High-Accuracy Analysis of Compton Scattering off Protons and Deuterons in Chiral EFT

Transcription

1 High-Accuracy Analysis of Compton Scattering off Protons and Deuterons in Chiral EFT H. W. Grießhammer Institute for Nuclear Studies The George Washington University, DC, USA 1 Compton Scattering Explores Low-Energy Dynamics 2 One Nucleon 3 The Other Nucleon 4 Concluding Questions How do constituents of the nucleon react to external fields? How to reliably extract neutron and spin polarisabilities? Comprehensive Theory Effort: hg, J. McGovern (Manchester), D. R. Phillips (Ohio U) arxiv: (proton) + G. Feldman (GW): Prog. Part. Nucl. Phys. 67 (212) 841 Precursors: Hildebrandt/Hemmert/Pasquini/hg ,...,Beane/Malheiro/McGovern/Phillips/van Kolck ; Choudhury Shukla/Phillips 25-8; Friar 1975, Arenhövel/Weyrauch , Karakowski/Miller 1999, Levchuk/L vov Polarisabilities, INT workshop, 35, Grießhammer, INS@GWU 1-1

2 1. Compton Scattering Explores Low-Energy Dynamics (a) Energy-Dependent (Dynamical) Polarisabilities hg/hemmert/+hildebrandt/pasquini 22/3 Example: induced electric dipole radiation from harmonically bound charge, damping Γ Lorentz/Drude 19/195 E in (ω) m,q d ind (ω)= q2 1 E ω,γ m ω 2 ω 2 in (ω) iγω }{{} =: 4π α E1 (ω) [ ] L pol = 2π α E1 (ω) E 2 + β M1 (ω) B 2 }{{} electric, magnetic scalar dipole +... Energy- (ω)-dependent multipole-decomposition dis-entangles scales, symmetries & mechanisms of interactions with & among constituents. = Clean, perturbative probe of (1232) properties, nucleon spin-constituents, χiral symmetry of pion-cloud & its breaking (proton-neutron difference). q µ =(ω, q) proton neutron iso-spin breaking: = elmag. p-n self-energy difference from β p M1 β n M1 2γ contribution to Lamb shift in muonic H (β M1 ) Walker-Loud/ Polarisabilities, INT workshop, 35, Grießhammer, INS@GWU 2-1

3 (b) Towards Polarisabilities from First Principles: Lattice QCD Pioneering: Quenched, chiral fermions Lee/Zhou/Wilcox/Christensen neutron α n E1 [1 4 fm 3 ] E.1 m π [ MeV] _ Ongoing: spin-polarisabilities, unquenching, m π ց 2 MeV, larger volumes, more statistics,... Lee/ , LHPC 26-, Detmold/Tiburzi/Walker-Loud 26- [1-4 fm] 4 E1 γ γe1e1 n Engelhardt (LHPC) fully dynamical vs. χeft with dyn m [MeV] Polarisabilities, INT workshop, 35, Grießhammer, INS@GWU 3-1

4 (c) Separation of Scales: Effective Field Theory from QCD Wilson, Weinberg,... Theory of strong interactions: Quantum Chromo Dynamics QCD L QCD = Ψ q [i / + g /A m q ]Ψ q 1 4 G µν G µν = Effective low-energy degrees of freedom: Nucleons, Pions, (1232) Systematic ordering in Q= typ. momentum m π breakdown scale 1 GeV Controlled approximation: model-independent, error-estimate. π L χeft =(D µ π a )(D µ π a ) m 2 π π a π a N [i D + D 2 2M + g ( ) A 2+ ( σ Dπ+...]N+ C N N H N N) 2f π Correct long-range Physics + all interactions allowed by symmetries. Short-range: encode ignorance into minimal parameter-set at given order. E [MeV] λ[fm=1 15m] p,n (94).2 ω,ρ (77) gauge, Lorentz, iso-spin,... symmetries chiral: pions light & weakly coupled: Goldstone bosons of Chiral SSB = Chiral Effective Field Theory χeft low-energy QCD π (14) M M N 2 H R λ Polarisabilities, INT workshop, 35, Grießhammer, INS@GWU 4-1

