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
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
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
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
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
Muonic hydrogen Regular hydrogen: Muonic hydrogen: electron e − + muon µ − proton p + proton p electron Randolf Pohl Birmingham, 8 Feb 2017 14
Muonic hydrogen Regular hydrogen: Muonic hydrogen: electron e − + muon µ − proton p + proton p electron ✍ from Wikipedia Randolf Pohl Birmingham, 8 Feb 2017 14
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
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
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
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
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
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
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
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
Disk amplifier laser heads Randolf Pohl Birmingham, 8 Feb 2017 17
Disk laser doubling stages Randolf Pohl Birmingham, 8 Feb 2017 18
TiSa lasers and Raman cell Randolf Pohl Birmingham, 8 Feb 2017 19
Laser beam tube Randolf Pohl Birmingham, 8 Feb 2017 20
Swiss muons ❘ Randolf Pohl Birmingham, 8 Feb 2017 21
Swiss muons ❘ Randolf Pohl Birmingham, 8 Feb 2017 21
Swiss muons q Randolf Pohl Birmingham, 8 Feb 2017 21
Setup Randolf Pohl Birmingham, 8 Feb 2017 22
Setup Play movie: “Muon beam” Randolf Pohl Birmingham, 8 Feb 2017 22
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
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
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
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
Muon beam line Randolf Pohl Birmingham, 8 Feb 2017 24
Target, cavity and detectors Muons Laser pulse Randolf Pohl Birmingham, 8 Feb 2017 25
Target, cavity and detectors Play movie: “The Search” Muons Laser pulse Randolf Pohl Birmingham, 8 Feb 2017 25
Yeah! Randolf Pohl Birmingham, 8 Feb 2017 26
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
(Electronic) hydrogen. Randolf Pohl Birmingham, 8 Feb 2017 42
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
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
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
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
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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