Deepshikha Shukla (Daniel Phillips, Andreas Nogga)

Transkript

1 Compton Scattering from He- Deepshikha Shukla (Daniel Phillips, ndreas Nogga)

2 Outline Neutron polarizabilities very brief summary Chiral perturbation theory Our calculation and prediction Summary and future direction

3 Options? dpn - lot of work has already been done (a long list of people have been involved). He-ppn Elastic OR breakup Possible benefits of quasi-free remain to be explored. Here, just elastic.

4 The State of Neutron Pols. SL, Kolb et al. PRL85 (000), 88 IN, Kossert et al. EPJ 6 (00), 59 IN, Kossert et al. EPJ 6 (00), 59 Sandorfi et al. PR D50 (99), ( ), π ( )

5 Exciting time for neutron pol. New Experiments XLab (Elastic d Compton Scattering) lready Running HIS (Elastic Compton Scattering on p, d, He) Starting soon Theoretically First He Compton scattering calculations 5

6 ission neutron polarizabilities In this talk Compton Scattering on Light Nuclei (He-) at Low Energies (E~m π ) using χpt(upto NLO: O(Q )) 6

7 HBχPT (Reminder) Degrees of freedom: pions & nucleons Expansion parameter: Q/Λ, Q~(p,m π ) Heavy Baryon formalism: Baryons included as heavy objects vq; v(,0,0,0) Thus, the generic contribution to a matrix element can be expressed as Q ν F(Q/μ) Low Energy Constants (LECs) 7

8 He He p q O(Q ) d p d p ' d qd q ' Ψ ' ˆ He O Ψ He O(Q ) d p d p ' d q Ψ ' ˆ He O Ψ He Ψ α α J T He ( l s ) j m ; l j m ;( j j ) t p qα T T p qα J α T J Wfns from. Nogga 8

9 natomy of the Calculation He He DC,. Nogga, D. Phillips PRL98 (007) 0 Oˆ T NN T NN T B T B 9

10 The scattering amplitude T NN has a chiral expansion. Naïve dimensional analysis- - - Q Q n for a vertex with n powers of p or m π Q - for pion propagator (/(p -m π )) Q - for nucleon propagator (/(E-p /)) 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. 0

11 Points to note! No new LECs at O(Q ) Theory is predictive at this order Breakdown of theory Lightest omitted degree of freedom Low-energy breakdown (~m π /) Does not give the correct Thomson limit.

12 Results for dcs at 60 and 0 ev

13 [ ] cos cos cos κ κ κ θ θ κ κ β θ β α π π π How do the polarizabilites enter into the calculations? Α 6 i i i B t T

14 How do the polarizabilites enter into the calculations? [ ] 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 Α 6 i i i B t T

15 5 How do the polarizabilites enter into the calculations? [ ] 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 Α 6 i i i B t T fm fm fm fm fm fm n p n p n p n p n p n p β β α α BK, PRL 67 55

16 Observables Cross-section: σ Differential cross-section: dσ/dω k r,εˆ k r k r ', ˆ' ε ŷ xˆ θ ẑ t Co frame 6

17 Observable (Double Polarization Observables, Δ z & Δ x ) k r k r k r ' ŷ xˆ θ ẑ h ẑ ẑ Δ z dσ dω dσ dω h± RCP h- LCP xˆ xˆ Δ x dσ dω dσ dω h± 7

18 Sensitivity at 80 ev 8

19 DCS vs cm angle at 0eV (Effect of α n ) 9

20 DCS vs cm angle at 0eV (Effect of β n ) 0

21 Δ z vs cm angle at 0 ev

22 Δ x vs cm angle at 0 ev

23 Neutron spin pols at 0 ev

24 Transversely polarized target

25 HIS projection with polarized He target symmetry in symmetry in C angle (deg) C angle (deg) symmetry in symmetry in ΔE ev 5eV C angle (deg) C angle (deg) Photon flux: 5*0 7 /s, target.0*0 /cm, 5% polarization 500 hours E Slide from H.Gao 6 NaI 5

26 Theoretical Issues Wavefunction dependence Effect of the Delta Correct Low energy limits. Boost corrections (really small) Recoil corrections 6

27 Wavefunction Dependence (He-) DS,. Nogga, D. Phillips (to be published) 7

28 Not so Simple! Proton Spin polarizabilities not well known Experiment scheduled at HIS (R. iskimen) easure double polarization observables for Compton scattering on proton. Neutron electric and magnetic polarizabilities not accurately known Unpolarized Compton scattering experiment on d at XLab (Lund). 8

29 Contributions to the cause of neutron polarizabilities! RODP: Proton spin polarizabilities should be measured first (HIS scheduled, R iskimen). α n & β n should be pinned down Lund) α n & β n should be extracted from He- dcs as a check Neutron spin polarizabilities through polarized d (HIS - scheduled) prediction from χpt: linear combination of and (DC, D. Phillips, PRC 7, 000) He- (HIS - scheduled) these calculations. 9

30 Summary & Future Direction Elastic scattering promising avenue to extract polarizabilities. We have taken the first step with 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. Future effort Delta-ful, O(Q ) calculations Effort required to reduce theoretical uncertainties. 0

31 ND, of course we are all eagerly waiting for Lattice QCD!!! Thank You!