Nuclear structure and the proton radius puzzle

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Nuclear structure and the proton radius puzzle Nir Nevo Dinur 1,2 Chen Ji 2,3, Javier Hernandez 2,5, Sonia Bacca 2,4, Nir Barnea 1 1 The Hebrew University of Jerusalem, Israel 2 TRIUMF, Vancouver,

1 Nuclear structure and the proton radius puzzle Nir Nevo Dinur 1,2 Chen Ji 2,3, Javier Hernandez 2,5, Sonia Bacca 2,4, Nir Barnea 1 1 The Hebrew University of Jerusalem, Israel 2 TRIUMF, Vancouver, BC, Canada 3 ECT* and INFN-TIFPA, Trento, Italy 4 University of Manitoba, Winnipeg, Canada 5 University of British Columbia, BC, Canada INT May 5th 2016 Nir Nevo Dinur (TRIUMF) Nuclear structure and the proton radius puzzle 1 / 47

2 Outline Introduction The proton radius puzzle Lamb shift, charge radius & nuclear structure Calculation details Results µd µ 4 He + µ 3 He + µ 3 H Uncertainty estimates Summary Outlook Nir Nevo Dinur (TRIUMF) Nuclear structure and the proton radius puzzle 2 / 47

3 The proton radius puzzle How big is the proton? R. CREMA Nir Nevo Dinur (TRIUMF) Nuclear structure and the proton radius puzzle 3 / 47

4 Origins of the discrepancy? What is the source of the discrepancy? µh experiment / theory? eh spectroscopy? ep scattering? overlooked/underestimated effects? (e.g., exotic hadron structure) beyond standard model? (extra dimensions, quantum gravity, new force-carriers,... ) Nir Nevo Dinur (TRIUMF) Nuclear structure and the proton radius puzzle 4 / 47

5 Origins of the discrepancy? Problem with µh experiment / theory? Nir Nevo Dinur (TRIUMF) Nuclear structure and the proton radius puzzle 4 / 47

6 Origins of the discrepancy? Problem with µh experiment / theory? probably not Nir Nevo Dinur (TRIUMF) Nuclear structure and the proton radius puzzle 4 / 47

7 Problem with eh spectroscopy? Origins of the discrepancy? Pohl et al., Annu. Rev. Nucl. Part. Sci. (2013) Nir Nevo Dinur (TRIUMF) Nuclear structure and the proton radius puzzle 4 / 47

8 Problem with eh spectroscopy? possible Origins of the discrepancy? Pohl et al., Annu. Rev. Nucl. Part. Sci. (2013) Nir Nevo Dinur (TRIUMF) Nuclear structure and the proton radius puzzle 4 / 47

9 Origins of the discrepancy? Problem(s) with ep scattering? G p E (Q2 ) = r2 p Q r 2 p 6dGp E (Q2 ) dq 2 Q 2 =0 Problem with measurements? Q 2 not small enough? Problem with fits? extrapolation to Q 2 = 0 depends on fit various groups obtain contradicting results Nir Nevo Dinur (TRIUMF) Nuclear structure and the proton radius puzzle 4 / 47

10 Origins of the discrepancy? Problem(s) with ep scattering? possible G p E (Q2 ) = r2 p Q r 2 p 6dGp E (Q2 ) dq 2 Q 2 =0 Problem with measurements? Q 2 not small enough? Problem with fits? extrapolation to Q 2 = 0 depends on fit various groups obtain contradicting results Nir Nevo Dinur (TRIUMF) Nuclear structure and the proton radius puzzle 4 / 47

11 Origins of the discrepancy? What is the source of the discrepancy? µh experiment / theory? probably not eh spectroscopy? possible ep scattering? possible overlooked/underestimated effects? Birse & McGovern, EPJA 12 vs. Miller, PLB 13 Hill & Paz, PRD 10; PRL 11 & Jentschura PRA 13 beyond standard model? new force carriers, address also (g 2) µ puzzle Tucker-Smith & Yavin, PRD 11; Batell, McKeen & Pospelov, PRL 11; Carlson & Rislow, PRD 12; PRD 14;... Nir Nevo Dinur (TRIUMF) Nuclear structure and the proton radius puzzle 4 / 47

Origins of the discrepancy? What is the source of the discrepancy? µh experiment / theory? probably not eh spectroscopy? possible ep scattering? possible overlooked/underestimated effects?

12 Origins of the discrepancy? What is the source of the discrepancy? µh experiment / theory? probably not eh spectroscopy? possible ep scattering? possible overlooked/underestimated effects? possible Birse & McGovern, EPJA 12 vs. Miller, PLB 13 Hill & Paz, PRD 10; PRL 11 & Jentschura PRA 13 beyond standard model? possible (very constrained) new force carriers, address also (g 2) µ puzzle Tucker-Smith & Yavin, PRD 11; Batell, McKeen & Pospelov, PRL 11; Carlson & Rislow, PRD 12; PRD 14;... Nir Nevo Dinur (TRIUMF) Nuclear structure and the proton radius puzzle 4 / 47

13 Tucker-Smith & Yavin s prediction for µ 4 He + Nir Nevo Dinur (TRIUMF) Nuclear structure and the proton radius puzzle 5 / 47

14 Origins of the discrepancy? - more data! New scattering experiments to shed light on the puzzle JLab (windowless target) & MAMI (initial state radiation) ep scattering for Q GeV 2 (in progress) MUSE collaboration at PSI µ ± p (& e ± p) scattering experiment (in development) MAMI electron-deuteron experiment e d scattering (data taken) JLab 3 He & 3 H form factors extract 3 He 3 H charge radii difference (planned) Nir Nevo Dinur (TRIUMF) Nuclear structure and the proton radius puzzle 6 / 47

15 Origins of the discrepancy? - more data! New H-spectroscopy experiments to shed light on the puzzle York Univ. (Toronto) 2S-2P Ordinary Lamb shift aim at 0.6% accuracy for r p MPQ (Garching) 2S-4P Ordinary transitions (+ 1S-2S) aim at 2% accuracy for r p NPL (UK) 2S-nS,D Ordinary transitions (+ 1S-2S) LKB (Paris) & MPQ (Garching) 1S-3S Ordinary transitions (+ 1S-2S) two different methods, aim at 1% accuracy for r p NIST & ETHZ Rydberg const. using circular Rydberg atoms & positronium Nir Nevo Dinur (TRIUMF) Nuclear structure and the proton radius puzzle 7 / 47

