Antimatter tests of Lorentz violation
Encyclopedia
High-precision experiments could reveal
small previously unseen differences between the behavior
of matter and antimatter.
This prospect is appealing to physicists because it may
show that nature is not Lorentz symmetric.
The quantum behavior of these particles can be predicted with excellent accuracy
using the Dirac equation
, named after P.A.M. Dirac.
One of the triumphs of the Dirac equation is
its prediction of the existence of antimatter particles.
Antiprotons, positrons, and antineutron
s
are now well understood,
and can be created and studied in experiments.
High-precision experiments have been unable to
detect any difference between the masses
of particles and
those of the corresponding antiparticles.
They also have been unable to detect any difference between the magnitudes of
the charges,
or between the lifetimes,
of particles and antiparticles.
These mass, charge, and lifetime symmetries
are required in a Lorentz and CPT symmetric universe,
but are only a small number of the properties that need to match
if the universe is Lorentz and CPT symmetric.
The Standard-Model Extension
(SME
),
a comprehensive theoretical framework for Lorentz and CPT violation,
makes specific predictions
about how particles and antiparticles
would behave differently in a universe
that is very close to,
but not exactly,
Lorentz symmetric.
In loose terms,
the SME
can be visualized
as being constructed from
fixed background fields
that interact weakly, but differently,
with particles and antiparticles.
The behavioral differences between
matter and antimatter
are specific to each individual experiment.
Factors that determine the behavior include
the particle species involved,
the electromagnetic, gravitational, and nuclear fields controlling the system.
Furthermore,
for any Earth-bound experiment,
the rotational and orbital motion of the Earth is important,
leading to sidereal and seasonal signals.
For experiments conducted in space, the orbital motion of the craft
is an important factor in determining the signals
of Lorentz violation
that might arise.
To harness the predictive power of the SME
in any specific system,
a calculation has to be performed
so that all these factors can be accounted for.
These calculations are facilitated by the reasonable assumption that Lorentz
violations, if they exist,
are small. This makes it possible to use perturbation theory to obtain results
that would otherwise be extremely difficult to find.
The SME
generates a modified Dirac equation
that breaks Lorentz symmetry
for some types of particle motions, but not others.
It therefore holds important information
about how Lorentz violations
might have been hidden
in past experiments,
or might be revealed in future ones.
is a research apparatus
capable of trapping individual charged particles
and their antimatter counterparts.
The trapping mechanism is
a strong magnetic field that keeps the particles near a central axis,
and an electric field that turns the particles around
when they stray too far along the axis.
The motional frequencies of the trapped particle
can be monitored and measured with astonishing precision.
One of these frequencies is the anomaly frequency,
which has played an important role in the measurement
of the gyromagnetic ratio of the electron.
The first calculations of SME
effects
in Penning trap
s
were published in 1997
and 1998.
They showed that,
in identical Penning traps,
if the
anomaly frequency of an electron
was increased,
then the anomaly frequency of a positron
would be decreased.
The size of the increase or decrease
in the frequency
would be a measure of
the strength of one of the SME
background fields.
More specifically,
it is a measure
of the component of the background field
along the direction of the axial magnetic field.
In tests of Lorentz symmetry,
the noninertial nature of the laboratory
due to the rotational and orbital motion of the Earth
has to be taken into account.
Each Penning-trap measurement
is the projection of the background SME
fields
along the axis of the experimental magnetic field
at the time of the experiment.
This is further complicated if the experiment takes
hours, days, or longer to perform.
One approach is to seek instantaneous differences,
by comparing anomaly frequencies
for a particle and an antiparticle
measured at the same time on different days.
Another approach is to seek
sidereal variations,
by continuously monitoring
the anomaly frequency for just one species of particle
over an extended time.
Each offers different challenges.
For example,
instantaneous comparisons
require the electric field in the trap to be
precisely reversed,
while sidereal tests are limited
by the stability of the magnetic field.
An experiment conducted by Harvard University
physicist Gerald Gabrielse
involved two particles confined in a Penning trap
.
The idea was to compare a proton and an antiproton,
but to overcome the technicalities of having opposite charges,
a negatively charged hydrogen ion was used in place of the proton.
The ion, two electrons bound electrostatically with a proton
,
and the antiproton have the same charge
and can therefore be simultaneously trapped.
This design allows for quick interchange
of the proton and the antiproton
and so an instantaneous-type Lorentz test can be performed.
