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.