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Recent progress in determination of fundamental constants (CODATA 2010)
Savely G Karshenboim Pulkovo observatory () (St. Petersburg) and Max-Planck-Institut fЭr Quantenoptik (Garching)


Outline
structure of input and output auxiliary data

Rydberg and Rp me/mp

independent constants
G k

h mass of a particle

progress: 2006 vs. 2010 problems


Structure of the input data and output values
Auxiliary input data
Auxiliary data = exact + the most accurate data which are to be evaluated prior the adjustment: R, me/mp, atomic masses. related data: h/m, hNA ... data h related data: e, e/h, ... data The lines ( ) are equations: e.g., theoretical expressions for h/M, the Lamb shift, ... Some data are measured, a lot are derived: mp [kg], me [Mev/c2], ... G is uncorrelated,...

related data
h & related data

derived values independent data


Structure of the input data and output values
Auxiliary input data: c, 0; R, Rp, me/mp Auxiliary data = exact + the most accurate data which are to be evaluated prior the adjustment: R, me/mp, atomic masses. related data: h/m, hNA ... data h related data: e, e/h, NA ... data The lines ( ) are equations: e.g., theoretical expressions for h/M, the Lamb shift, ... Some data are measured, a lot are derived: mp [kg], me [Mev/c2], ... G is uncorrelated; k, a, ...

& related data: h/me, h·NA h & related data: h, e, NA derived values independent data: G, k, a


Structure of the input data and output values
Auxiliary input data: c, 0; R, Rp, me/mp Auxiliary data = exact + the most accurate data which are to be evaluated prior the adjustment: R, me/mp, atomic masses. related data: h/m, hNA ... data h related data: e, e/h, NA ... data The lines ( ) are equations: e.g., theoretical expressions for h/M, the Lamb shift, ... Some data are measured, a lot are derived: mp [kg], me [Mev/c2], ... G is uncorrelated; k, a, ...

& related data: h/me, h·NA h & related data: h, e, NA derived values independent data G k a


Auxiliary data
exact: the most accurate


Example: multiplicative vs. additive: R vs.
equations: uncertainties:
R ~ 10-11 ~ 10-9 ­ 10-10
1/2

2 10-4 в 10

-9


Example: multiplicative vs. additive: R vs.
equations: uncertainties:
R ~ 10-11 ~ 10-9 ­ 10-10
1/2

2 10-4 в 10

-9

`almostґ
exact


Auxiliary data
exact the most accurate:


Auxiliary data
exact the most accurate:


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 collaboration @ PSI


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.

The idea is based on theoretical study of which we understand much better since any short distance effect vanishes for (2).
Theory of p and d states is also simple. That leaves only two variables to determine: the 1s Lamb shift L1s & R.

(2) = L1s ­ 23в L2s

Now we have more data and more unknown variables.


The Lamb shift in muonic hydrogen: experiment


The Lamb shift in muonic hydrogen: experiment


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 frequency) @ Mainz antiprotonic He spectroscopy (ASACUSA @ CERN)


block
equations: input data
h/me


block
equations: input data
h/me h/mp

me/mp


block
equations: input data
h/me h/mp h/mat

me/mp mp in u mat in u


block
equations: input data
h/me h/mp h/mat

me/mp mp in u mat in u

output
h·NA


block
equations: input data
h/me h/mp h/mat

me/mp mp in u mat in u

output
h·NA


block


block
QED vs. Penning trap: ae recoil spectroscopy quatum Hall standard vs calculable capacitor: RK
h/mRb h/mCs


block
QED vs Penning trap: ae recoil spectroscopy
h/mRb h/mCs


block
2006:


block
2006:

old CODATA = old ae


block
2006:

ae theory jump


block
2006:

not sensitive


block
2006:

sensitive


block
QED vs Penning trap: ae recoil spectroscopy
h/mRb h/mCs

5-loop corrections to (g-2)e


me/mp vs : accuracy is close!


block
QED vs. Penning trap: ae recoil spectroscopy quatum Hall standard vs calculable capacitor: RK
h/mRb h/mCs


Quantum Hall effect and a standard of resistance

W. Poirier, Les Houches, 2007


Needs for a `theoryґ for QHE
steps rational universal relation to


h block
known from block input:
h e N

A

h·NA h/me

output
me B


h block


h block


h block: the most important data


h block: the most important data
watt ballance Avogadro constant from ehrhiched Si


watt-ballance

B. Jeanneret, Les Houches, 2007


Josephson effect and quantum volt stardard

B. Jeanneret, Les Houches, 2007


watt-ballance

B. Jeanneret, Les Houches, 2007


h block: the most important data
watt ballance Avogadro constant from ehrhiched Si


Monocrystale of
monocrystale ~ 1 kg

28

Si

isotopic composition 28Si: 92% 29Si: 5% 30Si: 3%


Monocrystale of
monocrystale ~ 1 kg

28

Si

isotopic composition 28Si: 92% 99.985% 29Si: 5% 30Si: 3%


Monocrystale of
monocrystale ~ 1 kg

28

Si

isotopic composition 28Si: 92% 99.985% 29Si: 5% 30Si: 3%


Monocrystale of
monocrystale ~ 1 kg

28

Si

isotopic composition 28Si: 92% 99.985% 29Si: 5% 30Si: 3%


h block: the most important data
watt ballance Avogadro constant from ehrhiched Si problem remains


h block: the most important data
watt ballance Avogadro constant from ehrhiched Si
2006

problem remains


Mass of a proton in different units


Mass of a proton in different units

auxiliary data


Mass of a proton in different units

block


Mass of a proton in different units

h block


Independent constants


Independent constants: G
G/G ~ 10
-4

IESR, 2010

BIPM 1889

Kramer et al., 2006


Independent constants: G
2002 1998

2006

2010


Independent constants: G
2002 1998

2006

2010


Independent constants: k

Fixsen, 2009: COBE


Independent constants: k
2010 2006


Progress


Progress


Progress


Progress


Problems
R & Rp me/mp h G k


Problems
R & Rp me/mp h G k + better accuracy in scattering + new method for Rp - discrepancy in data


Problems
R & Rp me/mp h G k + slow progress in two methods + no discrepancies overlap with data


Problems
R & Rp me/mp h G k + better accuracy + two methods + sensitivity to 5 loops ­ 6-sigma jump


Problems
R & Rp me/mp h G k + natural-silicon discrepacy resolved + better accuracy for Avodagro - new discrepancy NPL NRC


Problems
R & Rp me/mp h G k a + natural-silicon discrepacy resolved + better accuracy for Avodagro - new discrepancy NPL NRC


Problems
R & Rp me/mp h G k + more accurate results ­ bigger scatter


Problems
R & Rp me/mp h G k + more accurate results + more methods + efforts for atomic/molecular spectroscopy