16 Origins of the discrepancy? - more data! New µ-spectroscopy experiments to shed light on the puzzle CREMA collaboration at PSI Lamb shift (2S-2P) in µd (finishing) Lamb shift in µ 4 He + and µ 3 He + (both measured in 2014) Lamb shift in µ 3 H, µ 6 He +, and Z = 3, 4, 5 (wanted since 85) = Extract charge radii with high precision = proton puzzle, QED tests, He isotope shift, nuclear ab initio,... Hyperfine splitting (HFS) in µh & µ 3 He + (approved) = Extract magnetic radii Nir Nevo Dinur (TRIUMF) Nuclear structure and the proton radius puzzle 8 / 47

17 Origins of the discrepancy? - more data! New µ-spectroscopy experiments to shed light on the puzzle CREMA collaboration at PSI Lamb shift (2S-2P) in µd (finishing) Lamb shift in µ 4 He + and µ 3 He + (both measured in 2014) Lamb shift in µ 3 H, µ 6 He +, and Z = 3, 4, 5 (wanted since 85) = Extract charge radii with high precision = proton puzzle, QED tests, He isotope shift, nuclear ab initio,... Hyperfine splitting (HFS) in µh & µ 3 He + (approved) = Extract magnetic radii RIKEN / (J-PARC?) HFS in µh (planned) Nir Nevo Dinur (TRIUMF) Nuclear structure and the proton radius puzzle 8 / 47

18 Origins of the discrepancy? - more data! New µ-spectroscopy experiments to shed light on the puzzle CREMA collaboration at PSI Lamb shift (2S-2P) in µd (finishing) Lamb shift in µ 4 He + and µ 3 He + (both measured in 2014) Lamb shift in µ 3 H, µ 6 He +, and Z = 3, 4, 5 (wanted since 85) = Extract charge radii with high precision = proton puzzle, QED tests, He isotope shift, nuclear ab initio,... Hyperfine splitting (HFS) in µh & µ 3 He + (approved) = Extract magnetic radii RIKEN / (J-PARC?) HFS in µh (planned) high-precision measurements accurate theoretical inputs Nir Nevo Dinur (TRIUMF) Nuclear structure and the proton radius puzzle 8 / 47

19 Lamb shift, charge radius & nuclear TPE Extract R c r 2 from Lamb shift measurement E 2S 2P = δ QED + δ size (R c ) + δ Zem + δ pol Nir Nevo Dinur (TRIUMF) Nuclear structure and the proton radius puzzle 9 / 47

20 Lamb shift, charge radius & nuclear TPE Extract R c r 2 from Lamb shift measurement E 2S 2P = δ QED + δ size (R c ) + δ Zem + δ pol QED corrections: vacuum polarization lepton self energy relativistic recoil effects Theory of µ-p, D, 3,4 He + reexamined Martynenko et al. 07, Borie 12, Krutov et al. 15 Karshenboim et al. 15, Krauth et al Nir Nevo Dinur (TRIUMF) Nuclear structure and the proton radius puzzle 9 / 47

21 Lamb shift, charge radius & nuclear TPE Extract R c r 2 from Lamb shift measurement E 2S 2P = δ QED + δ size (R c ) + δ Zem + δ pol Nuclear finite-size corrections (elastic): leading term: δ size = m3 r 12 (Zα)4 R 2 c Zemach/Friar term: δ Zem = m4 r 24 (Zα)5 r 3 (2) R 3 c can be calculated from g.s. charge distribution, Friar 79, Borie 12( 14), Krutov et al. 15 extracted from experimental form factors, Sick 14 or avoided due to cancellations with δ pol Pachucki 11 & Friar 13 (µd) Nir Nevo Dinur (TRIUMF) Nuclear structure and the proton radius puzzle 9 / 47

22 Lamb shift, charge radius & nuclear TPE Extract R c r 2 from Lamb shift measurement E 2S 2P = δ QED + δ size (R c ) + δ Zem + δ pol Nuclear polarization corrections (inelastic): least well-known related to nuclear response functions: S O (ω) = ψf Ô ψ 0 2 δ(e f E 0 ω) can be calculated (continuum few-body problem) or extracted from data (very imprecise) sometimes rewritten as: δ TPE δ Zem + δ pol lepton Nucleus Nir Nevo Dinur (TRIUMF) Nuclear structure and the proton radius puzzle 9 / 47

23 Update from CREMA Case study µd Krauth et al., Ann. Phys. (Mar. 2016) Nir Nevo Dinur (TRIUMF) Nuclear structure and the proton radius puzzle 10 / 47

24 Previous calculations of S O (ω) & δ pol µd ( 2 H) Modern forces: AV14 - Leidemann & Rosenfelder 95 State-of-the-art: AV18 - Pachucki 11 underestimates nuclear physics uncertainty includes nucleon polarizability δ p pol (partial) π/eft: zero-range expansion - Friar 13 (under?) estimated uncertainty 1 2% includes nucleon-size corrections From e D scattering: Dispersion relations - Carlson et al. 14 estimate nuclear uncertainty 40% Nir Nevo Dinur (TRIUMF) Nuclear structure and the proton radius puzzle 11 / 47

25 Previous calculations of S O (ω) & δ pol µd ( 2 H) Modern forces: AV14 - Leidemann & Rosenfelder 95 State-of-the-art: AV18 - Pachucki 11 underestimates nuclear physics uncertainty includes nucleon polarizability δ p pol (partial) π/eft: zero-range expansion - Friar 13 (under?) estimated uncertainty 1 2% includes nucleon-size corrections From e D scattering: Dispersion relations - Carlson et al. 14 estimate nuclear uncertainty 40% µ 3,4 He + From photoabsorption: Bernabeu & Jarlskog 74; Rinker 76; Friar 77 δ A=3/4 pol = 4.9/ 3.1 mev ±20% (c.f. experimental requirement ±5%) Nir Nevo Dinur (TRIUMF) Nuclear structure and the proton radius puzzle 11 / 47

26 Previous calculations of S O (ω) & δ pol µd ( 2 H) Modern forces: AV14 - Leidemann & Rosenfelder 95 State-of-the-art: AV18 - Pachucki 11 underestimates nuclear physics uncertainty includes nucleon polarizability δ p pol (partial) π/eft: zero-range expansion - Friar 13 (under?) estimated uncertainty 1 2% includes nucleon-size corrections From e D scattering: Dispersion relations - Carlson et al. 14 estimate nuclear uncertainty 40% µ 3,4 He + From photoabsorption: Bernabeu & Jarlskog 74; Rinker 76; Friar 77 δ A=3/4 pol = 4.9/ 3.1 mev ±20% (c.f. experimental requirement ±5%) µt ( 3 H) Very crude theoretical estimation: C. Joachain 61 (in French) Nir Nevo Dinur (TRIUMF) Nuclear structure and the proton radius puzzle 11 / 47

