Nucleon Polarisabilities from Compton Scattering Off the Deuteron

Transcription

1 Nucleon Polarisabilities from Compton Scattering Off the Deuteron H. W. Grießhammer Center for Nuclear Studies The George Washington University, DC, USA 1 From Compton Scattering to Dynamical Polarisabilities 2 Previous Successes, Old Worries & a Solution 3 Spin-Polarisabilities in the Deuteron 4 Concluding Questions How do constituents of the nucleon react to external fields? How to reliably extract neutron-polarisabilities? hg/t. R. Hemmert, + R. Hildebrandt, + B. Pasquini, + D. R. Phillips R. Hildebrandt/hg/T. R. Hemmert: [nucl-th/ ] R. Hildebrandt: Ph.D thesis [nucl-th/ ] Friar 1975, Arenhövel/Weyrauch , Karakowski/Miller 1999, Levchuk/L vov 2000, Beane/Malheiro/McGovern/Phillips/van Kolck Polarisabilities, Soft γs & Light Ns INT, Grießhammer, CNS@GWU 1-1

2 1. From Compton Scattering to Dynamical Polarisabilities (a) Polarisabilities: Neutron in a Capacitor Polarisabilities parameterise stiffness of charged constituents in electric/magnetic field. _ π+ π+ π+ S S S S S S S S S S S S E π+ B π+ π+ π+ π+ π Nucleon between conducting plates N N N N N N N N N N N N Nucleon between poles of a magnet Proton: ᾱ p := α E1 (ω = 0) fm 3 β p := β M1 (ω = 0) fm 3 Neutron: not so well known Olmos de Leon 2001 spin-polarisabilities & higher multipoles unknown Polarisabilities, Soft γs & Light Ns INT, Grießhammer, CNS@GWU 2-1

3 1. From Compton Scattering to Dynamical Polarisabilities (a) Polarisabilities: Neutron in a Capacitor Polarisabilities parameterise stiffness of charged constituents in electric/magnetic field N N N N N N N N N N N N π E π+ B π+ π+ π+ π+ π+ π+ π+ _ Nucleon between conducting plates S S S S S S S S S S S S Nucleon between poles of a magnet Proton: ᾱ p := α E1 (ω = 0) fm 3 β p := β M1 (ω = 0) fm 3 Neutron: not so well known Olmos de Leon 2001 spin-polarisabilities & higher multipoles unknown Dis-entangle scales and mechanisms by ω-dependence. hg/hemmert, + Hildebrandt, + Pasquini Polarisabilities, Soft γs & Light Ns INT, Grießhammer, CNS@GWU 2-2

4 (b) Microscopic processes hg/t.r.h./hildebrandt/pasquini 2002/03 Powell: point-like spin- 1 2 with anom. mag. moment [ Dynamical Polarisabilities: 2π α E1 (ω) E 2 + β M1 (ω) B 2 + γ E1E1 (ω) σ ( E E)+γ M1M1 (ω) σ ( B B)+... ] Chiral Dynamics: Cusp at 1-π production threshold. = Nπ Large para-magnetism from N-to- M1 transition. δ β fm 3 = β p 2 fine-tuned, π = + permutations + crossed Core Contribution only for α E1, β M1 : ω-independent dia-magnetism. C.T. Polarisabilities, Soft γs & Light Ns INT, Grießhammer, CNS@GWU 3-1

5 (c) Extracting Dynamical Polarisabilities hg/trh 2002, Hildebrandt/hg/TRH/Pasquini 2003 (3) Multipole decomposition into photon transitions Tl T l (T = E,M) at fixed energy ω: static: α E1 (ω = 0) = 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, Soft γs & Light Ns INT, Grießhammer, CNS@GWU 4-1

6 (d) Spin-Independent Polarisabilities: Quantitative Understanding hg/ /03 Dynamical Polarisabilities: Multipole decomposition of real Compton scattering at fixed energy. Neither more nor less information about response of constituents, but information more readily accessible. α E1 (ω): Pion cusp well captured by single-nπ. β M1 (ω): para-magnetic N-to- M1-transition. Disp. Rel. χdyn. (Nπ) Nπ + + stat. error Here: Strong dispersive effects especially by s para-magnetism fully taken into account. Polarisabilities, Soft γs & Light Ns INT, Grießhammer, CNS@GWU 5-1

7 (d) Spin-Independent Polarisabilities: Quantitative Understanding hg/ /03 Dynamical Polarisabilities: Multipole decomposition of real Compton scattering at fixed energy. Neither more nor less information about response of constituents, but information more readily accessible. α E1 (ω): Pion cusp well captured by single-nπ. β M1 (ω): para-magnetic N-to- M1-transition. Disp. Rel. Nπ + Polarisabilities, Soft γs & Light Ns INT, Grießhammer, CNS@GWU 5-2

