Manifestations of Neutron Spin Polarizabilities in Compton Scattering on d and He- Deepshikha Choudhury (Collaborators: D. Phillips,. Nogga, R. Hildebrandt) Supported by US-DOE
Focus Neutron Spin Polarizabilities Neutron- particularly challenging Polarizabilities- EM properties- Compton Scattering Polarization observables in Compton Scattering on d and He- Chiral Perturbation Theory (χpt)- pions and nucleons- ~m π
Polarizabilities LO: NLO: NNLO:
State of affairs Proton Proton EM polarizabilities are well established. α ( 1.0 ± 0.7) 10 fm β ( 1.6 ± 0.6) 10 fm p Spin polarizabilities less known (only 0 and π ) Neutron still remains elusive Even electric and magnetic polarizabilities not known to desired accuracy Spin polarizabilities less known (only 0 and π ) Problems: Neutron charge 0 Lifetime ~887 secs Experiments @ HIS p
HIS @ TUNL Circularly polarized photons 10 8 /sec 5
Thus, we study Compton Scattering on Light Nuclei (d & He-) at Low Energies (E~m π ) using HBχPT(upto O(Q )) 6
d d DC, D.Phillips (PRC 71, 000) 1B B T NN TNN T NN d pd ( π ) 6 p d σ d Ω ' ' T Ψ d NN Ψ d & 7
The scattering amplitude T NN has a chiral expansion. Naïve dimensional analysis- 1 - -1 1 Q Q n for a vertex with n powers of p or m π Q - for pion propagator (1/(p -m π )) Q -1 for nucleon propagator (1/(E-p /M)) Q for loop (loop integral) Q for a two-body diagram (δ (p -p ) absent) The wavefunctions are derived from potential model or chiral potential. 8
9 ( ) ( ) ( ) [ ] ( ) ( ) ( ) ( ) ( ) 6 6 5 5 1 1 0 0 0 cos cos cos κ κ κ θ θ κ κ β θ β α π π π M M M M M M How do the polarizabilites enter into the calculations? ( ) ( ) ( ) ( ) [ ] ( ) ( ) ( ) ( ) ( ) ( ) ( ) 6 6 5 5 1 1 1 0 0 0 cos cos cos cos cos κ κ κ θ θ θ κ κ β β θ β α θ β α π π π Δ Δ Δ Δ Δ Δ Δ Δ Δ M M M M M M Α 6 1 1 i i i B t T t O(Q ) the calculations are predictive. 1 1 10 1.1 10 1.1 10. 10. 10 1. 10 1. fm fm fm fm fm fm n p n p n p n p n p n p β β α α BKM, PRL 67 1515
Observable (Double Polarization symmetries, Δ z & Δ x ) k r k r k r ' ŷ xˆ θ ẑ h1 ẑ ẑ Δ z dσ dω dσ dω h±1 RCP h-1 LCP xˆ xˆ Δ x dσ dω dσ dω h±1 10
V. Bernard, N. Kaiser, Ulf-G. Meissner, Int. J. of Mod. Phys. E, 19 Born Born π 0 Born π 0 loops Born loops 11
Effect of varying s on Δ z at 15 MeV (lab) 1
Effect of varying s on Δ x at 15 MeV (lab) 1
He He 1 p 1 q O(Q ) d p 1 d p ' Ψ α α 1 J T He d qd ( l s ) j m ; l j m ;( j j ) t p 1 q ' 1 1 qα 1 1 Ψ ' He O 1 TM ˆ 1 T p Ψ 1 He qα J 1 O(Q ) α T d 1 p 1 d JM p ' 1 d q Ψ ' ˆ He O Ψ He Wfns from. Nogga DC,. Nogga, D. Phillips (submitted to PRL) 1
natomy of the Calculation He He DC, D. Phillips,. Nogga (in preparation) T T 1B T B 15
Polarized He- is interesting! T He Α i 6 Α i 1 1B i i t i, B i To the extent that polarized He- behaves as an effective neutron, contributions from i B (i..6) are negligible i 1B ~ i 1B (O(Q )) Δ i 1B Δ i 1B ~ Δ i 1B (n) 16
Comparison of dcs at different orders 17
Δ z vs cm angle at 10 MeV 18
Δ x vs cm angle at 10 MeV 19
DCS vs cm angle at 10MeV (Effect of α n and β n ) 0
Not so Simple! Proton Spin polarizabilities not well known Experiment scheduled at HIS (R. Miskimen) Measure double polarization observables for Compton scattering on proton. Neutron electric and magnetic polarizabilities not accurately known Unpolarized Compton scattering experiment on d at MXLab (Lund). 1
Theoretical mbiguities Boost corrections (really small) Included in d calculations. Effect studied for He- calculations. Recoil corrections Included in d calculations. Effect studied for He-. Wavefunction dependence Studied for both d and He-. Effect of the Delta Collaborated with R. Hildebrandt for polarized d Needs to be done for He-
Wavefunction Dependence For polarized d calculation
Wavefunction Dependence (He-)
Effect of the Delta (R. Hildebrandt) dditional diagrams at O(ε ) ε (p, m π, Δ 0 ) DC, R. Hildebrandt (in preparation) 5
Effect of varying s on Δ x at 15 MeV (lab): d No Delta 6
Effect of varying s on Δ z at 15 MeV (lab ): d No Delta 7
Summary Elastic scattering promising avenue to extract polarizabilities. We have taken the first step with He- and polarized d calculations. d d Double pol. Observables are sensitive to combination of neutron spin polarizabilities. He He Double pol. Observables are quite sensitive to combinations of neutron spin polarizabilities. dcs is sensitive to α n and β n and can be used to extract them if needed. 8
Outlook More needs to be done both in theory and experiment. Proton spin polarizabilities should be measured first (HIS - scheduled). α n & β n should be pinned down (Lund unpolarized d experiments). Neutron spin polarizabilities through polarized d and He- (HIS - scheduled). Theory: Delta-ful, O(Q ) calculations Effort required to reduce theoretical uncertainties. 9
Thank You! 0
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