Muonic Hydrogen and the Proton Radius Puzzle

The extremely precise extraction of the proton radius obtained by Pohl et al. from the measured energy difference between the 2P and 2S states of muonic hydrogen disagrees significantly with that extracted from electronic hydrogen or elastic electron–proton scattering. This discrepancy is the proton radius puzzle. In this review, we explain the origins of the puzzle and the reasons for believing it to be very significant. We identify various possible solutions of the puzzle and discuss future research needed to resolve the puzzle.

[1]  André Clairon,et al.  Optical Frequency Measurement of the 2S-12D Transitions in Hydrogen and Deuterium: Rydberg Constant and Lamb Shift Determinations , 1999 .

[2]  André Clairon,et al.  Absolute Frequency Measurement of the 2S-8S/D Transitions in Hydrogen and Deuterium: New Determination of the Rydberg Constant , 1997 .

[3]  W. Morse,et al.  THE BROOKHAVEN MUON ANOMALOUS MAGNETIC MOMENT EXPERIMENT , 2004 .

[4]  Ulf-G. Meißner,et al.  The size of the proton: Closing in on the radius puzzle , 2012, 1205.6628.

[5]  U. Jentschura,et al.  Lamb shift in muonic hydrogen—I. Verification and update of theoretical predictions , 2010, 1011.5275.

[6]  E. Bigot,et al.  Status of the muonic hydrogen Lamb-shift experiment , 2007 .

[7]  J. Rafelski,et al.  Nonperturbative relativistic calculation of the muonic hydrogen spectrum , 2011, 1104.2971.

[8]  C. Wong.  DEUTERON RADIUS AND NUCLEAR FORCES IN FREE SPACE , 1994 .

[9]  T. Hänsch,et al.  Improved measurement of the hydrogen 1S-2S transition frequency. , 2011, Physical review letters.

[10]  Electron self-energy for higher excited S levels (2 pages) , 2004, hep-ph/0405137.

[11]  U. Jentschura,et al.  Two-loop Bethe-logarithm correction in hydrogenlike atoms. , 2003, Physical review letters.

[12]  T. Hänsch,et al.  A deep-UV optical frequency comb at 205 nm. , 2009, Optics express.

[13]  S. Karshenboim,et al.  Second-order corrections to the wave function at the origin in muonic hydrogen and pionium , 2009, 0906.2632.

[14]  U. Jentschura.  Relativistic reduced-mass and recoil corrections to vacuum polarization in muonic hydrogen, muonic deuterium, and muonic helium ions , 2011, 1107.1737.

[15]  Randolf Pohl,et al.  Observation of long-lived muonic hydrogen in the 2S state. , 2006, Physical review letters.

[16]  F. Jegerlehner,et al.  The muon g ― 2 , 2009, 0902.3360.

[17]  A. P. Martynenko.  Proton-polarizability effect in the Lamb shift for the hydrogen atom , 2006 .

[18]  J. Khoury,et al.  Chameleon Cosmology , 2003, astro-ph/0309411.

[19]  Tobias Nebel,et al.  The Lamb shift in muonic hydrogen , 2011 .

[20]  J. J. Murphy,et al.  Erratum: Proton form factor from 0.15 to 0.79 fm -2 , 1974 .

[21]  G. Soff,et al.  Relativistic recoil correction to hydrogen energy levels. , 1998 .

[22]  T. Hänsch,et al.  Laser spectroscopy of the Lamb shift in muonic hydrogen , 1999 .

[23]  Thomas Graf,et al.  The size of the proton and the deuteron , 2011 .

[24]  N. Levinos,et al.  A continuously tunable sequential Stokes Raman laser , 1986 .

[25]  U. Meißner,et al.  Dispersion analysis of the nucleon form factors including meson continua , 2006, hep-ph/0608337.

[26]  T. Hänsch,et al.  Precision spectroscopy of the 2S‐4P transition in atomic hydrogen on a cryogenic beam of optically excited 2S atoms , 2013 .