8 (e) Determining Static Proton Polarisabilities from Data hg/hildebrandt/hemmert EJPA20, 329 MAMI, Moscow, Illinois ; Saskatoon Dispersion Relations, Nπ only (LO, NLO) Nπ and : δᾱ, δ β, b 1 fitted. Quantity free fit with Baldin-Σ-rule exp. (global) Olmos de Leon 2001 ᾱ p 11.5 ± 2.4 stat 11.0 ± 1.4 stat ± 0.4 Σ 12.1 ± 1.2 stat,mod ± 0.4 Σ β p 3.4 ± 1.7 stat stat ± 0.4 Σ stat,mod ± 0.4 Σ Consistent with Baldin-Σ-rule ᾱ p + β p = 13.8 ± 0.4 for proton. Beane et al. 2002/03: no explicit = disagree as low as ω 80 MeV (LO) [120 MeV (NLO) ] esp. at large momentum-transfer. Model-indep. extraction of spin-independent, static proton dipole polarisabilities from all data 170 MeV. Polarisabilities, Soft γs & Light Ns INT, Grießhammer, CNS@GWU 6-1

9 2. Previous Successes, Old Worries & a Solution (a) Iso-scalar Nucleon Polarisabilities: Theory and Experiments 2003 Iso-scalar target = extract only iso-scalar polarisabilities ᾱ s = 1 2 (ᾱp + ᾱ n ), β s = 1 2 ( β p + β n ) Experiment ᾱ s [10 4 fm 3 ] β s [10 4 fm 3 ] npb scattering (1) : (Schmiedmayer et al. 1991) 12.2 ± 2.0 Baldin npb scattering (2) : (Koester et al. 1995) 6.0 ± 2.8 Baldin dγ npγ: (Rose et al. 1990) Baldin (Kolb et al. 2000) ?? 3.8 Baldin (Kossert et al. 2003) 12.3 ±[3...4] Baldin dγ dγ Urbana 1994: (Lucas et al.) ω = 49;69 MeV 12 Baldin Lund 2002: (Ludin et al.) ω = 55;66 MeV 11.2 ± 2.0 Baldin χeft prediction ᾱ s ᾱ p 11 β s β p 3 Lattice QCD (quenched) Lee/ Nucleon Baldin Sum Rule: ᾱ s + β s = 1 2π 2 dν σ(γn X) ν 2 = 14.5 ± 0.6 ν 0 Polarisabilities, Soft γs & Light Ns INT, Grießhammer, CNS@GWU 7-1

10 (b) Towards Polarisabilities from First Principles: Lattice QCD Pioneering: Quenched, chiral fermions Lee/Zhou/Wilcox/Christensen neutron ᾱ n neutron β n proton β p E Ongoing: spin-polarisabilities, unquenching, m π ց 200 MeV, larger volumes, Engelhardt (LHPC) fully dynamical vs. χeft with dyn. more statistics,... Lee/ , LHPC 2006-, _ Detmold/Tiburzi/Walker-Loud Polarisabilities, Soft γs & Light Ns INT, Grießhammer, CNS@GWU 8-1

11 (c) Iso-Vector Polarisabilities Hildebrandt/TRH/hg/Pasquini 2002/ th of iso-scalar polarisabilities in DR; zero in χdyn. at LO. Probes accuracy of data set of Dispersion Relations: Limits by neutron data. Re[α E1 ] Disp. Rel. Re[β M1 ] Polarisabilities, Soft γs & Light Ns INT, Grießhammer, CNS@GWU 9-1

12 (d) Dynamical Solves the SAL Puzzle hg/hildebrandt/hemmert/phillips 2004, hg/rph/trh 2005 Predictions taking proton polarisabilities.δ β Illinois, Lund, Saskatoon Nπ only Nπ + with proton values Clear -signature at backward angles. χeft captures angular dependence without altering static values: full dispersion. Before: SAL puzzle ᾱ s = ᾱp +ᾱ n 2 β s = β p + β n 2 Hornidge et al (exp): 8.8 ± 1.0 Baldin Levchuk/L vov 2000: 11 ± 2 7 ± 2 Beane/Malheiro/McGovern/Phillips/van Kolck 2003 (NLO HBχPT): 13.0 ± ± Polarisabilities, Soft γs & Light Ns INT, Grießhammer, CNS@GWU 10-1

13 (e) The Problem With Deuteron Compton Scattering at Lower Energies naïve = Thomson on proton correct Thomson on deuteron Low-Energy Theorem: Thomson limit A(ω = 0) = e2 M d ε ε. Friar 1975: Thomson limit current conservation gauge invariance. χeft must give that automatically. Straight-forward for EFT(/π), 1-nucleon sector. Arenhövel 1980: NN phenomenology clear. = Back to basics. Polarisabilities, Soft γs & Light Ns INT, Grießhammer, CNS@GWU 11-1