27 Previous calculations of S O (ω) & δ pol µd ( 2 H) Modern forces: AV14 - Leidemann & Rosenfelder 95 State-of-the-art: AV18 - Pachucki 11 underestimates nuclear physics uncertainty includes nucleon polarizability δ p pol (partial) π/eft: zero-range expansion - Friar 13 (under?) estimated uncertainty 1 2% includes nucleon-size corrections From e D scattering: Dispersion relations - Carlson et al. 14 estimate nuclear uncertainty 40% µ 3,4 He + From photoabsorption: Bernabeu & Jarlskog 74; Rinker 76; Friar 77 δ A=3/4 pol = 4.9/ 3.1 mev ±20% (c.f. experimental requirement ±5%) µt ( 3 H) Very crude theoretical estimation: C. Joachain 61 (in French) Status of δ pol in light muonic atoms experimental input for S O is unsatisfactory Nir Nevo Dinur (TRIUMF) Nuclear structure and the proton radius puzzle 11 / 47

28 Previous calculations of S O (ω) & δ pol µd ( 2 H) Modern forces: AV14 - Leidemann & Rosenfelder 95 State-of-the-art: AV18 - Pachucki 11 underestimates nuclear physics uncertainty includes nucleon polarizability δ p pol (partial) π/eft: zero-range expansion - Friar 13 (under?) estimated uncertainty 1 2% includes nucleon-size corrections From e D scattering: Dispersion relations - Carlson et al. 14 estimate nuclear uncertainty 40% µ 3,4 He + From photoabsorption: Bernabeu & Jarlskog 74; Rinker 76; Friar 77 δ A=3/4 pol = 4.9/ 3.1 mev ±20% (c.f. experimental requirement ±5%) µt ( 3 H) Very crude theoretical estimation: C. Joachain 61 (in French) Status of δ pol in light muonic atoms experimental input for S O is unsatisfactory need to calculate δ pol using modern potentials and ab-initio methods Nir Nevo Dinur (TRIUMF) Nuclear structure and the proton radius puzzle 11 / 47

29 Our work: 2 < A We have performed the first ab-initio calculation of δ pol and δ Zem we use state-of-the-art forces AV18+UIX χeft = estimate nuclear physics uncertainty we employ established Few-body methods EIHH: Effective interaction Hyperspherical Harmonics (bound method) LIT: Lorentz Integral Transform (continuum method) LSR: A new method, based on the Lanczos algorithm NND et al., Phys. Rev. C (2016) Nir Nevo Dinur (TRIUMF) Nuclear structure and the proton radius puzzle 12 / 47

30 Nuclear potentials: two approaches Nir Nevo Dinur (TRIUMF) Nuclear structure and the proton radius puzzle 13 / 47

31 Nuclear potentials: Traditional (phen.) Argonne v18 fitted to 1787 pp & 2514 np observables for E lab 350 MeV with χ 2 /datum = 1.1 nn scattering length & D binding energy Urbana IX V ijk = Vijk 2πP + Vijk R Illinois +Vijk 2πS + V ijk 3π R Nir Nevo Dinur (TRIUMF) Nuclear structure and the proton radius puzzle 14 / 47

32 Nuclear potentials: Traditional (phen.) Nir Nevo Dinur (TRIUMF) Nuclear structure and the proton radius puzzle 15 / 47

33 Nuclear potentials: Chiral-EFT Nir Nevo Dinur (TRIUMF) Nuclear structure and the proton radius puzzle 16 / 47

34 Nuclear potentials: 4 He Photoabsorption electric dipole photoabsorption cross section σ γ (ω) = 4π 2 αωs D1 (ω) 5 Arkatov et al. (1979) Shima et al. (2005) AV18+UIX (2006) Nilsson et al. (2005) Nakayama et al. (2007) NN(N 3 LO)+3N(N 2 LO) (2007) 4 Tornow et al. (2012) σ γ [mb] ω [MeV] Nir Nevo Dinur (TRIUMF) Nuclear structure and the proton radius puzzle 17 / 47

35 Nuclear polarization: basic idea Hamiltonian for muonic atoms H = H nucl + H µ + H H µ = p2 Zα 2m r r p Ri 4 He n n p r µ Corrections to the point Coulomb from protons Z Z ( ) 1 H = α V (r, R i) α r 1 r R i i Evaluate inelastic effects of H on muonic spectrum i in 2 nd -order perturbation theory δ pol = 1 N 0 µ 0 H Nµ Nµ H µ 0 N 0 E N0 E N + ɛ µ0 ɛ µ N N 0,µ µ 0 : muon wave function for 2S/2P state Nir Nevo Dinur (TRIUMF) Nuclear structure and the proton radius puzzle 18 / 47

36 Nuclear polarization: contributions Systematic contributions to nuclear polarization δ NR Non-Relativistic limit δ L + δ T Longitudinal and Transverse relativistic corrections δ C Coulomb distortions δ NS Corrections from finite Nucleon Size Nir Nevo Dinur (TRIUMF) Nuclear structure and the proton radius puzzle 19 / 47

37 Non-relativistic limit Neglect Coulomb interactions in the intermediate state lepton Nucleus Nir Nevo Dinur (TRIUMF) Nuclear structure and the proton radius puzzle 20 / 47

38 Non-relativistic limit Neglect Coulomb interactions in the intermediate state Expand muon matrix element in powers of η 2m r ω R R lepton Nucleus Nir Nevo Dinur (TRIUMF) Nuclear structure and the proton radius puzzle 20 / 47

39 Non-relativistic limit Neglect Coulomb interactions in the intermediate state Expand muon matrix element in powers of η 2m r ω R R lepton Nucleus R R = virtual distance the proton travels in 2γ exchange uncertainty principal R R 1/ 2m N ω η mr m N 0.3 Nir Nevo Dinur (TRIUMF) Nuclear structure and the proton radius puzzle 20 / 47

40 Non-relativistic limit Neglect Coulomb interactions in the intermediate state Expand muon matrix element in powers of η 2m r ω R R lepton Nucleus R R = virtual distance the proton travels in 2γ exchange uncertainty principal R R 1/ 2m N ω η mr m N 0.3 P m3 r(zα) 5 [ 2mr R R 2 2mr ω R R 3 + m ] rω 12 ω 4 10 R R 4 δ NR = δ (0) NR + δ(1) NR + δ(2) NR = η2 + η 3 + η 4 Nir Nevo Dinur (TRIUMF) Nuclear structure and the proton radius puzzle 20 / 47