5 2. One Nucleon (a) Including the (1232) in χeft (1232) lowest hadronic excitation above 1-pion threshold m π, below χeft breakdown scale Λ χ 1 MeV = Expand in δ = M M N Λ χ mπ = p typ 1 ω (numerical fact) Pascalutsa/Phillips 22 and. Λ χ Λ χ Λ χ Low régime ω m π = ω δ 2 High régime ω M M N 3 MeV = ω δ 1 ω M M N : propagator enhanced 1 ω (M M N ) 1 δ 3 = Re-order & dress = 1 E (M M N ) + relativity Probe non-zero width, M1 and E2 transition strengths. Polarisabilities, INT workshop, 35, Grießhammer, INS@GWU 5-1

6 (b) All Contributions Bernard/Kaiser/Meißner 1994, Hemmert/ hg/hemmert/hildebrandt/pasquini 23, McGovern 21 McGovern/Phillips/hg 212 Low régime ω m π δ 2 High régime ω M M N δ 1 3 MeV ω m π M M N e 2 δ LO e 2 δ ցnlo π e 2 δ 2 N 2 LO e 2 δ 1 N 2 LO covariant with vertex corrections b 1 (M1) b 2 (E2) = LO NLO N 2 LO e 2 δ 3 N 3 LO e 2 δ 1 րlo e 2 δ 3 N 3 LO e 2 δ 1 N 2 LO etc. δα,δβ fit etc. e 2 δ 4 N 4 LO e 2 δ 2 N 3 LO Unified Amplitude: gauge & RG invariant set of all contributions which are in low régime ω m π at least N 4 LO (e 2 δ 4 ): accuracy δ 5 2%; or in high régime ω M M N at least NLO (e 2 δ ): accuracy δ 2 2%. Unknowns: δα,δβ α E1,β M1, γn strengths b 1 (M1), b 2 (E2) Polarisabilities, INT workshop, 35, Grießhammer, INS@GWU 6-1

7 (c) Elementary, Watson. Watson 1954 Watson s Theorem: Re[Amplitude] = at resonance peak by unitarity. = Unified Amplitude must contain additional pieces: πn loops order for γ N vertex corrections N 2 LO, N 4 LO for ω m π ω M M N N 7 LO, N 9 LO for ω m π + + e 2 δ 1 N 2 LO e 2 δ 2 N 3 LO = Keep these vertex corrections, albeit higher-order everywhere; check. Polarisabilities, INT workshop, 35, Grießhammer, INS@GWU 7-1

8 (d) Creating a Consistent Proton Compton Database hg/mcgovern/phillips/feldman PPNP Θ lab Θ lab Θ lab Θ lab 9 2 Θ lab Θ lab Θ lab Θ lab data, mostly New effort for better data: MAMI, MAXlab, HIγS,... Gaps for: ω [16;25] MeV; θ : Baldin check; θ 18 for (1232)! Small quoted systematics = tensions: MAMI vs. LEGS, but also others = no Not more, but more reliable data needed for unpolarised proton. χ 2 1 without pruning. d.o.f. Polarisabilities, INT workshop, 35, Grießhammer, INS@GWU 8-1

9 (e) Polarisabilities from Consistent Database McGovern/Phillips/hg 212 database: +Feldman PPNP b Θlab Θlab Θlab Θlab Θlab Θlab > 2 MeV: fix b 2 /b 1 =.34 Vanderhaeghen/ Pascalutsa 26, fit b 1 = 3.61±.2; = <17 MeV: polarisabilities α p E1 [1 4 fm 3 ] β p M1 [1 4 fm 3 ] χ 2 /d.o.f. Baldin constrained α p E1 + β p M1 = 13.8±.4 1.7±.4 stat ±.2 Σ ±.3 theory stat ±.2 Σ.3 theory 113.2/135 Polarisabilities, INT workshop, 35, Grießhammer, INS@GWU 9-1