14 (f) Messages for the Chiral Power-Counting Weinberg 1991, van Kolck 1992-; cf. hg forthcoming Only phenomenological input: Non-relativistic system with shallow (real/virtual) bound-state. k T NN (E p2,k 2 M ) Q 1 k p p = V NN + q V NN Q 1 Power-Counting: Q m Q m Q 2m+3 2! = Q m = m = 1 Examples: NRQCD/NRQED EFT(/π) χeft Coulomb A 0, p A A 0, p A v 1 C 0 Q 1 + g2 A σ 1 q σ 2 q 4fπ 2 τ 1 τ 2 q 2 + m 2 Q 1 π T NN non-perturbative only in bound-state dynamics: E Q2 M Polarisabilities, Soft γs & Light Ns INT, Grießhammer, CNS@GWU 12-1

15 (f) Messages for the Chiral Power-Counting Weinberg 1991, van Kolck 1992-; cf. hg forthcoming Only phenomenological input: Non-relativistic system with shallow (real/virtual) bound-state. k T NN (E p2,k 2 M ) Q 1 k p p = V NN + q V NN Q 1 Power-Counting: Q m Q m Q 2m+3 2! = Q m = m = 1 Examples: NRQCD/NRQED EFT(/π) χeft Coulomb A 0, p A A 0, p A v 1 C 0 Q 1 + g2 A σ 1 q σ 2 q 4fπ 2 τ 1 τ 2 q 2 + m 2 Q 1 π T NN non-perturbative only in bound-state dynamics: E Q2 M E m π T NN (E Q) Q 0 E m π Nstatic = perturbative, 2 orders down cf. soft photons/gluons in NRQED/NRQCD Polarisabilities, Soft γs & Light Ns INT, Grießhammer, CNS@GWU 12-2

16 (g) Deuteron Compton Scattering at ω = MeV Hildebrandt/hg/Hemmert 2005, hg 2006 One-body: electric, magnetic moment couplings ω Q2 M 20 MeV partial waves α s E1,β s M1 T NN LO Q 1 LO Q 1 Full LO T NN pivotal for d Thomson at LO. Arenhövel 1980 Iso-scalar polarisabilities N 3 LO χeft pion-exchange currents: Beane et al ; hg/ NLO NLO part. waves Full LO T NN pivotal for total zero NLO contrib. to LET. Arenhövel 1980 Polarisabilities, Soft γs & Light Ns INT, Grießhammer, CNS@GWU 13-1

17 (g) Deuteron Compton Scattering at ω = MeV Hildebrandt/hg/Hemmert 2005, hg 2006 One-body: electric, magnetic moment couplings ω Q2 M 20 MeV ω Q 100 MeV partial waves LO Q 1 LO Q 1 ց NLO, N 3 LO T NN Full LO T NN pivotal for d Thomson at LO. Arenhövel 1980 ց N 3 LO, perturbative α s E1,β s M1 Iso-scalar polarisabilities N 3 LO ր NLO χeft pion-exchange currents: Beane et al ; hg/ NLO NLO NLO ց N 2 LO part. waves Full LO T NN pivotal for total zero NLO contrib. to LET. Arenhövel 1980 ց N 3 LO, pert. Polarisabilities, Soft γs & Light Ns INT, Grießhammer, CNS@GWU 13-2

18 (h) The Consequences of NN-Rescattering Off-shell T NN by Green s function method Arenhövel/Weyrauch 1980/83, Karakowski/Miller 1999, Levchuk/L vov 2000 = Thomson limit built-in order-by-order. A(ω = 0) = e2 M N ε ε A(ω = 0) = e2 M d ε ε : without T NN (old) : with T NN (new) predicted Thomson Polarisabilities, Soft γs & Light Ns INT, Grießhammer, CNS@GWU 14-1

19 (h) The Consequences of NN-Rescattering Off-shell T NN by Green s function method Arenhövel/Weyrauch 1980/83, Karakowski/Miller 1999, Levchuk/L vov 2000 = Thomson limit built-in order-by-order. A(ω = 0) = e2 M N ε ε Statistically significant only for ω 70 MeV. Included higher-order diagrams indeed small. A(ω = 0) = e2 M d ε ε : without T NN (old) : with T NN (new) predicted Thomson Polarisabilities, Soft γs & Light Ns INT, Grießhammer, CNS@GWU 14-2

20 (h) The Consequences of NN-Rescattering Eliminate Dependence on Deuteron Wave-function also at high ω, for ω 0 clear from Thomson. Illinois, Lund, Saskatoon NNLO χpt AV18 CD-Bonn Nijmegen 93 without T NN with T NN without T NN with T NN Polarisabilities, Soft γs & Light Ns INT, Grießhammer, CNS@GWU 15-1

