The Lamb shift, `proton The Lamb shift, `proton charge radius - PowerPoint PPT Presentation

The Lamb shift, `proton The Lamb shift, `proton charge radius puzzle' etc. charge radius puzzle' etc. Savely Karshenboim Savely Karshenboim Pulkovo Observatory ( ГАО ГАО РАН РАН ) (St. Petersburg) ) (St. Petersburg) Pulkovo Observatory ( & & Max- -Planck Planck- -Institut f Institut fü ür Quantenoptik (Garching) r Quantenoptik (Garching) Max

Outline  Different methods to determine the proton charge radius  spectroscopy of hydrogen (and deuterium)  the Lamb shift in muonic hydrogen  electron-proton scattering  The proton radius: the state of the art  electric charge radius  magnetic radius

Electromagnetic interaction and structure of the proton Quantum Quantum  hadron structure hadron structure  electrodynamics: : electrodynamics  affects details of interactions;  kinematics of photons;  not calculable, to be measured;  kinematics,  space distribution structure and of charge and dynamics of magnetic moment; leptons;  form factors (in  hadrons as hadrons as  momentum compound objects: compound objects: space).

Atomic energy levels and the proton radius  Proton structure  The Lamb shift The Lamb shift in  affects hydrogen and muonic hydrogen  the Lamb shift the Lamb shift   splits 2s 1/2 & 2p 1/2  the hyperfine splitting  The proton finite size contribution 2 |  (0)| 2 ~ (Z  ) R p  shifts all s states

Different methods to determine the proton charge radius  Spectroscopy of  Electron-proton hydrogen (and scattering deuterium) Studies of scattering need theory of radiative  The Lamb shift in corrections, estimation of two-photon effects; muonic hydrogen the result is to depend on model applied to Spectroscopy produces a extrapolate to zero model-independent momentum transfer. result, but involves a lot of theory and/or a bit of modeling.

Different methods to determine the proton charge radius  Spectroscopy of  Electron-proton hydrogen (and scattering deuterium) Studies of scattering need theory of radiative  The Lamb shift in corrections, estimation of two-photon effects; muonic hydrogen the result is to depend on model applied to Spectroscopy produces a extrapolate to zero model-independent momentum transfer. result, but involves a lot of theory and/or a bit of modeling.

Energy levels in the hydrogen atom

Three fundamental spectra: n = 2

Three fundamental spectra: n = 2  The dominant effect is the fine structure .  The Lamb shift is about 10% of the fine structure.  The 2p line width (not shown) is about 10% of the Lamb shift.  The 2s hyperfine structure is about 15% of the Lamb shift.

Three fundamental spectra: n = 2  The Lamb shift originating from vacuum polarization effects dominates over fine structure (4% of the Lamb shift).  The fine structure is larger than radiative line width.  The HFS is more important than in hydrogen; it is ~ 10% of the fine structure (because m  /m p ~ 1/9).

QED tests in microwave  Lamb shift used to be measured either as a 2p 3/2 splitting between 2s 1/2 2s 1/2 and 2p 1/2 (1057 MHz) 2p 1/2 Lamb shift: 1057 MHz (RF)

QED tests in microwave  Lamb shift used to be measured either as a 2p 3/2 splitting between 2s 1/2 2s 1/2 and 2p 1/2 (1057 MHz) or a big contribution into the fine splitting 2p 3/2 – 2s 1/2 2p 1/2 11 THz (fine structure). Fine structure: 11 050 MHz (RF)

QED tests in microwave & optics  Lamb shift used to be measured either as a 2p 3/2 splitting between 2s 1/2 2s 1/2 and 2p 1/2 (1057 MHz) or RF a big contribution into the fine splitting 2p 3/2 – 2s 1/2 11 THz (fine 2p 1/2 structure).  However, the best result for the Lamb shift has 1s – 2s: been obtained up to now UV from UV transitions (such as 1s – 2s). 1s 1/2

Two-photon Doppler-free spectroscopy of hydrogen atom Two-photon spectroscopy All states but 2s are broad because of the E1 v decay.  , k  , - k The widths decrease with increase of n. However, higher levels is free of linear Doppler are badly accessible. effect. That makes cooling Two-photon transitions relatively not too double frequency and important problem. allow to go higher.

