Compton Scattering on Light Nuclei (A=2,3)

Deepshikha ShuklaUNC-Chapel Hill

Collaborators: H. Griesshammer (George Washington U.), J. McGovern (U. Manchester), D. Phillips (Ohio U.)

Previous Work:

Beane/Malheiro/McGovern/Phillips/VanKolck; Griesshammer/Hemmert/Hildebrandt/Pasquini/Phillips;

Choudhury(Shukla)/Phillips.

Choudhury(Shukla)/Nogga/Phillips

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Compton Scattering

~1Å

~few fm

~1 fm

NEUTRON

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Polarizabilities

ijjiij

jiijMEjiijEMMMEE

ME

eff

XXwhereX

EHHEHHEE

HE

ZeM

AZepH

2

1

222

2

2

21211111

21

21

2

Spin-independent

Spin-dependent

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Light Nuclei (?)

A=2,3: Access Neutron polarizabilities Not charged No ‘free neutron’ targets

HeHe

dd33

Computable problem Ongoing and planned experiments for both processes At these energies, PT is an effective tool

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Ingredients- 1B mechanisms

O(e2): LO

O(e2P): NLO

Bernard, Kaiser, Meissner (1992)

O(e2P2): N2LO

(, J. McGovern (2001)

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HBPT for Compton Scattering on light Nuclei

O'

Chiral expansion for

Naïve dimensional analysis- Pn for a vertex with n powers of p or mp

P-2 for pion propagator (1/(p2-m2))

P-1 for nucleon propagator (1/(E-p2/2M)) P4 for loop (loop integral) P3 for a two-body diagram (3(p2’-p2) absent)

Wavefunction derived from chiral potential or from potential model

n

n

nn

mpcO

,ˆ

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Ingredients- 2B mechanisms

O(e2P2: N2LO)

O(e2P: NLO)

Beane, Malheiro, McGovern, Phillips, VanKolck (2003)

Beane, Malheiro, Phillips, VanKolck (1999)

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Unpolarized d at O(e2P2)

341.2

9.0

349.35.1

109.18.1

109.10.13

fm

fm

N

N

Beane, Malheiro, McGovern, Phillips, VanKolck (2003)

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Ingredients – explicitly

Small Scale Expansion (SSE) – : /~m/M-MN

(, O(3): NLO

Alternative – -counting:

mm

~~ 2

Hemmert, Holstein, Kambor (1997) + Knochlein (1998)

Pascalutsa, Phillips (2003)

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Ingredients – Low-energy resummation

d only:

NLO:1B

2B

Griesshammer, Hemmert, Hildebrandt (2005)

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Unpolarized d at O(3)+Low-energy resumm.

Griesshammer, Hemmert, Hildebrandt (2005)

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Current Efforts: Polarized d - O(3 )+Low-energy resumm.

Slide from H. Griesshammer

Griesshammer, McGovern, Phillips, Shukla (2009)

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Polarized d - O(3 )+Low-energy resumm.

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Polarized d - O(3 )+Low-energy resumm.

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Ongoing Efforts

Comprehensive N2LO calculation with O(4) effects and low-energy resummation.

Map out all(?) possible observables in the entire kinematic range - would serve as a guide for future experiments (MAxLab, HIS, MAMI).

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3He at O(e2P) at 120 MeV (cm)Choudhury, Nogga, Phillips PRL98 (2007) 232303

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0 30 60 90 120 150 180

-0.2

-0.1

0.0

0.1

0.2

0.3

0.4A

sym

met

ry in

Z

CM angle (deg)

0 30 60 90 120 150 180

-0.2

-0.1

0.0

0.1

0.2

0.3

0.4

As

ym

me

try

in Z

CM angle (deg)

0 30 60 90 120 150 180

-0.2

-0.1

0.0

0.1

0.2

0.3

0.4

Asy

mm

etry

in Z

CM angle (deg)

0 30 60 90 120 150 180

-0.2

-0.1

0.0

0.1

0.2

0.3

0.4

Asy

mm

etry

in Z

CM angle (deg)

HIS projection with polarized 3He target

Photon flux: 5*107/s, target 1.0*1022/cm2, 45% polarization 500 hours

16 NaI

Slide from H.Gao

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Summary & Future Direction

Elastic scattering on A=2,3– “promising” avenue to extract neutron polarizabilities.

We have taken the first step with He-3 Delta degree of freedom Low-energy resumm.

Comprehensive NNLO d calculations in progress

Waiting for experimental data!

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TT

J

TJHe

TMt

JMjjmjlmjsl

qpqp

2

1

;2

1;

12

31233312121212

1212

HeHe 33

O(Q3)

HeHe Oqqddpdpd ˆ''' 3312

312

3HeHe Oqdpdpd ˆ'' 3

123

123O(Q3)

1

2

3

p12

q

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