21 (h) The Consequences of NN-Rescattering Dependence of T NN on NN-potential = short-distance, for ω 0 clear from Thomson. Illinois, Lund, Saskatoon LO χeft AV18 LO χeft-potential: + C 0,P Q 1 Consistent for Compton at NLO: O(Q 0 )-correction of NN-potential presumed zero. AV18 provides < 3% corrections = suggests higher-order indeed Q 1 ( ) Polarisabilities, Soft γs & Light Ns INT, Grießhammer, CNS@GWU 16-1

22 (i) Building Confidence: Partial Waves, Photon Multipoles, Optical Theorem J C 3 partial waves T NN Multipolarity of Photon Fields saturated result: L,L 2 L = L = 1 only 10% at SAL energies, for- & backward angles Polarisabilities, Soft γs & Light Ns INT, Grießhammer, CNS@GWU 17-1

23 (i) Building Confidence: Partial Waves, Photon Multipoles, Optical Theorem J C 3 partial waves T NN Optical Theorem relates rescattering to dγ np: σ tot (ω) = 1 6ω Im[M fi (θ = 0)] i=f Agrees with Arenhövel, Partovi, Karakowski/Miller to better than 1%. Polarisabilities, Soft γs & Light Ns INT, Grießhammer, CNS@GWU 17-2

24 (j) Determine Neutron Polarisabilities hg/hemmert/hildebrandt/phillips: 2004; hg/rph/trh 2005 δᾱ, δ β fit independently to all elastic data. Illinois, Lund, Saskatoon Nπ + + stat. error unconstrained: ᾱ s = 11.5 ± 1.3 stat β s = 3.4 ± 1.5 stat Consistent with iso-scalar Baldin Sum-Rule ᾱ s + β s = 14.5 ± 0.6 Polarisabilities, Soft γs & Light Ns INT, Grießhammer, CNS@GWU 18-1

25 (j) Determine Neutron Polarisabilities hg/hemmert/hildebrandt/phillips: 2004; hg/rph/trh 2005 Constrain fit of δᾱ, δ β to all elastic data: iso-scalar Baldin Sum-Rule ᾱ s + β s = 14.5 ± 0.6 Illinois, Lund, Saskatoon Nπ + + stat. error constrained: ᾱ s = 11.3 ± 0.7 stat ± 0.6 Σ ±1 theory β s = stat ± 0.6 Σ ±1 theory Proton hg/ : ᾱ p = 11.0 ± 1.4 stat ± 0.4 Σ ± 1 theory β p = stat ± 0.4 Σ ± 1 theory no T NN hg/ : ᾱ s = 12.6 ± 0.8 stat ± 0.6 Σ ± 1.1 wavefu β s = stat ± 0.6 Σ ± 0.1 wavefu estimate theory uncertainty ( ±1): higher-order 1N; AV18 vs. LO χeft, d wave-fu., with vs. without T NN. = neutron proton polarisabilities Polarisabilities, Soft γs & Light Ns INT, Grießhammer, CNS@GWU 18-2

26 (a) Reminder: Leading Dynamical Polarisabilities Response of spin-degrees of freedom in nucleon to real photon of definite multipolarity and non-zero energy ω. 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 spin-indep dipole [ γ E1E1 (ω) σ ( E E) + γ M1M1 (ω) σ ( B B) pure spin-dep dipole 2 γ M1E2 (ω) σ i B j E ij + 2 γ E1M2 (ω) σ i E j B ij ] } N mixed spin-dep 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, Soft γs & Light Ns INT, Grießhammer, CNS@GWU 19-1

27 (b) Iso-Scalar Spin-Dependent Dynamical Polarisabilities Predicted in χeft: No N-core contributions = no free parameters. Spin-physics dominated by pion-cloud + (γ M1M1, γ M1E2 ). Re[γ E1E1 ] Re[γ M1M1 ] Pure polarisabilities γ E1E1, γ M1M1 quite good. Disp. Rel. Nπ Nπ +. Re[γ E1M2 ] Re[γ M1E2 ] Mixed polarisabilities γ E1M2,γ M1E2 small. Uncertainties in DR? Static values (proton vs. iso-scalar) χeft iso-scalar DR iso-scalar MAMI proton LEGS proton γ 0 = (γ E1E1 +γ M1M1 +γ E1M2 +γ M1E2 ) γ π (π pole) = γ E1E1 +γ M1M1 γ E1M2 +γ M1E Polarisabilities, Soft γs & Light Ns INT, Grießhammer, CNS@GWU 20-1

