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Jul 01, 2023 •211 likes •1.58k views

Shrinking the Proton Exotic and not-so-exotic atoms for nuclear physics and fundamental constants Muonic news Muonic hydrogen and deuterium Randolf Pohl Randolf Pohl JGU, Mainz MPQ, Garching for the CREMA collaboration 1 Collaborators

  1. Muonic DEUTERIUM µ → Experiment: F=3/2 F=5/2 p + iso CODATA this value 2S 2P 10 1/2 3/2 signal [arb. units] RP et al. (CREMA), Science 353 , 417 (2016). ∆ E exp LS = 202 . 8785 ( 31 ) stat ( 14 ) syst meV 5 ⇒ r d = 2 . 12562 ( 13 ) exp ( 77 ) theo fm Theory: ∆ E theo LS = 228 . 7766 ( 10 ) meV ( QED ) + 1 . 7096 ( 200 ) meV ( TPE ) 0 − 100 0 100 ∆ ν (GHz) 3 ) r 2 d meV / fm 2 , − 6 . 1103 ( 8 µ → F=1/2 F=3/2 p + iso CODATA this value 2S 2P 1/2 3/2 signal [arb. units] Krauth, RP et al. , Ann. Phys. 366 , 168 (2016) F=1/2 → F=1/2 2S 2P 1/2 3/2 [arXiv 1506.01298] 6 based on papers and communication from Bacca, Barnea, Birse, Borie, Carlson, Eides, 4 Faustov, Friar, Gorchtein, Hernandez, Ivanov, Jentschura, Ji, Karshenboim, Korzinin, Krutov, 2 Martynenko, McGovern, Nevo Dinur, Pachucki, Shelyuto, Sick, Vanderhaeghen et al. 0 − 100 0 100 ∆ ν THANK YOU! (GHz) Randolf Pohl PhiPsi17 , 28 June 2017 13

  2. Deuteron charge radius H/D isotope shift: r 2 d − r 2 p = 3 . 82007 ( 65 ) fm 2 C.G. Parthey, RP et al. , PRL 104 , 233001 (2010) r d = 2 . 14130 ( 250 ) fm CODATA 2014 r p from µ H gives r d = 2 . 12771 ( 22 ) fm ← 5 . 4 σ from r p µ H + iso H/D(1S-2S) CODATA-2014 e-d scatt. 2.11 2.115 2.12 2.125 2.13 2.135 2.14 2.145 Deuteron charge radius [fm] Randolf Pohl PhiPsi17 , 28 June 2017 14

  3. Deuteron charge radius H/D isotope shift: r 2 d − r 2 p = 3 . 82007 ( 65 ) fm 2 C.G. Parthey, RP et al. , PRL 104 , 233001 (2010) r d = 2 . 14130 ( 250 ) fm CODATA 2014 r p from µ H gives r d = 2 . 12771 ( 22 ) fm ← 5 . 4 σ from r p µ H + iso H/D(1S-2S) CODATA-2014 ✛ ( 5 . 4 σ from µ H) ✲ e-d scatt. 2.11 2.115 2.12 2.125 2.13 2.135 2.14 2.145 Deuteron charge radius [fm] Randolf Pohl PhiPsi17 , 28 June 2017 14

  4. Deuteron charge radius H/D isotope shift: r 2 d − r 2 p = 3 . 82007 ( 65 ) fm 2 C.G. Parthey, RP et al. , PRL 104 , 233001 (2010) r d = 2 . 14130 ( 250 ) fm CODATA 2014 r p from µ H gives r d = 2 . 12771 ( 22 ) fm ← 5 . 4 σ from r p r d = 2 . 12562 ( 13 ) exp ( 77 ) theo fm RP et al. , Science 353 , 417 (2016) Muonic DEUTERIUM µ D µ H + iso H/D(1S-2S) CODATA-2014 ✛ ( 5 . 4 σ from µ H) ✲ e-d scatt. 2.11 2.115 2.12 2.125 2.13 2.135 2.14 2.145 Deuteron charge radius [fm] Randolf Pohl PhiPsi17 , 28 June 2017 14

  5. Deuteron charge radius H/D isotope shift: r 2 d − r 2 p = 3 . 82007 ( 65 ) fm 2 C.G. Parthey, RP et al. , PRL 104 , 233001 (2010) r d = 2 . 14130 ( 250 ) fm CODATA 2014 r p from µ H gives r d = 2 . 12771 ( 22 ) fm ← 5 . 4 σ from r p r d = 2 . 12562 ( 13 ) exp ( 77 ) theo fm RP et al. , Science 353 , 417 (2016) Muonic DEUTERIUM µ D another 6 σ discrepancy! ✛ ✲ µ H + iso H/D(1S-2S) CODATA-2014 ✛ ( 5 . 4 σ from µ H) ✲ e-d scatt. 2.11 2.115 2.12 2.125 2.13 2.135 2.14 2.145 Deuteron charge radius [fm] Randolf Pohl PhiPsi17 , 28 June 2017 14

  6. Conclusions µ p and µ d Pohl et al. , Nature 466, 213 (2010). Antognini et al. , Science 339, 417 (2013). Proton charge radius: r p = 0.84087 (39) fm Pohl et al. , Science 353, 669 (2016). Antognini et al. , Ann. Phys. 331, 127 (2013). Proton Zemach radius: R Z = 1.082 (37) fm Krauth et al. , Ann. Phys. 366, 168 (2016). Rydberg constant, using H(1S-2S): Pohl et al. , Metrologia 54, L1 (2017). R ∞ = 3 . 2898419602495 ( 10 ) radius ( 25 ) QED × 10 15 Hz / c Deuteron charge radius: r d = 2.12771 (22) fm using H/D(1S-2S) r p is 5 . 6 σ smaller than CODATA-2014 4 . 0 σ smaller than r p (H spectrosopy) r d is 5 . 4 σ smaller than CODATA-2014 (99% correlated with r p !) 3 . 5 σ smaller than r d (D spectrosopy) Proton and deuteron are consistently too small: h 2 3¯ r 2 d = r 2 struct + r 2 p + r 2 n + 4 m 2 p c 2 Randolf Pohl PhiPsi17 , 28 June 2017 15

  7. Conclusions µ p and µ d Pohl et al. , Nature 466, 213 (2010). Antognini et al. , Science 339, 417 (2013). Proton charge radius: r p = 0.84087 (39) fm Pohl et al. , Science 353, 669 (2016). Antognini et al. , Ann. Phys. 331, 127 (2013). Proton Zemach radius: R Z = 1.082 (37) fm Krauth et al. , Ann. Phys. 366, 168 (2016). Rydberg constant, using H(1S-2S): Pohl et al. , Metrologia 54, L1 (2017). R ∞ = 3 . 2898419602495 ( 10 ) radius ( 25 ) QED × 10 15 Hz / c Deuteron charge radius: r d = 2.12771 (22) fm using H/D(1S-2S) r p is 5 . 6 σ smaller than CODATA-2014 4 . 0 σ smaller than r p (H spectrosopy) r d is 5 . 4 σ smaller than CODATA-2014 (99% correlated with r p !) 3 . 5 σ smaller than r d (D spectrosopy) Proton and deuteron are consistently too small: h 2 3¯ r 2 d = r 2 struct + r 2 p + r 2 n + 4 m 2 p c 2 Randolf Pohl PhiPsi17 , 28 June 2017 15

  8. Muonic helium ions µ 4 He + µ 3 He + 2P 3/2 2P 3/2 F=1 2P F=2 2P 2P 1/2 F=0 F=1 2P 1/2 F=0 2S 1/2 F=1 2S 1/2 Randolf Pohl PhiPsi17 , 28 June 2017 16

  9. µ 4 He + ( 2 S 1 / 2 → 2 P 3 / 2 ) 1st µ 4 He-ion resonance at ∼ 812 nm wavelength -3 10 × 1 Events / Prompt 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 366 367 368 369 370 371 372 Frequency [THz] Randolf Pohl PhiPsi17 , 28 June 2017 17

