Compton Scattering and Nucleon Polarisabilities in Chiral EFT: Status and Future

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1 Compton Scattering and Nucleon Polarisabilities in Chiral EFT: Status and Future H. W. Grießhammer Institute for Nuclear Studies The George Washington University, DC, USA INS Institute for Nuclear Studies a 1 Two-Photon Response Explores Low-Energy Dynamics 2 Polarisabilities from Compton Scattering 3 The Future: Per Aspera Ad Astra 4 Concluding Questions a How do constituents of the nucleon react to external fields? How to reliably extract proton, neutron and spin polarisabilities? Comprehensive Theory Effort: hg, J. A. McGovern (Manchester), D. R. Phillips (Ohio U): Eur. Phys. J. A49 (213), 12 (proton) + G. Feldman (GW): Prog. Part. Nucl. Phys. 67 (212) 841 neutron in COMPTON@MAX-lab: Phys. Rev. Lett. 113 (214) 2626 [ [nucl-ex]] & Phys. Rev. C92 (2) 223 Polarisabilities, Hadrons JLab 2, Grießhammer, INS@GWU -1

2 1. Two-Photon Response Explores Low-Energy Dynamics (a) Polarisabilities: Stiffness of Charged Constituents in El.- Mag. Fields Example: induced electric dipole radiation from harmonically bound charge, damping Γ Lorentz/Drude 19/19 E in (ω) m,q d ind (ω) = q2 1 ω,γ m ω 2 E in (ω) ω2 iγω }{{} =: 4π α E1 (ω) [ ] L pol = 2π α E1 (ω) E 2 + β M1 (ω) B 2 }{{} electric, magnetic scalar dipole displaced volume [1 3 fm 3 ] +... = Clean, perturbative probe of (1232) properties, nucleon spin-constituents, χiral symmetry of pion-cloud & its breaking (proton-neutron difference). fundamental hadron property = link to emergent lattice-qcd results Alexandru/Lee/... 2-, NPLQCD 26-, LHPC 27-, Leinweber/ π Polarisabilities, Hadrons JLab 2, Grießhammer, INS@GWU 1-1

3 (b) Why the Magnetic Polarisability β M1 Matters modified from McGovern: plenary χdyn 2 2γ in Lamb shift: proton radius M p γ M n γ [1.1 ±.] MeV Cottingham Sum Rule and VVCS + dark-matter detection scenarios e.g. Appelquist/ Polarisabilities, Hadrons JLab 2, Grießhammer, INS@GWU 2-1

4 (c) Studying the Two-Photon Response 27 NSAC, 21 NuPECC LRPs: Compton pivotal to explore low-energy structure of hadrons. 2 QCD White Paper: Synergistic Blend of Theory and Experiment Lattice QCD: relate to fundamental interactions polarqcd (Alexandru/Lee) 2-; NPLQCD 26-; LHPC (Engelhardt) 27-; Leinweber/... (Adelaide) 213 Experiment: Significant investments; data taken/scheduled/approved: HIγS (DOE): a central goal; > 3 hrs committed at 6 1 MeV proton doubly & beam pol. (E-6-9/1) deuteron beam pol. (E-18-9) 3 He unpol & doubly pol. (E-7-1) 4 He unpol 6 Li unpol. (E--11, first!) MAMI (DFG: -year SFB): cooking, running and planned proton 1 4 MeV: beam & target pol. deuteron, 3 He, 4 He unpol., beam & target pol. MAXlab: cooking and running deuteron 1 16 MeV: unpol. Chiral EFT: data consistency, binding effects, analysis, extraction Goal: Unified framework with reliable error bars for proton, deuteron, 3 He (elastic & inelastic) into (1232) region. Polarisabilities, Hadrons JLab 2, Grießhammer, INS@GWU 3-1

5 (d) Understanding Energy Dependence hg/hildebrandt/hemmert/pasquini 22/3 Polarisabilities: Energy-dependent Multipoles of real Compton scattering. [ 2π α E1 (ω) E 2 + β M1 (ω) B 2 + γ E1E1 (ω) σ ( E E) + γ M1M1 (ω) σ ( B B) ] +... Neither more nor less information about two-photon response of constituents, but more readily accessible α E1 (ω): Pion cusp well captured by single-nπ. p data range d data range Re ΑE1 Ω Ω Π Ω Im β M1 (ω): para-magnetic N-to- M1-transition p data range d data range ΒM1 Ω Re Ω Π Ω Im π E π+ π+ π+ π+ _ Re: refraction; Im: absorption For ω m π more than static+slope! = Need to understand dynamics! Polarisabilities, Hadrons JLab 2, Grießhammer, INS@GWU 4-1

