Measurement of the Coulomb quadrupole amplitude in the * p (1232) - - PowerPoint PPT Presentation

Measurement of the Coulomb quadrupole amplitude in the *p(1232) reaction in the low momentum transfer region

David Anez Dalhousie University April 20, 2010

Introduction

Take measurements of the p(e,ep)0 (pion

electroproduction) reaction

At energies in the area of the resonance With low momentum transfer (Q2) between the electron

and proton

To better understand the Coulomb quadrupole

transition amplitude behavior in this region and how it affects nucleon deformation

David Anez – April 20th, 2010 2/29

Overview

Motivation: Constituent Quark Model Kinematics and Transition Amplitudes Response Functions and Amplitude Extraction World Data and Models Experimental Setup Conclusions

David Anez – April 20th, 2010 3/29

Motivation: Constituent Quark Model

Three “heavy” quarks in nucleon

Each quark has mass 1⁄3 of nucleon Each quark has intrinsic spin angular momentum of 1⁄2 Combines to give S = 1⁄2 or S = 3⁄2

If L = 0 S = 1⁄2, J = 1⁄2

+ corresponds to N(939)

S = 3⁄2, J = 3⁄2

+ corresponds to (1232)

If L = 2 S = 1⁄2, J = 3⁄2

+ corresponds to (1232)

S = 3⁄2, J = 1⁄2

+ corresponds to N(939)

David Anez – April 20th, 2010 4/29

Motivation: Constituent Quark Model

Wave functions created

• (

) ( )

( )

+ +

= = = + = = = =

2 1 2 3 2 1 2 1

2 , , 939

π π

J L S a J L S a N

D S

( )

( ) ( )

+ +

= = = + = = = = ∆

2 3 2 1 2 3 2 3

2 , , 1232

π π

J L S b J L S b

D S

David Anez – April 20th, 2010 5/29

Motivation: Constituent Quark Model

Measure non-spherical components by measuring

quadrupole moment

Cannot measure quadrupole moment directly Measure quadrupole moment of N transition

Three electromagnetic transitions

M1 – magnetic dipole E2 – electric quadrupole C2 – Coulomb/scalar quadrupole

David Anez – April 20th, 2010 6/29

Motivation: Constituent Quark Model

Magnetic Dipole

Spin-flip Dominant

David Anez – April 20th, 2010 7/29

Motivation: Constituent Quark Model

Electric quadrupole Coulomb quadrupole

Only with virtual photons

David Anez – April 20th, 2010 8/29

Motivation: Constituent Quark Model

One-body interactions

• Two-body interactions
• ( )

( )

• −

= =

= i i i i i i i i

r z e r Y r e Q

2 2 3 1 2 2 ] 1 [

3 5 16 ˆ

• π

( )

• =

≠

⋅ − =

3 1 ] 2 [

3 ˆ

j i j i jz iz i

e B Q σ σ σ σ

• David Anez – April 20th, 2010

9/29

Motivation: Constituent Quark Model

Pion Cloud

David Anez – April 20th, 2010 10/29

Kinematics – Electronic Vertex

Incoming electron

Energy E Momentum ki

Scattered electron

Energy E Momentum kf Angle e

Virtual photon

Energy Momentum q Angle q

i

k

• f

k

• q
• David Anez – April 20th, 2010

11/29

Kinematics – Electronic Vertex

Momentum transfer, Q2

• )

(

2 2 2 2

q q Q

• −

− = − = ω 2 sin 4

2 2 e

E E Q θ ′ ≈

David Anez – April 20th, 2010 12/29

Kinematics – Hadronic Vertex

Recoil proton

Energy Ep Momentum pp Angle pq

Recoil pion

Energy E Momentum p Angle Not detected

p

p

• π

p

• David Anez – April 20th, 2010

13/29

Kinematics – Planes

Scattering plane – ki and kf Recoil plane – pp and p Azimuthal angle – φpq

i

k

• f

k

• p

p

• π

p

• David Anez – April 20th, 2010

14/29

Multipole Amplitudes

General form of N Multipoles:

X – type of excitation (M, E, S) I – isospin of excited intermediate state ± – J = ± 1⁄2

