Upload
grant-hunter
View
217
Download
3
Tags:
Embed Size (px)
Citation preview
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
31/08/2009FB19: Compton Scattering on Light Nuclei 2
Compton Scattering
~1Å
~few fm
~1 fm
NEUTRON
31/08/2009FB19: Compton Scattering on Light Nuclei 3
Polarizabilities
ijjiij
jiijMEjiijEMMMEE
ME
eff
XXwhereX
EHHEHHEE
HE
ZeM
AZepH
2
1
222
2
2
21211111
21
21
2
Spin-independent
Spin-dependent
31/08/2009FB19: Compton Scattering on Light Nuclei 4
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
31/08/2009FB19: Compton Scattering on Light Nuclei 5
Ingredients- 1B mechanisms
O(e2): LO
O(e2P): NLO
Bernard, Kaiser, Meissner (1992)
O(e2P2): N2LO
(, J. McGovern (2001)
31/08/2009FB19: Compton Scattering on Light Nuclei 6
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
31/08/2009FB19: Compton Scattering on Light Nuclei 7
Ingredients- 2B mechanisms
O(e2P2: N2LO)
O(e2P: NLO)
Beane, Malheiro, McGovern, Phillips, VanKolck (2003)
Beane, Malheiro, Phillips, VanKolck (1999)
31/08/2009FB19: Compton Scattering on Light Nuclei 8
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)
31/08/2009FB19: Compton Scattering on Light Nuclei 9
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)
31/08/2009FB19: Compton Scattering on Light Nuclei 10
Ingredients – Low-energy resummation
d only:
NLO:1B
2B
Griesshammer, Hemmert, Hildebrandt (2005)
31/08/2009FB19: Compton Scattering on Light Nuclei 11
Unpolarized d at O(3)+Low-energy resumm.
Griesshammer, Hemmert, Hildebrandt (2005)
31/08/2009FB19: Compton Scattering on Light Nuclei 12
Current Efforts: Polarized d - O(3 )+Low-energy resumm.
Slide from H. Griesshammer
Griesshammer, McGovern, Phillips, Shukla (2009)
31/08/2009FB19: Compton Scattering on Light Nuclei 13
Polarized d - O(3 )+Low-energy resumm.
31/08/2009FB19: Compton Scattering on Light Nuclei 14
Polarized d - O(3 )+Low-energy resumm.
31/08/2009FB19: Compton Scattering on Light Nuclei 15
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).
31/08/2009FB19: Compton Scattering on Light Nuclei 16
3He at O(e2P) at 120 MeV (cm)Choudhury, Nogga, Phillips PRL98 (2007) 232303
31/08/2009FB19: Compton Scattering on Light Nuclei 17
31/08/2009FB19: Compton Scattering on Light Nuclei 18
31/08/2009FB19: Compton Scattering on Light Nuclei 19
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
31/08/2009FB19: Compton Scattering on Light Nuclei 20
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!
31/08/2009FB19: Compton Scattering on Light Nuclei 21
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
31/08/2009FB19: Compton Scattering on Light Nuclei 22