28 (c) Spin-Polarisabilities from Circularly Polarised Compton hg/trh/hildebrandt 2003 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 = clear γ i -dep. no l 2 = higher pols negligible proton neutron Also good signal for linear polarisations. Extraction from 2 H/ 3 He needs model-independent subtraction of binding & exchange currents. Polarisabilities, Soft γs & Light Ns INT, Grießhammer, CNS@GWU 21-1

29 (d) Starting on Deuteron Asymmetries Choudhuri/Phillips 2005, Choudhury/hg 2008 x Circularly polarised γ on vector-polarised d, ω lab = 120 MeV O(Q 3 ) + Rescat. O(ε 3 ) + Rescat O(Q 3 ) + Rescat. O(ε 3 ) + Rescat. Σ x O(Q 3 ) + Rescat. O(ε 3 ) + Rescat O(Q 3 ) + Rescat. O(ε 3 ) + Rescat. z 0-10 Σ z CM Angle (deg) CM Angle (deg) More pronounced by explicit (1232) Σ x sensitive to neutron-γ E1E1,γ M1M1 Σ z in-sensitive to γs Polarisabilities, Soft γs & Light Ns INT, Grießhammer, CNS@GWU 22-1

30 (d) Starting on Deuteron Asymmetries Choudhuri/Phillips 2005, Choudhury/hg 2008 Circularly polarised γ on vector-polarised d, ω lab = 120 MeV γ E1E1 (x10-4 fm 4 ) varying γ E1M2 (x10-4 fm 4 ) varying 0 γ E1E1 =2 γ E1E1 =0 γ E1E1 =-2 0 γ E1M2 =2 γ E1M2 =0 γ E1M2 =-2 x γ M1M1 (x10-4 fm 4 ) varying γ M1E2 (x10-4 fm 4 ) varying x γ M1M1 =2 γ M1M1 =0 γ M1M1 = CM Angle (deg) γ M1E2 =2 γ M1E2 =0 γ M1E2 = CM Angle (deg) More pronounced by explicit (1232) Σ x sensitive to neutron-γ E1E1,γ M1M1 Σ z in-sensitive to γs Polarisabilities, Soft γs & Light Ns INT, Grießhammer, CNS@GWU 22-2

31 (d) Starting on Deuteron Asymmetries Choudhuri/Phillips 2005, Choudhury/hg 2008 Circularly polarised γ on vector-polarised d, ω lab = 120 MeV Σ z Σ z γ E1E1 (x10-4 fm 4 ) varying γ E1E1 =2 γ E1E1 =0 γ E1E1 = γ M1M1 (x10-4 fm 4 ) varying γ M1M1 =2 γ M1M1 =0 γ M1M1 = CM Angle (deg) γ E1M2 (x10-4 fm 4 ) varying γ E1M2 =2 γ E1M2 =0 γ E1M2 = γ M1E2 (x10-4 fm 4 ) varying γ M1E2 =2 γ M1E2 =0 γ M1E2 = CM Angle (deg) More pronounced by explicit (1232) Σ x sensitive to neutron-γ E1E1,γ M1M1 Σ z in-sensitive to γs Polarisabilities, Soft γs & Light Ns INT, Grießhammer, CNS@GWU 22-3

32 (e) 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 Assumptions: α E1 (ω), β M1 (ω) well captured, only two spin-polarisabilities γ E1E1 (ω), γ M1M1 (ω) large; superficial fit to existing data. = precision experiments on p, d, 3 He: TUNL/HIγS, MAMI, MAXLab, S-DALINAC, LARA,... Polarisabilities, Soft γs & Light Ns INT, Grießhammer, CNS@GWU 23-1

33 4. Concluding Questions Dynamical polarisabilities by multipole-decomposition of real Compton scattering at fixed energy. Propose polarised and un-polarised precision experiments at given ω and varying angle: extract ω-dependence of dynamical spin-polarisabilities: 6 parameters α E1 (ω), β M1 (ω), γ i (ω) at given ω. χeft predicts strong dispersive effects at ω 70 MeV: resonance and 1-π-production threshold not captured by static + slope at ω = 0 Polarisabilities from all Compton data below 200 MeV: ᾱ p = 11.0 ± 1.4 stat ± 0.4 Σ ± 1 theory ᾱ n = 11.6 ± 1.0 stat ± 0.6 Σ ± 1 theory β p = stat ± 0.4 Σ ± 1 theory β n = stat ± 0.6 Σ ± 1 theory The Future: Experiment: Call for data answered by MAXlab, HIγS,?? precision experiments on p, d, 3 H, 3 He polarised = spin-polarisabilities. Theory: N 2 LO, resonance region: -resummation; Short-distance origin of C.T.s δᾱ, δ β. Test your model and your equipment! Polarisabilities, Soft γs & Light Ns INT, Grießhammer, CNS@GWU 24-1

