High-Accuracy Analysis of Compton Scattering in Chiral EFT: Status and Future H. W. Grießhammer INS Institute for Nuclear Studies Institute for Nuclear Studies The George Washington University, DC, USA Two-Photon Response Explores Low-Energy Dynamics 1 Polarisabilities from Compton Scattering 2 a a The Future: Per Aspera Ad Astra 3 Concluding Questions 4 How do constituents of the nucleon react to external fields? How to reliably extract neutron and spin polarisabilities? Comprehensive Theory Effort: hg, J. A. McGovern (Manchester), D. R. Phillips (Ohio U): Eur. Phys. J. A49 (2013), 12 (proton) + G. Feldman (GW): Prog. Part. Nucl. Phys. 67 (2012) 841 neutron in C OMPTON @MAX-lab: Phys. Rev. Lett. 113 (2014) 262506 [1409.3705 [nucl-ex]] & subm. to PRC [1503.08094 [nucl-ex]] Polarisabilities, GHP Baltimore (18+2)’, 10.04.2015 Grießhammer, INS@GWU 0-1
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 1900/1905 � � � � � m , q E in ( ω ) � � d ind ( ω ) = q 2 1 � � E in ( ω ) 0 − ω 2 − i Γ ω ω 2 ω 0 , Γ m � �� � = : 4 π α E 1 ( ω ) � � E 2 + β M 1 ( ω ) � α E 1 ( ω ) � B 2 L pol = 2 π + ... � �� � electric, magnetic scalar dipole “displaced volume” [ 10 − 3 fm 3 ] = ⇒ Clean, perturbative probe of ∆ ( 1232 ) properties, nucleon spin-constituents, χ iral symmetry of pion-cloud & its breaking (proton-neutron difference). – fundamental hadron property = ⇒ link to emergent lattice-QCD results Alexandru/Lee/. . . 2005-, Detmold/. . . 2006-, LHPC 2007-, Leinweber/. . . 2013 – β p M 1 in elmag. p-n mass split M p M 1 − β n γ − M n γ ≈ [ 1 . 1 ± 0 . 5 ] MeV – 2 γ contribution to Lamb shift in muonic H ( β M 1 ), proton radius π – dark-matter detection scenarios e.g. Appelquist/. . . 2014- Polarisabilities, GHP Baltimore (18+2)’, 10.04.2015 Grießhammer, INS@GWU 1-1
(b) Understanding Energy Dependence hg/Hildebrandt/Hemmert/Pasquini 2002/03 Polarisabilities : Energy-dependent Multipoles of real Compton scattering. � � E × ˙ B × ˙ E 2 + β M 1 ( ω ) � B 2 + γ E 1 E 1 ( ω ) � α E 1 ( ω ) � σ · ( � � σ · ( � � E )+ γ M 1 M 1 ( ω ) � 2 π B )+ ... Neither more nor less information about response of constituents, but more readily accessible. α E 1 ( ω ) : Pion cusp well captured by single- N π . β M 1 ( ω ) : para-magnetic N -to- ∆ M 1 -transition. Ω Π Ω � Ω Π Ω � 30 p data range p data range 30 25 d data range d data range 20 20 Re Im Re 10 15 Im 0 10 � 10 Β M1 � Ω � Α E1 � Ω � 5 � 20 0 0 50 100 150 200 250 300 0 50 100 150 200 250 300 + + + + + + + + + + + + + + + + _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ Re : refraction ; Im : absorption π + π + π − π + For ω �≪ m π more than “static + slope”! = ⇒ Need to understand dynamics! π + E Polarisabilities, GHP Baltimore (18+2)’, 10.04.2015 Grießhammer, INS@GWU 2-1
