Recent progress in determination of fundamental constants (CODATA and afterwards ) Savely G Karshenboim Pulkovo observatory (ГАО) (St. Petersburg) and Max-Planck-Institut für Quantenoptik (Garching)

Outline structure of input and output auxiliary data Rydberg and R p m e /m p  h mass of a particle independent constants G k (g-2)  progress: 2006 vs problems

Structure of the input data and output values Auxiliary dataexact prior Auxiliary data = exact + the most accurate data which are to be evaluated prior the adjustment: R , m e /m p, atomic masses.  related data  related data: h/m, hN A... h related data h related data: e, e/h,... The lines (  ) are equations: e.g., theoretical expressions for h/M, the Lamb shift,... Some data are measured, a lot are derived: m p [kg], m e [Mev/c 2 ],... G is uncorrelated,... Auxiliary input data  related data h & related data data derived values independent data

Structure of the input data and output values Auxiliary dataexact prior Auxiliary data = exact + the most accurate data which are to be evaluated prior the adjustment: R , m e /m p, atomic masses.  related data  related data: h/m, hN A... h related data h related data: e, e/h, N A... The lines (  ) are equations: e.g., theoretical expressions for h/M, the Lamb shift,... Some data are measured, a lot are derived: m p [kg], m e [Mev/c 2 ],... G is uncorrelated; k, a ,...  & related data: h/m e, h·N A h & related data: h, e, N A derived values independent data: G, k, a  Auxiliary input data: c,  0 ; R ∞, R p, m e /m p

Structure of the input data and output values Auxiliary dataexact prior Auxiliary data = exact + the most accurate data which are to be evaluated prior the adjustment: R , m e /m p, atomic masses.  related data  related data: h/m, hN A... h related data h related data: e, e/h, N A... The lines (  ) are equations: e.g., theoretical expressions for h/M, the Lamb shift,... Some data are measured, a lot are derived: m p [kg], m e [Mev/c 2 ],... G is uncorrelated; k, a ,...  & related data: h/m e, h·N A h & related data: h, e, N A derived values independent data Auxiliary input data: c,  0 ; R ∞, R p, m e /m p k aa G

Example: multiplicative vs. additive: R ∞ vs.  equations: uncertainty: R ∞ ~  ~ –  2 ~ × ` almost´ exact

Auxiliary data exact the most accurate:

Atomic & nuclear masses

Rydberg constant hydrogen & deuterium spectroscopy electron-proton elastic scattering Lamb shift in muonic hydrogen

Rydberg constant hydrogen & deuterium spectroscopy electron-proton elastic scattering Lamb shift in muonic hydrogen LKP (Paris), MPQ (Garching),...

Rydberg constant hydrogen & deuterium spectroscopy electron-proton elastic scattering Lamb shift in muonic hydrogen MAMI = Mainzer Mikrotron old world data

Rydberg constant hydrogen & deuterium spectroscopy electron-proton elastic scattering Lamb shift in muonic hydrogen CREMA PSI

Proton radius puzzle

electron-to-proton mass ratio cyclotron frequencies of e & p (UWash) g factor of a bound e in H-like ion (magnetic moment precession vs. ion cyclotron Mainz antiprotonic He spectroscopy CERN)

[A r (e)– ] × Electron mass: TGFC meeting A r (e) CODATA 2010 GSI-02 (C) Uwash-95 GSI-04 (O) CERN-06/10 MPIK parts in image charges interaction correction not applied 2010 Anti-protonic Helium

 –related data equations: m e /m p m p in u m at in u input data  h/m e h/m p h/m at

 –related data equations: m e /m p m p in u m at in u input data  h/m e h/m p h/m at output h·N A

 –related data

QED vs. Penning trap: a e recoil spectroscopy h/m Rb h/m Cs quantum Hall standard vs calculable capacitor: R K

 –related data QED vs Penning trap: a e recoil spectroscopy h/m Rb h/m Cs

 –related data QED vs Penning trap: a e recoil spectroscopy h/m Rb h/m Cs 5-loop corrections to (g-2) e

 –related data QED vs. Penning trap: a e recoil spectroscopy h/m Rb h/m Cs quantum Hall standard vs calculable capacitor: R K

2014 Input data related to the Fine-structure constant: TGFC meeting  2 : 5.82 DOF: 2 Prob.  2 : 5.8 % R B : 1.71 Max. reduced residuals: 1.51, 1.70 ‘CODATA-14’ Rel. Unc.: 2.3 ×