34 4. Concluding Questions Dynamical polarisabilities by multipole-decomposition of real Compton scattering at fixed energy. Propose polarised and un-polarised precision experiments at given ω and varying angle: extract ω-dependence of dynamical spin-polarisabilities: 6 parameters α E1 (ω), β M1 (ω), γ i (ω) at given ω. χeft predicts strong dispersive effects at ω 70 MeV: resonance and 1-π-production threshold not captured by static + slope at ω = 0 Polarisabilities from all Compton data below 200 MeV: ᾱ p = 11.0 ± 1.4 stat ± 0.4 Σ ± 1 theory ᾱ n = 11.6 ± 1.0 stat ± 0.6 Σ ± 1 theory β p = stat ± 0.4 Σ ± 1 theory β n = stat ± 0.6 Σ ± 1 theory The Future: Experiment: Call for data answered by MAXlab, HIγS,?? precision experiments on p, d, 3 H, 3 He polarised = spin-polarisabilities. Theory: Comprehensive Compton picture p, d, 3 H, 3 He d, 3 He: N 2 LO HBχPT ; beyond 1π threshold; breakup : N 2 LO (δ,ε), resonance resummation, N 2,3 -forces; best kinematics for spin-pols; Thomson in 3 He Gee-WhAM-collaboration George Washington-Athens-Manchester McGovern/Phillips/Shukla/hg Test your model and your equipment! Polarisabilities, Soft γs & Light Ns INT, Grießhammer, CNS@GWU 24-2

35 (a) What Jerry Will Measure: deuteron Compton scattering in the cm frame dσ dω cm [nbarn/sr] Polarisabilities, Soft γs & Light Ns INT, Grießhammer, CNS@GWU 25-1

36 (a) Extracting Dynamical Polarisabilities hg/trh 2002, Hildebrandt/hg/TRH/Pasquini 2003 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 k ˆ ) + i A 3 (ω,z) σ ( ε ε)+ i A 4 (ω,z) σ (ˆ k k) ˆ ( ε ε) [( + i A 5 (ω,z) σ ε k ˆ ) ( ε k ˆ ) ( ε k ˆ ) ( ε k ˆ )] [( + i A 6 (ω,z) σ ε k ˆ ) ( ε k ˆ ) ( ε k ˆ ) ( ε k ˆ )] (1) Choose frame of reference: centre of mass; θ = ( k, k ), z = cosθ. (2) Subtract nucleon pole terms in π 0 s-channel, u-channel, t-channel, : two-photon interaction with point-like spin- 1 2 = Structure-dependent part of Compton amplitude: nucleon of magnetic moment κ (Powell) + pion-pole term. Ā i (ω,cosθ) = A i (ω,cosθ) A pole i (ω,cosθ) Polarisabilities, Soft γs & Light Ns INT, Grießhammer, CNS@GWU 26-1

37 (a) Extracting Dynamical Polarisabilities hg/trh 2002, Hildebrandt/hg/TRH/Pasquini 2003 (3) Multipole decomposition into photon transitions Tl T l (T = E,M) at fixed energy ω: static: α E1 (ω = 0) = 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, Soft γs & Light Ns INT, Grießhammer, CNS@GWU 26-2

38 (b) Real, Virtual, Dynamical, Generalised, Static: Who is Who Virtual Compton Scattering: Q 2 > 0, ω = 0 = Q 2 = q 2 Generalised Polarisabilities spatial resolution of internal d.o.f. s (?) Where? most experiments q µ = (ω, q) Static Polarisabilities ᾱ p = fm 3 β p = fm 3 but from where? ω Real Compton Scattering: Q 2 = 0, ω > 0 = Dynamical Polarisabilities temporal resolution/response of internal d.o.f. s Which? Neutron: not so well known spin-polarisabilities and higher multipoles unknown Polarisabilities, Soft γs & Light Ns INT, Grießhammer, CNS@GWU 27-1

39 (c) The NLO HBχPT-Hypothesis Bernard/Kaiser/Meißner/Schmidt: Phys. Lett. B319 (1993), 269 and Z. Phys. A348 (1993), 317: Aspects of Nucleon Compton Scattering (Citations) ᾱ p,n, β ) p,n = # (c p,n 2 #p,n g 2 A M N ln m π λ + δ(ᾱ, β) p,n (λ) from,, C.T. etc. We are not in that fortunate position but [... ] must resort to the resonance saturation hypothesis to estimate [... ] the constants [... ] at the scale λ equal to some resonance scale. [... ] there is some spurious sensitivity on the value of λ as shown in Fig. 6. While the neutron polarizabilities are quite insensitive to the choice of λ, the much larger coefficients [... ] induce some scale dependence for the proton case. Since most of the counterterms are in fact given by exchange, we have chosen λ = M [= 1232 MeV] (which gives our best values). L (2) L (2) The main sources of uncertainty stem from the choice of the values for g A, the scale λ and the kaon and contributions to the various low-energy constants. Adding these in quadrature leads to ᾱ p E1 = 10.5 ± 2.0, ᾱn E1 = 13.4 ± 1.5, p β M1 = 3.5 ± 3.6, β M1 n = 7.8 ± 3.6 [... ] Notice also that at present the theoretical uncertainties are larger than the experimental ones. Polarisabilities, Soft γs & Light Ns INT, Grießhammer, CNS@GWU 28-1