Magnetic dipole – M1 / Electric quadrupole – E2 / Coulomb quadrupole – C2 /

• 2

/ 3 1+

E

2 / 3 1+

S

+ + = 1 1

L q S

• ω

2 / 3 1+

M

I

X ±

• David Anez – April 20th, 2010

15/29

Multipole Amplitudes

M2+ 2−

1⁄2 +

D35 D15

5⁄2 − 1⁄2 +

M2− 2−

1⁄2 +

D33 D13

3⁄2 − 1⁄2 +

2− M2 L3−, E3− 3+

1⁄2 +

F35 F15

5⁄2 + 1⁄2 +

L1+, E1+ 1+

1⁄2 +

P33 P13

3⁄2 + 1⁄2 +

2+ C2, E2 M1+ 1+

1⁄2 +

P33 P13

3⁄2 + 1⁄2 +

M1− 1+

1⁄2 +

P31 P11

1⁄2 + 1⁄2 +

1+ M1 L2−, E2− 2−

1⁄2 +

D33 D13

3⁄2 − 1⁄2 +

L0+, E0+ 0−

1⁄2 +

S31 S11

1⁄2 − 1⁄2 +

1− C1,E1 L1− 1+

1⁄2 +

P31 P11

1⁄2 + 1⁄2 +

0+ C0 L±, E±, M± N* I2I2J C, E, M N-Multipoles Final State Excited State Initial State N-Multipoles

π γ

L

π N

s

π R

J

π π

I

π N

s

David Anez – April 20th, 2010 16/29

Multipole Amplitudes

E1+ and S1+ at same magnitude as background

amplitudes

Measure ratio to dominant M1+ EMR = CMR =

( )

2 1 1 * 1 2 / 3 1 2 / 3 1 2 / 3

Re Re

+ + + + +

=

• =

M M E M E REM

( )

2 1 1 * 1 2 / 3 1 2 / 3 1 2 / 3

Re Re

+ + + + +

=

• =

M M S M S RCM

David Anez – April 20th, 2010 17/29

Response Functions

Unpolarized cross section made up of four

independent partial cross sections

p p

m m W k 2

2 2 −

=

γ

( )

TT LT T L e f

q k d d dk d σ σ σ σ σ

γ

+ + + Γ = Ω Ω

* 5

ε π α

γ γ

− = Γ 1 1 2

2 2

Q k k k

i f 1 2 2 2

2 tan 2 1

−

• +

=

e

Q q θ ε

2 2 2 2 2

4

π π

m W m m W k

p −

− + = W m W q

p

2

2 2

− = ε ε

2 2

q Q

S =

David Anez – April 20th, 2010 18/29

Response Functions

Unpolarized cross section made up of four

independent partial cross sections

( )

TT LT T L e f

q k d d dk d σ σ σ σ σ

γ

+ + + Γ = Ω Ω

* 5 L S L

R ε σ =

T T

R = σ

( )

* * cos

sin 1 2

pq pq LT S LT

R φ θ ε ε σ + =

* * 2

2 cos sin

pq pq TT TT

R φ θ ε σ =

David Anez – April 20th, 2010 19/29

Response Functions

• {

}

( )

{ } { }

( )

− + + − + + − + − + +

+ + + + − + + =

1 * 1 2 1 2 1 1 * 1 * 1 2 1 2 1 2 2 2

Re cos 12 4 Re cos 2 Re 4 4 L L L L L L L L L L L Q R

cm L

θ θ ω

( )

{ }

− + + + − + + − + +

− + + + − + + + =

1 1 1 * 2 1 1 1 2 1 2 1 1 2 1 2

3 Re cos 2 3 2 M M E E M M E M M E RT θ

( )

2 1 1 1 2 1 2 1 1 2 1 2 1 1 1 2

3 2 3 cos

− + + − + − + +

− − − + − − + + M M E M M M M E θ

( ) (

)

( )

( ) { }

+ − − + + + + − + − + + +

+ + − + − − + − − =

1 * 1 1 1 1 * 1 * 1 * 1 1 1 1 * 2 2

cos 6 2 3 Re sin E L M M E L E L L M M E L Q R

cm LT

θ θ ω

( )

{ }

( )

