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Lamb Shift in Muonic Hydrogen the Proton Radius Puzzle Muonic News Muonic Deuterium and Helium Muonic Hydrogen and Deuterium Lamb shift in muonic hydrogen The Proton Radius Puzzle Muonic news Muonic deuterium and helium Muonic hydrogen and deuterium Randolf Pohl Randolf Pohl Max-Planck-Institut fur¨ Quantenoptik Garching 1 7.9 p 2013 electron avg. scatt. JLab p 2010 scatt. Mainz H spectroscopy 0.83 0.84 0.85 0.86 0.87 0.88 0.89 0.9 Proton charge radius R [fm] There is the muon g-2 puzzle. RandolfPohl LeptonMoments,July222014 2 ––––––––––––––––There is the muon g-2 puzzle. RandolfPohl LeptonMoments,July222014 2 There are TWO muon puzzles. RandolfPohl LeptonMoments,July222014 2 Two muon puzzles • Anomalous magnetic moment of the muon ∼ 3.6σ J. Phys. G 38, 085003 (2011). RandolfPohl LeptonMoments,July222014 3 Two muon puzzles • Anomalous magnetic moment of the muon ∼ 3.6σ • Proton radius from muonic hydrogen RandolfPohl LeptonMoments,July222014 3 Two muon puzzles • Anomalous magnetic moment of the muon ∼ 3.6σ • Proton radius from muonic hydrogen ∼ 7.9σ The measured value of the proton rms charge radius from muonic hydrogen µ p is 10 times more accurate, but 4% smaller than the value from both hydrogen spectroscopy and elastic electron proton scattering. 7.9 σ µp 2013 electron avg. scatt. JLab µp 2010 scatt. Mainz H spectroscopy 0.83 0.84 0.85 0.86 0.87 0.88 0.89 0.9 Proton charge radius R [fm] ch RP et al., Nature 466, 213 (2010); Science 339, 417 (2013); ARNPS 63, 175 (2013). RandolfPohl LeptonMoments,July222014 3 Two muon puzzles • Anomalous magnetic moment of the muon ∼ 3.6σ • Proton radius from muonic hydrogen ∼ 7.9σ • These 2 discrepancies may be connected. rp aµ Karshenboim, McKeen, Pospelov, arXiv 1401.6156 RandolfPohl LeptonMoments,July222014 3 Outline Introduction: Proton radius, hydrogen and all that Muonic hydrogen The proton radius puzzle (Electronic) hydrogen Proton polarizability aka two-photon-exchange BSM Muonic deuterium Muonic helium RandolfPohl LeptonMoments,July222014 4 Proton radius vs. time The proton rms charge radius is not the most accurate quantity in the universe. 0.920 • • electron scattering 0.900 • 2 slope of GE at Q = 0 0.880 • 0.860 • hydrogen spectr. 0.840 Lamb shift (S-states) 0.820 Orsay Sick, 2003 Proton radius (fm) Stanford Hydrogen 0.800 Saskatoon CODATA 2006 Mainz Bonn VMD 0.780 Mergell VMD year → 2006 2007 2010 1962 1963 1974 1980 1994 1996 1997 1999 2000 2001 2003 e-p scattering: rp = 0.895(18)fm (ur = 2 %) Hydrogen: rp = 0.8760(78)fm (ur = 0.9 %) RandolfPohl LeptonMoments,July222014 5 Proton radius vs. time The proton rms charge radius is not the most accurate quantity in the universe. 0.920 Electron scattering: • 0.900 • electron scattering dG Q2 • 2 2 E ( ) 2 2 hr i = −6h¯ ⇒ slope of GE at Q = 0 p 2 2 slope of GE at Q = 0 0.880 dQ Q =0 • 0.860 • hydrogen spectr. 0.840 Lamb shift (S-states) 0.820 Orsay Sick, 2003 Proton radius (fm) Stanford Hydrogen 0.800 Saskatoon CODATA 2006 Mainz Bonn VMD 0.780 Mergell VMD year → 2006 2007 2010 1962 1963 1974 1980 1994 1996 1997 1999 2000 2001 2003 e-p scattering: rp = 0.895(18)fm (ur = 2 %) Hydrogen: rp = 0.8760(78)fm (ur = 0.9 %) Vanderhaeghen, Walcher 1008.4225 RandolfPohl LeptonMoments,July222014 5 Proton radius vs. time The proton rms charge radius is not the most accurate quantity in the universe. 0.920 Hydrogen spectroscopy (Lamb shift): • • electron scattering 0.900 • 2 2 L1S(rp)= 8171.636(4)+ 1.5645hrpi MHz slope of GE at Q = 0 0.880 8S 0.860 4S • hydrogen spectr. 3S 3D • 2S-8S 2S-8D 0.840 Lamb shift (S-states) 2S 2P 0.820 R∞ L1S OrsayEnS ≃− 2 +Sick,3 2003 Proton radius (fm) Stanford n Hydrogenn 0.800 Saskatoon CODATA 2006 Mainz Bonn VMD 2 unknowns 2 transitions 0.780 1S-2S Mergell VMD⇒ → year • Rydberg constant R∞ 2006 2007 2010 1962 1963 1974 1980 1994 1996 1997 1999 2000 2001 2003 e-p scattering: rp = 0.895(18)fm• Lamb shift (uLr1=S ←2 %)rp Hydrogen: rp = 0.8760(78)fm (ur = 0.9 %) 1S RandolfPohl LeptonMoments,July222014 5 Proton radius vs. time The proton rms charge radius is not the most accurate quantity in the universe. 0.920 • • electron scattering 0.900 • 2 our goal slope of GE at Q = 0 0.880 • 0.860 • hydrogen spectr. 0.840 Lamb shift (S-states) 0.820 Orsay Sick, 2003 Proton radius (fm) Stanford Hydrogen 0.800 Saskatoon CODATA 2006 Mainz Bonn VMD 0.780 Mergell VMD year → 2006 2007 2010 1962 1963 1974 1980 1994 1996 1997 1999 2000 2001 2003 e-p scattering: rp = 0.895(18)fm (ur = 2 %) 20x improvement Hydrogen: rp = 0.8760(78)fm (ur = 0.9 %) (aim: 10x better QED test in H) muonic hydrogen goal (1998): ur = 0.1 % RandolfPohl LeptonMoments,July222014 5 Atomic physics Spectrum of atomic hydrogen 8S ... 4S Bohr model quantum mechanics → 3S 3D n=2 2S 2P n=1 1S RandolfPohl LeptonMoments,July222014 6 Atomic physics Bohr model → quantum mechanics 8S ... 4S planetary orbits wave function → 3S 3D n=2 2S 2P n=1 1S Orbital pictures from Wikipedia RandolfPohl LeptonMoments,July222014 6 Atomic and nuclear physics Wave functions of S and P states: 8S ... 1 4S 2S 3S 3D 2P radial w.f. 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 RandolfPohl LeptonMoments,July222014 6 Atomic and nuclear physics 8S ... 4S arb. units 3S 3D 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 RandolfPohl LeptonMoments,July222014 6 Atomic and nuclear physics 8S ... proton charge 4S arb. units 3S 3D 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 RandolfPohl LeptonMoments,July222014 6 Atomic and nuclear physics 8S ... proton charge 4S arb. units 3S 3D 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 RandolfPohl LeptonMoments,July222014 6 Muonic hydrogen Regular hydrogen: Muonic hydrogen: electron e− + proton p muon µ− + proton p electron RandolfPohl LeptonMoments,July222014 7 Muonic hydrogen Regular hydrogen: Muonic hydrogen: electron e− + proton p muon µ− + proton p electron ✒ from Wikipedia RandolfPohl LeptonMoments,July222014 7 Muonic hydrogen Regular hydrogen: Muonic hydrogen: electron e− + proton p muon µ− + proton p muon mass mµ ≈ 200 ×me Bohr radius rµ ≈ 1/200 ×re electron µ inside the proton: 2003 ≈ 107 muon muon much is more sensitive to rp RandolfPohl LeptonMoments,July222014 7 Proton charge radius and muonic hydrogen µp(n=2) levels: 8.4 meV F=2 Lamb shift in µp [meV]: 2P3/2 F=1 2P1/2 F=1 F=0 2 ∆E = 206.0668(25) − 5.2275(10)rp [meV] 206 meV 50 THz 6 µm Proton size effect is 2% of the µ p Lamb shift 225 meV Measure to 10−5 ⇒ r to 0.05% p 55 THz 5.5 µm Experiment: R. Pohl et al., Nature 466, 213 (2010). fin. size: A. Antognini, RP et al., Science 339, 417 (2013). 3.7 meV F=1 2S1/2 Theory summary: 23 meV A. Antognini, RP et al., Ann. Phys. 331, 127 (2013). F=0 RandolfPohl LeptonMoments,July222014 8 Muonic measurements. RandolfPohl LeptonMoments,July222014 9 Setup RandolfPohl LeptonMoments,July222014 10 The resonance: discrepancy, sys., stat. Water-line/laser wavelength: ∆ν water-line to resonance: 300 MHz uncertainty 200 kHz uncertainty 7 CODATA-06 our value ] -4 6 e-p scattering H2O Statistics: 700 MHz 5 calib. Systematics: 300 MHz 4 delayed / prompt events [10 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). 5.0σ ↔ 75 GHz ↔ δν/ν = 1.5 × 10−3 A. Antognini, RP et al.,Science 339, 417 (2013). RandolfPohl LeptonMoments,July222014 11 The proton radius puzzle. RandolfPohl LeptonMoments,July222014 12 The proton radius puzzle The proton rms charge radius measured with electrons: 0.8770 ± 0.0045 fm muons: 0.8409 ± 0.0004 fm 7.9 σ µp 2013 electron avg. scatt. JLab µp 2010 scatt. Mainz H spectroscopy 0.83 0.84 0.85 0.86 0.87 0.88 0.89 0.9 Proton charge radius R [fm] RP, Gilman, Miller, Pachucki, Annu. Rev. Nucl. Part. Sci. 63, 175 (2013). ch RandolfPohl LeptonMoments,July222014 13 The proton radius puzzle The proton rms charge radius measured with electrons: 0.8770 ± 0.0045 fm muons: 0.8409 ± 0.0004 fm 7.9 σ µp 2013 electron avg. scatt. JLab µp 2010 scatt.
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