40 (d) Determining Static Proton Polarisabilities from Data hg/hildebrandt/hemmert EJPA20, 329 Dispersion Relations MAMI, Moscow, Illinois ; Saskatoon Nπ and : δᾱ, δ β, b 1 fitted. Quantity free fit α δᾱ E1 5.4 ± 2.4 stat naïvely NLO: δα E1, δβ M1 δ β Λ 2 χ M 1 M ± 1.7 stat Large nucleon-core contributions. Polarisabilities, Soft γs & Light Ns INT, Grießhammer, CNS@GWU 29-1

41 (e) Spin-Averaged Compton Scattering on Proton Target Recall dependence on Dispersion Relations Nπ only Nπ + sensitivity to -physics Polarisabilities, Soft γs & Light Ns INT, Grießhammer, CNS@GWU 30-1

42 (e) Spin-Averaged Compton Scattering on Proton Target Dependence on spin- and higher polarisabilities Nπ + full no spin-pols γ i no quadrupole pols clear γ i -dep. higher pols negligible = Dynamics by fitting 6 free functions α E1 (ω), β M1 (ω), γ i (ω) to precise data at fixed ω, varying angle? But: only linear combinations seen in un-polarised exp. Polarisabilities, Soft γs & Light Ns INT, Grießhammer, CNS@GWU 30-2

43 (f) Spin-Averaged Compton Scattering on Free Neutron Target Dependence on -physics Nπ + no not sensitive to -physics below 130 MeV Polarisabilities, Soft γs & Light Ns INT, Grießhammer, CNS@GWU 31-1

44 (f) Spin-Averaged Compton Scattering on Free Neutron Target Spin- and higher polarisabilities Nπ + (full) no γ i s no l 2 clear γ i -dep. higher pols negligible Polarisabilities, Soft γs & Light Ns INT, Grießhammer, CNS@GWU 31-2

45 (g) Asymmetries in Circularly Polarised Compton Scattering hg/t.r.h./hildebrandt 2003/04 Incoming nucleon & photon polarised, sum over final states. Kinematics: cm frame; right-handed, circularly polarised photon; nucleon-spin in reaction plane ( k, k ) vs. : Nucleon spin parallel vs. anti-parallel to k vs. : Nucleon spin perpendicular to k Observables: D z = 1 2 ( dσ dω dσ ) dω Σ z = T 2 T 2 T 2 + T 2 D x = 1 2 ( dσ dω dσ ) dω Σ x = T 2 T 2 T 2 + T 2 Extraction of neutron pols from 3 He? (proposal H. Gao, TUNL/HIGS) Polarisabilities, Soft γs & Light Ns INT, Grießhammer, CNS@GWU 32-1

46 (g) Asymmetries in Circularly Polarised Compton Scattering hg/t.r.h./hildebrandt 2003/04 Proton Spin Asymmetry Σ z = : Born term and -physics + Born SSE no dominated by Born term insensitive to -physics Polarisabilities, Soft γs & Light Ns INT, Grießhammer, CNS@GWU 32-2

47 (g) Asymmetries in Circularly Polarised Compton Scattering hg/t.r.h./hildebrandt 2003/04 Proton Spin Asymmetry Σ z = : Spin and higher order polarisabilities + full SSE no γ i s no l 2 γ i -dep. small higher pols negligible Polarisabilities, Soft γs & Light Ns INT, Grießhammer, CNS@GWU 32-3

48 (g) Asymmetries in Circularly Polarised Compton Scattering hg/t.r.h./hildebrandt 2003/04 Proton Spin Asymmetry D z = : Spin and higher order polarisabilities full SSE no γ i s no l 2 Polarisabilities, Soft γs & Light Ns INT, Grießhammer, CNS@GWU 32-4

49 (g) Asymmetries in Circularly Polarised Compton Scattering hg/t.r.h./hildebrandt 2003/04 Proton Spin Asymmetry Σ x = : Born term and -physics + Born SSE no sensitive to -physics Polarisabilities, Soft γs & Light Ns INT, Grießhammer, CNS@GWU 32-5