6 2. Polarisabilities from Compton Scattering (a) The Method: Chiral Effective Field Theory Degrees of freedom π, N, (1232) + all interactions allowed by symmetries: Chiral SSB, gauge, iso-spin,... = Chiral Effective Field Theory χeft low-energy QCD 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) f π Controlled approximation = model-independent, error-estimate. E [MeV] λ[fm=1 m] p,n (94).2 ω,ρ (77) π π (14) M M N 2 H 1 8 Expand in δ = M M N Λ χ 1GeV mπ Λ χ = p typ Λ χ 1 (numerical fact) Pascalutsa/Phillips 22. Polarisabilities, Hadrons JLab 2, Grießhammer, INS@GWU -1

7 (b) All 1N Contributions to N 4 LO Bernard/Kaiser/Meißner , Butler/Savage/Springer , Hemmert/ McGovern 21, hg/hemmert/hildebrandt/pasquini 23 McGovern/Phillips/hg 213 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 2%; or in high régime ω M M N at least NLO (e 2 δ ): accuracy δ 2 2%. ω m π M M N 3 MeV e 2 δ LO e 2 δ NLO 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 LO 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 Unknowns: short-distance δα,δβ static α E1,β M1 Polarisabilities, Hadrons JLab 2, Grießhammer, INS@GWU 6-1

8 Θlab 4 (c) Nucleon Polarisabilities from a Consistent Database 4 dσ d lab Θlab Θlab Θlab 6 Θlab Θlab 11 Θlab Θlab 6 Θlab Θlab Ω lab McGovern/Phillips/hg 213 Θlab 11 database: +Feldman PPNP Θlab Θlab 11 Θlab 133 Θlab Ω lab Θlab Θlab Ω lab 2 2 Θlab 6 Θlab Polarisabilities, Hadrons JLab 2, Grießhammer, INS@GWU 7-1

9 (d) Fit Discussion: Parameters and Uncertainties McGovern/Phillips/hg 213 exp(stat+sys) 1σ-error 1σ -contours βm1 [1-4 fm 3 ] Baldin Σ rule N2LO (Baldin) NLO (Baldin) NLO (free) N2LO (free) LO (no fit) α E1 [1-4 fm 3 ] Consistent with Baldin Σ Rule α E1 + β M1 = 1 σ(γp X) 2π 2 dν ν 2 ν = 13.8 ±.4 Olmos de Leon 21 need more forward data to constrain. Residual Theoretical Uncertainty McGovern/Phillips/hg: EPJA49 12 (213); many before Convergence pattern of α E1 β M1 by most conservative/worst-case of: (1) δ 2 (2) δ (3) δ Fit Stability: floating norms within exp. sys. errors; vary dataset, b 1, vertex dressing,... of of NLO N 2 LO; LO NLO; of LO N 2 LO. = α p E1 [1 4 fm 3 ] β p M1 [1 4 fm 3 ] χ 2 /d.o.f. N 2 LO Baldin constrained α p E1 + β p M1 = 13.8 ± ±.4 stat ±.2 Σ ±.3 theory 3..4 stat ±.2 Σ.3 theory 113.2/13 Polarisabilities, Hadrons JLab 2, Grießhammer, INS@GWU 8-1

10 (e) Neutron Polarisabilities and Nuclear Binding hg/... /+Phillips/+McGovern MECs: Beane/ Need model-independent, systematic subtraction of binding effects. = χeft: reliable uncertainties. Nucleon structure: average of neutron & proton polarisabilities: χeft, Disp. Rel.: p-n difference is small hg/pasquini/... 2 Parameter-free one-nucleon contributions: partial waves S NN Parameter-free charged meson-exchange currents dictated in χeft by gauge & chiral symmetry: π + π Test charged-pion component of NN force. Rescattering pivotal for Thomson limit A(ω = ) = e2 M d ɛ ɛ. = tiny dep. on d wave fu. & NN pot. Polarisabilities, Hadrons JLab 2, Grießhammer, INS@GWU 9-1

11 (f) Myers et al. 214: MAX-lab Doubles & Improves Database PRL 214 & PRC 2 Illinois 1994, Lund 23, Saskatoon 2, Lund 214 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 Baldin constrained α s E1 + β s M1 = 14. ± ±.6 stat ±.2 Σ ±.8 theory stat ±.2 Σ.8 theory 4.2/44 Before Myers 214: 1.9 ±.9 stat ±.2 Σ ±.8 theory stat ±.2 Σ.8 theory 24.4/ Pruning: World data statistically consistent after 2 points with χ 2 > 9 removed. number of points per χ 2 compared to analytic χ 2 distribution Polarisabilities, Hadrons JLab 2, Grießhammer, INS@GWU 1-1

12 (g) Scalar Dipole Polarisabilities: Values, Data and Theory Errors in χeft Need better neutron data: proton-neutron differences test interplay short-distance χsb in pion cloud. exp(stat+sys)+theory/model 1σ-error in quadrature 6 n BΣR p Baldin Σ rule n PDG 213 This extraction: α (p) E1 α(n) E1 =.9 ± 1.6 tot??? β M1 [1-4 fm 3 ] 4 3 proton neutron n Kossert 23 via γd γnp Cottingham Sum Rule explains p-n self-energy difference if α (p) E1 α(n) E1 = 1.7 ±.4 tot 2 p PDG Gasser/ Grießhammer Nov α E1 [1-4 fm 3 ] Polarisabilities, Hadrons JLab 2, Grießhammer, INS@GWU 11-1

13 3. The Future: Per Aspera Ad Astra (a) Improve on the Neutron: Target 3 He Experiment: dσ dω (target-charge)2 to 1 = more & easier targets & counts Theory: Reliable extraction needs accurate description of nuclear binding & levels Shukla/Phillips/Nogga 29 +Sandberg/hg/McG/Ph 214- = heavier nuclei = lighter nuclei Find sweet-spot between competing forces: 3 He at HIγS, MAMI, MAXlab, 4 He, 6 Li? Example unpolarised 3 He: Sensitivity on (1232) and α n E1 at ω lab = 12 MeV 3 ω lab =12 MeV, δαe1=±2 etc. dσ /dω [nb/sr] no Δ(1232) with Δ(1232) 3 He as effective neutron spin target. 1 θ lab [deg] Beyond ω [8;12] MeV: rescattering (Thomson, T NN ); explicit (1232) also in MECs Polarisabilities, Hadrons JLab 2, Grießhammer, INS@GWU 12-1

14 (b) En Route to Static Polarisabilities from Lattice QCD: Chiral Extrapolations Towards comparable uncertainties in experiment, χeft and lattice QCD: χeft at O(e 2 δ 4 ) provides reliable error estimate for m π Λ χ extrapolation. hg/mcgovern/phillips in prep. Pick fully dynamical, m π Λ χ 8 MeV, volume: mostly neutron Example: static electric neutron polarisability α n E1 E _ Active lattice groups: Alexandru/Lee/... 2-; Engelhardt/LHPC 26-; Detmold/Tiburzi/Walker-Loud/NPLQCD 26-, 2; Leinweber/Primer/Hall/ This is Not A Fit to Lattice Simulation! Polarisabilities, Hadrons JLab 2, Grießhammer, INS@GWU 13-1

15 (c) Magnetic Polarisabilities: Surprises and Numerology χeft predicts substantial isospin splitting for m π 2 MeV: At m π = 14 MeV, paramagnetic (1232) accidentally fine-tuned against diamagnetic NLO πn loops. Why m π -independent offset? Polarisabilities, Hadrons JLab 2, Grießhammer, INS@GWU 14-1

16 (c) Magnetic Polarisabilities: Surprises and Numerology χeft predicts substantial isospin splitting for m π 2 MeV: At m π = 14 MeV, paramagnetic (1232) accidentally fine-tuned against diamagnetic NLO πn loops. Why m π -independent offset? Why isoscalar off by exactly π 1 4 fm 3? Why isovector exactly matched? Principle of Chiral Persistence? Polarisabilities, Hadrons JLab 2, Grießhammer, INS@GWU 14-2

17 (d) Spin-Polarisabilities: Nucleonic Bi-Refringence and Faraday Effect Optical Activity: Response of spin-degrees of freedom, experimental frontier. S S S S S S S S S S S S π+ π+ σ π+ π+ L pol = 4π N { 1 2 [α E1 E 2 + β M1 B 2 ] [ γ E1E1 σ ( E E) + γ M1M1 σ ( B B) scalar dipole pure spin-dependent dipole } 2 γ M1E2 σ i B j E ij + 2 γ E1M2 σ i E j B ij ] +... N E ij := 1 2 ( ie j + j E i ) etc. mixed spin-dependent dipole + quadrupole etc. N N N N N N N N N N N N O(e 2 δ 4 ) χeft prediction hg/mcgovern/phillips 214 vs. MAMI extraction Martel/ static [1 4 fm 4 ] γ E1E1 γ M1M1 γ E1M2 γ M1E2 MAMI 214 proton 3. ± ±.9.7 ± ±.3 χeft proton 1.1 ± 1.9 th 2.2 ±. stat ±.6 th fit to unpol..4 ±.6 th 1.9 ±. th χeft neutron 4. ± 1.9 th 1.3 ±. stat ±.6 th.1 ±.6 th 2.4 ±. th Polarisabilities, Hadrons JLab 2, Grießhammer, INS@GWU -1