Quantum Hall effect and a standard of resistance W. Poirier, Les Houches, 2007

Needs for a `theory´ for QHE steps rational universal relation to 

Needs for a `theory´ for QHE steps rational universal relation to 

h, e, N A and related data known from  block h·N A h/m e input: h e N A output m e  B

h, e, N A and related data

h, e, N A : the most important data watt balance Avogadro constant from ehrhiched Si

watt-balance B. Jeanneret, Les Houches, 2007

Josephson effect and quantum volt stardard B. Jeanneret, Les Houches, 2007

watt-balance B. Jeanneret, Les Houches, 2007

h, e, N A : the most important data watt balance Avogadro constant from ehrhiched Si

Monocrystale of 28 Si monocrystale ~ 1 kgisotopic composition 28 Si: 92% 29 Si: 5% 30 Si: 3%

Monocrystale of 28 Si monocrystale ~ 1 kgisotopic composition 28 Si: 92% % 29 Si: 5% 30 Si: 3%

Monocrystale of 28 Si monocrystale ~ 1 kgisotopic composition 28 Si: 92% % 29 Si: 5% 30 Si: 3%

Monocrystale of 28 Si monocrystale ~ 1 kgisotopic composition 28 Si: 92% % 29 Si: 5% 30 Si: 3%

h, e, N A : the most important data watt balance Avogadro constant from ehrhiched Si problem remains 

h, e, N A : the most important data watt balance Avogadro constant from ehrhiched Si the problem remains in 2010

2014 Input data related to the Planck constant: TGFC meeting

Planck constant (2015) 5.6  10 –8 1.8  10 –8 Relative combined standard uncertainty 2.0  10 –8

h = (81) × J sec [1.2 × ]  2 : 8.49 DOF: 4 Prob.  2 : 7.52% R B : 1.45 Max. reduced residuals: 1.96, 1.84 The problem is resolved

Independent constants

Independent constants: G  G/G ~ Kramer et al., 2006 IESR, 2010 BIPM 1889

Independent constants: G    

Independent constants: G    

G = (31)× m 3 kg -1 s -2 [4.7×10 -5 ]: TGFC meeting With expansion factor of 6.3  2 : 8.05 DOF: 13 Prob.  2 : 84% R B : 0.79 Max. reduced residuals: -1.98, 1.44

Independent constants: k  

4b) 2014 Input data related to the Boltzmann constant: TGFC meeting  2 : 5.50 DOF: 7 Prob.  2 : 60.0% R B : 0.89 Max. reduced residuals: -1.28, 1.55

“Improving acoustic determinations of the Boltzmann constant with mass spectrometer measurements of the molar mass of argon,” I. Yang, L. Pitre, M. R. Moldover, J. Zhang, X. Feng, and J. S. Kim1, Metrologia, available online November 2015

k = (79) × J K -1 [5.7 × ]  2 : 1.98 DOF: 8 Prob.  2 : 98.0% R B : 0.50 Max. reduced residuals: -0.72, 0.66

Progress

Problems R ∞ & R p m e /m p  h G k

Problems R ∞ & R p m e /m p  h G k a  + better accuracy in scattering + new method for R p - discrepancy in data

Problems R ∞ & R p m e /m p  h G k + slow progress in two methods + no discrepancies overlap with  data

Problems R ∞ & R p m e /m p  h G k + better accuracy + two methods sensitivity to 5 loops + sensitivity to 5 loops

Problems R ∞ & R p m e /m p  h G k + natural-silicon discrepacy resolved by better accuracy for Avodagro + discrepancy with NIST watt-balance resolved

Problems R ∞ & R p m e /m p  h G k + natural-silicon discrepacy resolved by better accuracy for Avodagro + discrepancy with NIST watt-balance resolved

Problems R ∞ & R p m e /m p  h G k + more accurate results – bigger scatter

Problems R ∞ & R p m e /m p  h G k + more accurate results + more methods consistency fixed with isotopic abundance of Ar + consistency fixed with isotopic abundance of Ar + efforts for atomic/molecular spectroscopy

Towards a quantum SI system the ampere to be defined via a fixed value of e the kilogram to be defined via a fixed value of h the kelvin it to be defined via a fixed value of k to be reproduced from ohm (quantum Hall effect) and volt (Josephson effect) to be reproduced with watt balances and Avogadro spheres