  10. µ 4 He + ( 2 S 1 / 2 → 2 P 3 / 2 ) 1st µ 4 He-ion resonance at ∼ 812 nm wavelength ∆ E ( 2 S − 2 P ) = 1668 . 487 ( 14 ) meV ( QED ) -3 10 × − 106 . 358 ( 7 ) meV / fm 2 ·� r 2 � 1 Events / Prompt 0.9 0.8 + 6 . 761 ( 77 ) meV ( Friar ) 0.7 + 3 . 296 ( 189 ) meV ( polarizability ) 0.6 0.5 + 146 . 197 ( 12 ) meV ( fine structure ) 0.4 Diepold et al., 1606.05231 0.3 Thanks to the theorists! 0.2 0.1 0 expt’l accuracy: 17 GHz ≡ 0.066 meV 366 367 368 369 370 371 372 Frequency [THz] r( 4 He) = 1.68xxx ( 19) exp ( 58) theo fm PRELIMINARY vs. 1.68100 (400) fm from e-He scattering (plus the other transition µ 4 He + ( 2 S 1 / 2 → 2 P 1 / 2 ) ) Randolf Pohl PhiPsi17 , 28 June 2017 17

  11. 4 He charge radii PRELIMINARY This work Sick 2008 wrong µ 4 He Carboni 1977 Ottermann 1985 1.66 1.665 1.67 1.675 1.68 1.685 alpha charge radius [fm] Randolf Pohl PhiPsi17 , 28 June 2017 18

  12. µ 3 He + resonances signal [arb. units] transition #1 6 4 2 0 346.5 347 347.5 348 8 frequency [THz] signal [arb. units] transition #3 transition #2 6 4 2 ν ν 3 2 0 310 311 312 313 frequency [THz] Randolf Pohl PhiPsi17 , 28 June 2017 19

  13. µ 3 He + resonances signal [arb. units] ∆ E ( 2 S − 2 P 1 / 2 ) = transition #1 6 1644 . 347 ( 15 ) meV ( QED ) − 103 . 518 ( 10 ) meV / fm 2 ·� r 2 � 4 + 0 . 118 ( 3 ) meV ( radius ) + 15 . 300 ( 520 ) meV ( polarizability ) 2 Franke, Krauth et al., 1705.00352 Thanks to the theorists! 0 346.5 347 347.5 348 8 frequency [THz] signal [arb. units] transition #3 transition #2 expt’l accuracy: each ∼ 20 GHz 6 ⇒ 0.082/ √ 3 meV = 0.050 meV 4 r( 3 He) = 1.97xxx ( 12) exp (128) theo fm 2 PRELIMINARY ν ν 3 2 0 310 311 312 313 frequency [THz] Randolf Pohl PhiPsi17 , 28 June 2017 19

  14. 3 He charge radii PRELIMINARY This work Sick 2001 Amroun 1994 Ottermann 1985 Retzlaff 1984 Collard 1965 Dunn 1983 1.82 1.84 1.86 1.88 1.9 1.92 1.94 1.96 1.98 2 helion charge radius [fm] Randolf Pohl PhiPsi17 , 28 June 2017 20

  15. Muonic summary Muonic hydrogen gives: Proton charge radius: r p = 0.84087 (39) fm 7 σ away from electronic average (CODATA: H, e-p scatt.) Deuteron charge radius: r d = 2 . 12771 ( 22 ) fm from µ H + H/D(1S-2S) Muonic deuterium: Deuteron charge radius: r d = 2 . 12562 ( 13 ) exp ( 77 ) theo fm consistent with muonic proton radius, but again 7 σ away from CODATA: 2 . 14240 ( 210 ) fm “Proton” Radius Puzzle is in fact “Z=1 Radius Puzzle” muonic helium-3 and -4 ions: No big discrepancy (PRELIMINARY) Randolf Pohl PhiPsi17 , 28 June 2017 21

  16. Muonic summary Muonic hydrogen gives: Proton charge radius: r p = 0.84087 (39) fm 7 σ away from electronic average (CODATA: H, e-p scatt.) Deuteron charge radius: r d = 2 . 12771 ( 22 ) fm from µ H + H/D(1S-2S) Muonic deuterium: Deuteron charge radius: r d = 2 . 12562 ( 13 ) exp ( 77 ) theo fm consistent with muonic proton radius, but again 7 σ away from CODATA: 2 . 14240 ( 210 ) fm “Proton” Radius Puzzle is in fact “Z=1 Radius Puzzle” muonic helium-3 and -4 ions: No big discrepancy (PRELIMINARY) Could ALL be solved if the Rydberg constant [ and hence the (electronic) proton radius ] was wrong. Plus ∼ 2 . 6 σ change in deuteron polarizabililty. Plus: accept dispersion fits of e-p scattering Or: BSM physics, e.g. Tucker-Smith & Yavin (2011) Randolf Pohl PhiPsi17 , 28 June 2017 21

  17. (Electronic) hydrogen. Randolf Pohl PhiPsi17 , 28 June 2017 22

  18. Hydrogen spectroscopy = 8171 . 636 ( 4 )+ 1 . 5645 � r 2 L 1 S ( r p ) p � MHz Lamb shift : ≃ L 1 S L nS n 3 8S 4S 3S 3D 2S 2P 1S RP et al. arXiv 1607.03165 Randolf Pohl PhiPsi17 , 28 June 2017 23

  19. Hydrogen spectroscopy = 8171 . 636 ( 4 )+ 1 . 5645 � r 2 L 1 S ( r p ) p � MHz Lamb shift : ≃ L 1 S L nS n 3 8S 4S 3S 3D F=2 2P 3/2 F=1 2S 2P classical Lamb shift: 2S-2P 2S-2P Lamb, Retherford 1946 Lundeen, Pipkin 1986 9910 MHz = 40 µ eV Hagley, Pipkin 1994 Hessels et al. , 201x F=1 2S 1/2 1058 MHz = 4 µ eV F=0 F=1 2P 1/2 F=0 1S RP et al. arXiv 1607.03165 Randolf Pohl PhiPsi17 , 28 June 2017 23

  20. Hydrogen spectroscopy = 8171 . 636 ( 4 )+ 1 . 5645 � r 2 L 1 S ( r p ) p � MHz Lamb shift : ≃ L 1 S L nS n 3 8S 4S 3S 3D 2S-4P 2S-8D 2S 2P E nS ≃ − R ∞ n 2 + L 1 S n 3 1S-2S 2 unknowns ⇒ 2 transitions • Rydberg constant R ∞ • Lamb shift L 1 S ⇒ r p 1S RP et al. arXiv 1607.03165 Randolf Pohl PhiPsi17 , 28 June 2017 23

  21. Hydrogen spectroscopy 2S 1/2 - 2P 1/2 2S 1/2 - 2P 1/2 2S 1/2 - 2P 3/2 1S-2S + 2S- 4S 1/2 1S-2S + 2S- 4D 5/2 1S-2S + 2S- 4P 1/2 1S-2S + 2S- 4P 3/2 1S-2S + 2S- 6S 1/2 1S-2S + 2S- 6D 5/2 1S-2S + 2S- 8S 1/2 1S-2S + 2S- 8D 3/2 1S-2S + 2S- 8D 5/2 1S-2S + 2S-12D 3/2 1S-2S + 2S-12D 5/2 1S-2S + 1S - 3S 1/2 0.8 0.85 0.9 0.95 1 proton charge radius (fm) Randolf Pohl PhiPsi17 , 28 June 2017 24

  22. Hydrogen spectroscopy 2S 1/2 - 2P 1/2 2S 1/2 - 2P 1/2 2S 1/2 - 2P 3/2 1S-2S + 2S- 4S 1/2 1S-2S + 2S- 4D 5/2 1S-2S + 2S- 4P 1/2 1S-2S + 2S- 4P 3/2 1S-2S + 2S- 6S 1/2 1S-2S + 2S- 6D 5/2 1S-2S + 2S- 8S 1/2 1S-2S + 2S- 8D 3/2 1S-2S + 2S- 8D 5/2 1S-2S + 2S-12D 3/2 µ p : 0.84087 +- 0.00039 fm 1S-2S + 2S-12D 5/2 1S-2S + 1S - 3S 1/2 0.8 0.85 0.9 0.95 1 proton charge radius (fm) Randolf Pohl PhiPsi17 , 28 June 2017 24