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 χ EFT ≡ low-energy QCD � D 2 � � 2 2 M + g A π π a π a + ··· + N † [ i D 0 + L χ EFT = ( D µ π a )( D µ π a ) − m 2 σ · � N † N � D π + ... ] N + C 0 + ... 2 f π Controlled approximation = ⇒ model-independent, error-estimate. −15 E [MeV] λ [fm=10 m] 0.2 p,n (940) ω,ρ (770) π M −M ∆ N 1 π (140) 2 H 5 0 8 � m π M ∆ − M N = p typ Expand in δ = Λ χ ≈ 1GeV ≈ ≪ 1 (numerical fact) Pascalutsa/Phillips 2002 . Λ χ Λ χ Polarisabilities, GHP Baltimore (18+2)’, 10.04.2015 Grießhammer, INS@GWU 3-1
Bernard/Kaiser/Meißner 1992-4, Butler/Savage/Springer 1992-3, Hemmert/. . . 1998 (b) All 1N Contributions to N 4 LO McGovern 2001, hg/Hemmert/Hildebrandt/Pasquini 2003 McGovern/Phillips/hg 2013 Unified Amplitude: gauge & RG invariant set of all contributions which are at least N 4 LO ( e 2 δ 4 ): accuracy δ 5 � 2% ; ω � m π in low régime ( e 2 δ 0 ): accuracy δ 2 � 20% . in high régime ω ∼ M ∆ − M N at least NLO or π 0 b 1 ( M 1 ) covariant with vertex NLO N 2 LO b 2 ( E 2 ) LO corrections = δα , δβ fit etc. etc. Unknowns: short-distance δα , δβ ⇐ ⇒ static α E 1 , β M 1 Polarisabilities, GHP Baltimore (18+2)’, 10.04.2015 Grießhammer, INS@GWU 4-1
McGovern/Phillips/hg 2013 (c) Nucleon Polarisabilities from a Consistent Database database: + Feldman PPNP 2012 250 400 250 250 35 25 25 25 20 20 20 30 b 200 200 200 300 15 15 15 25 20 10 150 10 150 10 150 200 5 5 5 15 100 100 100 10 0 0 0 40 60 80 100 120 140 160 40 60 80 100 120 140 160 40 60 80 100 120 140 160 40 60 80 100 120 140 160 100 50 50 50 Θ lab � 85° Θ lab � 110° Θ lab � 155° Θ lab � 45° 0 0 0 0 0 50 100 150 200 250 300 350 0 50 100 150 200 250 300 350 0 50 100 150 200 250 300 350 0 50 100 150 200 250 300 350 250 25 300 35 20 30 250 200 15 25 200 10 20 150 5 150 15 100 0 10 100 40 60 80 100 120 140 160 40 60 80 100 120 140 160 50 50 Θ lab � 60° Θ lab � 133° 0 0 0 50 100 150 200 250 300 350 0 50 100 150 200 250 300 350 Polarisabilities, GHP Baltimore (18+2)’, 10.04.2015 Grießhammer, INS@GWU 5-1
(d) Fit Discussion: Parameters and Uncertainties McGovern/Phillips/hg 2013 exp ( stat + sys ) 1 σ - error 5 B a l d i n Σ N2LO ( free ) r u 4 l e 1 σ -contours β M1 [ 10 - 4 fm 3 ] N2LO ( Baldin ) Consistent with Baldin Σ Rule ∞ 3 NLO ( Baldin ) � d ν σ ( γ p → X ) 1 α E 1 + β M 1 = 2 π 2 ν 2 ν 0 NLO ( free ) = 13 . 8 ± 0 . 4 Olmos de Leon 2001 2 need more forward data to constrain. LO ( no fit ) 1 9 10 11 12 13 α E1 [ 10 - 4 fm 3 ] Fit Stability: floating norms within exp. sys. uncertainties; vary dataset, b 1 , vertex dressing,. . . Residual Theoretical Uncertainty from convergence pattern: δ 2 ≈ 1 6 of LO → NLO change δ ( α − β ) = 3 . 5 E 1 [ 10 − 4 fm 3 ] M 1 [ 10 − 4 fm 3 ] α p β p χ 2 / d.o.f. N 2 LO Baldin constrained 10 . 65 ± 0 . 4 stat ± 0 . 2 Σ ± 0 . 3 theory 3 . 15 ∓ 0 . 4 stat ± 0 . 2 Σ ∓ 0 . 3 theory 113 . 2 / 135 α p E 1 + β p M 1 = 13 . 8 ± 0 . 4 Polarisabilities, GHP Baltimore (18+2)’, 10.04.2015 Grießhammer, INS@GWU 6-1