41 NR limit at LO: δ (0) NR δ NR = δ (0) NR + δ(1) NR + δ(2) NR δ (0) NR η2 δ (0) D1 = 2πm3 r (Zα) 5 dω 9 ω th 2mr ω S D 1 (ω) S D1 (ω) = electric dipole response function [ ˆD 1 = R Y 1 ( ˆR) ] δ (0) D1 is the dominant contribution to δ pol Nir Nevo Dinur (TRIUMF) Nuclear structure and the proton radius puzzle 21 / 47

42 NR limit at LO: δ (0) NR δ NR = δ (0) NR + δ(1) NR + δ(2) NR δ (0) NR η2 δ (0) D1 = 2πm3 r (Zα) 5 dω 9 ω th 2mr ω S D 1 (ω) S D1 (ω) = electric dipole response function [ ˆD 1 = R Y 1 ( ˆR) ] δ (0) D1 is the dominant contribution to δ pol = Rel. and Coulomb corrections added at this order Nir Nevo Dinur (TRIUMF) Nuclear structure and the proton radius puzzle 21 / 47

43 NR limit at NLO: δ (1) NR δ NR = δ (0) NR + δ(1) NR + δ(2) NR δ (1) NR η3 δ (1) NR = δ(1) R3pp + δ(1) Z3 δ (1) R3pp = m4 r 24 (Zα)5 δ (1) Z3 = m4 r 24 (Zα)5 drdr R R 3 N 0 ˆρ (R)ˆρ(R ) N 0 drdr R R 3 ρ 0(R)ρ 0(R ) δ (1) R3pp 3rd-order proton-proton correlation δ (1) Z3 = 3rd Zemach moment Nir Nevo Dinur (TRIUMF) Nuclear structure and the proton radius puzzle 22 / 47

44 NR limit at NLO: δ (1) NR δ NR = δ (0) NR + δ(1) NR + δ(2) NR δ (1) NR η3 δ (1) NR = δ(1) R3pp + δ(1) Z3 δ (1) R3pp = m4 r 24 (Zα)5 δ (1) Z3 = m4 r 24 (Zα)5 δ (1) R3pp 3rd-order proton-proton correlation δ (1) Z3 drdr R R 3 N 0 ˆρ (R)ˆρ(R ) N 0 drdr R R 3 ρ 0(R)ρ 0(R ) = m4 r 24 (Zα)5 r 3 (2) = 3rd Zemach moment cancels elastic Zemach moment of finite-size corrections c.f. Pachucki 11 & Friar 13 (µd) Nir Nevo Dinur (TRIUMF) Nuclear structure and the proton radius puzzle 22 / 47

45 NR limit at NLO: δ (1) NR δ NR = δ (0) NR + δ(1) NR + δ(2) NR δ (1) NR η3 δ (1) NR = δ(1) R3pp + δ(1) Z3 δ (1) R3pp = m4 r 24 (Zα)5 δ (1) Z3 = m4 r 24 (Zα)5 δ (1) R3pp 3rd-order proton-proton correlation δ (1) Z3 drdr R R 3 N 0 ˆρ (R)ˆρ(R ) N 0 drdr R R 3 ρ 0(R)ρ 0(R ) = m4 r 24 (Zα)5 r 3 (2) = 3rd Zemach moment cancels elastic Zemach moment of finite-size corrections c.f. Pachucki 11 & Friar 13 (µd) = δ TPE δ Zem + δ pol Nir Nevo Dinur (TRIUMF) Nuclear structure and the proton radius puzzle 22 / 47

46 NR limit at N 2 LO: δ (2) NR δ NR = δ (0) NR + δ(1) NR + δ(2) NR δ (2) NR η4 δ (2) NR = m5 r 18 (Zα)5 ω dω ω th 2m r S R 2(ω) = monopole response function S Q (ω) = quadrupole response function [ S R 2(ω) + 16π 25 S Q(ω) + 16π ] 5 S D 1D 3 (ω) S D1D 3 (ω) = interference between D 1 and D 3 [ ˆD 3 = R 3 Y 1 ( ˆR) ] Nir Nevo Dinur (TRIUMF) Nuclear structure and the proton radius puzzle 23 / 47

47 Test: δ (0) in µd Test Run: electric-dipole polarization effects in µd previous δ pol in µd (AV18): Pachucki 11 we calculate δ (0) from dipole response of D (AV18) [S D1 (ω) from Bampa, Leidemann & Arenhövel 11] The difference in δ (0) L δ (0) [mev] Pachucki 11 Our work non-rel dipole δ (0) D relativistic δ (0) L δ (0) T Coulomb δ (0) C is due to small energy expansion used in Pachucki 11 Nir Nevo Dinur (TRIUMF) Nuclear structure and the proton radius puzzle 24 / 47

48 4 He: Calculating few-body response functions Few-body bound-states: EIHH Effective Interaction Hyperspherical Harmonics Rapidly converging, based on symmetrized hyperspherical functions Barnea & Novoselsky, Ann. Phys. (1997); Barnea et al., Phys. Rev. C (2000)... Nir Nevo Dinur (TRIUMF) Nuclear structure and the proton radius puzzle 25 / 47

49 4 He: Calculating few-body response functions Few-body bound-states: EIHH Effective Interaction Hyperspherical Harmonics Rapidly converging, based on symmetrized hyperspherical functions Barnea & Novoselsky, Ann. Phys. (1997); Barnea et al., Phys. Rev. C (2000)... Few-body continuum: LIT Lorentz Integral Transform Transforms calculation of response S(ω) into two-steps: 1. Solving a Schroedinger-like (bound-state) equation 2. Inverting an integral transform (with Lorentzian kernel) Efros, Leidemann, & Orlandini, Phys. Lett. B (1994) Efros, Leidemann, Orlandini & Barnea, J. Phys. G (2007) Nir Nevo Dinur (TRIUMF) Nuclear structure and the proton radius puzzle 25 / 47