18 (e) Spin-Polarisabilities from Polarised Photons O(e 2 δ 3 ): hg/hildebrandt/ O(e 2 δ 4 ): hg/mcgovern/phillips in prep. exp: Martel/... (MAMI) PRL 214 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 Compare to Martel/... (MAMI) PRL 214 γ E1E1 = 1.1: χeft prediction; ; = 3.1 Martel fit: 3. ± 1.2 ω lab = 288 MeV ω lab = 33 MeV DATA PRELIMINARY Polarisabilities beyond dipoles negligible ω-dependence important. Also good signal for linear polarisations. Polarisabilities, Hadrons JLab 2, Grießhammer, INS@GWU 16-1

19 (f) Plethora of Polarised Compton Observables: Proton/Spin- 1 2 Babusci/ linpol. γ, unpol. target: dσ lin k k θ dσ lin dω x dω y k k θ circpol. γ, vecpol. target: circ x y x z φ k k k σ θ k σ θ φ circ z y x z k σ θ k k σ θ k linpol. γ, vecpol. target: lin x y x z k σ θ k φ k σ θ k φ lin z y x z k σ θ k φ k σ θ k φ Differences and asymmetries Σ = sum 2 6 observables, 6 polarisabilities, 3 kinemat. variables ω, θ, φ + additional constraints: scalar polarisabilities α E1, β M1 γ, γ π (???) experiment: detector settings,... = Kill too many trees when all presented. Polarisabilities, Hadrons JLab 2, Grießhammer, INS@GWU 17-1

20 (g) Plethora of Polarised Compton Observables: Deuteron/Spin-1 hg 213 Parametrise dγ X: unpol./linear/circular beam on scalar/vector/tensor target. [ dσ dω unpol + I=1,2 M I + I=1,2 M I + I=1,2 I M I 1 + Σ lin (ω,θ) P (γ) lin cos2φ lin 1 beam asymmetry T IM (ω,θ) P (d) I dm(θ I d ) cos[mφ d π 2 δ I1] 4 target asymmetries T circ IM (ω,θ) P (γ) circ P(d) I d I M(θ d ) sin[mφ d + π 2 δ I1] 4 circpol. double asymmetries 8 linpol. T lin IM(ω,θ) P (γ) lin P(d) I d I M(θ d ) cos[mφ d 2φ lin π 2 δ I1] Differences and asymmetries sum ] ϕ lin ϑ d k k 2 18 observables, 6 polarisabilities, 2 kinemat. variables ω, θ + additional constraints: x d θ ϕ d z scalar polarisabilities α E1, β M1 γ, γ π (???) experiment: P 1 9%, P 2 7%, detector settings,... = Interactive mathematica 9. notebooks. hg/ Polarisabilities, Hadrons JLab 2, Grießhammer, INS@GWU 18-1

21 (h) Guide, Support, Analyse, Predict Polarised Experiments hg hg/mcgovern/phillips 212- = Interactive mathematica 9. notebooks from hgrie@gwu.edu Example double-polarised on deuteron Goal: guide & analyse polarised experiments extend deuteron analysis to 3 MeV Compton@Web on DAC/SAID website In progress. When all in place. Polarisabilities, Hadrons JLab 2, Grießhammer, INS@GWU 19-1

22 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. Experiment, Low-Energy Theory, Lattice QCD in sync. = χeft: unified frame-work off light nuclei: model-independent, systematic, reliable errors. Goals: Guide, support, analyse, predict experiments. hg, J. McGovern (U. Manchester), D.R. Phillips (Ohio U.) Compton amplitude to 3 MeV Scalar Dipole Polarisabilities from all Compton data below 2 MeV: proton N 2 LO α p = 1.6 ±.3 stat ±.2 Σ ±.3 theory β p = 3..3 stat ±.2 Σ.3 theory neutron NLO α n = 11. ± 1.2 stat ±.2 Σ ±.8 theory β n = stat ±.2 Σ.8 theory Theory To-Do List: explore host of observables; expansion p typ Λ χ 1 for credible error-bars. math notebooks Opportunities for high intensities, polarised beam and/or target: p, d, 3 He; 4 He?, 6 Li? We Need Data: elastic & inelastic cross-sections & asymmetries reliable systematics! ω [8;18] MeV: Single- & double-polarisation observables, elastic & inelastic: p, d, 3 He; 4 He?, 6 Li? = sweet-spot increased count-rates accurate theory; proton neutron differences; cross-checks Clean probe to explore strong force at low energies. Polarisabilities, Hadrons JLab 2, Grießhammer, INS@GWU 2-1

23 no Polarisabilities, Hadrons JLab 2, Grießhammer, 21-1