[27]  Cheng-Wei Chiang,et al.  Proton size anomaly. , 2010, Physical review letters.

[28]  B. Taylor,et al.  CODATA recommended values of the fundamental physical constants: 2006 | NIST , 2007, 0801.0028.

[29]  L. Hand,et al.  Electric and Magnetic Form Factors of the Nucleon , 1963 .

[30]  J.F.C.A. Veloso,et al.  Planar LAAPDs: temperature dependence, performance, and application in low energy X-ray spectroscopy , 2004, IEEE Symposium Conference Record Nuclear Science 2004..

[31]  E. Borie,et al.  The energy levels of muonic atoms , 1982 .

[32]  E. Borie.  Lamb shift in light muonic atoms — Revisited , 2011, 1103.1772.

[33]  M. Pospelov,et al.  Secluded WIMP Dark Matter , 2007, 0711.4866.

[34]  B. Barbiellini,et al.  Muonium emission into vacuum from mesoporous thin films at cryogenic temperatures. , 2011, Physical review letters.

[35]  Thomas Graf,et al.  Proton Structure from the Measurement of 2S-2P Transition Frequencies of Muonic Hydrogen , 2013, Science.

[36]  G. A. Miller,et al.  Transverse Charge Densities , 2010, 1002.0355.

[37]  K. Eikema,et al.  XUV Frequency Comb Metrology and the Ground State of Helium , 2011, 1109.3228.

[38]  Adolf Giesen,et al.  Scalable concept for diode-pumped high-power solid-state lasers , 1994 .

[39]  C. Zimmermann,et al.  Isotope-shift measurements of stable and short-lived lithium isotopes for nuclear-charge-radii determination , 2010, 1009.0393.

[40]  Douglas P. Finkbeiner,et al.  Exciting dark matter and the INTEGRAL/SPI 511 keV signal , 2007, astro-ph/0702587.

[41]  W. Melnitchouk,et al.  Review of two-photon exchange in electron scattering , 2011, 1105.0951.

[42]  T. Hänsch,et al.  Powerful fast triggerable 6 μm laser for the muonic hydrogen 2S-Lamb shift experiment , 2005 .

[43]  Pachucki,et al.  Pure recoil corrections to hydrogen energy levels. , 1995, Physical review. A, Atomic, molecular, and optical physics.

[44]  Randolf Pohl,et al.  2S state and Lamb shift in muonic hydrogen , 2009 .

[45]  B. Rislow,et al.  New Physics and the Proton Radius Problem , 2012, 1206.3587.

[46]  Recoil corrections of order (Z alpha)**6 (m / M) m to the hydrogen energy levels revisited , 1996, hep-ph/9611399.

[47]  J. Martorell,et al.  HADRONIC VACUUM POLARIZATION AND THE LAMB SHIFT , 1999 .

[48]  G. A. Miller,et al.  Charge densities of the neutron and proton. , 2007, Physical review letters.

[49]  V. Shabaev.  Mass corrections in a strong nuclear field , 1985 .

[50]  Three-loop radiative corrections to Lamb shift and hyperfine splitting , 2006, physics/0612244.

[51]  L. Eyraud,et al.  Phenomenology of the deuteron electromagnetic form factors , 2000, nucl-ex/0002003.

[52]  P. Fayet.  Light spin-1/2 or spin-0 Dark Matter particles , 2004, hep-ph/0403226.

[53]  C. Burrage,et al.  Atomic Precision Tests and Light Scalar Couplings , 2010, 1010.5108.

[54]  C. Perdrisat,et al.  Nucleon Form Factors – A Jefferson Lab Perspective , 2011, 1102.2463.

[55]  H. Bethe.  The Electromagnetic shift of energy levels , 1947 .

[56]  A. P. Martynenko.  Fine and hyperfine structure of P-wave levels in muonic hydrogen , 2008 .

[57]  J. Wallenius,et al.  Decay rates of excited muonic molecular ions , 2003 .

[58]  R. Pohl,et al.  N ov 2 01 2 Theory of the 2 S-2 P Lamb shift and 2 S hyperfine splitting in muonic hydrogen , 2014 .

