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Jan 28, 2024 •379 likes •1.63k views

Shrinking the Proton Laser spectroscopy 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 CREMA (Charge

  1. Atomic and nuclear physics Wave functions of S and P states: ... 8S 4S 1 radial w.f. 3D 2S 3S 2P 0.5 2S 2P 0 0 1 2 3 4 5 6 7 8 r [Zr/a0] S states: max. at r=0 P states: zero at r=0 Electron sometimes inside the proton. Electron is not inside the proton. S states are shifted. Shift ist proportional to the size of the proton 1S Orbital pictures from Wikipedia Randolf Pohl Birmingham, 8 Feb 2017 12

  2. Atomic and nuclear physics arb. units ... 8S 4S 3D 3S Coulomb potential: V = 1/r 2S 2P 0 0.5 1 1.5 2 2.5 radius [fm] S states: max. at r=0 P states: zero at r=0 Electron sometimes inside the proton. Electron is not inside the proton. S states are shifted. Shift ist proportional to the size of the proton 1S Orbital pictures from Wikipedia Randolf Pohl Birmingham, 8 Feb 2017 12

  3. Atomic and nuclear physics arb. units ... 8S proton charge 4S 3D 3S Coulomb potential: V = 1/r 2S 2P 0 0.5 1 1.5 2 2.5 radius [fm] S states: max. at r=0 P states: zero at r=0 Electron sometimes inside the proton. Electron is not inside the proton. S states are shifted. Shift ist proportional to the size of the proton 1S Orbital pictures from Wikipedia Randolf Pohl Birmingham, 8 Feb 2017 12

  4. Atomic and nuclear physics arb. units ... 8S proton charge 4S 3D 3S true potential Coulomb potential: V = 1/r 2S 2P 0 0.5 1 1.5 2 2.5 radius [fm] S states: max. at r=0 P states: zero at r=0 Electron sometimes inside the proton. Electron is not inside the proton. S states are shifted. Shift ist proportional to the size of the proton 1S Orbital pictures from Wikipedia Randolf Pohl Birmingham, 8 Feb 2017 12

  5. Charge radii of light nuclei 7 8 9 10 11 12 Be Be Be Be Be Be Proton Number Z 6 9 11 7 8 Li Li Li Li Li 2.5890 (390) 3 4 6 8 He He He He 1.9730 (160) 1.6810 ( 40) 2.0680 (110) 1.9290 (260) 1 2 3 rms charge radii in fm H T D • electron scattering 0.8775 (51) 2.1424 (21) 1.7550 (860) • muonic atom spectroscopy (medium-to-high Z) n • H/D: precision laser spectroscopy + theory (a lot!) • 6 He, 8 He, ...: laser spectroscopy of isotope shift Neutron number N Randolf Pohl Birmingham, 8 Feb 2017 13

  6. Muonic hydrogen Regular hydrogen: Muonic hydrogen: electron e − + muon µ − proton p + proton p electron Randolf Pohl Birmingham, 8 Feb 2017 14

  7. Muonic hydrogen Regular hydrogen: Muonic hydrogen: electron e − + muon µ − proton p + proton p electron ✍ from Wikipedia Randolf Pohl Birmingham, 8 Feb 2017 14

  8. Muonic hydrogen Regular hydrogen: Muonic hydrogen: electron e − + muon µ − proton p + proton p muon mass m µ ≈ 200 × m e Bohr radius r µ ≈ 1/200 × r e electron µ inside the proton: 200 3 ≈ 10 7 muon muon much is more sensitive to r p Randolf Pohl Birmingham, 8 Feb 2017 14

  9. Proton charge radius and muonic hydrogen µ p (n=2) levels: 8.4 meV F=2 2P 3/2 Lamb shift in µ p [meV]: F=1 2P 1/2 F=1 F=0 = 206 . 0668 ( 25 ) − 5 . 2275 ( 10 ) r 2 ∆ E [meV] p 206 meV 50 THz 6 µ m Proton size effect is 2% of the µ p Lamb shift 225 meV Measure to 10 − 5 ⇒ r p to 0.05 % 55 THz 5.5 µ m Experiment: R. Pohl et al. , Nature 466, 213 (2010). fin. size: 3.7 meV A. Antognini, RP et al. , Science 339, 417 (2013). F=1 2S 1/2 Theory summary: 23 meV A. Antognini, RP et al. , Ann. Phys. 331, 127 (2013). F=0 Randolf Pohl Birmingham, 8 Feb 2017 15

  10. The laser system Yb:YAG thin−disk laser Main components: cw TiSa laser Oscillator Oscillator Wave 1030 nm 1030 nm 200 W 200 W Verdi meter • Thin-disk laser 9 mJ 9 mJ 5 W fast response to detected µ − Amplifier Amplifier cw TiSa 500 W 500 W FP 708 nm 43 mJ 43 mJ • Frequency doubling 400 mW SHG SHG I / Cs 2 SHG • TiSa laser: frequency stabilized cw laser 7 mJ 1.5 mJ 23 mJ 515 nm 23 mJ injection seeded oscillator TiSa Osc. multipass amplifier TiSa Amp. 708 nm, 15 mJ • Raman cell µ µ 6 m monitoring H O 6 m 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 µ − 6 m cavity A. Antognini, RP et. al. , Opt. Comm. 253, 362 (2005). Randolf Pohl Birmingham, 8 Feb 2017 16

  11. The laser system Yb:YAG thin−disk laser cw TiSa laser Oscillator Oscillator Thin-disk laser Wave 1030 nm 1030 nm 200 W 200 W Verdi meter 9 mJ 9 mJ • Large pulse energy: 85 (160) mJ 5 W Amplifier Amplifier cw TiSa • Short trigger-to-pulse delay: � 400 ns 500 W 500 W FP 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 µ µ 6 m monitoring H O 6 m 2 0.25 mJ 20 m Raman cell Ge−filter A. Antognini, RP et. al. , µ µ − IEEE J. Quant. Electr. 45, 993 (2009). 6 m cavity Randolf Pohl Birmingham, 8 Feb 2017 16

  12. The laser system Yb:YAG thin−disk laser MOPA TiSa laser: cw TiSa laser Oscillator Oscillator Wave 1030 nm 1030 nm 200 W 200 W Verdi 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 - FP cavity calibrated with I 2 , Rb, Cs lines 43 mJ 43 mJ 400 mW SHG SHG I / Cs ν FP = N · FSR 2 SHG FSR = 1497 . 344 ( 6 ) MHz ν cw TiSa absolutely known to 30 MHz 7 mJ 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 µ µ 6 m monitoring H O 6 m TiSa TiSa 2 0.25 mJ (frequency chirp ≤ 200 MHz) 20 m Raman cell Ge−filter Multipass amplifier (2f- configuration) gain=10 µ µ − 6 m cavity Randolf Pohl Birmingham, 8 Feb 2017 16

  13. The laser system Yb:YAG thin−disk laser Raman cell: cw TiSa laser Oscillator Oscillator Wave 1030 nm 1030 nm 200 W 200 W Verdi µ 708 nm 6.02 m meter H 2 9 mJ 9 mJ 5 W Amplifier Amplifier cw TiSa 500 W 500 W FP 708 nm 43 mJ 43 mJ st nd 400 mW rd SHG 1 Stokes 2 Stokes 3 Stokes SHG I / Cs 2 SHG 708 nm 7 mJ µ 1.00 m 1.5 mJ 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 µ µ 6 m monitoring H O 6 m 2 ν 6 µ m = ν 708nm − 3 · ¯ 0.25 mJ h ω vib 20 m Raman cell Ge−filter tunable ω vib ( p , T ) = const µ µ − 6 m cavity P . Rabinowitz et. al. , IEEE J. QE 22 , 797 (1986) Randolf Pohl Birmingham, 8 Feb 2017 16

  14. The laser system Yb:YAG thin−disk laser cw TiSa laser 12 190 mm Oscillator Oscillator Wave 1030 nm 1030 nm 200 W 200 W Verdi − µ meter 9 mJ 9 mJ 25 5 W Amplifier Amplifier cw TiSa 500 W 500 W FP α 708 nm β 43 mJ 43 mJ Laser pulse 400 mW SHG SHG I / Cs 2 2 mm SHG 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 µ µ 6 m monitoring H O 6 m 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 µ − 6 m cavity J. Vogelsang, RP et. al. , Opt. Expr. 22 , 13050 (2014) Randolf Pohl Birmingham, 8 Feb 2017 16

  15. The laser system Yb:YAG thin−disk laser Water absorption cw TiSa laser 0.7 Oscillator Oscillator 0.6 Wave 1030 nm 1030 nm 200 W 200 W Verdi meter 0.5 9 mJ 9 mJ 5 W 0.4 Amplifier Amplifier cw TiSa 500 W 500 W FP 708 nm 0.3 43 mJ 43 mJ 400 mW 0.2 SHG SHG I / Cs 2 0.1 SHG 0 1200 1300 1400 1500 1600 1700 1800 1900 2000 2100 wavenumber (cm -1 ) 7 mJ 0.7 1.5 mJ 23 mJ 515 nm 23 mJ scan region 0.6 0.5 TiSa Osc. TiSa Amp. 0.4 708 nm, 15 mJ 0.3 0.2 µ µ 6 m monitoring H O 6 m 2 0.1 0.25 mJ 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 µ − 6 m cavity • Direct frequency calibration at 6 µ m. Randolf Pohl Birmingham, 8 Feb 2017 16

  16. Disk amplifier laser heads Randolf Pohl Birmingham, 8 Feb 2017 17

  17. Disk laser doubling stages Randolf Pohl Birmingham, 8 Feb 2017 18

  18. TiSa lasers and Raman cell Randolf Pohl Birmingham, 8 Feb 2017 19

  19. Laser beam tube Randolf Pohl Birmingham, 8 Feb 2017 20

  20. Swiss muons ❘ Randolf Pohl Birmingham, 8 Feb 2017 21

  21. Swiss muons ❘ Randolf Pohl Birmingham, 8 Feb 2017 21

  22. Swiss muons q Randolf Pohl Birmingham, 8 Feb 2017 21

  23. Setup Randolf Pohl Birmingham, 8 Feb 2017 22

  24. Setup Play movie: “Muon beam” Randolf Pohl Birmingham, 8 Feb 2017 22

  25. µ p Lamb shift experiment: Principle ( ∼ 13 hours of data @ 1 laser wavelength) time spectrum of 2 keV x-rays events in 25 ns 4 10 3 10 2 10 10 1 0.5 1 1.5 2 2.5 3 3.5 4 time [us] Randolf Pohl Birmingham, 8 Feb 2017 23

  26. µ p Lamb shift experiment: Principle “prompt” ( t ∼ 0 ) time spectrum of 2 keV x-rays n~14 1 % 99 % events in 25 ns 2 P 4 2 S 10 2 keV � 1 S 3 10 2 10 10 1 0.5 1 1.5 2 2.5 3 3.5 4 time [us] Randolf Pohl Birmingham, 8 Feb 2017 23

  27. µ p Lamb shift experiment: Principle “prompt” ( t ∼ 0 ) “delayed” ( t ∼ 1 µ s) time spectrum of 2 keV x-rays n~14 2 P Laser 1 % 99 % 2 S events in 25 ns 2 P 4 2 S 2 keV � 10 2 keV � 1 S 1 S 3 10 r u o h 2 10 r e p s t n e v e 6 10 1 0.5 1 1.5 2 2.5 3 3.5 4 time [us] Randolf Pohl Birmingham, 8 Feb 2017 23

  28. µ p Lamb shift experiment: Principle “prompt” ( t ∼ 0 ) “delayed” ( t ∼ 1 µ s) time spectrum of 2 keV x-rays n~14 2 P Laser 1 % 99 % 2 S events in 25 ns 2 P 4 2 S 2 keV � 10 2 keV � 1 S 1 S 3 10 normalize delayed K α ⇒ Resonance prompt K α 7 2 10 delayed / prompt events [1e−4] 6 5 4 10 3 2 1 1 0.5 1 1.5 2 2.5 3 3.5 4 0 49.75 49.8 49.85 49.9 49.95 time [us] laser frequency [THz] Randolf Pohl Birmingham, 8 Feb 2017 23

  29. Muon beam line Randolf Pohl Birmingham, 8 Feb 2017 24

  30. Target, cavity and detectors Muons Laser pulse Randolf Pohl Birmingham, 8 Feb 2017 25

  31. Target, cavity and detectors Play movie: “The Search” Muons Laser pulse Randolf Pohl Birmingham, 8 Feb 2017 25

  32. Yeah! Randolf Pohl Birmingham, 8 Feb 2017 26

  33. The resonance: discrepancy, sys., stat. ∆ ν water-line to resonance: Water-line/laser wavelength: 300 MHz uncertainty 200 kHz uncertainty our value CODATA-06 7 ] -4 delayed / prompt events [10 e-p scattering 6 H O Statistics: 700 MHz 2 5 calib. Systematics: 300 MHz 4 3 2 1 0 49.75 49.8 49.85 49.9 49.95 laser frequency [THz] Discrepancy: R. Pohl et al. , Nature 466, 213 (2010). 5 . 0 σ ↔ 80 GHz ↔ δν / ν = 1 . 5 × 10 − 3 A. Antognini, RP et al. ,Science 339, 417 (2013). Randolf Pohl Birmingham, 8 Feb 2017 27

  34. Muonic hydrogen results ν t = ν ( 2 S F = 1 1 / 2 − 2 P F = 2 2P fine structure 3 / 2 ) 8 CODATA this value 2P 3/2 F=2 signal [arb. units] F=1 F=1 6 2P 1/2 F=0 4 ν triplet 2 Lamb shift 0 750 800 850 900 950 ν singlet ν - 49.0 THz (GHz) ν s = ν ( 2 S F = 0 1 / 2 − 2 P F = 1 3 / 2 ) 8 CODATA this value signal [arb. units] 6 F=1 2S 1/2 4 2S hyperfine splitting F=0 2 Exp.: R. Pohl et al. , Nature 466, 213 (2010). A. Antognini, RP et al. , Science 339, 417 (2013). 0 450 500 550 600 650 Theo: A. Antognini, RP et al ., Ann. Phys. 331, 127 (2013). ν - 54.0 THz (GHz) Randolf Pohl Birmingham, 8 Feb 2017 28

  35. Muonic hydrogen results 2P fine structure • two transitions measured 2P 3/2 F=2 ν t = 49881.35( 65) GHz F=1 F=1 2P 1/2 ν s = 54611.16(1.05) GHz F=0 • Lamb shift ⇒ charge radius ν triplet ∆ E LS = 206 . 0668 ( 25 ) − 5 . 2275 ( 10 ) r 2 [meV, fm] E � d 3 r r 2 ρ E ( r ) Lamb r 2 E = shift ν singlet r E = 0 . 84087 ( 26 ) exp ( 29 ) th fm = 0.84087 (39) fm 10x more precise than CODATA-2010 4% smaller ( 7 σ ) F=1 proton radius puzzle 2S 1/2 2S hyperfine splitting F=0 Exp.: R. Pohl et al. , Nature 466, 213 (2010). A. Antognini, RP et al. , Science 339, 417 (2013). Theo: A. Antognini, RP et al ., Ann. Phys. 331, 127 (2013). Randolf Pohl Birmingham, 8 Feb 2017 28

  36. Muonic hydrogen results 2P fine structure • two transitions measured 2P 3/2 F=2 ν t = 49881.35( 65) GHz F=1 F=1 2P 1/2 ν s = 54611.16(1.05) GHz F=0 • Lamb shift ⇒ charge radius ν triplet ∆ E LS = 206 . 0668 ( 25 ) − 5 . 2275 ( 10 ) r 2 [meV, fm] E � d 3 r r 2 ρ E ( r ) Lamb r 2 E = shift ν singlet r E = 0 . 84087 ( 26 ) exp ( 29 ) th fm = 0.84087 (39) fm • 2S-HFS ⇒ Zemach radius F=1 ∆ E HFS = 22 . 9843 ( 30 ) − 0 . 1621 ( 10 ) r Z [meV, fm] 2S 1/2 2S hyperfine splitting � d 3 r � d 3 r ′ r ρ E ( r ) ρ M ( r − r ′ ) r Z = F=0 r Z = 1.082 (31) exp (20) th fm = 1.082 (37) fm Exp.: R. Pohl et al. , Nature 466, 213 (2010). A. Antognini, RP et al. , Science 339, 417 (2013). Theo: A. Antognini, RP et al ., Ann. Phys. 331, 127 (2013). Randolf Pohl Birmingham, 8 Feb 2017 28

  37. Proton Zemach radius 2S hyperfine splitting in µ p is: ∆ E HFS = 22 . 9843 ( 30 ) − 0 . 1621 ( 10 ) r Z [ fm ] meV � d 3 r � d 3 r ′ r ρ E ( r ) ρ M ( r − r ′ ) with r Z = ∆ E HFS = 22 . 8089 ( 51 ) meV We measured This gives a proton Zemach radius r Z = 1.082 (31) exp (20) th = 1.082 (37) fm 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 A. Antognini, RP et al. , Science 339, 417 (2013) Randolf Pohl Birmingham, 8 Feb 2017 29

  38. Proton Zemach radius 2S hyperfine splitting in µ p is: ∆ E HFS = 22 . 9843 ( 30 ) − 0 . 1621 ( 10 ) r Z [ fm ] meV � d 3 r � d 3 r ′ r ρ E ( r ) ρ M ( r − r ′ ) with r Z = ∆ E HFS = 22 . 8089 ( 51 ) meV We measured This gives a proton Zemach radius r Z = 1.082 (31) exp (20) th = 1.082 (37) fm goal R-16-02 (CREMA-3) µ p 2013 e-p, Mainz H, Volotka I S P t a d e-p, Friar e v o r p p a H, Dupays 3 - A M 1 1.02 1.04 1.06 1.08 1.1 1.12 E R C Proton Zemach radius R [fm] Z A. Antognini, RP et al. , Science 339, 417 (2013) Randolf Pohl Birmingham, 8 Feb 2017 29

  39. Muonic deuterium F=5/2 0.7534 meV 2P 3/2 F=1/2 0.3634 meV F=3/2 FS: 8.86412 meV F=3/2 2P 1/2 F=1/2 LS: 202.88 meV F=3/2 2S 1/2 2S-HFS: 6.27 meV F=1/2 Randolf Pohl Birmingham, 8 Feb 2017 30

  40. 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 F=5/2 2P 3/2 F=1/2 F=3/2 0 � 100 0 100 ∆ ν (GHz) F=3/2 8 2P 1/2 µ � F=1/2 F=3/2 p + iso CODATA this value 2S 2P 1/2 3/2 signal [arb. units] F=1/2 F=1/2 � F=1/2 2S 2P 1/2 3/2 6 4 F=3/2 2S 1/2 2 0 � 100 0 100 ∆ ν F=1/2 (GHz) Randolf Pohl Birmingham, 8 Feb 2017 31

  41. 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 Birmingham, 8 Feb 2017 31

  42. 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 . 14240 ( 210 ) fm CODATA 2010 r p from µ H gives r d = 2 . 12771 ( 22 ) fm ← 7 σ from r p µ H + iso H/D(1S-2S) CODATA-2010 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 Birmingham, 8 Feb 2017 32

  43. 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 . 14240 ( 210 ) fm CODATA 2010 r p from µ H gives r d = 2 . 12771 ( 22 ) fm ← 7 σ from r p µ H + iso H/D(1S-2S) CODATA-2010 ( 7 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 Birmingham, 8 Feb 2017 32

  44. 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 . 14240 ( 210 ) fm CODATA 2010 r p from µ H gives r d = 2 . 12771 ( 22 ) fm ← 7 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-2010 ( 7 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 Birmingham, 8 Feb 2017 32

  45. 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 . 14240 ( 210 ) fm CODATA 2010 r p from µ H gives r d = 2 . 12771 ( 22 ) fm ← 7 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 7 σ discrepancy! ✛ ✲ µ H + iso H/D(1S-2S) CODATA-2010 ( 7 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 Birmingham, 8 Feb 2017 32

  46. 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 . 14240 ( 210 ) fm CODATA 2010 r p from µ H gives r d = 2 . 12771 ( 22 ) fm ← 7 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. arXiv 1607.03165 D spectr. µ D another 7 σ discrepancy! ✛ ✲ µ H + iso H/D(1S-2S) CODATA-2010 ( 7 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 Birmingham, 8 Feb 2017 32

  47. 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 . 14240 ( 210 ) fm CODATA 2010 r p from µ H gives r d = 2 . 12771 ( 22 ) fm ← 7 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. arXiv 1607.03165 ✛ ✲ 3 . 5 σ indep. of r p D spectr. µ D another 7 σ discrepancy! ✛ ✲ µ H + iso H/D(1S-2S) CODATA-2010 ( 7 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 Birmingham, 8 Feb 2017 32

  48. Results from muonic deuterium (prel.) 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 (preliminary) 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 . 14240 ( 210 ) fm 7 . 5 σ to ∆ E LS ( r d ( CODATA )) = 0.438(59) meV Disprepancy (“proton radius puzzle” ( µ p discrepancy) = 0.329(47) meV) Randolf Pohl Birmingham, 8 Feb 2017 33

  49. 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 Birmingham, 8 Feb 2017 34

  50. 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 Birmingham, 8 Feb 2017 35

  51. 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-2010 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 Birmingham, 8 Feb 2017 36

  52. 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-2010 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 Birmingham, 8 Feb 2017 36

  53. 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 (accepted 2016). 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 ∼ 7 σ smaller than CODATA-2010 4 . 0 σ smaller than r p (H spectrosopy) r d is 7 . 5 σ smaller than CODATA-2010 (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 Birmingham, 8 Feb 2017 37

  54. 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 (accepted 2016). 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 ∼ 7 σ smaller than CODATA-2010 4 . 0 σ smaller than r p (H spectrosopy) r d is 7 . 5 σ smaller than CODATA-2010 (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 Birmingham, 8 Feb 2017 37

  55. 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 Birmingham, 8 Feb 2017 38

  56. Lamb shift in muonic helium Goal: Measure ∆ E(2S-2P) in µ 4 He, µ 3 He to ∼ 50 ppm ⇒ alpha particle and helion charge radius to 3 × 10 − 4 ( ± 0.0005 fm), This is 10 times better than from electron scattering. Solve discrepancy in 3 He - 4 He isotope shift. Randolf Pohl Birmingham, 8 Feb 2017 39

  57. Lamb shift in muonic helium Goal: Measure ∆ E(2S-2P) in µ 4 He, µ 3 He to ∼ 50 ppm ⇒ alpha particle and helion charge radius to 3 × 10 − 4 ( ± 0.0005 fm), This is 10 times better than from electron scattering. Solve discrepancy in 3 He - 4 He isotope shift. 146 meV 145 meV 8.4 meV 2P 3/2 F=1 2P 3/2 F=2 2P 3/2 F=1 F=2 2P 2P 1/2 F=1 2P F=0 2P 1/2 F=0 µ 4 He µ 3 He F=1 2P 1/2 µ p 206 meV 812 nm 50 THz 6 µ m 898 nm 225 meV 55 THz 5.5 µ m F=0 167 meV 2S 1/2 F=1 fin. size: 2S 1/2 3.7 meV fin. size effect F=1 fin. size effect 2S 1/2 397 meV 23 meV 290 meV F=0 Randolf Pohl Birmingham, 8 Feb 2017 39

  58. 1st resonance in muonic He-4 µ 4 He ( 2S 1 / 2 → 2P 3 / 2 ) at ∼ 813 nm wavelength � -3 10 Events / Prompt 1.2 Preliminary 1 0.8 0.6 0.4 0.2 0 -3 -2 -1 0 1 2 3 4 Frequency [THz] Randolf Pohl Birmingham, 8 Feb 2017 40

  59. 1st resonance in muonic He-4 µ 4 He ( 2S 1 / 2 → 2P 3 / 2 ) at ∼ 813 nm wavelength � -3 10 Events / Prompt 1.2 e−He scattering Preliminary 1 0.8 0.6 0.4 0.2 0 -3 -2 -1 0 1 2 3 4 Frequency [THz] Sick, PRD 77, 040302(R) (2008) Borie, Ann. Phys. 327, 733 (2012) Randolf Pohl Birmingham, 8 Feb 2017 40

  60. 1st resonance in muonic He-4 µ 4 He ( 2S 1 / 2 → 2P 3 / 2 ) at ∼ 813 nm wavelength � -3 10 Events / Prompt 1.2 Zavattini Preliminary 1 0.8 0.6 0.4 0.2 0 -3 -2 -1 0 1 2 3 4 Frequency [THz] Carboni et al, Nucl. Phys. A273, 381 (1977) Randolf Pohl Birmingham, 8 Feb 2017 40

  61. 1st resonance in muonic He-4 µ 4 He ( 2S 1 / 2 → 2P 3 / 2 ) at ∼ 813 nm wavelength � -3 10 Events / Prompt 1.2 Batell, McKeen, Pospelov Preliminary 1 0.8 0.6 0.4 0.2 0 -3 -2 -1 0 1 2 3 4 Frequency [THz] Batell, McKeen, Pospelov, PRL 107, 011803 (2011) Randolf Pohl Birmingham, 8 Feb 2017 40

  62. 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 Birmingham, 8 Feb 2017 41

  63. 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 Birmingham, 8 Feb 2017 41

  64. (Electronic) hydrogen. Randolf Pohl Birmingham, 8 Feb 2017 42

  65. Rydberg constant R ∞ = α 2 m e c 2 h − 6 10 fractional uncertainty − 7 10 − 8 10 − 9 10 single measurements least-square adjustments − 10 10 − 11 10 − 12 10 1930 1940 1950 1960 1970 1980 1990 2000 2010 year Randolf Pohl Birmingham, 8 Feb 2017 43

  66. Hydrogen spectroscopy ≃ − R ∞ n 2 + L 1 S Hydrogen : E nS n 3 = 8171 . 636 ( 4 )+ 1 . 5645 � r 2 L 1 S ( r p ) p � MHz Lamb shift : 8S 4S 3S 3D 2S 2P 1S RP et al. arXiv 1607.03165 Randolf Pohl Birmingham, 8 Feb 2017 44

  67. Rydberg constant Hydrogen spectroscopy (Lamb shift): − 6 10 fractional uncertainty L 1 S ( r p ) = 8171 . 636 ( 4 )+ 1 . 5645 � r 2 p � MHz − 7 10 8S 4S 3S 3D − 8 10 2S 2P E nS ≃ − R ∞ n 2 + L 1 S − 9 10 single measurements n 3 least-square adjustments 2 unknowns ⇒ − 10 10 1S-2S • use r p from muonic H − 11 10 to calculate Lamb shift L 1 S • combine with H(1S-2S) − 12 10 ⇒ Rydberg constant R ∞ 1S 1930 1940 1950 1960 1970 1980 1990 2000 2010 year Randolf Pohl Birmingham, 8 Feb 2017 45

  68. Rydberg constant R ∞ = 3 . 289 841 960 249 5 ( 10 ) r p ( 25 ) QED × 10 15 Hz/c [8 parts in 10 13 ] − 6 10 fractional uncertainty − 7 10 − 8 10 − 9 10 single measurements least-square adjustments − 10 10 muonic hydrogen + H(1S-2S) discrepancy − 11 10 − 12 10 1930 1940 1950 1960 1970 1980 1990 2000 2010 year H(1S-2S): C.G. Parthey, RP et al. , PRL 107, 203001 (2011). r p : A. Antognini, RP et al. , Science 339, 417 (2013). Randolf Pohl Birmingham, 8 Feb 2017 45

  69. 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 Birmingham, 8 Feb 2017 46

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