Spectroscopy of hydrogen (and deuterium) Two-photon spectroscopy involves a number of levels strongly affected by QED. In “old good time” we had to deal only with 2s Lamb shift. Theory for p states is simple since their wave functions vanish at r=0. Now we have more data and more unknown variables.

Spectroscopy of hydrogen (and deuterium) Two-photon spectroscopy The idea is based on involves a number of theoretical study of levels strongly affected  (2) = L 1s – 2 3 × L 2s by QED. which we understand In “old good time” we had much better since any to deal only with 2s short distance effect Lamb shift. vanishes for  (2). Theory for p states is Theory of p and d states simple since their wave is also simple. functions vanish at r=0. That leaves only two Now we have more data variables to determine: and more unknown the 1s Lamb shift L 1s & variables. R ∞ .

Spectroscopy of hydrogen (and deuterium) Two-photon spectroscopy The idea is based on involves a number of theoretical study of levels strongly affected  (2) = L 1s – 2 3 × L 2s by QED. which we understand In “old good time” we had much better since any to deal only with 2s short distance effect Lamb shift. vanishes for  (2). Theory for p states is Theory of p and d states simple since their wave is also simple. functions vanish at r=0. That leaves only two Now we have more data variables to determine: and more unknown the 1s Lamb shift L 1s & variables. R ∞ .

Spectroscopy of hydrogen (and deuterium)

Lamb shift (2s 1/2 – 2p 1/2 ) in the hydrogen atom Uncertainties: There are data on a number of  Experiment: 2 ppm transitions, but  QED: < 1 ppm most of them are  Proton size: 2 ppm correlated.

Proton radius from hydrogen

Proton radius from hydrogen

The Lamb shift in muonic hydrogen  Used to believe: since  Scaling of contributions  nuclear finite size nuclear finite size a muon is heavier than  effects: ~ m 3 ; effects: an electron, muonic  standard Lamb-shift atoms are more QED and its sensitive to the nuclear uncertainties: ~ m ; structure.  width of the 2p state: ~  Not quite true. What is What is m ; important: scaling of important  nuclear finite size effects various contributions for HFS: ~ m 3 with m .

The Lamb shift in muonic hydrogen: experiment

The Lamb shift in muonic hydrogen: experiment

The Lamb shift in muonic hydrogen: experiment

The Lamb shift in muonic hydrogen: theory

The Lamb shift in muonic hydrogen: theory  Discrepancy ~ 0.300 meV.  Only few contributions are important at this level.  They are reliable They are reliable. . 

Electron-proton scattering: new Mainz experiment

Electron-proton scattering: evaluations of `the World data’  Mainz:  Charge radius: JLab  JLab (similar results also from Ingo Sick) Magnetic radius does not agree! Magnetic radius does not agree !

Electron-proton scattering: evaluations of `the World data’  Mainz:  Charge radius: JLab  JLab (similar results also from Ingo Sick) Magnetic radius does not agree! ! Magnetic radius does not agree

Different methods to determine the proton charge radius  Comparison:  spectroscopy of hydrogen (and deuterium) JLab  the Lamb shift in muonic hydrogen  electron-proton scattering

Present status of proton radius: three convincing results magnetic radius: magnetic radius charge radius and the charge radius Rydberg constant: a a strong discrepancy strong discrepancy. between different If I would bet: evaluation of the  data and maybe  systematic effects in between the data hydrogen and deuterium spectroscopy  error or underestimation of uncalculated terms in 1s Lamb shift theory Uncertainty and model-  independence of scattering results.

Present status of proton radius: three convincing results magnetic radius: magnetic radius charge radius and the charge radius Rydberg constant: a a strong discrepancy strong discrepancy. between different If I would bet: evaluation of the  data and maybe  systematic effects in between the data hydrogen and deuterium spectroscopy  error or underestimation of uncalculated terms in 1s Lamb shift theory Uncertainty and model-  independence of scattering results.

What is next?  new evaluations of scattering data (old and new evaluations of scattering data (old and  new) new)  new spectroscopic experiments on new spectroscopic experiments on  hydrogen and deuterium hydrogen and deuterium  evaluation of data on the Lamb shift in evaluation of data on the Lamb shift in  muonic deuterium (from PSI) and new value muonic deuterium (from PSI) and new value of the Rydberg constant of the Rydberg constant  systematic check on muonic hydrogen and deuterium theory

Where we are