50 4 He: Calculating few-body response functions Few-body bound-states: EIHH Effective Interaction Hyperspherical Harmonics Rapidly converging, based on symmetrized hyperspherical functions Barnea & Novoselsky, Ann. Phys. (1997); Barnea et al., Phys. Rev. C (2000)... Few-body continuum: LIT Lorentz Integral Transform Transforms calculation of response S(ω) into two-steps: 1. Solving a Schroedinger-like (bound-state) equation 2. Inverting an integral transform (with Lorentzian kernel) Efros, Leidemann, & Orlandini, Phys. Lett. B (1994) Efros, Leidemann, Orlandini & Barnea, J. Phys. G (2007) Uses Lanczos to diagonalize low-energy spectrum of H nucl Marchisio, Barnea, Leidemann, & Orlandini, Few-body Sys. (2003) Nir Nevo Dinur (TRIUMF) Nuclear structure and the proton radius puzzle 25 / 47

51 LSR: Lanczos sum rule method Nuclear polarization = energy-dependent sum rules of the response functions δ pol I O = 0 dω S O (ω) g (ω) Nir Nevo Dinur (TRIUMF) Nuclear structure and the proton radius puzzle 26 / 47

52 LSR: Lanczos sum rule method Nuclear polarization = energy-dependent sum rules of the response functions δ pol I O = 0 dω S O (ω) g (ω) The Lanczos algorithm is an efficient method calculate the LIT of S O. It can be extended to calculate the sum rules. Nir Nevo Dinur (TRIUMF) Nuclear structure and the proton radius puzzle 26 / 47

53 LSR: Lanczos sum rule method Nuclear polarization = energy-dependent sum rules of the response functions δ pol I O = 0 dω S O (ω) g (ω) The Lanczos algorithm is an efficient method calculate the LIT of S O. It can be extended to calculate the sum rules. With the Lanczos sum rule (LSR) method, we directly calculate I O, without explicitly solving S O. Nir Nevo Dinur (TRIUMF) Nuclear structure and the proton radius puzzle 26 / 47

54 LSR: Lanczos sum rule method Nuclear polarization = energy-dependent sum rules of the response functions δ pol I O = 0 dω S O (ω) g (ω) The Lanczos algorithm is an efficient method calculate the LIT of S O. It can be extended to calculate the sum rules. With the Lanczos sum rule (LSR) method, we directly calculate I O, without explicitly solving S O. The calculated I O converges as the LIT of S O, if g (ω) is smooth. NND, Barnea, Ji, and Bacca, Phys. Rev. C 89, (2014) Nir Nevo Dinur (TRIUMF) Nuclear structure and the proton radius puzzle 26 / 47

55 LSR: Example 4 He dipole response sum-rules (Model space size M 10 5 ) NND, Barnea, Ji, and Bacca, Phys. Rev. C 89, (2014) Nir Nevo Dinur (TRIUMF) Nuclear structure and the proton radius puzzle 27 / 47

56 Nuclear polarization in µ 4 He + [mev] AV18+UIX χeft δ (0) δ (0) D δ (0) L δ (0) T δ (0) C NN: N 3 LO-EM 3N: N 2 LO (c D=1, c E=-0.029) Nir Nevo Dinur (TRIUMF) Nuclear structure and the proton radius puzzle 28 / 47

57 Nuclear polarization in µ 4 He + [mev] AV18+UIX χeft δ (0) δ (0) D δ (0) L δ (0) T δ (0) C δ (1) δ (1) R3pp δ (1) Z NN: N 3 LO-EM 3N: N 2 LO (c D=1, c E=-0.029) Nir Nevo Dinur (TRIUMF) Nuclear structure and the proton radius puzzle 28 / 47

58 Nuclear polarization in µ 4 He + [mev] AV18+UIX χeft δ (0) δ (0) D δ (0) L δ (0) T δ (0) C δ (1) δ (1) R3pp δ (1) Z δ (2) (2) δr δ (2) Q δ (2) D1D NN: N 3 LO-EM 3N: N 2 LO (c D=1, c E=-0.029) Nir Nevo Dinur (TRIUMF) Nuclear structure and the proton radius puzzle 28 / 47

59 Nuclear polarization in µ 4 He + [mev] AV18+UIX χeft δ (0) δ (0) D δ (0) L δ (0) T δ (0) C δ (1) δ (1) R3pp δ (1) Z δ (2) δ NS (2) δr δ (2) Q δ (2) D1D (1) δr1pp δ (1) Z δ (2) NS NN: N 3 LO-EM 3N: N 2 LO (c D=1, c E=-0.029) Nir Nevo Dinur (TRIUMF) Nuclear structure and the proton radius puzzle 28 / 47

60 Nuclear polarization in µ 4 He + [mev] AV18+UIX χeft δ (0) δ (0) D δ (0) L δ (0) T δ (0) C δ (1) δ (1) R3pp δ (1) Z δ (2) δ NS (2) δr δ (2) Q δ (2) D1D (1) δr1pp δ (1) Z δ (2) NS δ pol NN: N 3 LO-EM 3N: N 2 LO (c D=1, c E=-0.029) Nir Nevo Dinur (TRIUMF) Nuclear structure and the proton radius puzzle 28 / 47

61 Nuclear polarization in µ 4 He + [mev] AV18+UIX χeft δ (0) Convergence from δ (0) to δ (2) from an expansion in η m r /M N 0.3 δ (1) δ (2) δ NS NN: N 3 LO-EM 3N: N 2 LO (c D=1, c E=-0.029) δ pol Nir Nevo Dinur (TRIUMF) Nuclear structure and the proton radius puzzle 28 / 47

62 Nuclear polarization in µ 4 He + [mev] AV18+UIX χeft δ (0) δ (1) Convergence from δ (0) to δ (2) from an expansion in η m r /M N 0.3 δ pol with AV18+UIX & χeft differ: 5.5% (0.134 mev) δ (2) δ NS NN: N 3 LO-EM 3N: N 2 LO (c D=1, c E=-0.029) δ pol Nir Nevo Dinur (TRIUMF) Nuclear structure and the proton radius puzzle 28 / 47

63 Nuclear physics uncertainty 4 He obesrvable AV18+UIX χeft-em Difference µ 4 He + nuclear polarization δ pol [mev] % Nir Nevo Dinur (TRIUMF) Nuclear structure and the proton radius puzzle 29 / 47

64 Nuclear physics uncertainty 4 He obesrvable AV18+UIX χeft-em Difference binding energy B 0 [MeV] % point-proton nuclear radius R pp [fm] % electric-dipole polarizability α E [fm 3 ] % µ 4 He + nuclear polarization δ pol [mev] % B 0, R pp & α E in good agreement with previous calculations Kievsky et al. 08, Gazit et al. 06 & Stetcu et al. 09 Nir Nevo Dinur (TRIUMF) Nuclear structure and the proton radius puzzle 29 / 47

