The Lamb Shift, `Proton Charge Radius Puzzle' Etc

TheThe LambLamb shift,shift, `proton`proton chargecharge radiusradius puzzle'puzzle' etc.etc.

Savely Karshenboim Pulkovo Observatory (ГАО РАН) (St. Petersburg) & Max-Planck-Institut für Quantenoptik (Garching) 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 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 muonic hydrogen of two-photon effects; the result is to depend Spectroscopy produces a on model applied to model-independent extrapolate to zero result, but involves a lot momentum transfer. 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 muonic hydrogen of two-photon effects; the result is to depend Spectroscopy produces a on model applied to model-independent extrapolate to zero result, but involves a lot momentum transfer. of theory and/or a bit of modeling. The proton charge radius: spectroscopy vs. empiric fits

 Lamb shift used to be

measured either as a 2p3/2 splitting between 2s1/2 2s1/2 and 2p1/2 (1057 MHz)

2p1/2

Lamb shift: 1057 MHz (RF) Lamb shift measurements in microwave

 Lamb shift used to be

measured either as a 2p3/2 splitting between 2s1/2 2s1/2 and 2p1/2 (1057 MHz) or a big contribution into the fine splitting 2p3/2 – 2s1/2 2p 11 THz (fine structure). 1/2

Fine structure: 11 050 MHz (RF) Lamb shift measurements in microwave & optics

 Lamb shift used to be

measured either as a 2p3/2 splitting between 2s1/2 2s1/2 and 2p1/2 (1057 MHz) or RF a big contribution into the fine splitting 2p3/2 – 2p1/2 2s1/2 11 THz (fine structure).  However, the best result for the Lamb shift has 1s – 2s: been obtained up to UV now from UV transitions (such as 1s – 2s). 1s1/2 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. is free of linear Doppler However, higher levels effect. are badly accessible. 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 3 (2) = L1s – 2 × L2s 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 is simple since their wave 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 L1s & variables. R∞. Spectroscopy of hydrogen (and deuterium)

Uncertainties: There are data on a  Experiment: 2 ppm number of transitions, but  QED: < 1 ppm most of them are  Proton size: 2 ppm correlated. H & D spectroscopy

 Complicated theory  Some contributions are not cross checked  More accurate than experiment  No higher-order nuclear structure effects H & D spectroscopy

 Complicated theory  Some contributions are not cross checked  More accurate than experiment  No higher-order nuclear structure effects Proton radius from hydrogen Optical determination of Rydberg constant and proton radius D, 1s-2s D, 2s-8s H, 1s-2s H, 2s-8s

ELamb(D,1s)

Ry ELamb(H,1s)

ELamb(H,1s) H, 1s-2s

QED Rp QED Rp Proton radius from hydrogen Proton radius from hydrogen The Lamb shift in muonic hydrogen

 Used to believe: since  Scaling of contributions a muon is heavier than  nuclear finite size an electron, muonic effects: ~ m3; atoms are more  standard Lamb-shift sensitive to the nuclear QED and its uncertainties: ~ m; structure.  width of the 2p state: ~  Not quite true. What is m; importantimportant: scaling of  nuclear finite size effects various contributions for HFS: ~ m3 with m. The Lamb shift in muonic hydrogen: experiment The Lamb shift in muonic hydrogen: experiment The Lamb shift in muonic hydrogen: experiment Theoretical summary The Lamb shift in muonic hydrogen: theory

 Discrepancy ~ 0.300 meV.  Only few contributions are important at this level.  TheyThey areare reliable.reliable. Theory of H and H:

 Rigorous  Rigorous  Ab initio  Ab initio  Complicated  Transparent  Very accurate  Very accurate  Partly not cross  Cross checked checked  Needs higher-order  Needs no higher- proton structure order proton (much below the structure discrepancy) Theory of H and H:

 Rigorous  Rigorous  Ab initio  Ab initio  Complicated  Transparent The th uncertainty is much below the level of the discrepancy  Very accurate  Very accurate  Partly not cross  Cross checked checked  Needs higher-order  Needs no higher- proton structure order proton (much below the structure discrepancy) Spectroscopy of H and H:

 Many transitions in  One experiment different labs.  A correlated  One dominates. measurement on D  Correlated.  No real metrology  Metrology involved.  Discrepancy is of few  The discrepancy is line widths. much below the line  Not sensitive to width. many perturbations.  Sensitive to various systematic effects. H vs H:

 H: muchmuch more sensitive to the Rp term: less accuracy in theory and experiment is required; easier for estimation of systematic effects etc.  H experiment: easy to see a signal, hard to interpret.  H experiment: hard to see a signal, easy to interpret. Elastic electron-proton scattering Elastic electron-proton scattering 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) Electron-proton scattering: evaluations of `the World data’

 Mainz:  Charge radius:

JLab  JLabThe (similar consistency of the results resultson alsothe proton from charge radius is good, Ingo butSick) not sufficient. The agreement is required between the form factors, which is an open question for the moment. Electron-proton scattering: evaluations of `the World data’

 Mainz:  Charge radius:

JLab  JLab (similar results also from Ingo Sick)

Magnetic radius does not agree! Certainty of the derivatives

 f/t – we can  Data are roughly find it in a model with 1%. independent way  Rp is wanted if we have within 1%. accurate data and  We need fits! an estimation of the higher-order  We can use fits Taylor terms. only if we know the exact shape. Certainty of the derivatives

 f/t – we can  Data are roughly find it in a model with 1%. independent way  Rp is wanted if we have within 1%. accurate data and Narrowing the area  We need fits! estimation of the increases the uncertainty: higher-order  We can use fits e.g.: Taylor terms. only if we know Hill and Paz, 2010 the exact shape. Kraus et al., 2014 Certainty of the derivatives

Fifty f/ years:t – we can  Data are roughly •datafind improved it in a model (quality, quantity);with 1%. •accuracyindependent of radius way stays the same;  Rp is wanted •systematicif we have effects: within 1%. accurate increasing data complicity and of the fit.  We need fits! estimation of the higher-order  We can use fits Taylor terms. only if we know the exact shape. Analytic properties: is that important?

 The form factors  The form factors are measured in a fits in time-like finite space-like region are wrong. region.  Their analytic  The fits present properties are the form factors inappropriate. for all the  Their behavior at momenta. larger momenta is unreasonable. Analytic properties: `Dispersionis that fits’important? always produce smaller values The of theform radius,factors but The usually form factors they have badare measured 2. in a fits in time-like finite space-like region are wrong. Mergellregion. et al., 1995; Belushkin Their et analytic all, 2007, Lorenz Theet al., fits 2012;present Adamuscin properties et al., are 2012 the form factors inappropriate. for all the  Their behavior at Is it possible to produce a fit with a good Is it possiblemomenta. to produce a fitlarger with momenta a good is 2 valuevalue ofof  andand consistentconsistent withwithunreasonable. ourour knowledgeknowledge aboutabout thethe imaginaryimaginary partpart ?? Asymptotic behavior: is that important?

 The form factors  The form factors are measured in a in time-like region finite space-like are wrong. region.  Their analytic  The fits presents properties are the form factors inappropriate. for all the  Their behavior at momenta. high momenta is unreasonable. Analytic properties and the data q2 Convergence radius |q2|=(2m ) 2  Key area for G’(0)

branch cut 0 0.1 GeV2 e-p data (2 continuum) Different methods to determine the proton charge radius

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

 newnew evaluationsevaluations ofof scatteringscattering datadata (old(old andand new)new)  newnew spectroscopicspectroscopic experimentsexperiments onon hydrogenhydrogen andand deuteriumdeuterium  evaluationevaluation ofof datadata onon thethe LambLamb shiftshift inin muonicmuonic deuteriumdeuterium (from(from PSI)PSI) andand newnew valuevalue ofof thethe RydbergRydberg constantconstant

 systematic check on muonic hydrogen and deuterium theory Where we are What’s new?

 Hydrogen:  Scattering data:  A preliminary  Jlab’s people and MPQ result on 2s- I. Sick state that 4p is consistent world data and with H. MAMI’s are not  Muonic atoms: quite consistent.   D is consistent More studies of with H (PSI) + different shapes isotopic H-D 1s-2s (conformal (MPQ). mapping etc.) What’s new?

 Hydrogen:  Scattering data:  A preliminary  Jlab’s people and MPQresult on 2s- I. Sick state that 4p is consistent world data and with H. MAMI’s are not  Muonic atoms: quite consistent.   D is consistent More studies of with H (PSI) + different shapes isotopic H-D 1s-2s (conformal (MPQ_. mapping etc.) Conferences

PrecisionPrecision physicsphysics PrecisionPrecision physicsphysics ofof andand fundamentalfundamental simplesimple atomsatoms constantsconstants (FFK)(FFK) (PSAS)(PSAS)

Oct., 12-16, 2015 May, 22-26, 2016 Budapest Jerusalem