− + − + + + +

+ − − − =

1 * 1 1 1 * 1 2 1 2 1 2 1 2 3 2

Re sin 3 M M M M E M E RTT θ

David Anez – April 20th, 2010 20/29

Response Functions

Truncated Multipole Expansion

• Model Dependent Extraction

Fit theoretical model to existing data Insert model values for background amplitudes

{ } { } ( ) { }

( )

− + + + + + + + + + + + +

+ + − ≈ − ≈ − + ≈ ≈

1 * 1 1 * 1 2 1 2 1 2 1 * 1 1 * 2 1 2 2 3 1 * 2 1 2 5

Re sin 3 cos 6 Re sin cos Re cos 2 M M M E M R M L M L R M M E M R R

TT LT T L

θ θ θ θ θ

David Anez – April 20th, 2010 21/29

World Data and Models

Models

MAID SAID DMT Sato-Lee Chiral EFT Lattice QCD

p(e,ep)0 experiments

CEA – 1969 DESY – 1970-1972 NINA – 1971 ELSA – 1997 MIT-Bates – 2000 MAMI – 2001 CLAS – 2002 MAMI – 2005-2006

David Anez – April 20th, 2010 22/29

World Data and Models

David Anez – April 20th, 2010 23/29

World Data and Models

David Anez – April 20th, 2010 24/29

World Data and Models

David Anez – April 20th, 2010 24/29

World Data and Models

Q2 = 0.040 (GeV/c)2

New lowest CMR value e = 12.5°

David Anez – April 20th, 2010 24/29

World Data and Models

Q2 = 0.040 (GeV/c)2

New lowest CMR value e = 12.5°

Q2 = 0.125 (GeV/c)2

Validate previous

measurements

David Anez – April 20th, 2010 24/29

World Data and Models

Q2 = 0.040 (GeV/c)2

New lowest CMR value e = 12.5°

Q2 = 0.125 (GeV/c)2

Validate previous

measurements

Q2 = 0.090 (GeV/c)2

Bridge previous

measurements

David Anez – April 20th, 2010 24/29

World Data and Models

Sato and Lee

Suggest separating nucleon

into quark core and pion cloud

“bare” quark core links to

lattice QCD

“full” nucleon links to

experimental data

David Anez – April 20th, 2010 25/29

The Experiment

Jefferson Lab, Hall A April 3rd – April 8th, 2011 1115 MeV, 75A e− beam 6 cm LH2 target Two high resolution

spectrometers

HRSe and HRSh

David Anez – April 20th, 2010 26/29

High Resolution Spectrometers

Vertical drift chambers

Particle tracking

Scintillators

Timing information Triggering DAQ

Cerenkov detectors

Aerogel and gas Particle identification

Lead glass showers

Particle identification

David Anez – April 20th, 2010 27/29

Settings

72 Total: 8 Calibrations 17 Configuration changes 2 622.63 34.06 750.16 22.29 1200 0.125 3 575.57 37.31 788.05 21.74 1170 0.125 3.5 596.43 49.19 708.69 22.94 55 1232 0.125 3.5 596.43 12.52 708.69 22.94 55 1232 0.125 7 649.23 41.03 708.69 22.94 30 1232 0.125 7 649.23 20.68 708.69 22.94 30 1232 0.125 3.5 672.56 30.86 708.69 22.94 1232 0.125 4.5 589.08 43.74 729.96 19.14 40 1230 0.090 3 589.08 14.99 729.96 19.14 40 1230 0.090 1.5 627.91 29.37 729.96 19.14 1230 0.090 1.5 614.44 21.08 716.42 12.96 1260 0.040 3.5 528.12 36.48 767.99 12.52 30 1221 0.040 2 528.12 12.52 767.99 12.52 30 1221 0.040 1.5 547.54 24.50 767.99 12.52 1221 0.040 Time (hrs) (MeV/c) (MeV/c) W (MeV) Q2 (GeV/c)2

°

* pq

θ °

e

θ

e

P′ °

p

θ

p

P′

David Anez – April 20th, 2010 28/29

Conclusion

Important step forward in understanding

nucleon’s internal structure

Help bridge and validate experimental world data Help theoretical models better understand

role of pion cloud in nucleon deformation role of QCD in low momentum transfer region

David Anez – April 20th, 2010 29/29