65 Nuclear physics uncertainty 4 He obesrvable AV18+UIX χeft-em Difference binding energy B 0 [MeV] % point-proton nuclear radius R pp [fm] % electric-dipole polarizability α E [fm 3 ] % µ 4 He + nuclear polarization δ pol [mev] % B 0, R pp & α E in good agreement with previous calculations Kievsky et al. 08, Gazit et al. 06 & Stetcu et al. 09 systematic uncertainty in δ pol from nuclear physics: 5.5% 2 = ±4% (1σ) Nir Nevo Dinur (TRIUMF) Nuclear structure and the proton radius puzzle 29 / 47

66 Numerical accuracy Convergence with model space size Compare δ (Kmax) pol AV18+UIX 0.4% χeft-em 0.2% with δ (Kmax 4) pol -2.4 δ pol AV18 + UIX 2N(N 3 LO) + 3N(N 2 LO) K max Nir Nevo Dinur (TRIUMF) Nuclear structure and the proton radius puzzle 30 / 47

67 Error budget µ 4 He + Nuclear physics 4% from two potentials Numerical accuracy 0.4% from convergence Additional corrections (Zα) 6 terms (beyond 2nd-order perturbation theory) Rel. & Coulomb corrections (other than dipole) higher-order nucleon-size corrections 4% estimated from additional corrections Final result (quadratic sum) our prediction: δ pol = 2.47 mev ±6% previous estimates: δ pol = 3.1 mev ±20% experimental needs: δ pol uncertainty 5% Nir Nevo Dinur (TRIUMF) Nuclear structure and the proton radius puzzle 31 / 47

68 Reflections on µ 4 He + The accuracy of δ pol in µ 4 He + is limited by the nuclear physics (AV18+UIX vs. χeft-em) To study this we can further vary the nuclear potentials Use χeft at different orders to track the convergence At each order vary the cutoff to estimate the theoretical error (χeft-egm: Epelbaum, Glöckle, & Meißner, Nucl. Phys. A 05) Nir Nevo Dinur (TRIUMF) Nuclear structure and the proton radius puzzle 32 / 47

69 Reflections on µd Pachucki only used AV18 No nuclear physics uncertainty We can add χeft-em & χeft-egm 2-body problem only N N interaction simple numerics Other issues Pachucki did not include nucleon-size corrections Pachucki did not treat nucleon-polarization correctly We already reproduced Pachucki s leading term as a check for µ 4 He + There is also a Magnetic contribution Pachucki only calculated δ TPE δ Zem + δ pol Nir Nevo Dinur (TRIUMF) Nuclear structure and the proton radius puzzle 33 / 47

70 Nuclear polarization in µd Pachucki 11 (AV18) our work (AV18) δ (0) D δ (0) L δ (0) T δ (0) C δ (2) R δ (2) Q δ (2) D1D δ (1) NS δ (2) NS δ M δ TPE δ pol + δ Zem compare: δ (0) L & δ(0) T ; δ (2) ; δ M ; δ NS Nir Nevo Dinur (TRIUMF) Nuclear structure and the proton radius puzzle 34 / 47

71 Nuclear polarization in µd Pachucki 11 our work (AV18) (AV18) N 3 LO-EM N 3 LO-EGM δ (0) D (-1.911,-1.926) δ (0) L ( 0.029, 0.030) δ (0) T δ (0) C ( 0.262, 0.264) δ (2) R δ (2) Q δ (2) D1D (-0.139,-0.140) δ (1) NS δ (2) NS δ M δ TPE δ pol + δ Zem (1.660,1.674) compare: δ (0) L & δ(0) T ; δ (2) ; δ M ; δ NS Nir Nevo Dinur (TRIUMF) Nuclear structure and the proton radius puzzle 34 / 47

72 Improved nuclear uncertainty in µd Nir Nevo Dinur (TRIUMF) Nuclear structure and the proton radius puzzle 35 / 47

73 Error budget µd Nuclear physics 1.1% from a range of potentials Numerical accuracy (negligible) Additional corrections 0.95% (as estimated by Pachucki) Final result (quadratic sum) our prediction: δ TPE δ pol + δ Zem = 1.66 mev ±1.5% includes nuclear error & nucleon-size corrections improved result and error estimate Nir Nevo Dinur (TRIUMF) Nuclear structure and the proton radius puzzle 36 / 47

74 µd theory: Krauth et al., Ann. Phys. (Mar. 2016) Nir Nevo Dinur (TRIUMF) Nuclear structure and the proton radius puzzle 37 / 47

Hot from the press: A = 3 AV18/UIX EFT 3 He 3 H Drop Times (Seconds) OBJECT A OBJECT B -6.48-6.63 Table 6 0.23 0.24-0.10-0.11 OBJECT C OBJECT D 1.00 1.02-0.77-0.78 0.08 0.05 0.03 0.03-8.54-8.71-0.

75 Hot from the press: A = 3 AV18/UIX EFT 3 He 3 H Drop Times (Seconds) OBJECT A OBJECT B Table OBJECT C OBJECT D (0) D1 (0) L (0) T (0) C (0) M (1) R3 (1) Z3 (2) R 2 (2) Q (2) D1D3 (1) R1 (1) Z1 (2) NS A pol A Zem A TPE NND et al., Phys. Lett. B (Apr. 2016) mev mev Nir Nevo Dinur (TRIUMF) Nuclear structure and the proton radius puzzle 38 / 47

76 Hot from the press: δ pol in µ 3 He + [mev] AV18+UIX χeft Convergence from δ (0) to δ (2)? δ (0) δ (1) δ (2) δ NS δ Mag δ pol NN: N 3 LO-EM 3N: N 2 LO (c D=1, c E=-0.029) Nir Nevo Dinur (TRIUMF) Nuclear structure and the proton radius puzzle 39 / 47

77 Hot from the press: δ pol in µ 3 He + [mev] AV18+UIX χeft δ (0) δ (1) Convergence from δ (0) to δ (2)? AV18+UIX vs. χeft: 1% (±0.04 mev) c.f. µ 4 He + : 2.47 ± 0.15 mev δ (2) δ NS δ Mag δ pol NN: N 3 LO-EM 3N: N 2 LO (c D=1, c E=-0.029) Nir Nevo Dinur (TRIUMF) Nuclear structure and the proton radius puzzle 39 / 47