10 (f) Fit Discussion: Parameters and Uncertainties McGovern/Phillips/hg 212 Fit to α, β only: Combined πn loops and pushes intermed. angles too high. = Must also fit γ M1M1 2.2±.5 stat for good χ 2, fwd. spin-polarisability γ p 1 (cf. Disp. Rel.). 1σ -contours N 2 LO marginalised over γ M1M1 Consistent with Baldin Σ Rule α E1 + β M1 = 1 2π 2 ν dν σ(γp X) ν 2 = 13.8±.4 Olmos de Leon 21 need more forward data to constrain. Fit Stability: floating norms within exp. sys. uncertainties; vary dataset, b 1, vertex dressing,... Residual Theoretical Uncertainty from convergence pattern: δ of LO NLO change δ(α β)=3.5 LO parameter-free Bernard/Kaiser/Meißner 1994 α p E1 [1 4 fm 3 ] β p M1 [1 4 fm 3 ] χ 2 /d.o.f no fit N 2 LO Baldin constrained α p E1 + β p M1 = 13.8±.4 1.7±.4 stat ±.2 Σ ±.3 theory stat ±.2 Σ.3 theory 113.2/135 Olmos de Leon ±1.2 stat+model ±.4 Σ stat+model ±.4 Σ Polarisabilities, INT workshop, 35, Grießhammer, INS@GWU 1-1

11 (g) Spin-Polarisabilities: Nucleonic Bi-Refringence and Faraday Effect Optical Activity: Response of spin-degrees of freedom, experimentally untested. S S S S S S S S S S S S π+ π+ σ π+ π+ L pol = 4π N { ] [α E1 (ω) E 2 + β M1 (ω) B scalar dipole [ γ E1E1 (ω) σ ( E E) + γ M1M1 (ω) σ ( B B) pure spin-dependent dipole 2 γ M1E2 (ω) σ i B j E ij + 2 γ E1M2 (ω) σ i E j B ij ] } N mixed spin-dependent dipole quadrupole etc. N N N N N N N N N N N N E ij := 1 2 ( ie j + j E i ) etc. Polarisabilities, INT workshop, 35, Grießhammer, INS@GWU 11-1

12 (h) Spin-Polarisabilities from Circular-Polarised Photon O(e 2 δ 3 ): hg/hildebrandt/ O(e 2 δ 4 ): hg/mcgovern in prep. exp: MAMI 211- Proton Best: Incoming γ circularly polarised, sum over final states. N-spin in( k, k )-plane, perpendicular to k: Σ x = ( ) ( ) ( )+( ) σ k k ε θ vs. σ k k ε θ full Nπ+ no γ i s no l 2 proton proton Dominated by structure Clear γ i -dep. Higher pols negligible HIγS? Also good signal for linear polarisations. Polarisabilities, INT workshop, 35, Grießhammer, INS@GWU 12-1

13 3. The Other Nucleon (a) Iso-Vector Polarisabilities Proton-neutron difference αe1 v := αp E1 αn E1 etc. probes details: Explicit χiral-symmetry-breaking in pion-cloud,..., elmag. p-n self-energy difference[±1] MeV β p M1 β n M1 Appears only in NLO χeft; compatible with 1 1 th of iso-scalar polarisabilities in Dispersion Relations. No free neutron targets = χeft for model-independent subtraction of nuclear binding. Polarisabilities, INT workshop, 35, Grießhammer, INS@GWU 13-1

14 (b) Deuteron Compton Scattering at ω =... 2 MeV Hildebrandt/hg/Hemmert 25-1, hg 212 One-body: electric, magnetic moment couplings α s E1,β s M1 ω Q2 M 2 MeV ω Q 1 MeV LO, N 3 LO LO,րNLO partial waves T NN LO ց NLO, N 3 LO 2N correlated i B d ± ω q2 M uncorrelated χeft pion-exchange currents: Beane et al ; hg/ NLO NLO NLO ց N 2 LO part. waves NLO ց N 3 LO, pert. Full LO T NN pivotal for current conservation. Arenhövel 198 Polarisabilities, INT workshop, 35, Grießhammer, INS@GWU 14-1

15 (c) Consequence of NN-Rescattering: An Exact Low-Energy Theorem hg/... 21, 212 Low-Energy Theorem: Thomson limita(ω = )= e2 M d ε ε. Thirring 195, Friar 1975, Arenhövel 198: Thomson limit current conservation gauge invariance. Exact Theorem = At each χeft order = Checks numerics. 25 dσ d nbarn sr Θ Ω lab MeV Significantly reduces cross section for ω 7 MeV. Numerically confirmed to.2%, irrespective of deuteron wave function & potential. Urbana, Lund data model-independence Wave function & potential dependence significantly reduced even as ω 15 MeV = gauge invariance. Polarisabilities, INT workshop, 35, Grießhammer, INS@GWU 15-1

