Post on 27-Jan-2016
description
Higher order Higher order
forward forward
spin polarizabilitiesspin polarizabilities
Barbara PasquiniBarbara Pasquini
Pavia U. and INFN PaviaPavia U. and INFN Pavia
Paolo Pedroni Dieter DrechselPaolo Pedroni Dieter Drechsel
INFN Pavia Mainz U.INFN Pavia Mainz U.
OutlineOutline
Real Compton scattering off the proton and polarizabilities
Status of theoretical and experimental analysis
Forward spin-dependent amplitude
Real Compton scattering off the neutron
GDH sum rule and dispersion integrals for leading and higher order forward spin polarizabilities
dispersion analysis from helicity-dependent photon absorption cross section: experimental data and phenomenological studies
B.P., P. Pedroni, D. Drechsel, arXiv:1001.4230 [hep-ph], to appear in PLB
Static polarizabilities in Real Compton ScatteringStatic polarizabilities in Real Compton Scattering
Powell cross section: photon scattering off a pointlike nucleon with anomalous magnetic momentStatic polarizabilities: response of the internal nucleon degrees of freedom to a static electric and magnetic field
spin-independent dipole
spin-dependent dipole
spin-dependent dipole-quadrupole
Spin independent dipole polarizabilitiesSpin independent dipole polarizabilities
Baldin Sum Rule (1960)
Olmos de Leon et al., EPJ A10 (2001)
Compton scattering
Spin polarizabilitiesSpin polarizabilities
forward spin polarizability
GDH Coll. (MAMI & ELSA)
Ahrens et al., PRL87 (2001)Dutz et al. PRL91 (2003)
backward spin polarizability(unpolarized Compton scattering)
TAPS, LARA, SENECASchumacher, Prog. Part. Nucl. Phys. 55(2005)
HB3: Heavy Baryon ChPT at O(p3) [Hemmert et al, 1998]
HB4: Heavy Baryon ChPT at O(p4) [Kumar et al, 2000]
SSE: Heavy Baryon with at O(p3) [Hemmert et al, 1998]
LC: Lorentz covariant ChPT [Djukanovic, PhD Thesis, Mainz, 2008]
DRs: Dispersion Relations [Drechsel et al., 2003]
HB3 HB4 SSE LC3 LC4 DRs Exp.
E1E1 -5.7 -1.4 -5.4 -3.2 -2.8 -4.3 no data
M1M1 -1.1 3.3 1.4 -1.4 -3.1 2.9 no data
E1M2 1.1 0.2 1.0 0.7 0.8 0.0 no data
M1E2 1.1 1.8 1.0 0.7 0.3 2.1 no data
0 4.6 -3.9 2.0 3.1 4.8 -0.7 -1.00 0.08 0.10
4.6 6.3 6.8 1.8 -0.8 9.3 -38.7 1.8
Spin PolarizabilitiesSpin Polarizabilities
Double and single polarization experiments at MAMIDouble and single polarization experiments at MAMI
(proposal A2/11-2009-contact person D. Hornidge)(proposal A2/11-2009-contact person D. Hornidge)
leading spin polarizabilities are treated as free parameters
higher order polarizabilities are fixed by subtracted dispersion relations based on pion-photoproduction multipoles
How well is the model dependence under control?
0 40 80 120 160
1.2
0.8
0.4
0.
M1M1
0 40 80 120 160
0.8
0.4
0.
-0.4
-0.8
E1E1
0 40 80 120 160
0.1
0.06
0.02
-0.02
-0.06
-0.1
M1M1
circularly pol. photons
longitudinally pol. target
circularly pol. photons
transversely pol. target beam asymmetry
E=240 MeV E=240 MeV E=240 MeV
Forward Real Compton Scattering
Forward scattering: k=k’, p=p’
Photon crossing:
Optical theorem:
Dispersion relations:
Make a Low Energy Expansion of both left and right hand sides of DRs
Sum Rules for Forward Scattering Amplitude
Forward Spin Polarizability
Higher order Forward Spin Polarizab.