78 Hot from the press: δ pol in µ 3 He + [mev] AV18+UIX χeft δ (0) δ (1) Convergence from δ (0) to δ (2)? AV18+UIX vs. χeft: 1% (±0.04 mev) c.f. µ 4 He + : 2.47 ± 0.15 mev δ Zem =? δ (2) δ NS δ Mag δ pol NN: N 3 LO-EM 3N: N 2 LO (c D=1, c E=-0.029) Nir Nevo Dinur (TRIUMF) Nuclear structure and the proton radius puzzle 39 / 47

79 Hot from the press: δ pol in µ 3 He + [mev] AV18+UIX χeft δ (0) δ (1) δ (2) Convergence from δ (0) to δ (2)? AV18+UIX vs. χeft: 1% (±0.04 mev) c.f. µ 4 He + : 2.47 ± 0.15 mev δ Zem = 10.5(2) mev w/r p (µ ) δ NS δ Mag δ pol NN: N 3 LO-EM 3N: N 2 LO (c D=1, c E=-0.029) Nir Nevo Dinur (TRIUMF) Nuclear structure and the proton radius puzzle 39 / 47

80 Hot from the press: δ pol in µ 3 He + [mev] AV18+UIX χeft δ (0) δ (1) δ (2) Convergence from δ (0) to δ (2)? AV18+UIX vs. χeft: 1% (±0.04 mev) c.f. µ 4 He + : 2.47 ± 0.15 mev δ Zem = 10.5(2) mev w/r p (µ ) 10.7(2) mev w/r p (e ) δ NS δ Mag δ pol NN: N 3 LO-EM 3N: N 2 LO (c D=1, c E=-0.029) Nir Nevo Dinur (TRIUMF) Nuclear structure and the proton radius puzzle 39 / 47

81 Hot from the press: δ pol in µ 3 He + [mev] AV18+UIX χeft δ (0) δ (1) δ (2) δ NS Convergence from δ (0) to δ (2)? AV18+UIX vs. χeft: 1% (±0.04 mev) c.f. µ 4 He + : 2.47 ± 0.15 mev δ Zem = 10.5(2) mev w/r p (µ ) 10.7(2) mev w/r p (e ) both agree with 10.87(27) mev from scattering data (Sick, PRC 14) δ Mag δ pol NN: N 3 LO-EM 3N: N 2 LO (c D=1, c E=-0.029) Nir Nevo Dinur (TRIUMF) Nuclear structure and the proton radius puzzle 39 / 47

82 Hot from the press: δ pol in µ 3 He + [mev] AV18+UIX χeft δ (0) δ (1) δ (2) δ NS Convergence from δ (0) to δ (2)? AV18+UIX vs. χeft: 1% (±0.04 mev) c.f. µ 4 He + : 2.47 ± 0.15 mev δ Zem = 10.5(2) mev w/r p (µ ) 10.7(2) mev w/r p (e ) 10.9 both agree with 10.87(27) mev from scattering data (Sick, PRC 14) δ Mag δ pol NN: N 3 LO-EM 3N: N 2 LO (c D=1, c E=-0.029) Nir Nevo Dinur (TRIUMF) Nuclear structure and the proton radius puzzle 39 / 47

83 Hot from the press: δ pol in µ 3 H [mev] AV18+UIX χeft Convergence from δ (0) to δ (2)? δ (0) δ (1) AV18+UIX vs. χeft: 1.5% (±7.5 µev) Probe δpol N of the nucleons? δ (2) δ N pol 34(16) µev δ NS Precise triton radius δ Mag δ pol NN: N 3 LO-EM 3N: N 2 LO (c D=1, c E=-0.029) Nir Nevo Dinur (TRIUMF) Nuclear structure and the proton radius puzzle 40 / 47

84 Uncertainty estimates Nir Nevo Dinur (TRIUMF) Nuclear structure and the proton radius puzzle 41 / 47

85 Summary of results: 2 A 4 System Ref. δ pol err. exptl. status µ 2 H Phys. Lett. B % measured, unpublished µ 4 He + Phys. Rev. Lett % 6% measured, unpublished µ 3 He + Phys. Lett. B 16 20% 4% measured, unpublished µ 3 H Phys. Lett. B 16 4% measurable? δ Zem agree with other values calculated or extracted from data δ pol more accurate than previous estimates δ pol err. comparable to the 5% experimental needs will significantly improve the precision of R c extracted from the measured Lamb shifts may help shed light on the proton radius puzzle Nir Nevo Dinur (TRIUMF) Nuclear structure and the proton radius puzzle 42 / 47

86 Work in progress The work is not completed yet... Nir Nevo Dinur (TRIUMF) Nuclear structure and the proton radius puzzle 43 / 47

87 Outlook Study higher-order terms (in progress) Quantify & reduce nuclear physics uncertainty (in progress) understand why various nuclear Hamiltonians differ further explore the phase-space of nuclear Hamiltonians include higher-order or otherwise improved nuclear forces include many-body currents Improve treatment of nucleon finite sizes (in progress) Investigate nuclear corrections in µ 6 Li +2, µ 6 He +, Investigate nuclear corrections in HFS of µ 3 He + Nir Nevo Dinur (TRIUMF) Nuclear structure and the proton radius puzzle 44 / 47

88 Quantitative nuclear physics uncertainty B. D. Carlsson et al., Phys. Rev. X (2016) Nir Nevo Dinur (TRIUMF) Nuclear structure and the proton radius puzzle 45 / 47

89 Update from CREMA: µd status 2015 Courtesy of Randolf CREMA Nir Nevo Dinur (TRIUMF) Nuclear structure and the proton radius puzzle 46 / 47

90 Update from CREMA: µd status 2015 Courtesy of Randolf CREMA Nir Nevo Dinur (TRIUMF) Nuclear structure and the proton radius puzzle 46 / 47

91 Update from CREMA: µd status 2015 Courtesy of Randolf CREMA Nir Nevo Dinur (TRIUMF) Nuclear structure and the proton radius puzzle 46 / 47

92 The muonic Lamb shift is still puzzling!!! Nir Nevo Dinur (TRIUMF) Nuclear structure and the proton radius puzzle 47 / 47

93 The muonic Lamb shift is still puzzling!!! Nir Nevo Dinur (TRIUMF) Nuclear structure and the proton radius puzzle 47 / 47