[59]  M. D. Hoogerland,et al.  Frequency Metrology in Quantum Degenerate Helium: Direct Measurement of the 2 3S1 → 2 1S0 Transition , 2011, Science.

[60]  L. Hilico,et al.  Coulombic and radiative decay rates of the resonances of the exotic molecular ions pp{mu}, pp{pi}, dd{mu}, dd{pi}, and dt{mu} , 2004 .

[61]  J. J. Murphy,et al.  Proton form factor from 0.15 to 0.79 fm-2 , 1974 .

[62]  J. Rafelski,et al.  Toward a resolution of the proton size puzzle , 2011, 1101.4073.

[63]  G. Drake,et al.  Lamb shift s and fine-s tructure splitt ings for the muonic ions - Li, - Be, and - B: A proposed experiment , 1985 .

[64]  U. Jentschura,et al.  Lamb shift in muonic hydrogen-II. Analysis of the discrepancy of theory and experiment , 2010, 1011.5453.

[65]  C. Petitjean,et al.  Observation of the Molecular Quenching of μp(2S) Atoms , 2001 .

[66]  S. Karshenboim,et al.  Contribution of light-by-light scattering to energy levels of light muonic atoms , 2010, 1005.4880.

[67]  M. Vanderhaeghen,et al.  Higher order proton structure corrections to the Lamb shift in muonic hydrogen , 2011, 1101.5965.

[68]  Final report of the E821 muon anomalous magnetic moment measurement at BNL , 2006, hep-ex/0602035.

[69]  G. Paz,et al.  Model-independent extraction of the proton charge radius from electron scattering , 2010, 1008.4619.

[70]  Howard Grotch,et al.  Theory of light hydrogenlike atoms , 2000, hep-ph/0002158.

[71]  F. Dittus,et al.  Measurement of the K-line intensity ratios in muonic hydrogen between 0.25 and 150 torr gas pressures , 1984 .

[72]  F. Borkowski,et al.  Absolute electron Proton Cross-Sections at Low Momentum Transfer Measured with a High Pressure Gas Target System , 1980 .

[73]  T. Hänsch,et al.  Experiment to measure the Lamb shift in muonic hydrogen , 2000 .

[74]  Pachucki.  Theory of the Lamb shift in muonic hydrogen. , 1996, Physical review. A, Atomic, molecular, and optical physics.

[75]  Coulomb corrections to elastic electron–proton scattering and the proton charge radius , 1999, nucl-th/9912031.

[76]  R. Rattazzi,et al.  Galileon as a local modification of gravity , 2008, 0811.2197.

[77]  Nucleon electromagnetic form factors , 2006, hep-ph/0612014.

[78]  G. A. Miller,et al.  Nuclear quasielastic electron scattering limits nucleon off-mass shell properties , 2012, 1207.0549.

[79]  S. Karshenboim,et al.  Relativistic recoil corrections to the electron-vacuum-polarization contribution in light muonic atoms , 2011, 1112.2739.

[80]  Jeff L. Flowers,et al.  The NPL Rydberg Constant Experiment , 2007, IEEE Transactions on Instrumentation and Measurement.

[81]  A. Giacomo.  A sensitive test of quantum electrodynamics. The 2S–2P energy difference of muonic hydrogen , 1969 .

[82]  Ingo Sick,et al.  ON THE RMS RADIUS OF THE DEUTERON , 1998 .

[83]  Ingo Sick.  On the RMS radius of the proton , 2003 .

[84]  Theodor W. Hänsch,et al.  Illuminating the proton radius conundrum: The mu He+ Lamb shift , 2011 .

[85]  I. Sick.  Precise root-mean-square radius of He 4 , 2008 .

[86]  I. Yavin,et al.  Muonic hydrogen and MeV forces , 2010, 1011.4922.

[87]  Ulf-G. Meissner,et al.  Dispersion-Theoretical Analysis of the Nucleon Electromagnetic Formfactors , 1995, hep-ph/9506375.