Low Energy TheoremLow, Gell-Mann, Goldberger (1954)
GDH Sum Rule (1966)
Sum Rule for FSP
Sum Rule for Higher Order FSP
helicity-dependent data for the total inclusive cross section ¾1/2 -¾3/2 in the energy range (0.204 0.009) – (2.82 0.09) GeV
GDH Coll. and A2 Coll. (MAMI and ELSA)
Experimental Data Base
helicity-dependent differential cross section data for the n ¼+ channel in the angular range µ*
= 45o – 109o at E= (0.18 0.005) and E = (0.19 0.005)
SAID
MAID
HDTHanstein, Drechsel, Tiator, NPA(1998)
Drechsel, Hanstein, Kamalov, Tiator, NPA(1999)
Arndt, Briscoe, Strakovsky, Workman (2002)
Ahrens, et al, GDH Coll., EPJA 21(2004) 323
use HDT to extrapolate the data in the whole angular range and obtain the total cross section with error bar estimated by comparison with other models
very good agreement with HDT
n ¼+
p ¼0
E, min= 0.158 GeV
E, min= 0.175 GeV
Running Integral for Higher Order FSP
extrapolation of differential cross sections
S-wave contribution to ¢¾
large contribution from the S-wave multipole E0+ in the threshold region
unmeasured region 0.15 0.175 GeV
low energy theorems for pion photo-production constrain the value of E0+ at threshold
good agreement between predictions of HBChPT and other multipole analysis, except for MAID
contribution below 0.175 evaluated with HDT
systematic error estimated by comparison with other models, excluded MAID
Forward Spin Polarizabilities
Recent calculation at NNLO order in Lorentz covariant ChPT with the ¢ 0 = -0.90 0.15 (Pascalutsa & Lensky, in preparation)
Dispersion Relations and Multipole analysis
o simple model to estimate of the multipion contribution by assuming the same helicity structure of the one-pion channel
o contribution to the GDH from exp. data at 325 < E < 800 MeV: 39 1 3 ¹b
HDT
SAID
MAID
DMT
sd
syst.
Running Integrals
GDH
S wave P waves TOT
Multipole decomposition
Dynamic Forward Spin Polarizability
MAID
DMT
sd
syst.
HDT
SAID
LEX
Neutron Polarizabilities
Baldin Sum Rule (1960) [Levchuk, L’vov, 2001]
Quasi-free Compton scattering and electromagnetic neutron scattering: [MAMI,Lund,SAL]M. Schumacher,
Prog. Part. Nucl. Phys. 55 (2005)[MAMI]
no experimental information on the other spin polarizabilities
Dispersion relation analysis requires more precise information for the input from multipoles of neutron pion-photoproduction ! test like dispersion analysis of spin-dependent forward scattering amplitude from polarized inclusive cross section
planned measurements at His: o Unpolarized Compton scattering from the deuteron at photon energies between 30 and 80 MeV ! and
o Double polarized Compton scattering from the He3 target at photon energies between 5 and 114 MeV ! neutron spin polarizabilities
planned measurements at Lund: unpol. RCS on deuterium target at E < 115 MeV
-4.0-6.0
-8.0E1E
1
5.863.861.86
M1M
1
Circularly pol. Photon - Neutron pol. along z or along xCircularly pol. Photon - Neutron pol. along z or along x
fixed values for other polarizabilities
neutron pol. along z neutron pol. along x
Summary
spin polarizabilities require:
double polarization experiments above pion threshold ! upcoming data from MAMI
theoretical framework which goes beyond the low energy expansion, such as subtracted dispersion relations with input from pion photoproduction data
electric and magnetic dipole polarizabilities of the proton known quite preciselyfrom low-energy Compton scattering
Necessary independent test of the model dependence of dispersion analysis
GDH sum rule:
dispersion analysis of the forward spin-dependent amplitude from helicity dependent photoabsorption cross section data (MAMI and ELSA)
o good agreement up to photon energy of 300 MeV for the one-pion channel
o deviations at higher energies up to 10-20% due to multi-pion production
Higher order forward spin polarizability: o higher energy contribution suppressed ! very good agreement with experimental analysis
Analysis of RCS with SUBtracted dispersion relations is well under control
Spin PolarizabilitiesSpin Polarizabilities
HB3: Heavy Baryon ChPT at O(p3) [Hemmert et al, 1998]
HB4: Heavy Baryon ChPT at O(p4) [Kumar et al, 2000]
SSE: Heavy Baryon with at O(p3) [Hemmert et al, 1998]
LC: Lorentz covariant ChPT [Djukanovic, PhD Thesis, Mainz, 2008]
DRs: Dispersion Relations [Drechsel et al., 2003]
LC3 + -resonance: expansion in » m/ M » M/M; no free-parameters[Lensky, Pascalutsa, 2008]
HB3 HB4 SSE LC3 LC4 DRs LC3 + ¢
Exp.
E1E1 -5.7 -1.4 -5.4 -3.2 -2.8 -4.3 no data
M1M
1
-1.1 3.3 1.4 -1.4 -3.1 2.9 no data
E1M2 1.1 0.2 1.0 0.7 0.8 0.0 no data
M1E2 1.1 1.8 1.0 0.7 0.3 2.1 no data
0 4.6 -3.9 2.0 3.1 4.8 -0.7 -1.00 0.08 0.10
4.6 6.3 6.8 1.8 -0.8 9.3 -38.7 1.8
-4.0-6.0
-8.0E1E
1
5.863.86
1.86M1M
1
Circularly pol. Photon - Neutron pol. along zCircularly pol. Photon - Neutron pol. along z
fixed values for other polarizabilities
Similar effects in the beam asymmetry and asymmetry with circularly polarized photon and transversely polarized neutron