94 BACK UP Nir Nevo Dinur (TRIUMF) Nuclear structure and the proton radius puzzle 48 / 47

95 Energy (MeV) H 1/2+ 3 H He 1 + AV /2 Li 3/2 IL2 7 Li 5/2 7/2 Exp 8 Li Phenomenological potentials 8 Be Li Argonne v 18 With Illinois-2 GFMC Calculations 7/2 5/2 1/2 3/2 9 Be 9/2 7/2 + 1/2 + 7/2 5/2 + 3/2 + 1/2 5/2 3/2 10 Be , B C Nir Nevo Dinur (TRIUMF) Nuclear structure and the proton radius puzzle 49 / 47

96 4 He photoabsorption cross sections electric-dipole photoabsorption cross section σ γ (ω) = 4π 2 αωs D1 (ω) 3 Shima et al. (2005) Nilsson et al. (2005) Nakayama et al. (2007) Tornow et al. (2012) Arkatov (1979) σ γ [mb] ω [MeV] Nir Nevo Dinur (TRIUMF) Nuclear structure and the proton radius puzzle 50 / 47

97 4 He photoabsorption cross sections electric-dipole photoabsorption cross section σ γ (ω) = 4π 2 αωs D1 (ω) σ γ [mb] 3 2 Shima et al. (2005) Nilsson et al. (2005) Nakayama et al. (2007) Tornow et al. (2012) Arkatov (1979) AV18/UIX 2N(N 3 LO) + 3N(N 2 LO) ω [MeV] Nir Nevo Dinur (TRIUMF) Nuclear structure and the proton radius puzzle 50 / 47

98 Non-Relativistic Approximation Coulomb interactions in the (virtual) intermediate state are neglected Results are expressed in an expansion of 2m r ω R R E NR = E (2) NR + E(3) NR + E(4) NR Nir Nevo Dinur (TRIUMF) Nuclear structure and the proton radius puzzle 51 / 47

99 Non-Relativistic Approximation Coulomb interactions in the (virtual) intermediate state are neglected Results are expressed in an expansion of 2m r ω R R E NR = E (2) NR + E(3) NR + E(4) NR 1. R 2 term: E (2) NR is the dominant polarizability contribution E (2) NR = 2πm3 r (Zα) 5 9 ω th dω 2mr ω SD 1 (ω) S D 1 (ω) = 1 2J 0 +1 ˆD 1 = 1 Z N N 0,J Z R iy 1( ˆR i) i N 0J 0 ˆD 1 NJ 2 δ(ω E N + E N0 ) Nir Nevo Dinur (TRIUMF) Nuclear structure and the proton radius puzzle 51 / 47

100 Non-Relativistic Approximation Coulomb interactions in the (virtual) intermediate state are neglected Results are expressed in an expansion of 2m r ω R R E NR = E (2) NR + E(3) NR + E(4) NR 2. R 3 term: E (3) NR = m4 r 24 (Zα)5 [ d 3 Rd 3 R R R 3 N 0 ˆρ (R)ˆρ(R ) N 0 r 3 (2) ] Nir Nevo Dinur (TRIUMF) Nuclear structure and the proton radius puzzle 52 / 47

101 Non-Relativistic Approximation Coulomb interactions in the (virtual) intermediate state are neglected Results are expressed in an expansion of 2m r ω R R E NR = E (2) NR + E(3) NR + E(4) NR 2. R 3 term: E (3) NR = m4 r 24 (Zα)5 [ 1st term: charge correlation function vanishes in point-nucleon limit d 3 Rd 3 R R R 3 N 0 ˆρ (R)ˆρ(R ) N 0 r 3 (2) ] Nir Nevo Dinur (TRIUMF) Nuclear structure and the proton radius puzzle 52 / 47

102 Non-Relativistic Approximation Coulomb interactions in the (virtual) intermediate state are neglected Results are expressed in an expansion of 2m r ω R R E NR = E (2) NR + E(3) NR + E(4) NR 2. R 3 term: E (3) NR = m4 r 24 (Zα)5 [ 1st term: charge correlation function vanishes in point-nucleon limit d 3 Rd 3 R R R 3 N 0 ˆρ (R)ˆρ(R ) N 0 r 3 (2) ] 2nd term: Zemach moment r 3 (2) = d 3 Rd 3 R R R 3 ρ 0 (R) ρ 0 (R ) ρ 0 (R) = N 0 ˆρ(R) N 0 cancels exactly the Zemach term in (elastic) finite-size corrections c.f. Pachucki PRL 2011 (µd) Nir Nevo Dinur (TRIUMF) Nuclear structure and the proton radius puzzle 52 / 47

103 3. R 4 term: E (4) NR corresponds to higher-multipole corrections Non-Relativistic Approximation [ E (4) NR = m5 r ω 18 (Zα)5 dω S Q 0 (ω) + 16π ω th 2m r 25 SQ 2 (ω) + 16π ] 5 SD 13 (ω) S R2 (ω) = 1 2J 0 +1 S Q 2 (ω) = 1 2J 0 +1 S D 13 (ω) = 1 2J 0 +1 N N 0,J N 0J 0 ˆR 2 NJ 2 δ(ω E N + E N0 ) N 0J 0 ˆQ 2 NJ 2 δ(ω E N + E N0 ) N N 0,J ( 1) J 0 J N N 0,J ( Re N 0J 0 ˆD 3 NJ NJ ˆD ) 1 N 0J 0 δ(ω E N + E N0 ) ˆR 2 = 1 Z ˆQ 2 = 1 Z Z i R 2 i Z Ri 2 Y 2( ˆR i) i ˆD 1 = 1 Z ˆD3 = 1 Z Z R iy 1( ˆR i) i Z R 3 Y 1( ˆR i) i Nir Nevo Dinur (TRIUMF) Nuclear structure and the proton radius puzzle 53 / 47

104 Convergence of Ab-initio calculations Convergence of ω -3.6 δ (0) [mev] AV18 / UIX Γ = 10 MeV AV18 / UIX Γ = 20 MeV EFT 2N / 3N Γ = 10 MeV EFT 2N / 3N Γ = 20 MeV ω [MeV] Nir Nevo Dinur (TRIUMF) Nuclear structure and the proton radius puzzle 54 / 47

105 Convergence of Ab-initio calculations δ (0) δ (0) convergence with the largest model space K max AV18 + UIX 2N(N 3 LO) + 3N(N 2 LO) K max Nir Nevo Dinur (TRIUMF) Nuclear structure and the proton radius puzzle 55 / 47

Understanding the proton radius puzzle: Nuclear structure corrections in light muonic atoms

Canada s national laboratory for particle and nuclear physics Laboratoire national canadien pour la recherche en physique nucléaire et en physique des particules Understanding the proton radius puzzle: