Precision tests of QED

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Quantum
electrodynamics (QED) is the most stringently tested theory in physics (after special relativity
which currently is tested to 10-15).

Precision tests of QED consist of measurements of the electromagnetic fine structure
constant, α, in different physical systems. Checking the consistency of such
measurements tests the theory.

Tests of a theory are normally carried out by comparing experimental results
to theoretical predictions. In QED, there is some subtlety in this comparison,
because theoretical predictions require as input an extremely precise value of
α, which can only be obtained from another precision QED experiment. Because of
this, the comparisons between theory and experiment are usually quoted as
independent determinations of α. QED is then confirmed to the extent that these
measurements of α from different physical sources agree with each other.

Contents

1 Precision QED
experiments

1.1 Low-energy
measurements

1.1.1 Anomalous magnetic
dipole moments

1.1.2 Atom-recoil
measurements

1.1.3 Neutron Compton
wavelength

1.1.4 Hyperfine
splitting

1.1.5 Lamb
shift

1.1.6 Positronium

1.2 High-energy QED
processes

1.3 Condensed matter
systems

2 References

[edit]
Precision QED experiments

Precision tests of QED have been performed in low-energy atomic
physics experiments, high-energy collider experiments, and condensed matter
systems. The value of α is obtained in each of these experiments by fitting an
experimental measurement to a theoretical expression (including higher-order radiative corrections)
that includes α as a parameter. The uncertainty in the extracted value of α
includes both experimental and theoretical uncertainties. This program thus
requires both high-precision measurements and high-precision theoretical
calculations. Unless noted otherwise, all results below are from [1].

[edit]
Low-energy measurements

[edit]
Anomalous magnetic dipole moments

The most precise measurement of α comes from the anomalous
magnetic dipole moment, or g-2 ("g minus 2"), of the electron.[2]
To make this measurement, two ingredients are needed:

1) A precise measurement of the anomalous magnetic dipole moment, and

2) A precise theoretical calculation of the anomalous magnetic dipole
moment in terms of α.

As of February 2007, the best measurement of the anomalous magnetic dipole
moment of the electron was made by Gabrielse et al.[3]
using a single electron caught in a Penning trap. The
difference between the electron's cyclotron frequency and its spin precession
frequency in a magnetic field is proportional to g-2. An extremely high
precision measurement of the quantized energies of the cyclotron orbits, or
Landau levels, of the
electron, compared to the quantized energies of the electron's two possible spin orientations, gives
a value for the electron's spin g-factor:

g/2 = 1.001 159 652 180 85 (76),

a precision of better than one part in a trillion. (The digits in parentheses
indicate the uncertainty in the last listed digits of the measurement.)

The current state-of-the-art theoretical calculation of the anomalous
magnetic dipole moment of the electron includes QED diagrams with up to four
loops. Combining this with the experimental measurement of g yields the most
precise value of α:[4]

α-1 = 137.035 999 710 (96),

a precision of better than a part in a billion. This uncertainty is ten times
smaller than the nearest rival method involving atom-recoil measurements.

A value of α can also be extracted from the anomalous magnetic dipole moment
of the muon. The
g-factor of the muon is extracted using the same physical principle as for the
electron above -- namely, that the difference between the cyclotron frequency
and the spin precession frequency in a magnetic field is proportional to g-2.
The most precise measurement comes from Brookhaven
National Laboratory's muon g-2 experiment,[5]
in which polarized muons are stored in a cyclotron and their spin orientation is
measured by the direction of their decay electrons. As of February 2007, the
current world average muon g-factor measurement is,[6]

g/2 = 1.001 165 920 8 (6),

a precision of better than one part in a billion. The difference between the
g-factors of the muon and the electron is due to their difference in mass.
Because of the muon's larger mass, contributions to the theoretical calculation
of its anomalous magnetic dipole moment from Standard Model weak interactions and
from contributions involving hadrons are important at the
current level of precision, whereas these effects are not important for the
electron. The muon's anomalous magnetic dipole moment is also sensitive to
contributions from new physics beyond the
Standard Model, such as supersymmetry. For this
reason, the muon's anomalous magnetic moment is normally used as a probe for new
physics beyond the Standard Model rather than as a test of QED.[7]

[edit]
Atom-recoil measurements

This is an indirect method of measuring α, based on measurements of the
masses of the electron, certain atoms, and the Rydberg constant. The
Rydberg constant is known to seven parts in a trillion. The mass of the electron
relative to that of cesium and rubidium atoms is also known
with extremely high precision. If the mass of the electron can be gotten with
high enough precision, then α can be found from the Rydberg constant according
to

.

To get the mass of the electron, this method actually measures the mass of an
86Rb atom by measuring the recoil
speed of the atom after it emits a photon of known wavelength in an atomic
transition. Combining this with the ratio of electron to 86Rb atom,
the result for α is,[8]

α-1 = 137.035 998 78 (91).

Because this measurement is the next-most-precise after the measurement of α
from the electron's anomalous magnetic dipole moment described above, their
comparison provides the most stringent test of QED, which is passed with flying
colors: the value of α obtained here is within one standard deviation of that
found from the electron's anomalous magnetic dipole moment, an agreement to
within ten parts in a billion.

