L/T separation in the 3He(e,e’p) reaction

Javier R. Vignote and Eric Voutier

Laboratoire de Physique Subatomique et de Cosmologie, Grenoble, France

Jlab Hall A Collaboration Meeting, January, 4-5 2007

L/T separation in the 3He(e,e’p) reaction

• Motivations

• Quasi-elastic scattering• 3He(e,e’p) cross section• L/T separation

• Cross section extraction• Monte Carlo simulation• Results

• L/T separation

• Conclusion and prospects

Motivations

E89-044 experiment: Previous analyses performed by M.Rvachev, E.Penel, F.Benmokhtar and F.Descamps

Free nucleon Bound nucleonChange in structure?

Study bound nucleon by (e,e’p) quasi-elastic scattering

Extract electromagnetic response functions for various transfered four-momenta Q (i.e. various probing resolutions).

Quasi-elastic scattering: 3He(e,e’p)B

Bpm ppqp

BpHeBpm TTMmmE 3*

Missing momentum : undetected momentum

Missing energy : separation energy

GeV/c5.1 ppqGeV837.0

Leptonic plane

Hadronic plane

• Only e’ and p are detected

• Residual system B:

Quasi-elastic: 12

2

pm

Qx

Parallel: 0pq

pm ≈ 0

• Kinematical regime

2 body break-up peak2-bbu

3 body break-up threshold3-bbu

Quasi-elastic scattering

3He(e,e’p)d cross section

)2(cos)(cos)2( 3

5

TTTTLTLTTTLLM

pp

pff

RVRVRVRVREp

dddE

d

),,,( TTLTTL RRRR : Nuclear response functions

R: Recoil factor

σM: Mott cross section

),,,( TTLTTL VVVV : Kinematic electron coupling coefficients

L/T separation:

•Separation of longitudinal/transverse response functions

•Interference terms ! 0 if pq! 0 (parallel kinematics)

•Averaging over out-of-plane angle: ! 0

Separation using Rosenbluth method:

•Extraction of the 3He(e,e’p)d cross section at different kinematic settings

•Keep same hadronic vertex and change leptonic vertex.

TL RR and

)cos(2),cos(

)2(cos)(cos)2( 3

5

TTTTLTLTTTLLM

pp

pff

RVRVRVRVREp

dddE

d

KIN01≠ KIN03 change photon polarization

2 points in space

T

M

VR,

Experimental setup

e He3

p

e

d, np

Experimental setup

3 Monte Carlo simulation: matrix-method

Em

Vertex

Em

Asymptotic

Binning in EmV

BinningIn

EmA

Radiation effects

Resolution effects

Weights associated to each vertex

bin

3 Monte Carlo simulation: example

Em

Vertex

Em

Asymptotic

Binning in EmV

BinningIn

EmA

Radiation effects

Resolution effects

Eventdrawn in 2nd bin

Vertex

Resolution effect to

1st asymptotic bin

Contributionto N12

Monte Carlo simulation: example

Em

Vertex

Em

Asymptotic

Binning in EmV

BinningIn

EmA

Radiation effects

Resolution effects

Eventdrawn in 2nd bin

Vertex

Resolution effect to

1st asymptotic bin

Contributionto N12

Eventdrawn in 2-bbu bin

Vertex (1)

Radiation to

3rd asymptotic bin

Contributionto N31

Cross section results

1w

Kin 03 Kin 01

L/T Separation

• Kin01, Kin03: keep same hadronic vertex

•ω/q and pm/q phase spaces need to be matched

•Mean values have to be checked to be equal for Kin01 and Kin03

•Extract 2-bbu cross sections for the two kinematics at the average kinematic point.

q vs ω for Kin01 and Kin03

L/T Separation

TTLLMpp RVRVREp 3333

3

)2(

)2(cos)(cos)2( 3

5

TTTTLTLTTTLLM

pp

pff

RVRVRVRVREp

dddE

d

σ TTLLMpp RVRVREp 1113

1

)2(

34.0/7.30

34.0/2.2

/01.0/29.27

35.0/4.32

36.0/7.2

/07.0/96.21

fmR

fmR

cMeVP

fmR

fmR

cMeVP

T

L

miss

T

L

miss

Conclusion and prospects

• Next steps?

• Generalization of the matrix-method to deconvolute radiative effects between pm bins

• Additional binning in Q2

• Cross section extractions and L/T separations for the remaining Q2 at parallel kinematics

• Matrix method• Results consistent with previous analysis

• Understanding of the different aspects concerning the separation

• 3He(e,e’p)d Cross section extraction

• L/T separation