16 (d) Determine Neutron Polarisabilities from all Deuteron Data hg/mcgovern/phillips/ Feldman PPNP 212 Illinois, Lund, Saskatoon Nπ + free fit Nπ + + stat. error, Baldin constrained α s E1 [1 4 fm 3 ] β s M1 [1 4 fm 3 ] χ 2 /d.o.f. NLO free fit 1.5±2. stat ±.8 theory 3.6±1. stat ±.8 theory 24.3/24 NLO Baldin constrained α s E1 + β s M1 = 14.5±.3 1.9±.9 stat ±.2 Σ ±.8 theory stat ±.2 Σ.8 theory 24.4/25 N 2 LO proton (Baldin) hg/... PPNP ±.4 stat ±.2 Σ ±.3 theory stat ±.2 Σ.3 theory 113.2/135 = neutron proton polarisabilities Need better data: MAXlab taken, HIγS approved theory: N 2 LO, beyond pion threshold Polarisabilities, INT workshop, 35, Grießhammer, INS@GWU 16-1

17 (e) Goal: Guide, Support, Analyse, Predict Experiments hg/shukla 21- hg/mcgovern/phillips independent observables for proton; 23 for deuteron = Interactive mathematicia 8. notebooks from hgrie@gwu.edu Example double-polarised on deuteron Θcm 16,9, Γ E1E1 ±2 2 First scatt. angle Θ 16 Second scatt. angle Θ 9 Reference frame cm lab x circ nbarn sr Ωcm MeV Deuteron polarisation axis x z Variation by ±2 of Γ E1E1 ΧEFT order Ε 3 Deuteron wave function NNLO Epelbaum 65MeV AV18 NN potential AV18 Range y axis Automatic Γ E1E1 ; Γ E1E1 2; Γ E1E1 2 Future: guide/support experiments at HIγS, MAMI, MAXlab extend analysis proton to 3 MeV full analysis deuteron (tensor-polarised), 3 He Compton@Web on DAC/SAID website Polarisabilities, INT workshop, 35, Grießhammer, INS@GWU 17-1

18 (f) Spin-Polarisabilities from Circularly Pol. Photons at 125 MeV Shukla/Phillips 25 Shukla/hg 21; hg 212 Deuteron Best: Incoming γ circularly polarised, sum over final states. N-spin in( k, k )-plane, perpendicular to k: difference circ x, asymmetry Σ circ x = circ x sum σ k k ε θ vs. σ k k ε θ Sensitivity on neutron γ E1E1 x circ nbarn sr Sensitivity on neutron α E1 β M1 ; Baldin-Σ fixed 5.2; 5.2+2; ; 8.2+2; Ω lab 125 MeV, Γ E1E1 ± Θ deg x circ nbarn sr Ω lab 125 MeV, Α E1 Β M1 ±2, Baldin fixed Θ deg Sensitive to γ E1E1, but must nail down α E1, β M1 at lower energy. (1232) and re-scattering increase signal. Polarisabilities, INT workshop, 35, Grießhammer, INS@GWU 18-1

19 (g) Inelastic Compton Scattering on Nuclei theory: Levckuk/L vov/petrunkin ; Demissie/hg 212- exp: (Rose/ ); Kolb/... SAL 2; Kossert/... MAMI 22 Nucleon polarisabilities from centre of quasi-inelastic peak in A(γ,γA )N 9 data for d(γ,γp)n for ω [23;4] MeV d 3 σ / dω γ dω p de p [nb / MeV sr 2 ] MAID2 MAID2 (scaled) SAID-SMK SAID-SM99K SAL- SENECA γd γ pn s lab θ γ = Kossert et al. 23 found α n E1 = 12.5±1.8(stat) (syst)±1.1(model), β M1 from Baldin sys. & model-error under-estimated?: π production, SAID/MAID-2 amplitudes, π-exchange currents not chirally consistent, E γ [MeV] To Do: Theory starting up: Demissie PhD Analyse elastic & inelastic in unified χeft frame, test quasi-free hypothesis. Enhancement by (1232) peak = accurate theory. To Do: Experiment Better data. Lower energies. Sensitivity of single-/double-polarised observables, breakup asymmetries. Alternative targets: 3 He, 4 He, 6 Li,..., also for proton? Polarisabilities, INT workshop, 35, Grießhammer, INS@GWU 19-1