[88]  Willis E. Lamb,et al.  Fine Structure of the Hydrogen Atom by a Microwave Method , 1947 .

[89]  G. Ron.  The proton form factor ratio at low Q**2: New results from Jefferson Lab , 2011 .

[90]  P. Crivelli,et al.  Advances towards a new measurement of the 1S–2S transition of positroniumThis paper was presented at the International Conference on Precision Physics of Simple Atomic Systems, held at École de Physique, les Houches, France, 30 May – 4 June, 2010. , 2011 .

[91]  I. Sick.  Problems with proton radii , 2012 .

[92]  Three-Loop Slope of the Dirac Form Factor and the 1S Lamb Shift in Hydrogen. , 1999, Physical review letters.

[93]  I. Sick.  Troubles with the Proton rms-Radius , 2011 .

[94]  L. Ludhova,et al.  Behaviour of large-area avalanche photodiodes under intense magnetic fields for VUV- visible- and X-ray photon detection , 2003 .

[95]  H. Bethe,et al.  Quantum Mechanics of One- and Two-Electron Atoms , 1957 .

[96]  M. Pospelov,et al.  New parity-violating muonic forces and the proton charge radius. , 2011, Physical review letters.

[97]  Thomas Graf,et al.  The size of the proton , 2010, Nature.

[98]  Hagley,et al.  Separated oscillatory field measurement of hydrogen 2S1/2-2P3/2 fine structure interval. , 1994, Physical review letters.

[99]  Theodor W. Hänsch,et al.  The muonic hydrogen Lamb-shift experiment , 2005 .

[100]  C. Petitjean,et al.  Kinetic energies of exotic H atoms at formation and cascade , 1999 .

[101]  R. Barbieri,et al.  Evidence Against the Existence of a Low Mass Scalar Boson from Neutron-Nucleus Scattering , 1975 .

[102]  G. A. Miller,et al.  Proton Polarizability Contribution: Muonic Hydrogen Lamb Shift and Elastic Scattering , 2012, 1209.4667.

[103]  Chameleon fields: awaiting surprises for tests of gravity in space. , 2003, Physical review letters.

[104]  J. McGovern,et al.  Proton polarisability contribution to the Lamb shift in muonic hydrogen at fourth order in chiral perturbation theory , 2012, 1206.3030.

[105]  Theodor W. Hänsch,et al.  Feasibility of Coherent xuv Spectroscopy on the 1S-2S Transition in Singly Ionized Helium , 2009 .

[106]  Pachucki.  Radiative recoil correction to the Lamb shift. , 1995, Physical review. A, Atomic, molecular, and optical physics.

[107]  A. Mills,et al.  Positronium hyperfine interval measured via saturated absorption spectroscopy. , 2012, Physical review letters.

[108]  F. Wilczek.  Decays of Heavy Vector Mesons into Higgs Particles , 1977 .

[109]  G. Paz,et al.  Model independent analysis of proton structure for hydrogenic bound states. , 2011, Physical review letters.

[110]  Nonrelativistic QED approach to the Lamb shift , 2005, physics/0603123.

[111]  Lamb shift in muonic hydrogen , 2004, physics/0410051.

[112]  C. Chiang,et al.  Constraint on parity-violating muonic forces. , 2011, Physical review letters.

[113]  Lucile Julien,et al.  Optical frequency measurement of the 1S–3S two-photon transition in hydrogen , 2010, 1007.4794.

[114]  D. Bosnar,et al.  High-precision determination of the electric and magnetic form factors of the proton , 2010, 1108.3533.

[115]  J. J. Kelly.  Simple parametrization of nucleon form factors , 2004 .

[116]  J. Schwinger,et al.  Electrodynamic Displacement of Atomic Energy Levels. II. Lamb Shift , 1952 .

[117]  T. Graf,et al.  Thin-Disk Yb:YAG Oscillator-Amplifier Laser, ASE, and Effective Yb:YAG Lifetime , 2009, IEEE Journal of Quantum Electronics.