(e) Fit Discussion: Comparison McGovern/Phillips/hg 2013 exp � stat � sys � � theory � model 1 Σ� error in quadrature 6 Baldin � rule McG � DRP � hg free 5 Zieger � Pascalutsa � Lensky 2010 4 Β M1 � 10 � 4 fm 3 � 3 McG � DRP � hg PDG 2012 2 TAPS free 1 OdeL global 0 Grießhammer 2013 7 8 9 10 11 12 13 14 Α E1 � 10 � 4 fm 3 � McGovern/Lensky 2014: covariant χ EFT gives same results. Polarisabilities, GHP Baltimore (18+2)’, 10.04.2015 Grießhammer, INS@GWU 7-1
(e) Fit Discussion: Comparison McGovern/Phillips/hg 2013 exp � stat � sys � � theory � model 1 Σ� error in quadrature 6 Baldin � rule McG � DRP � hg free 5 Zieger � Pascalutsa � Lensky 2010 4 Β M1 � 10 � 4 fm 3 � 3 McG � DRP � hg PDG 2012 2 PDG 2013 TAPS free 1 OdeL global 0 Grießhammer 2013 7 8 9 10 11 12 13 14 Α E1 � 10 � 4 fm 3 � McGovern/Lensky 2014: covariant χ EFT gives same results. Polarisabilities, GHP Baltimore (18+2)’, 10.04.2015 Grießhammer, INS@GWU 7-2
(f) Creating a Consistent Proton Compton Database hg/McGovern/Phillips/Feldman PPNP 2012 300 250 250 200 Θ lab � 75 200 Θ lab � 35 200 Θ lab � 65 150 150 150 100 100 100 50 50 50 0 0 0 50 100 150 200 250 300 350 50 100 150 200 250 300 350 50 100 150 200 250 300 350 250 200 Θ lab � 105 200 Θ lab � 90 200 Θ lab � 115 150 150 150 100 100 100 50 50 50 0 0 0 50 100 150 200 250 300 350 50 100 150 200 250 300 350 50 100 150 200 250 300 350 250 250 200 Θ lab � 125 200 Θ lab � 135 ∼ 300 data, mostly 1991-2001 150 150 100 100 New effort for better data: 50 50 MAMI, MAXlab, HI γ S,. . . 0 0 50 100 150 200 250 300 350 50 100 150 200 250 300 350 Gaps: ω ∈ [ 160;250 ] MeV ; θ → 0 ◦ : Baldin check; θ → 180 ◦ for ∆ ( 1232 ) ! χ 2 Quoted stat+sys too small for quoted fluctuations; tensions MAMI vs. LEGS; etc. = ⇒ d . o . f . ≈ 1 needs pruning . Not more , but more reliable data needed for unpolarised proton. Polarisabilities, GHP Baltimore (18+2)’, 10.04.2015 Grießhammer, INS@GWU 8-1
(g) Neutron Polarisabilities and Nuclear Binding hg/. . . / + Phillips/ + McGovern 2004-2014 Need model-independent, systematic subtraction of binding effects. = ⇒ χ EFT: reliable uncertainties. – Nucleon structure: averaged neutron & proton polarisabilities: χ EFT, Disp. Rel.: p-n difference is small hg/Pasquini/. . . 2005 S NN ∑ – Parameter-free one-nucleon contributions: partial waves – Parameter-free charged meson-exchange currents dictated in χ EFT by gauge & chiral symmetry: + π − Test charged-pion component of NN force. Rescattering pivotal for Thomson limit A ( ω = 0 ) = − e 2 ǫ ′ . � ǫ · � π M d = ⇒ tiny dep. on d wave fu. & NN pot. Polarisabilities, GHP Baltimore (18+2)’, 10.04.2015 Grießhammer, INS@GWU 9-1
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