(e,e'K+)L process is of sufficient interest to warrant measurement at both angles. The PAC did not find the argument for the measurement of 16O(e,e'K+)16NL at all angles equally compelling.

PAC 31 Report

Something new

We might be able to have 5 degrees

Ei=3.660 GeV; Ef=1.450 GeV; teta = 6 teta = 5

theta(gamma-e)   3.91                    3.26theta(K-gamma) =  2.09                   1.74virtual photon flux =                   0.0172                0.0250Pk (GeV/c) 1.970 1.970 q (GeV.c) 0.264 0.257 16O(e,e'K+) (nb/sr^2/GeV) =                  1.45          2.551H(e,e'K+)  (nb/sr^2/GeV) =                  36.2          55.9

Hall A - Two High Resolution SpectrometersHall A - Two High Resolution SpectrometersQDQ - Momentum Range: 0.3 –4 GeV/c p/p : 1 x 10-4 – p = =-5% - –mr

1 (+1) Cherenkov threshold aerogels

+ RICH in the hadron

spectrometer + septum magnet

QuickTime™ and aMotion JPEG OpenDML decompressor

are needed to see this picture.

PID

electron arm:gas Cherenkov + shower counter

--> 105 pion rejection hadron arm

2 aerogel detectors (n=1.015 and n=1.025)

RICH detector

pion rejection ~ 10.000 !!

RICH upgrade

this proposal

Summary and ConclusionsSummary and Conclusions

- UnderstandingUnderstanding the the elementary cross sectionelementary cross section in an unexplored in an unexplored kinematical kinematical region fundamentalregion fundamental for the for the hypernuclear spectroscopyhypernuclear spectroscopy experiments experiments

- Obtaining informationObtaining information about the about the importance of hadron f.fimportance of hadron f.f. . - Is the concept of the hadronic form factors used in the isobaric models correct? - Is the hypernuclear angular dependence the same as the elementary dependence?

- What is the angular dependence of the hypernuclear form factor at forward angles?

- The ratio of the hypernuclear and elementary cross section is only weakly sensitive to the models of elementary production -> -> direct accessdirect access to the hypernuclear to the hypernuclear structurestructure in a model independent way (in a model independent way (unique feature of this experimentunique feature of this experiment))

- These questions areThese questions are very important for our very important for our understanding of understanding of dynamicsdynamics of the of the process and process and vitalvital for the hypernuclear calculations and for the hypernuclear calculations and interpretation of the interpretation of the datadata

- The proposed experimental technique has been fully and The proposed experimental technique has been fully and successfully proven in the previous experiment, E94-107, successfully proven in the previous experiment, E94-107, where very clean, background free, high resolution spectra where very clean, background free, high resolution spectra have been obtained.have been obtained.

Measuring Measuring simultaneouslysimultaneously the the angular dependenceangular dependence of electroproduction on of electroproduction on OxygenOxygen and and HydrogenHydrogen is is

importantimportant