20 (h) Per Aspera Ad Astra: 3 He Experiment: dσ dω (target-charge)2 to 1, more & easier targets Theory: Reliable extraction needs accurate description of nuclear binding & levels = heavier nuclei = lighter nuclei Find sweet-spot between competing forces: 3 He at HIγS, MAMI, MAXlab Example: Sensitivity of unpolarised 3 He cross-section at ω lab = 12 MeV on α n, β n Shukla/Phillips/Nogga α n =-4 α n =-2 α n = α n = 2 α n = β n =-2 β n = β n = 2 β n = 4 β n = cm angle (deg) cm angle (deg) First Compton cross section on 3 He. 3 He as effective neutron spin target. Extend beyond ω [8;12] MeV: re-scattering (Thomson, T NN ), explicit (1232), threshold corrections = Effects will become more pronounced. Polarisabilities, INT workshop, 35, Grießhammer, INS@GWU 2-1

21 (i) Understanding Energy Dependence Dynamical Polarisabilities: Multipole decomposition of real Compton scattering at fixed energy. Neither more nor less information about response of constituents, but more readily accessible. α E1 (ω): Pion cusp well captured by single-nπ. β M1 (ω): para-magnetic N-to- M1-transition. 3 Ω Π Ω Ω Π Ω Re ΑE1 Ω χeft with (1232) Im ΒM1 Ω Re Im Disp. Rel. Re: refraction; Im: absorption = pion photo-production multipoles. Polarisabilities, INT workshop, 35, Grießhammer, INS@GWU 21-1

22 (j) Iso-Scalar Spin-Dependent Dynamical Polarisabilities Hildebrandt/TRH/hg/Pasquini 22/3 Predicted in χeft: No N-core contributions = Spin-physics dominated by pion-cloud+ (γ M1M1, γ M1E2 ) ΓE1E1 Ω Ω Π ΓE1M2 Ω Ω Π Ω Ω ΓM1M1 Ω Ω Π Ω Π Ω Ω Pure polarisabilities γ E1E1, γ M1M1 agree. Nπ+ Nπ Disp. Rel.. Mixed polarisabilities γ E1M2,γ M1E2 small. Uncertainties in DR? 4 4 ΓM1E2 Ω Static values χeft DR MAMI LEGS MAMI units: [1 4 fm 4 ] iso-scalar iso-scalar proton proton neutron γ = (γ E1E1 +γ M1M1 +γ E1M2 +γ M1E2 ).7.4 1?? γ π (π pole)= γ E1E1 +γ M1M1 γ E1M2 +γ M1E [ ]±4 model Polarisabilities, INT workshop, 35, Grießhammer, INS@GWU 22-1

23 4. Concluding Questions Dynamical polarisabilities: Energy-dependent multipole-decomposition dis-entangles scales, symmetries & mechanisms of interactions with & among constituents: χiral symmetry of pion-cloud, iso-spin breaking, (1232) properties, nucleon spin-constituents. = χeft: unified frame-work off light nuclei: model-independent, systematic, reliable errors. Compton amplitude to 35 MeV Scalar Dipole Polarisabilities from all Compton data below 2 MeV: proton N 2 LO α p = 1.7±.35 stat ±.2 Σ ±.3 theory β p = stat ±.2 Σ.3 theory iso-scalar NLO α s = 1.9±.9 stat ±.2 Σ ±.8 theory β s = stat ±.2 Σ.8 theory neutron NLO α n = 11.1±1.8 stat ±.4 Σ ±.8 theory β n = stat ±.4 Σ.8 theory Theory To-Do List: explore host of observables: expansion p typ Λ χ 1 for credible error-bars. math notebooks One Nucleon: polarisation observables, higher-order in resonance region near-done; long-term Deuteron: embed N 2 LO; extend beyond 1π-threshold into (1232) region; break-up now focus of attention 3 He & heavier: Thomson limit; into (1232) region; break-up starting Data Needed: cross-sections & asymmetries reliable systematics. = spin-polarisabilities. Clean probe to explore the strong force at low energies. Polarisabilities, INT workshop, 35, Grießhammer, INS@GWU 23-1