50 (g) Asymmetries in Circularly Polarised Compton Scattering hg/t.r.h./hildebrandt 2003/04 Proton Spin Asymmetry Σ x = : Spin and higher order polarisabilities + full SSE no γ i s no l 2 clear γ i -dep. higher pols negligible Polarisabilities, Soft γs & Light Ns INT, Grießhammer, CNS@GWU 32-6

51 (g) Asymmetries in Circularly Polarised Compton Scattering hg/t.r.h./hildebrandt 2003/04 Proton Spin Asymmetry D x = : Spin and higher order polarisabilities full SSE no γ i s no l 2 stronger γ i - dep. Polarisabilities, Soft γs & Light Ns INT, Grießhammer, CNS@GWU 32-7

52 (g) Asymmetries in Circularly Polarised Compton Scattering hg/t.r.h./hildebrandt 2003/04 Neutron Spin Asymmetry Σ z = : Born term and -physics + Born SSE no dominated by structure term (uncharged!) sensitive to -physics Polarisabilities, Soft γs & Light Ns INT, Grießhammer, CNS@GWU 32-8

53 (g) Asymmetries in Circularly Polarised Compton Scattering hg/t.r.h./hildebrandt 2003/04 Neutron Spin Asymmetry Σ z = : Spin and higher order polarisabilities + full SSE no γ i s no l 2 γ i -dep. higher pols negligible Polarisabilities, Soft γs & Light Ns INT, Grießhammer, CNS@GWU 32-9

54 (g) Asymmetries in Circularly Polarised Compton Scattering hg/t.r.h./hildebrandt 2003/04 Neutron Spin Asymmetry D z = : Spin and higher order polarisabilities full SSE no γ i s no l 2 Polarisabilities, Soft γs & Light Ns INT, Grießhammer, CNS@GWU 32-10

55 (g) Asymmetries in Circularly Polarised Compton Scattering hg/t.r.h./hildebrandt 2003/04 Neutron Spin Asymmetry Σ x = : Born term and -physics + Born SSE no dominated by structure term (uncharged!) sensitive to -physics Polarisabilities, Soft γs & Light Ns INT, Grießhammer, CNS@GWU 32-11

56 (g) Asymmetries in Circularly Polarised Compton Scattering hg/t.r.h./hildebrandt 2003/04 Neutron Spin Asymmetry Σ x = : Spin and higher order polarisabilities + full SSE no γ i s no l 2 strong γ i -dep. higher pols negligible Extraction from deuteron/ 3 He needs model-independent subtraction of binding effects & exchange currents. Polarisabilities, Soft γs & Light Ns INT, Grießhammer, CNS@GWU 32-12

57 (g) Asymmetries in Circularly Polarised Compton Scattering hg/t.r.h./hildebrandt 2003/04 Neutron Spin Asymmetry D x = : Spin and higher order polarisabilities full SSE no γ i s no l 2 stronger γ i - dep. Polarisabilities, Soft γs & Light Ns INT, Grießhammer, CNS@GWU 32-13

58 (h) Asymmetries in Linearly Polarised Compton Scattering hg/t.r.h./hildebrandt 2003/04 Incoming nucleon & photon polarised, sum over final states. Kinematics: cm frame; linearly polarised photon; nucleon-spin N-spin k vs. : Photon polarisation parallel vs. perpendicular to nucleon spin Observables: T 2 T 2 T 2 + T 2 Extraction of neutron pols from 3 He? (proposal H. Gao, TUNL/HIGS) Polarisabilities, Soft γs & Light Ns INT, Grießhammer, CNS@GWU 33-1

59 (h) Asymmetries in Linearly Polarised Compton Scattering hg/t.r.h./hildebrandt 2003/04 Spin Asymmetry : Spin and higher order polarisabilities + proton full SSE no γ i s no l 2 γ i -dep. small higher pols negligible neutron Polarisabilities, Soft γs & Light Ns INT, Grießhammer, CNS@GWU 33-2

60 (i) The SAL Puzzle hg/hemmert/hildebrandt/phillips 2004 All low-ω Compton, dγ npγ consistent with ᾱ s ᾱ p ᾱ n, β s β p β n. Rose/..., Kolb/..., Kossert/..., Urbana Conflicting analyses of SAL data ω = [ MeV]. 30 E γ =50 MeV 30 E γ =94.2 MeV dσ/dω γ (nb/sr) dσ/dω γ (nb/sr) Θ γ (deg) Θ γ (deg) ᾱ s = ᾱp +ᾱ n 2 β s = β p + β n 2 Hornidge et al (exp): 8.8 ± 1.0 Baldin Levchuk/L vov 2000: 11 ± 2 7 ± 2 Beane/Malheiro/McGovern/Phillips/van Kolck 2003 (NLO HBχPT): 13.0 ± ± Polarisabilities, Soft γs & Light Ns INT, Grießhammer, CNS@GWU 34-1