  23. Hydrogen spectroscopy 2S 1/2 - 2P 1/2 2S 1/2 - 2P 1/2 2S 1/2 - 2P 3/2 1S-2S + 2S- 4S 1/2 1S-2S + 2S- 4D 5/2 1S-2S + 2S- 4P 1/2 1S-2S + 2S- 4P 3/2 1S-2S + 2S- 6S 1/2 1S-2S + 2S- 6D 5/2 1S-2S + 2S- 8S 1/2 1S-2S + 2S- 8D 3/2 1S-2S + 2S- 8D 5/2 H avg = 0.8779 +- 0.0094 fm 1S-2S + 2S-12D 3/2 µ p : 0.84087 +- 0.00039 fm 1S-2S + 2S-12D 5/2 1S-2S + 1S - 3S 1/2 0.8 0.85 0.9 0.95 1 proton charge radius (fm) Randolf Pohl PhiPsi17 , 28 June 2017 24

  24. Hydrogen spectroscopy 2S 1/2 - 2P 1/2 2S 1/2 - 2P 1/2 2S 1/2 - 2P 3/2 1S-2S + 2S- 4S 1/2 1S-2S + 2S- 4D 5/2 1S-2S + 2S- 4P 1/2 1S-2S + 2S- 4P 3/2 1S-2S + 2S- 6S 1/2 1S-2S + 2S- 6D 5/2 1S-2S + 2S- 8S 1/2 1S-2S + 2S- 8D 3/2 1S-2S + 2S- 8D 5/2 H avg = 0.8779 +- 0.0094 fm 1S-2S + 2S-12D 3/2 µ p : 0.84087 +- 0.00039 fm 1S-2S + 2S-12D 5/2 1S-2S + 1S - 3S 1/2 0.8 0.85 0.9 0.95 1 proton charge radius (fm) Randolf Pohl PhiPsi17 , 28 June 2017 24

  25. Rydberg constant from hydrogen 2S – 4P resonance at 88 ± 0 . 5 ◦ and 90 ± 0 . 08 ◦ A. Beyer, L. Maisenbacher, K. Khabarova, C.G. Parthey, A. Matveev, J. Alnis, R. Pohl, N. Kolachevsky, Th. Udem and T.W. Hänsch C.G. Parthey, RP et al. , PRL 104 , 233001 (2010) Apparatus used for H/D(1S-2S) C.G. Parthey, RP et al. , PRL 107 , 203001 (2011) 486 nm at 90 ◦ + Retroreflector ⇒ Doppler-free 2S-4P excitation 1st oder Doppler vs. ac-Stark shift ∼ 2 . 5 kHz accuracy (vs. 15 kHz Yale, 1995) cryogenic H beam, optical excitation to 2S A. Beyer, RP et al. , Ann. d. Phys. 525 , 671 (2013) Randolf Pohl PhiPsi17 , 28 June 2017 25

  26. Quantum interference shifts Horbatsch & Hessels, PRA 82, 052519 (2010); PRA 84, 032508 (2011), PRA 86, 040501 (2012), etc. Sansonetti et al. , PRL 107, 023001 (2011); Brown et al. , PRA 87, 032504 (2013) Amaro, RP et al. , PRA 92, 022514 (2015); PRA 92, 062506 (2015) Randolf Pohl PhiPsi17 , 28 June 2017 26

  27. Quantum interference shifts 2 ω 1 − ω L + i γ 1 / 2 + ( � ( � d 1 · � E 0 ) � d 2 · � E 0 ) � d 2 e i ∆ φ � � d 1 P ( ω ) ∝ � � ω 2 − ω L + i γ 2 / 2 � � = Lorentzian(1) + Lorentzian(2) + cross-term (QI) Horbatsch & Hessels, PRA 82, 052519 (2010); PRA 84, 032508 (2011), PRA 86, 040501 (2012), etc. Sansonetti et al. , PRL 107, 023001 (2011); Brown et al. , PRA 87, 032504 (2013) Amaro, RP et al. , PRA 92, 022514 (2015); PRA 92, 062506 (2015) Randolf Pohl PhiPsi17 , 28 June 2017 26

  28. Quantum interference shifts 2 ω 1 − ω L + i γ 1 / 2 + ( � ( � d 1 · � E 0 ) � d 2 · � E 0 ) � d 2 e i ∆ φ � � d 1 P ( ω ) ∝ � � ω 2 − ω L + i γ 2 / 2 � � = Lorentzian(1) + Lorentzian(2) + cross-term (QI) Horbatsch & Hessels, PRA 82, 052519 (2010); PRA 84, 032508 (2011), PRA 86, 040501 (2012), etc. Sansonetti et al. , PRL 107, 023001 (2011); Brown et al. , PRA 87, 032504 (2013) Amaro, RP et al. , PRA 92, 022514 (2015); PRA 92, 062506 (2015) Randolf Pohl PhiPsi17 , 28 June 2017 26

  29. Quantum interference shifts 2S-4P setup Beyer, RP et al. , submitted (2016) Randolf Pohl PhiPsi17 , 28 June 2017 26

  30. Cross-damping A. Beyer, RP et al. , submitted. Randolf Pohl PhiPsi17 , 28 June 2017 27

  31. 2S – 4P results PRELIMINARY PRELIMINARY A. Beyer, RP et al. , submitted. Randolf Pohl PhiPsi17 , 28 June 2017 28

  32. 2S – 4P results PRELIMINARY PRELIMINARY Proton can be small in regular hydrogen, too! Proton radius puzzle is NOT “solved”. Our main systematics do NOT affect the previous measurements. Note: We split an asymmetric line to 10 − 4 ! A. Beyer, RP et al. , submitted. Randolf Pohl PhiPsi17 , 28 June 2017 28

  33. The nuclear chart 7 8 9 10 11 12 Be Be Be Be Be Be Proton Number Z 2.6460 (150) 2.5190 (120) 2.3600 (140) 2.4650 (150) 2.5020 (150) 6 9 11 7 8 Li Li Li Li Li 2.5890 (390) 2.4440 (420) 2.3390 (440) 2.2450 (460) 2.4820 (430) 3 4 6 8 He He He He 1.9730 (160) 1.6810 ( 40) 2.0680 (110) 1.9290 (260) 1 2 3 T H D electron scattering muonic atom spectroscopy 0.8775 (51) 2.1424 (21) 1.7550 (860) H/D: precision laser spectroscopy + theory (a lot!) n 6 He, 8 He, ...: laser spectroscopy of isotope shift Neutron number N Randolf Pohl PhiPsi17 , 28 June 2017 29

  34. The nuclear chart - new charge radii 7 7 8 8 9 9 10 10 11 11 12 12 Be Be Be Be Be Be Be Be Be Be Be Be Proton Number Z Proton Number Z 2.6460 (150) 2.6460 (150) 2.5190 (120) 2.5190 (120) 2.3600 (140) 2.4650 (150) 2.3600 (140) 2.4650 (150) 2.5020 (150) 2.5020 (150) 6 6 9 9 11 11 7 7 8 8 Li Li Li Li Li Li Li Li Li Li 2.5890 (390) 2.4440 (420) 2.5890 (390) 2.4440 (420) 2.3390 (440) 2.3390 (440) 2.2450 (460) 2.2450 (460) 2.4820 (430) 2.4820 (430) 3 3 4 4 6 6 8 8 He He He He He He He He * * * * 1.96xx ( 10) 1.67xx ( 5) 2.06xx ( 80) 1.9xxx (246) 1.9730 (160) 1.9730 (160) 1.6810 ( 40) 1.6810 ( 40) 2.0680 (110) 2.0680 (110) 1.9290 (260) 1.9290 (260) 1 1 2 2 3 3 T T H H D D electron scattering muonic atom spectroscopy 0.8409 ( 4) 2.1277 ( 2) 0.8775 (51) 0.8775 (51) 2.1424 (21) 2.1424 (21) 1.7550 (860) 1.7550 (860) H/D: precision laser spectroscopy + theory (a lot!) n n 6 He, 8 He, ...: laser spectroscopy of isotope shift laser spectroscopy of muonic atoms/ions * = preliminary Neutron number N Neutron number N Randolf Pohl PhiPsi17 , 28 June 2017 29