24 no Claude Monet: Rock Arch West of Etretat (The Manneport), 1883 Polarisabilities, INT workshop, 35, Grießhammer, 24-1

25 (a) Extracting Dynamical Polarisabilities hg/trh 22, Hildebrandt/hg/TRH/Pasquini 23 Rigorous definition from spin-independent Compton scattering amplitudes T(ω,z) = A 1 (ω,z)( ε ε)+a ( 2 (ω,z) ε k ˆ )( ε ˆ k ) + i A 3 (ω,z) σ ( ε ε)+ i A 4 (ω,z) σ (ˆ k k)( ε ˆ ε) [( + i A 5 (ω,z) σ ε k ˆ )( ε k ˆ ) ( ε ˆ k )( ε k ˆ )] [( + i A 6 (ω,z) σ ε k ˆ )( ε k ˆ ) ( ε ˆ k )( ε k ˆ )] (1) Choose frame of reference: centre of mass; θ = ( k, k ), z=cosθ. (2) Subtract nucleon pole terms in π s-channel, u-channel, t-channel, : two-photon interaction with point-like spin- 1 2 nucleon of magnetic moment κ (Powell)+pion-pole term. = Structure-dependent part of Compton amplitude: Ā i (ω,cosθ)=a i (ω,cosθ) A pole i (ω,cosθ) Polarisabilities, INT workshop, 35, Grießhammer, INS@GWU 25-1

26 (a) Extracting Dynamical Polarisabilities hg/trh 22, Hildebrandt/hg/TRH/Pasquini 23 (3) Multipole decomposition into photon transitions Tl T l (T = E,M) at fixed energy ω: static: α E1 (ω = )=ᾱ etc. Ā 1 (ω,z) = 4π W M W = ω+ M 2 + ω 2 : cm energy [ ] ( ) α E1(ω)+cosθ β M1(ω) ω ( ) cosθ α E2 (ω)+(2cos 2 θ 1)β M2 (ω) ω Ā 2 (ω, z) = 4π W M β M1(ω)ω , Ā 3 (ω, z) = 4π W [ ] γ E1E1 (ω)+cosθ γ M1M1 (ω)+γ E1M2 (ω)+cosθ γ M1E2 (ω) ω M Ā 4 (ω, z) = 4π W [ ] γ M1M1 (ω)+γ M1E2 (ω) ω M Ā 5 (ω, z) = 4π W M γ M1M1(ω)ω Ā 6 (ω, z)= 4π W M γ E1M2(ω)ω Dynamical polarisabilities: Response of internal degrees of freedom to external, real photon field of definite multipolarity & non-zero energy. Neither more nor less information about temporal response/dispersive effects of nucleon constituents, but information more readily accessible. Polarisabilities, INT workshop, 35, Grießhammer, INS@GWU 25-2

27 (b) Imaginary Parts of Iso-Scalar Polarisabilities LO MSSE: without width; only pion production threshold (Nπ graphs). Non-zero width clearly seen in DR. Im[α E1 ] Disp. Rel. SSE. Im[β M1 ] Im[α E2 ] Im[β M2 ] Polarisabilities, INT workshop, 35, Grießhammer, INS@GWU 26-1

28 (c) Spin-Dependent Dynamical Polarisabilities from Multipole Analysis hg/ { ] 4π N 1 2 [α E1 (ω) E 2 + β M1 (ω) B 2 [ γ E1E1 (ω) σ ( E E)+γ M1M1 (ω) σ ( B B) } 2 γ M1E2 (ω) σ i B j E ij + 2 γ E1M2 (ω) σ i E j B ij ]+... N spin-indep dipole pure spin-dep dipole mixed spin-dep dipole Assumptions: α E1 (ω), β M1 (ω) well captured, only γ E1E1 (ω), γ M1M1 (ω) large = superficial fit to data. Polarisabilities, INT workshop, 35, Grießhammer, INS@GWU 27-1

29 (c) Spin-Dependent Dynamical Polarisabilities from Multipole Analysis hg/ Spin-physics dominated by pion-cloud +. No N-core contributions. { ] 4π N 1 2 [α E1 (ω) E 2 + β M1 (ω) B 2 [ γ E1E1 (ω) σ ( E E)+γ M1M1 (ω) σ ( B B) } 2 γ M1E2 (ω) σ i B j E ij + 2 γ E1M2 (ω) σ i E j B ij ]+... N spin-indep dipole pure spin-dep dipole mixed spin-dep dipole Polarisabilities, INT workshop, 35, Grießhammer, INS@GWU 27-2

30 (c) Spin-Dependent Dynamical Polarisabilities from Multipole Analysis hg/ Spin-physics dominated by pion-cloud +. No N-core contributions. { ] 4π N 1 2 [α E1 (ω) E 2 + β M1 (ω) B 2 [ γ E1E1 (ω) σ ( E E)+γ M1M1 (ω) σ ( B B) } 2 γ M1E2 (ω) σ i B j E ij + 2 γ E1M2 (ω) σ i E j B ij ]+... N spin-indep dipole pure spin-dep dipole mixed spin-dep dipole Large error-bars because γ i -effects cos 2 θ, while data nearly linear. Polarisabilities, INT workshop, 35, Grießhammer, INS@GWU 27-3

31 (c) Spin-Dependent Dynamical Polarisabilities from Multipole Analysis Dependence of T NN on NN-potential = short-distance, for ω clear from Thomson. Illinois, Lund, Saskatoon LO χeft AV18 LO χeft-potential: + C,P Q 1 Consistent for Compton at NLO:O(Q )-correction of NN-potential presumed zero. AV18 provides<3% corrections = suggests higher-order indeed Q 1 ( ) Polarisabilities, INT workshop, 35, Grießhammer, INS@GWU 28-1

32 (d) Spin-Polarisabilities from Circularly Pol. Photons at 125 MeV Shukla/Phillips 25 Shukla/hg 21; hg 212 Deuteron Best: Incoming γ circularly polarised, sum over final states. N-spin in( k, k )-plane, perpendicular to k: difference circ x, asymmetry Σ circ x = circ x sum σ k k ε θ vs. σ k k ε θ Sensitivity on & NN-rescattering: Sensitivity on wave-function: Nπ, no NN; Nπ+, no NN; Nπ+ +NN NNLO Epelbaum 65 MeV, AV18, Nijmegen 93 Ω lab 125 MeV 2 x nb sr x circ nbarn sr Θcm deg Θ deg More pronounced by explicit (1232) No residual deuteron wave-function dependence Thomson (NN rescatt.) important even at high ω = 125 MeV Higher pols negligible Polarisabilities, INT workshop, 35, Grießhammer, INS@GWU 29-1

33 (d) Spin-Polarisabilities from Circularly Pol. Photons at 125 MeV Shukla/Phillips 25 Shukla/hg 21; hg 212 Deuteron Best: Incoming γ circularly polarised, sum over final states. N-spin in( k, k )-plane, perpendicular to k: difference circ x, asymmetry Σ circ x = circ x sum σ k k ε θ vs. σ k k ε θ Sensitivity on neutron γ E1E1 x circ nbarn sr Sensitivity on neutron α E1 β M1 ; Baldin-Σ fixed 5.2; 5.2+2; ; 8.2+2; Ω lab 125 MeV, Γ E1E1 ± Θ deg x circ nbarn sr Ω lab 125 MeV, Α E1 Β M1 ±2, Baldin fixed Θ deg Sensitive to γ E1E1, but must nail down α E1, β M1 at lower energy. Similarly good signal for linear polarisation lin x. Polarisabilities, INT workshop, 35, Grießhammer, INS@GWU 29-2

34 (d) Spin-Polarisabilities from Circularly Pol. Photons at 125 MeV Shukla/Phillips 25 Shukla/hg 21; hg 212 Deuteron Best: Incoming γ circularly polarised, sum over final states. N-spin in( k, k )-plane, perpendicular to k: difference circ x, asymmetry Σ circ x = circ x sum σ k k ε θ vs. σ k k ε θ Sensitivity on neutron γ E1E1 x circ nbarn sr Sensitivity on neutron α E1 β M1 ; Baldin-Σ fixed 5.2; 5.2+2; ; 8.2+2; Ω lab 125 MeV, Γ E1E1 ± Θ deg x circ nbarn sr Ω lab 125 MeV, Α E1 Β M1 ±2, Baldin fixed Θ deg Sensitive to γ E1E1, but must nail down α E1, β M1 at lower energy. (1232) and re-scattering increase signal. Polarisabilities, INT workshop, 35, Grießhammer, INS@GWU 29-3

35 (d) Spin-Polarisabilities from Circularly Pol. Photons at 125 MeV Shukla/Phillips 25 Shukla/hg 21; hg 212 Deuteron Best: Incoming γ circularly polarised, sum over final states. N-spin in( k, k )-plane, perpendicular to k: x circ nbarn sr x circ nbarn sr Ω lab 125 MeV, Γ E1E1 ± Θ deg x circ nbarn sr Ω lab 125 MeV, Γ M1M1 ±2 δγ E1E1 =±2 δγ M1M1 =±2 Ω lab 125 MeV, Γ E1M2 ± Θ deg x circ nbarn sr Θ deg Ω lab 125 MeV, Γ M1E2 ±2 δγ E1M2 =±2 δγ M1E2 =± Θ deg Polarisabilities, INT workshop, 35, Grießhammer, INS@GWU 29-4

36 (e) Spin-Polarisabilities from Linearly Pol. Photons at 125 MeV Shukla/Phillips 25 Shukla/hg 21 Deuteron Best: Incoming γ linearly polarised, sum over final states. N-spin in( k, k )-plane, parallel to k: difference lin z, asymmetry Σlin z = lin z sum y x z k σ θ k φ k σ θ k φ Polarisabilities, INT workshop, 35, Grießhammer, INS@GWU 3-1

37 (e) Spin-Polarisabilities from Linearly Pol. Photons at 125 MeV Shukla/Phillips 25 Shukla/hg 21 Deuteron Best: Incoming γ linearly polarised, sum over final states. N-spin in( k, k )-plane, parallel to k: difference lin z, asymmetry Σlin z = lin z sum y x z k σ θ k φ k σ θ k φ Sensitivity on neutron γ M1M1 2 Sensitivity on neutron α E1 3.2; 3.2+2; ; ; Ω lab 125 MeV, Γ M1M1 ±2 z lin nbarn sr Θ deg Sensitive to γ M1M1, but must nail down α E1, β M1 at lower energy. Polarisabilities, INT workshop, 35, Grießhammer, INS@GWU 3-2

38 (f) Per Aspera Ad Astra: 3 He Example: Sensitivity of unpolarised cross-section at ω lab = 12 MeV on α n, β n Shukla/Phillips/Nogga α n =-4 α n =-2 α n = α n = 2 α n = β n =-2 β n = β n = 2 β n = 4 β n = cm angle (deg) cm angle (deg) First Compton cross section on 3 He. 3 He as effective neutron spin target. Extend beyond ω [8;12] MeV: re-scattering (Thomson, T NN ), explicit (1232), threshold corrections = Effects will become more pronounced. Polarisabilities, INT workshop, 35, Grießhammer, INS@GWU 31-1

39 (f) Per Aspera Ad Astra: 3 He Experiment: dσ dω (target-charge)2 to 1, more & easier targets Theory: Reliable extraction needs accurate description of nuclear binding & levels = heavier nuclei = lighter nuclei Find sweet-spot between competing forces: 3 He at HIγS, MAMI, MAXlab Example: Sensitivity of unpolarised 3 He cross-section at ω lab = 12 MeV on α n, β n Shukla/Phillips/Nogga α n =-4 α n =-2 α n = α n = 2 α n = β n =-2 β n = β n = 2 β n = 4 β n = cm angle (deg) cm angle (deg) First Compton cross section on 3 He. 3 He as effective neutron spin target. Extend beyond ω [8;12] MeV: re-scattering (Thomson, T NN ), explicit (1232), threshold corrections = Effects will become more pronounced. Polarisabilities, INT workshop, 35, Grießhammer, INS@GWU 31-2

40 (g) Starting with 3 He: Doubly-Polarised Choudhury Shukla/Phillips/Nogga 26-9 Example: Sensitivity of polarised cross-section at ω lab = 12 MeV on γ n i s First Compton cross section on 3 He. 3 He as effective neutron spin target. Extend beyond ω [8;12] MeV: re-scattering (Thomson, T NN ), explicit (1232), threshold corrections = Effects will become more pronounced. Polarisabilities, INT workshop, 35, Grießhammer, INS@GWU 32-1