[edit]
Neutron Compton wavelength

This method of measuring α is very similar in principle to the atom-recoil
method. In this case, the accurately known mass ratio of the electron to the neutron is used.
The neutron mass is measured with high precision through a very precise
measurement of its Compton wavelength.
This is then combined with the value of the Rydberg constant to extract α. The
result is,

α-1 = 137.036 010 1 (5 4).

[edit]
Hyperfine splitting

Hyperfine splitting
is a splitting in the energy levels of an atom caused by the interaction
between the magnetic moment of the
nucleus and the combined
spin and orbital magnetic
moment of the electron. The hyperfine splitting in hydrogen, measured using Ramsey's hydrogen maser, is the most
precisely known quantity in physics. Unfortunately, the influence of the proton's internal
structure limits how precisely the splitting can be predicted theoretically.
This leads to the extracted value of α being dominated by theoretical
uncertainty:

α-1 = 137.036 0 (3).

The hyperfine splitting in muonium, an "atom" consisting of
an electron and an antimuon, provides a more precise measurement of α because
the muon has no internal structure:

α-1 = 137.035 994 (18).

[edit]
Lamb shift

The Lamb
shift is a small difference in the energies of the 2 S1/2 and 2
P1/2 energy levels of hydrogen,
which arises from a one-loop effect in quantum electrodynamics. The Lamb shift
is proportional to α5 and its measurement yields the extracted
value:

α-1 = 137.036 8 (7).

[edit]
Positronium

Positronium is an "atom"
consisting of an electron and a positron. Whereas the
calculation of the energy levels of ordinary hydrogen is contaminated by
theoretical uncertainties from the proton's internal structure, the particles
that make up positronium have no internal structure so precise theoretical
calculations can be performed. The measurement of the splitting between the 2
3S1 and the 1 3S1 energy levels of
positronium yields

α-1 = 137.034 (16).

Measurements of α can also be extracted from the positronium decay rate.
Positronium decays through the annihilation of the electron and the positron
into two or more gamma-ray photons. The decay
rate of the singlet ("para-positronium") 1S0 state
yields

α-1 = 137.00 (6),

and the decay rate of the triplet ("ortho-positronium")
3S1 state yields

α-1 = 136.971 (6).

This last result is the only serious discrepancy among the numbers given
here, but there is some evidence that uncalculated higher-order quantum
corrections give a large correction to the value quoted here.

[edit]
High-energy QED processes

The cross sections
of higher-order QED reactions at high-energy electron-positron colliders provide
a determination of α. In order to compare the extracted value of α with the
low-energy results, higher-order QED effects including the running of α due to
vacuum polarization
must be taken into account. These experiments typically achieve only
percent-level accuracy, but their results are consistent with the precise
measurements available at lower energies.

The cross sections for
yields

α-1 = 136.5 (2.7),

and the cross section for
yields

α-1 = 139.9 (1.2).

[edit]
Condensed matter systems

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The quantum Hall effect
and the AC Josephson effect are
exotic quantum interference phenomena in condensed matter systems. These two
effects provide a standard electrical
resistance and a standard frequency, respectively, which
are believed[citation needed] to measure
the charge of the electron with corrections that are strictly zero for
macroscopic systems.

The quantum Hall effect yields

α-1 = 137.035 997 9 (3 2),

and the AC Josephson effect yields

α-1 = 137.035 977 0 (7 7).

[edit]
References

^
M.E. Peskin and D.V. Schroeder, An Introduction to Quantum Field Theory
(Westview, 1995), p. 198.

^
In Search of Alpha, New Scientist, 9 September 2006, p. 40-43.

^ B.
Odom, D. Hanneke, B. D'Urso, and G. Gabrielse, New Measurement of the
Electron Magnetic Moment Using a One-Electron Quantum Cyclotron, Phys.
Rev. Lett. 97, 030801 (2006).

^ G.
Gabrielse, D. Hanneke, T. Kinoshita, M. Nio, and B. Odom, New Determination
of the Fine Structure Constant from the Electron g Value and QED, Phys.
Rev. Lett. 97, 030802 (2006).

^
Pictorial overview of the Brookhaven muon g-2 experiment, [1].

^
Muon g-2 experiment homepage, [2].

^ K.
Hagiwara, A.D. Martin, Daisuke Nomura, and T. Teubner, Improved predictions
for g-2 of the muon and αQED(MZ2), hep-ph/0611102.

^
Pierre Cladé, Estefania de Mirandes, Malo Cadoret, Saïda Guellati-Khélifa,
Catherine Schwob, François Nez, Lucile Julien, and François Biraben,
Determination of the Fine Structure Constant Based on Bloch Oscillations of
Ultracold Atoms in a Vertical Optical Lattice, Phys. Rev. Lett. 96, 033001
(2006).

Quantum
electrodynamics

v • d • e

electron | positron | photon
self-energy | vacuum
polarization | vertex
function
Gupta-Bleuler
formalism | ξ gauge | Ward-Takahashi
identity
Compton
scattering | Bhabha
scattering | Møller
scattering
anomalous
magnetic dipole moment
bremsstrahlung | positronium

Retrieved from "http://en.wikipedia.org/wiki/Precision_tests_of_QED"

Categories: Physics
articles needing expert attention | Articles
with unsourced statements since February 2007 | All
articles with unsourced statements | Quantum
electrodynamics | Electrodynamics
| Quantum field
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