  35. Summary Results from muonic hydrogen and deuterium: Proton charge radius: r p = 0.84087 (39) fm Proton Zemach radius: R Z = 1.082 (37) fm Rydberg constant: R ∞ = 3 . 2898419602495 ( 10 ) r p ( 25 ) QED × 10 15 Hz / c Deuteron charge radius: r d = 2.12771 ( 22) fm from µ H + H/D(1S-2S) The “Proton radius puzzle” muonic helium-3 and -4: charge radius 10x more precise. No big discrepancy H(2S-4P) gives revised Rydberg ⇒ small r p PRELIMINARY New projects: 1S-HFS in muonic hydrogen / 3 He ⇐ PSI, J-PARC, RIKEN-RAL, ... LS in muonic Li, Be, B, T, ...; muonic high-Z, ... 1S-2S and 2S- n ℓ in Hydrogen/Deuterium/Tritium, He + He, H 2 , HD + ,... Positronium ≡ e + e − , Muonium ≡ µ + e − Electron scattering: H at lower Q 2 , D, He Muon scattering: MUSE @ PSI ... Randolf Pohl PhiPsi17 , 28 June 2017 30

  36. Future: Muonic The world’s most intense beam for low-energy µ − Randolf Pohl PhiPsi17 , 28 June 2017 31

  37. Future: Muonic The world’s most intense beam for low-energy µ − 1S-HFS in µ p , µ 3 He → Zemach (magnetic) radius goal R-16-02 (CREMA-3) µ p 2013 e-p, Mainz H, Volotka e-p, Friar H, Dupays 1 1.02 1.04 1.06 1.08 1.1 1.12 Proton Zemach radius R [fm] Z Randolf Pohl PhiPsi17 , 28 June 2017 31

  38. Future: Muonic The world’s most intense beam for low-energy µ − 1S-HFS in µ p , µ 3 He → Zemach (magnetic) radius goal R-16-02 (CREMA-3) µ p 2013 e-p, Mainz H, Volotka e-p, Friar H, Dupays 1 1.02 1.04 1.06 1.08 1.1 1.12 Proton Zemach radius R [fm] Z stop in µ g of (radioactive) material → charge radii of higher Z muX Collab @ PSI 187 75 Re prelim. 2016 data Randolf Pohl PhiPsi17 , 28 June 2017 31

  39. Future: Muonic The world’s most intense beam for low-energy µ − 1S-HFS in µ p , µ 3 He → Zemach (magnetic) radius goal R-16-02 (CREMA-3) µ p 2013 e-p, Mainz H, Volotka e-p, Friar H, Dupays 1 1.02 1.04 1.06 1.08 1.1 1.12 Proton Zemach radius R [fm] Z stop in µ g of (radioactive) material → charge radii of higher Z muX Collab @ PSI stop µ − in Penning trap 187 75 Re → charge radii of Li, Be, B, T prelim. 2016 data Randolf Pohl PhiPsi17 , 28 June 2017 31

  40. Future: Electronic Hydrogen apparatus in Garching Randolf Pohl PhiPsi17 , 28 June 2017 32

  41. Future: Electronic Hydrogen apparatus in Garching Tritium = “missing link” 3 4 He He * * 1.96xx ( 10) 1.67xx ( 5) 1.9730 (160) 1.6810 ( 40) 1 2 3 H T 0.8409 ( 4) 2.1277 ( 2) 0.8775 (51) 2.1424 (21) 1.7550 (860) r p = 0.8775( 51) fm → 0.8409( 4) fm r d = 2.1424( 21) fm → 2.1277( 2) fm r t = 1.7550(860) fm ⇒ potential improvement by 400! p = 3 . 82007 ( 65 ) fm 2 H/D(1S-2S) isotope shift to 15 Hz r 2 d − r 2 limit from theory : 1 kHz r t from T(1S-2S) to 10 kHz, later 1 kHz Randolf Pohl PhiPsi17 , 28 June 2017 32

  42. CREMA in 2009... Randolf Pohl PhiPsi17 , 28 June 2017 33

  43. ... and 2014 Randolf Pohl PhiPsi17 , 28 June 2017 34

  44. ... and 2017 Randolf Pohl PhiPsi17 , 28 June 2017 35

  45. Backup slides. Randolf Pohl PhiPsi17 , 28 June 2017 36

  46. Quantum interference shifts Horbatsch & Hessels, PRA 82, 052519 (2010); PRA 84, 032508 (2011), PRA 86, 040501 (2012), etc. Sansonetti et al. , PRL 107, 023001 (2011); Brown et al. , PRA 87, 032504 (2013) Amaro, RP et al. , PRA 92, 022514 (2015); PRA 92, 062506 (2015) Randolf Pohl PhiPsi17 , 28 June 2017 37

  47. Quantum interference shifts 2 ω 1 − ω L + i γ 1 / 2 + ( � ( � d 1 · � E 0 ) � d 2 · � E 0 ) � d 2 e i ∆ φ � � d 1 P ( ω ) ∝ � � ω 2 − ω L + i γ 2 / 2 � � = Lorentzian(1) + Lorentzian(2) + cross-term (QI) Horbatsch & Hessels, PRA 82, 052519 (2010); PRA 84, 032508 (2011), PRA 86, 040501 (2012), etc. Sansonetti et al. , PRL 107, 023001 (2011); Brown et al. , PRA 87, 032504 (2013) Amaro, RP et al. , PRA 92, 022514 (2015); PRA 92, 062506 (2015) Randolf Pohl PhiPsi17 , 28 June 2017 37

  48. Quantum interference shifts 2 ω 1 − ω L + i γ 1 / 2 + ( � ( � d 1 · � E 0 ) � d 2 · � E 0 ) � d 2 e i ∆ φ � � d 1 P ( ω ) ∝ � � ω 2 − ω L + i γ 2 / 2 � � = Lorentzian(1) + Lorentzian(2) + cross-term (QI) Horbatsch & Hessels, PRA 82, 052519 (2010); PRA 84, 032508 (2011), PRA 86, 040501 (2012), etc. Sansonetti et al. , PRL 107, 023001 (2011); Brown et al. , PRA 87, 032504 (2013) Amaro, RP et al. , PRA 92, 022514 (2015); PRA 92, 062506 (2015) Randolf Pohl PhiPsi17 , 28 June 2017 37

  49. Quantum interference shifts 2S-4P setup Beyer, RP et al. , submitted (2016) Randolf Pohl PhiPsi17 , 28 June 2017 37

  50. Cross-damping A. Beyer, RP et al. , submitted. Randolf Pohl PhiPsi17 , 28 June 2017 38

  51. 2S – 4P uncertainties A. Beyer, RP et al. , submitted. Randolf Pohl PhiPsi17 , 28 June 2017 39

  52. 2S – 4P results PRELIMINARY PRELIMINARY A. Beyer, RP et al. , submitted. Randolf Pohl PhiPsi17 , 28 June 2017 40

  53. 2S – 4P results PRELIMINARY PRELIMINARY Proton can be small in regular hydrogen, too! Proton radius puzzle is NOT “solved”. Our main systematics do NOT affect the previous measurements. Note: We split an asymmetric line to 10 − 4 ! A. Beyer, RP et al. , submitted. Randolf Pohl PhiPsi17 , 28 June 2017 40

  54. Hydrogen(-like) 1S-2S ✲ log(# atoms) Randolf Pohl PhiPsi17 , 28 June 2017 41

  55. Hydrogen(-like) 1S-2S Hydrogen apparatus in Garching 10 18 /s ✲ log(# atoms) Randolf Pohl PhiPsi17 , 28 June 2017 41

  56. Hydrogen(-like) 1S-2S Hydrogen apparatus in Garching ALPHA Antihydrogen 1S-2S 10 0 /s 10 18 /s ✲ log(# atoms) Randolf Pohl PhiPsi17 , 28 June 2017 41

  57. Hydrogen(-like) 1S-2S Hydrogen apparatus in Garching ALPHA Antihydrogen 1S-2S work here! 10 0 /s 10 9 /trial 10 18 /s ✲ log(# atoms) Randolf Pohl PhiPsi17 , 28 June 2017 41

  58. Towards T(1S-2S) I: Trapped H (BEC) PRL 70, 544 (1993), Walraven group Randolf Pohl PhiPsi17 , 28 June 2017 42

  59. Towards T(1S-2S) I: Trapped H (BEC) PRL 70, 544 (1993), Walraven group PRL 77, 255 (1996), Kleppner group Randolf Pohl PhiPsi17 , 28 June 2017 42

  60. Towards T(1S-2S) I: Trapped H (BEC) PRL 70, 544 (1993), Walraven group PRL 77, 255 (1996), Kleppner group PRL 81, 3811 (1998) Randolf Pohl PhiPsi17 , 28 June 2017 42

  61. Towards T(1S-2S) II: Matrix sublimation Rev. Sci. Instr. 86, 073109 (2015) C.L. Cesar (Kleppner @ MIT, 1990s) et al. Randolf Pohl PhiPsi17 , 28 June 2017 43

  62. The laser system Yb:YAG thin−disk laser Main components: cw TiSa laser Oscillator Oscillator 1030 nm Wave 1030 nm Verdi 200 W 200 W meter • Thin-disk laser 9 mJ 9 mJ 5 W Amplifier Amplifier cw TiSa fast response to detected µ − 500 W 500 W FP 708 nm 43 mJ 43 mJ • Frequency doubling 400 mW SHG SHG I / Cs 2 SHG • TiSa laser: 7 mJ frequency stabilized cw laser 1.5 mJ 23 mJ 515 nm 23 mJ injection seeded oscillator TiSa Osc. multipass amplifier TiSa Amp. 708 nm, 15 mJ • Raman cell 6 m monitoring H O µ 6 m µ 2 3 Stokes: 708 nm → 6 µ m 0.25 mJ 20 m λ calibration @ 6 µ m Raman cell Ge−filter • Target cavity µ 6 m cavity µ − A. Antognini, RP et. al. , Opt. Comm. 253, 362 (2005). Randolf Pohl PhiPsi17 , 28 June 2017 44

  63. The laser system Yb:YAG thin−disk laser cw TiSa laser Oscillator Oscillator Thin-disk laser 1030 nm Wave 1030 nm Verdi 200 W 200 W meter 9 mJ 9 mJ 5 W • Large pulse energy: 85 (160) mJ Amplifier Amplifier cw TiSa 500 W 500 W FP • Short trigger-to-pulse delay: � 400 ns 708 nm 43 mJ 43 mJ 400 mW • Random trigger SHG SHG I / Cs 2 • Pulse-to-pulse delays down to 2 ms SHG (rep. rate � 500 Hz) 7 mJ 1.5 mJ 23 mJ 515 nm 23 mJ TiSa Osc. • Each single µ − triggers the laser system TiSa Amp. 708 nm, 15 mJ • 2 S lifetime ≈ 1 µ s → short laser delay 6 m monitoring H O µ 6 m µ 2 0.25 mJ 20 m Raman cell Ge−filter A. Antognini, RP et. al. , µ 6 m cavity µ − IEEE J. Quant. Electr. 45, 993 (2009). Randolf Pohl PhiPsi17 , 28 June 2017 44

  64. The laser system Yb:YAG thin−disk laser MOPA TiSa laser: cw TiSa laser Oscillator Oscillator 1030 nm Wave 1030 nm Verdi 200 W 200 W cw laser, frequency stabilized meter 9 mJ 9 mJ 5 W - referenced to a stable FP cavity Amplifier Amplifier cw TiSa 500 W 500 W FP 708 nm 43 mJ - FP cavity calibrated with I 2 , Rb, Cs lines 43 mJ 400 mW SHG SHG I / Cs ν FP = N · FSR 2 SHG FSR = 1497 . 344 ( 6 ) MHz 7 mJ ν cw TiSa absolutely known to 30 MHz 1.5 mJ 23 mJ 515 nm 23 mJ Γ 2P − 2S = 18 . 6 GHz TiSa Osc. TiSa Amp. 708 nm, 15 mJ Seeded oscillator → ν pulsed = ν cw 6 m monitoring H O µ 6 m µ TiSa TiSa 2 0.25 mJ (frequency chirp ≤ 200 MHz) 20 m Raman cell Ge−filter Multipass amplifier (2f- configuration) gain=10 µ 6 m cavity µ − Randolf Pohl PhiPsi17 , 28 June 2017 44

  65. The laser system Yb:YAG thin−disk laser Raman cell: cw TiSa laser Oscillator Oscillator 1030 nm Wave 1030 nm Verdi 200 W 200 W µ 708 nm meter 6.02 m H 2 9 mJ 9 mJ 5 W Amplifier Amplifier cw TiSa 500 W 500 W FP 708 nm 43 mJ 43 mJ 400 mW st nd rd SHG 1 Stokes 2 Stokes 3 Stokes SHG I / Cs 2 SHG 708 nm 7 mJ µ 1.5 mJ 1.00 m 23 mJ 515 nm 23 mJ µ µ 1.72 m 6.02 m 4155 cm −1 v=1 TiSa Osc. H 2 TiSa Amp. 708 nm, 15 mJ v=0 6 m monitoring H O µ 6 m µ 2 0.25 mJ ν 6 µ m = ν 708nm − 3 · ¯ h ω vib 20 m Raman cell Ge−filter tunable ω vib ( p , T ) = const µ 6 m cavity µ − P . Rabinowitz et. al. , IEEE J. QE 22 , 797 (1986) Randolf Pohl PhiPsi17 , 28 June 2017 44

  66. The laser system Yb:YAG thin−disk laser cw TiSa laser 12 Oscillator Oscillator 190 mm 1030 nm Wave 1030 nm Verdi 200 W 200 W − µ meter 9 mJ 9 mJ 5 W 25 Amplifier Amplifier cw TiSa 500 W 500 W FP 708 nm α 43 mJ β 43 mJ Laser pulse 400 mW SHG SHG I / Cs 2 SHG 2 mm 3 mm Horiz. plane Vert. plane 7 mJ 1.5 mJ 23 mJ 515 nm 23 mJ Design: insensitive to misalignment TiSa Osc. Transverse illumination TiSa Amp. 708 nm, 15 mJ Large volume 6 m monitoring H O µ 6 m µ 2 Dielectric coating with R ≥ 99 . 9% (at 6 µ m ) 0.25 mJ 20 m → Light makes 1000 reflections Raman cell → Light is confined for τ =50 ns Ge−filter → 0.15 mJ saturates the 2 S − 2 P transition µ 6 m cavity µ − J. Vogelsang, RP et. al. , Opt. Expr. 22 , 13050 (2014) Randolf Pohl PhiPsi17 , 28 June 2017 44

  67. The laser system Yb:YAG thin−disk laser Water absorption cw TiSa laser 0.7 Oscillator Oscillator 1030 nm Wave 1030 nm Verdi 200 W 0.6 200 W meter 9 mJ 9 mJ 0.5 5 W Amplifier 0.4 Amplifier cw TiSa 500 W 500 W FP 708 nm 43 mJ 0.3 43 mJ 400 mW SHG 0.2 SHG I / Cs 2 0.1 SHG 0 1200 1300 1400 1500 1600 1700 1800 1900 2000 2100 wavenumber (cm -1 ) 7 mJ 1.5 mJ 0.7 23 mJ 515 nm 23 mJ scan region 0.6 TiSa Osc. 0.5 TiSa Amp. 708 nm, 15 mJ 0.4 0.3 0.2 6 m monitoring H O µ 6 m µ 2 0.25 mJ 0.1 20 m 0 1630 1640 1650 1660 1670 1680 1690 1700 wavenumber (cm -1 ) Raman cell Ge−filter • Vacuum tube for 6 µ m beam transport. µ 6 m cavity µ − • Direct frequency calibration at 6 µ m. Randolf Pohl PhiPsi17 , 28 June 2017 44

  68. Theory in µ d: TPE Deuteron structure contributions to the Lamb shift in muonic deuterium. µ µ d d µ µ d d Cancellation between elastic “Friar” (a.k.a. 3rd Zemach) terms and part of inelastic “polarizability” contributions. Friar & Payne, PRA 56, 5173 (1997) ; Pachucki, PRL 106, 193007 (2011) ; Friar, PRC 88, 034003 (2013) ; Hernandez et al. , PLB 736, 344 (2014) J.J. Krauth, RP et al. , Ann. Phys. 366 , 168 (2016) [1506.01298] Randolf Pohl PhiPsi17 , 28 June 2017 45

  69. Theory in µ d: TPE Table 3: Deuteron structure contributions to the Lamb shift in muonic deuterium. Values are in meV. Item Contribution Pachucki [55] Friar [60] Hernandez et al. [58] Pach.& Wienczek [65] Carlson et al. [64] Our choice N 3 LO † AV18 ZRA AV18 AV18 data value source Source 1 2 3 4 5 6 δ (0) p1 Dipole 1 . 910 δ 0 E 1 . 925 Leading C1 1 . 907 1 . 926 1 . 910 δ 0 E 1 . 9165 ± 0 . 0095 3-5 D 1 δ (0) p2 Rel. corr. to p1, longitudinal part − 0 . 035 δ R E − 0 . 037 Subleading C1 − 0 . 029 − 0 . 030 − 0 . 026 δ R E L δ (0) p3 Rel. corr. to p1, transverse part 0 . 012 0 . 013 T p4 Rel. corr. to p1, higher order 0 . 004 δ HO E sum Total rel. corr., p2+p3+p4 − 0 . 035 − 0 . 037 − 0 . 017 − 0 . 017 − 0 . 022 − 0 . 0195 ± 0 . 0025 3-5 p5 Coulomb distortion, leading − 0 . 255 δ C 1 E − 0 . 255 δ C 1 E p6 Coul. distortion, next order − 0 . 006 δ C 2 E − 0 . 006 δ C 2 E δ (0) sum Total Coulomb distortion, p5+p6 − 0 . 261 − 0 . 262 − 0 . 264 − 0 . 261 − 0 . 2625 ± 0 . 0015 3-5 C δ (2) p7 El. monopole excitation − 0 . 045 δ Q 0 E − 0 . 042 C0 − 0 . 042 − 0 . 041 − 0 . 042 δ Q 0 E R 2 δ (2) p8 El. dipole excitation 0 . 151 δ Q 1 E 0 . 137 Retarded C1 0 . 139 0 . 140 0 . 139 δ Q 1 E D 1 D 3 δ (2) p9 El. quadrupole excitation − 0 . 066 δ Q 2 E − 0 . 061 C2 − 0 . 061 − 0 . 061 − 0 . 061 δ Q 2 E Q sum Tot. nuclear excitation, p7+p8+p9 0 . 040 0 . 034 C0 + ret-C1 + C2 0 . 036 0 . 038 0 . 036 0 . 0360 ± 0 . 0020 2-5 δ (0) − 0 . 008 ♦ p10 Magnetic δ M E − 0 . 011 M1 − 0 . 008 − 0 . 007 − 0 . 008 δ M E − 0 . 0090 ± 0 . 0020 2-5 M SUM 1 Total nuclear (corrected) 1 . 646 1 . 648 1 . 656 1 . 676 1 . 655 1 . 6615 ± 0 . 0103 δ (2) 0 . 020 ♦ 0 . 021 ♦ ?? p11 Finite nucleon size 0 . 021 Retarded C1 f.s. 0 . 020 δ F S E NS δ (1) p12 n p charge correlation − 0 . 023 pn correl. f.s. − 0 . 017 − 0 . 017 − 0 . 018 δ F Z E np sum p11+p12 − 0 . 002 0 . 003 0 . 004 0 . 002 0 . 0010 ± 0 . 0030 2-5 � r 3 � pp � � p13 Proton elastic 3rd Zemach moment 0 . 030 0 . 0289 ± 0 . 0015 Eq.(13) 0 . 043(3) δ P E 0 . 043(3) δ P E (2) � � � p14 Proton inelastic polarizab. δ N 0 . 028(2)∆ E hadr 0 . 027(2) pol [64] 0 . 0280 ± 0 . 0020 6 p15 Neutron inelastic polarizab. 0 . 016(8) δ N E p16 Proton & neutron subtraction term − 0 . 0098 ± 0 . 0098 Eq.(15) sum Nucleon TPE, p13+p14+p15+p16 0 . 043(3) 0 . 030 0.027(2) 0 . 059(9) 0 . 0471 ± 0 . 0101 SUM 2 Total nucleon contrib. 0 . 043(3) 0 . 028 0.030(2) 0 . 061(9) 0 . 0476 ± 0 . 0105 Sum , published 1 . 680(16) 1 . 941(19) 1.690(20) 1 . 717(20) 2 . 011(740) Sum , corrected 1 . 697(19) 1.714(20) 1 . 707(20) 1 . 748(740) 1 . 7096 ± 0 . 0147 J.J. Krauth et al. , Ann. Phys. 366 , 168 (2016) [1506.01298] ∆ E TPE ( theo ) = 1 . 7096 ± 0 . 0200 meV ± 0 . 0034 meV vs. exp. uncertainty Randolf Pohl PhiPsi17 , 28 June 2017 45

  70. Theory in µ d: TPE using ∆ E theo r d = 2 . 12562 ( 13 ) exp ( 77 ) theo fm, TPE = 1 . 7096 ( 200 ) meV limited by deuteron structure (TPE) contributions to the µ d LS µ µ d d µ µ d d Cancellation between elastic “Friar” (a.k.a. 3rd Zemach) terms and part of inelastic “polarizability” contributions. Nucleon structure adds relevant contributions (and uncertainty). Friar & Payne, PRA 56, 5173 (1997) ; Pachucki, PRL 106, 193007 (2011) ; Friar, PRC 88, 034003 (2013) ; Hernandez et al. , PLB 736, 344 (2014) ; Pachucki & Wienczek, PRA 91, 040503(R) (2015) ; Carlson, Gorchtein, Vanderhaeghen, PRA 89, 022504 (2014) ; Birse & McGovern et al. J.J. Krauth, RP et al. , Ann. Phys. 366 , 168 (2016) [1506.01298] Randolf Pohl PhiPsi17 , 28 June 2017 46

  71. Theory in µ d: TPE Table 3: Deuteron structure contributions to the Lamb shift in muonic deuterium. Values are in meV. Item Contribution Pachucki [55] Friar [60] Hernandez et al. [58] Pach.& Wienczek [65] Carlson et al. [64] Our choice N 3 LO † AV18 ZRA AV18 AV18 data value source Source 1 2 3 4 5 6 δ (0) p1 Dipole 1 . 910 δ 0 E 1 . 925 Leading C1 1 . 907 1 . 926 1 . 910 δ 0 E 1 . 9165 ± 0 . 0095 3-5 D 1 δ (0) p2 Rel. corr. to p1, longitudinal part − 0 . 035 δ R E − 0 . 037 Subleading C1 − 0 . 029 − 0 . 030 − 0 . 026 δ R E L δ (0) p3 Rel. corr. to p1, transverse part 0 . 012 0 . 013 T p4 Rel. corr. to p1, higher order 0 . 004 δ HO E sum Total rel. corr., p2+p3+p4 − 0 . 035 − 0 . 037 − 0 . 017 − 0 . 017 − 0 . 022 − 0 . 0195 ± 0 . 0025 3-5 p5 Coulomb distortion, leading − 0 . 255 δ C 1 E − 0 . 255 δ C 1 E p6 Coul. distortion, next order − 0 . 006 δ C 2 E − 0 . 006 δ C 2 E δ (0) sum Total Coulomb distortion, p5+p6 − 0 . 261 − 0 . 262 − 0 . 264 − 0 . 261 − 0 . 2625 ± 0 . 0015 3-5 C δ (2) p7 El. monopole excitation − 0 . 045 δ Q 0 E − 0 . 042 C0 − 0 . 042 − 0 . 041 − 0 . 042 δ Q 0 E R 2 δ (2) p8 El. dipole excitation 0 . 151 δ Q 1 E 0 . 137 Retarded C1 0 . 139 0 . 140 0 . 139 δ Q 1 E D 1 D 3 δ (2) p9 El. quadrupole excitation − 0 . 066 δ Q 2 E − 0 . 061 C2 − 0 . 061 − 0 . 061 − 0 . 061 δ Q 2 E Q sum Tot. nuclear excitation, p7+p8+p9 0 . 040 0 . 034 C0 + ret-C1 + C2 0 . 036 0 . 038 0 . 036 0 . 0360 ± 0 . 0020 2-5 δ (0) − 0 . 008 ♦ p10 Magnetic δ M E − 0 . 011 M1 − 0 . 008 − 0 . 007 − 0 . 008 δ M E − 0 . 0090 ± 0 . 0020 2-5 M SUM 1 Total nuclear (corrected) 1 . 646 1 . 648 1 . 656 1 . 676 1 . 655 1 . 6615 ± 0 . 0103 δ (2) 0 . 020 ♦ 0 . 021 ♦ ?? p11 Finite nucleon size 0 . 021 Retarded C1 f.s. 0 . 020 δ F S E NS δ (1) p12 n p charge correlation − 0 . 023 pn correl. f.s. − 0 . 017 − 0 . 017 − 0 . 018 δ F Z E np sum p11+p12 − 0 . 002 0 . 003 0 . 004 0 . 002 0 . 0010 ± 0 . 0030 2-5 � r 3 � pp � � p13 Proton elastic 3rd Zemach moment 0 . 030 0 . 0289 ± 0 . 0015 Eq.(13) 0 . 043(3) δ P E 0 . 043(3) δ P E (2) � � � p14 Proton inelastic polarizab. δ N 0 . 028(2)∆ E hadr 0 . 027(2) pol [64] 0 . 0280 ± 0 . 0020 6 p15 Neutron inelastic polarizab. 0 . 016(8) δ N E p16 Proton & neutron subtraction term − 0 . 0098 ± 0 . 0098 Eq.(15) sum Nucleon TPE, p13+p14+p15+p16 0 . 043(3) 0 . 030 0.027(2) 0 . 059(9) 0 . 0471 ± 0 . 0101 SUM 2 Total nucleon contrib. 0 . 043(3) 0 . 028 0.030(2) 0 . 061(9) 0 . 0476 ± 0 . 0105 Sum , published 1 . 680(16) 1 . 941(19) 1.690(20) 1 . 717(20) 2 . 011(740) Sum , corrected 1 . 697(19) 1.714(20) 1 . 707(20) 1 . 748(740) 1 . 7096 ± 0 . 0147 J.J. Krauth et al. , Ann. Phys. 366 , 168 (2016) [1506.01298] ∆ E TPE ( theo ) = 1 . 7096 ± 0 . 0200 meV ∆ E TPE ( exp ) = 1 . 7638 ± 0 . 0068 meV Randolf Pohl PhiPsi17 , 28 June 2017 47

  72. Experimental TPE in µ d ∆ E TPE ( theo ) = 1 . 7096 ± 0 . 0200 meV ∆ E TPE ( exp ) = 1 . 7638 ± 0 . 0068 meV 2 . 6 σ , 3x more accurate = 228 . 7766 ( 10 ) meV ( QED )+ ∆ E TPE − 6 . 1103 ( 3 ) r 2 d meV / fm 2 , ∆ E LS • ∆ E exp LS = 202 . 8785 ( 31 ) stat ( 14 ) syst meV from µ D exp. p = 3 . 82007 ( 65 ) fm 2 [H/D(1S-2S) isotope shift] • r d = 2 . 12771 ( 22 ) fm from r 2 d − r 2 r p ( µ H) = 0.84087(39) fm using D spectr. µ D 2 . 6 σ from TPE ✛ ✲ µ H + iso H/D(1S-2S) CODATA-2014 e-d scatt. 2.11 2.115 2.12 2.125 2.13 2.135 2.14 2.145 Deuteron charge radius [fm] Randolf Pohl PhiPsi17 , 28 June 2017 48

  73. Experimental TPE in µ d ∆ E TPE ( theo ) = 1 . 7096 ± 0 . 0200 meV ∆ E TPE ( exp ) = 1 . 7638 ± 0 . 0068 meV 2 . 6 σ , 3x more accurate = 228 . 7766 ( 10 ) meV ( QED )+ ∆ E TPE − 6 . 1103 ( 3 ) r 2 d meV / fm 2 , ∆ E LS • ∆ E exp LS = 202 . 8785 ( 31 ) stat ( 14 ) syst meV from µ D exp. p = 3 . 82007 ( 65 ) fm 2 [H/D(1S-2S) isotope shift] • r d = 2 . 12771 ( 22 ) fm from r 2 d − r 2 r p ( µ H) = 0.84087(39) fm using D spectr. µ D 2 . 6 σ from TPE ✛ ✲ µ H + iso H/D(1S-2S) CODATA-2014 e-d scatt. 2.11 2.115 2.12 2.125 2.13 2.135 2.14 2.145 Deuteron charge radius [fm] Randolf Pohl PhiPsi17 , 28 June 2017 48

  74. Deuteron charge radius H/D isotope shift: r 2 d − r 2 p = 3 . 82007 ( 65 ) fm 2 C.G. Parthey, RP et al. , PRL 104 , 233001 (2010) r d = 2 . 14130 ( 250 ) fm CODATA 2014 r p from µ H gives r d = 2 . 12771 ( 22 ) fm ← 5 . 4 σ from r p µ H + iso H/D(1S-2S) CODATA-2014 e-d scatt. 2.11 2.115 2.12 2.125 2.13 2.135 2.14 2.145 Deuteron charge radius [fm] Randolf Pohl PhiPsi17 , 28 June 2017 49

  75. Deuteron charge radius H/D isotope shift: r 2 d − r 2 p = 3 . 82007 ( 65 ) fm 2 C.G. Parthey, RP et al. , PRL 104 , 233001 (2010) r d = 2 . 14130 ( 250 ) fm CODATA 2014 r p from µ H gives r d = 2 . 12771 ( 22 ) fm ← 5 . 4 σ from r p µ H + iso H/D(1S-2S) CODATA-2014 ✛ ( 5 . 4 σ from µ H) ✲ e-d scatt. 2.11 2.115 2.12 2.125 2.13 2.135 2.14 2.145 Deuteron charge radius [fm] Randolf Pohl PhiPsi17 , 28 June 2017 49

  76. Deuteron charge radius H/D isotope shift: r 2 d − r 2 p = 3 . 82007 ( 65 ) fm 2 C.G. Parthey, RP et al. , PRL 104 , 233001 (2010) r d = 2 . 14130 ( 250 ) fm CODATA 2014 r p from µ H gives r d = 2 . 12771 ( 22 ) fm ← 5 . 4 σ from r p r d = 2 . 12562 ( 13 ) exp ( 77 ) theo fm RP et al. , Science 353 , 417 (2016) Muonic DEUTERIUM µ D µ H + iso H/D(1S-2S) CODATA-2014 ✛ ( 5 . 4 σ from µ H) ✲ e-d scatt. 2.11 2.115 2.12 2.125 2.13 2.135 2.14 2.145 Deuteron charge radius [fm] Randolf Pohl PhiPsi17 , 28 June 2017 49

  77. Deuteron charge radius H/D isotope shift: r 2 d − r 2 p = 3 . 82007 ( 65 ) fm 2 C.G. Parthey, RP et al. , PRL 104 , 233001 (2010) r d = 2 . 14130 ( 250 ) fm CODATA 2014 r p from µ H gives r d = 2 . 12771 ( 22 ) fm ← 5 . 4 σ from r p r d = 2 . 12562 ( 13 ) exp ( 77 ) theo fm RP et al. , Science 353 , 417 (2016) Muonic DEUTERIUM µ D another 6 σ discrepancy! ✛ ✲ µ H + iso H/D(1S-2S) CODATA-2014 ✛ ( 5 . 4 σ from µ H) ✲ e-d scatt. 2.11 2.115 2.12 2.125 2.13 2.135 2.14 2.145 Deuteron charge radius [fm] Randolf Pohl PhiPsi17 , 28 June 2017 49

  78. Deuteron charge radius H/D isotope shift: r 2 d − r 2 p = 3 . 82007 ( 65 ) fm 2 C.G. Parthey, RP et al. , PRL 104 , 233001 (2010) r d = 2 . 14130 ( 250 ) fm CODATA 2014 r p from µ H gives r d = 2 . 12771 ( 22 ) fm ← 5 . 4 σ from r p r d = 2 . 12562 ( 13 ) exp ( 77 ) theo fm RP et al. , Science 353 , 417 (2016) Muonic DEUTERIUM r d = 2 . 14150 ( 450 ) fm electronic D ( r p indep.) RP et al. Metrologia 54 , L1 (2017) D spectr. µ D another 6 σ discrepancy! ✛ ✲ µ H + iso H/D(1S-2S) CODATA-2014 ✛ ( 5 . 4 σ from µ H) ✲ e-d scatt. 2.11 2.115 2.12 2.125 2.13 2.135 2.14 2.145 Deuteron charge radius [fm] Randolf Pohl PhiPsi17 , 28 June 2017 49

  79. Deuteron charge radius H/D isotope shift: r 2 d − r 2 p = 3 . 82007 ( 65 ) fm 2 C.G. Parthey, RP et al. , PRL 104 , 233001 (2010) r d = 2 . 14130 ( 250 ) fm CODATA 2014 r p from µ H gives r d = 2 . 12771 ( 22 ) fm ← 5 . 4 σ from r p r d = 2 . 12562 ( 13 ) exp ( 77 ) theo fm RP et al. , Science 353 , 417 (2016) Muonic DEUTERIUM r d = 2 . 14150 ( 450 ) fm ← 3 . 5 σ electronic D ( r p indep.) RP et al. Metrologia 54 , L1 (2017) 3 . 5 σ indep. of r p ✛ ✲ D spectr. µ D another 6 σ discrepancy! ✛ ✲ µ H + iso H/D(1S-2S) CODATA-2014 ✛ ( 5 . 4 σ from µ H) ✲ e-d scatt. 2.11 2.115 2.12 2.125 2.13 2.135 2.14 2.145 Deuteron charge radius [fm] Randolf Pohl PhiPsi17 , 28 June 2017 49

  80. Results from muonic deuterium Lamb shift in muonic deuterium: LS = 228 . 7766 ( 10 ) meV + ∆ E TPE − 6 . 1103 ( 3 ) r 2 ∆ E theo d meV / fm 2 with deuteron polarizability (TPE) ∆ E TPE ( theo ) = 1 . 7096 ( 200 ) meV J.J. Krauth et al. , Ann. Phys. 366 , 168 (2016) [1506.01298] compilation of original results from: Borie, Martynenko et al. , Karshenboim et al. , Jentschura, Bacca, Barnea, Nevo Dinur et al. , Pachucki et al. , Friar, Carlson, Gorchtein, Vanderhaeghen, and others r d ( µ d ) = 2 . 12562 ( 13 ) exp ( 77 ) theo fm RP et al. , Science 353 , 417 (2016) r d ( µ p + iso ) = 2 . 12771 ( 22 ) fm from r p ( µ p ) and H/D(1S-2S) 2 . 6 σ r d ( CODATA ) = 2 . 14130 ( 250 ) fm 6 . 0 σ to ∆ E LS ( r d ( CODATA )) Disprepancy = 0.409(68) meV (“proton radius puzzle” ( µ p discrepancy) = 0.329(47) meV) Randolf Pohl PhiPsi17 , 28 June 2017 50

  81. Theory in µ d: TPE Deuteron structure contributions to the Lamb shift in muonic deuterium. µ µ d d µ µ d d Cancellation between elastic “Friar” (a.k.a. 3rd Zemach) terms and part of inelastic “polarizability” contributions. Friar & Payne, PRA 56, 5173 (1997) ; Pachucki, PRL 106, 193007 (2011) ; Friar, PRC 88, 034003 (2013) ; Hernandez et al. , PLB 736, 344 (2014) J.J. Krauth, RP et al. , Ann. Phys. 366 , 168 (2016) [1506.01298] Randolf Pohl PhiPsi17 , 28 June 2017 51

  82. Theory in µ d: TPE Table 3: Deuteron structure contributions to the Lamb shift in muonic deuterium. Values are in meV. Item Contribution Pachucki [55] Friar [60] Hernandez et al. [58] Pach.& Wienczek [65] Carlson et al. [64] Our choice N 3 LO † AV18 ZRA AV18 AV18 data value source Source 1 2 3 4 5 6 δ (0) p1 Dipole 1 . 910 δ 0 E 1 . 925 Leading C1 1 . 907 1 . 926 1 . 910 δ 0 E 1 . 9165 ± 0 . 0095 3-5 D 1 δ (0) p2 Rel. corr. to p1, longitudinal part − 0 . 035 δ R E − 0 . 037 Subleading C1 − 0 . 029 − 0 . 030 − 0 . 026 δ R E L δ (0) p3 Rel. corr. to p1, transverse part 0 . 012 0 . 013 T p4 Rel. corr. to p1, higher order 0 . 004 δ HO E sum Total rel. corr., p2+p3+p4 − 0 . 035 − 0 . 037 − 0 . 017 − 0 . 017 − 0 . 022 − 0 . 0195 ± 0 . 0025 3-5 p5 Coulomb distortion, leading − 0 . 255 δ C 1 E − 0 . 255 δ C 1 E p6 Coul. distortion, next order − 0 . 006 δ C 2 E − 0 . 006 δ C 2 E δ (0) sum Total Coulomb distortion, p5+p6 − 0 . 261 − 0 . 262 − 0 . 264 − 0 . 261 − 0 . 2625 ± 0 . 0015 3-5 C δ (2) p7 El. monopole excitation − 0 . 045 δ Q 0 E − 0 . 042 C0 − 0 . 042 − 0 . 041 − 0 . 042 δ Q 0 E R 2 δ (2) p8 El. dipole excitation 0 . 151 δ Q 1 E 0 . 137 Retarded C1 0 . 139 0 . 140 0 . 139 δ Q 1 E D 1 D 3 δ (2) p9 El. quadrupole excitation − 0 . 066 δ Q 2 E − 0 . 061 C2 − 0 . 061 − 0 . 061 − 0 . 061 δ Q 2 E Q sum Tot. nuclear excitation, p7+p8+p9 0 . 040 0 . 034 C0 + ret-C1 + C2 0 . 036 0 . 038 0 . 036 0 . 0360 ± 0 . 0020 2-5 δ (0) − 0 . 008 ♦ p10 Magnetic δ M E − 0 . 011 M1 − 0 . 008 − 0 . 007 − 0 . 008 δ M E − 0 . 0090 ± 0 . 0020 2-5 M SUM 1 Total nuclear (corrected) 1 . 646 1 . 648 1 . 656 1 . 676 1 . 655 1 . 6615 ± 0 . 0103 δ (2) 0 . 020 ♦ 0 . 021 ♦ ?? p11 Finite nucleon size 0 . 021 Retarded C1 f.s. 0 . 020 δ F S E NS δ (1) p12 n p charge correlation − 0 . 023 pn correl. f.s. − 0 . 017 − 0 . 017 − 0 . 018 δ F Z E np sum p11+p12 − 0 . 002 0 . 003 0 . 004 0 . 002 0 . 0010 ± 0 . 0030 2-5 � r 3 � pp � � p13 Proton elastic 3rd Zemach moment 0 . 030 0 . 0289 ± 0 . 0015 Eq.(13) 0 . 043(3) δ P E 0 . 043(3) δ P E (2) � � � p14 Proton inelastic polarizab. δ N 0 . 028(2)∆ E hadr 0 . 027(2) pol [64] 0 . 0280 ± 0 . 0020 6 p15 Neutron inelastic polarizab. 0 . 016(8) δ N E p16 Proton & neutron subtraction term − 0 . 0098 ± 0 . 0098 Eq.(15) sum Nucleon TPE, p13+p14+p15+p16 0 . 043(3) 0 . 030 0.027(2) 0 . 059(9) 0 . 0471 ± 0 . 0101 SUM 2 Total nucleon contrib. 0 . 043(3) 0 . 028 0.030(2) 0 . 061(9) 0 . 0476 ± 0 . 0105 Sum , published 1 . 680(16) 1 . 941(19) 1.690(20) 1 . 717(20) 2 . 011(740) Sum , corrected 1 . 697(19) 1.714(20) 1 . 707(20) 1 . 748(740) 1 . 7096 ± 0 . 0147 J.J. Krauth et al. , Ann. Phys. 366 , 168 (2016) [1506.01298] ∆ E TPE ( theo ) = 1 . 7096 ± 0 . 0200 meV ± 0 . 0034 meV vs. exp. uncertainty Randolf Pohl PhiPsi17 , 28 June 2017 51

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