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