The cyclotron frequencies of the two trapped particles
were about 90 MHz,
and the apparatus was capable of resolving differences
in these of about 1 Hz.
The absence of Lorentz violating effects of this type
placed a limit on
combinations of
-type SME coefficients
that had not been accessed in other experiments.
The results
appeared in Physical Review Letters in 1999.
The Penning-trap group
at the University of Washington in Seattle,
headed by Nobel Laureate Hans Dehmelt,
conducted a search for sidereal variations
in the anomaly frequency of a trapped electron.
The results were extracted from
an experiment that ran for several weeks,
and the analysis required splitting the data
into bins according to the orientation of the apparatus
in the inertial reference frame of the Sun.
At a resolution of 0.20 Hz,
they were unable to discern any sidereal variations
in the anomaly frequency,
which runs around 185,000,000 Hz.
Translating this into an upper bound on the relevant
SME
background field,
places a
bound of about
10−24 GeV
on a
-type electron coefficient.
This work
was published in Physical Review Letters in 1999.
Another experimental result from the Dehmelt group
involved a comparison of the instantaneous
type.
Using data from a single trapped electron
and a single trapped positron,
they again found no difference
between the two anomaly frequencies
at a resolution of about 0.2 Hz.
This result placed a bound on a simpler combination of
-type coefficients at a level of about
10−24 GeV.
In addition to being a limit on Lorentz violation
,
this also limits CPT violation.
This result
appeared in
Physical Review Letters in 1999.
the antimatter counterpart of the hydrogen atom.
It has a negatively charged antiproton
at the nucleus
that attracts a positively charged positron
orbiting around it.
The spectral lines of hydrogen have frequencies
determined by the energy differences
between the quantum-mechanical orbital states
of the electron.
These lines
have been studied in thousands of spectroscopic experiments
and are understood in great detail.
The quantum mechanics of the positron orbiting an antiproton
in the antihydrogen atom is expected to be very similar
to that of the hydrogen atom.
In fact,
conventional physics predicts that the spectrum of antihydrogen
is identical to that of regular hydrogen.
In the presence of the background fields of the SME
,
the spectra of hydrogen and antihydrogen
are expected to show tiny differences
in some lines,
and no differences in others.
Calculations of these SME
effects
in antihydrogen and hydrogen
were published
in Physical Review Letters
in 1999.
One of the main results found
is that hyperfine transitions
are sensitive to Lorentz breaking effects.
Several experimental groups at CERN
are working on producing antihydrogen.
They are:
Creating trapped antihydrogen
in sufficient quantities
to do spectroscopy
is an enormous experimental challenge.
Signatures of Lorentz violation
are similar to those expected in Penning traps.
There would be sidereal effects
causing variations in the spectral frequencies
as the experimental laboratory turns with the Earth.
There would also be the possibility of finding instantaneous
Lorentz breaking signals
when antihydrogen spectra are compared directly with conventional hydrogen spectra
and its positively charged antiparticle
have been used to perform tests of Lorentz symmetry.
Since the lifetime of the muon
is only a few microseconds,
the experiments are quite different
from ones with electrons and positrons.
Calculations for muon
experiments
aimed at probing Lorentz violation
in the SME
were first published in 2000.
In 2001,
Hughes and collaborators published their results
from a search for sidereal signals in the spectrum
of muonium,
an atom consisting of an electron bound to an negatively-charged muon.
Their data,
taken over a two-year period,
showed no evidence for Lorentz violation
.
This placed a stringent constraint on
a combination of
-type coefficients in the SME
,
published in Physical Review Letters.
In 2008,
the Muon
Collaboration at Brookhaven National Laboratory
in New York state
published results
after searching for signals of Lorentz violation
with muons and antimuons.
In one type of analysis, they compared the anomaly frequencies
for the muon and its antiparicle.
In another,
they looked for sidereal variations
by allocating their data into one-hour bins
according to the orientation of the Earth
relative to the Sun-centered inertial reference frame.
Their results,
published in Physical Review Letters in 2008,
show no signatures of Lorentz violation
at the resolution of the Brookhaven experiment.
Experimental results in all sectors of the
SME
are summarized in the Data Tables for Lorentz and CPT violation.
small previously unseen differences between the behavior
of matter and antimatter.
This prospect is appealing to physicists because it may
show that nature is not Lorentz symmetric.
Introduction
Ordinary matter is made up of protons, electrons, and neutrons.The quantum behavior of these particles can be predicted with excellent accuracy
using the Dirac equation
Dirac equation
The Dirac equation is a relativistic quantum mechanical wave equation formulated by British physicist Paul Dirac in 1928. It provided a description of elementary spin-½ particles, such as electrons, consistent with both the principles of quantum mechanics and the theory of special relativity, and...
, named after P.A.M. Dirac.
One of the triumphs of the Dirac equation is
its prediction of the existence of antimatter particles.
Antiprotons, positrons, and antineutron
Antineutron
The antineutron is the antiparticle of the neutron with symbol . It differs from the neutron only in that some of its properties have equal magnitude but opposite sign. It has the same mass as the neutron, and no net electric charge, but has opposite baryon number...
s
are now well understood,
and can be created and studied in experiments.
High-precision experiments have been unable to
detect any difference between the masses
of particles and
those of the corresponding antiparticles.
They also have been unable to detect any difference between the magnitudes of
the charges,
or between the lifetimes,
of particles and antiparticles.
These mass, charge, and lifetime symmetries
are required in a Lorentz and CPT symmetric universe,
but are only a small number of the properties that need to match
if the universe is Lorentz and CPT symmetric.
The Standard-Model Extension
Standard-Model Extension
Standard-Model Extension is an effective field theory that contains the Standard Model, General Relativity, and all possible operators that break Lorentz symmetry.Violations of this fundamental symmetry can be studied within this general framework...
(SME
Standard-Model Extension
Standard-Model Extension is an effective field theory that contains the Standard Model, General Relativity, and all possible operators that break Lorentz symmetry.Violations of this fundamental symmetry can be studied within this general framework...
),
a comprehensive theoretical framework for Lorentz and CPT violation,
makes specific predictions
about how particles and antiparticles
would behave differently in a universe
that is very close to,
but not exactly,
Lorentz symmetric.
In loose terms,
the SME
Standard-Model Extension
Standard-Model Extension is an effective field theory that contains the Standard Model, General Relativity, and all possible operators that break Lorentz symmetry.Violations of this fundamental symmetry can be studied within this general framework...
can be visualized
as being constructed from
fixed background fields
that interact weakly, but differently,
with particles and antiparticles.
The behavioral differences between
matter and antimatter
are specific to each individual experiment.
Factors that determine the behavior include
the particle species involved,
the electromagnetic, gravitational, and nuclear fields controlling the system.
Furthermore,
for any Earth-bound experiment,
the rotational and orbital motion of the Earth is important,
leading to sidereal and seasonal signals.
For experiments conducted in space, the orbital motion of the craft
is an important factor in determining the signals
of Lorentz violation
Standard-Model Extension
Standard-Model Extension is an effective field theory that contains the Standard Model, General Relativity, and all possible operators that break Lorentz symmetry.Violations of this fundamental symmetry can be studied within this general framework...
that might arise.
To harness the predictive power of the SME
Standard-Model Extension
Standard-Model Extension is an effective field theory that contains the Standard Model, General Relativity, and all possible operators that break Lorentz symmetry.Violations of this fundamental symmetry can be studied within this general framework...
in any specific system,
a calculation has to be performed
so that all these factors can be accounted for.
These calculations are facilitated by the reasonable assumption that Lorentz
violations, if they exist,
are small. This makes it possible to use perturbation theory to obtain results
that would otherwise be extremely difficult to find.
The SME
Standard-Model Extension
Standard-Model Extension is an effective field theory that contains the Standard Model, General Relativity, and all possible operators that break Lorentz symmetry.Violations of this fundamental symmetry can be studied within this general framework...
generates a modified Dirac equation
Dirac equation
The Dirac equation is a relativistic quantum mechanical wave equation formulated by British physicist Paul Dirac in 1928. It provided a description of elementary spin-½ particles, such as electrons, consistent with both the principles of quantum mechanics and the theory of special relativity, and...
that breaks Lorentz symmetry
for some types of particle motions, but not others.
It therefore holds important information
about how Lorentz violations
Standard-Model Extension
Standard-Model Extension is an effective field theory that contains the Standard Model, General Relativity, and all possible operators that break Lorentz symmetry.Violations of this fundamental symmetry can be studied within this general framework...
might have been hidden
in past experiments,
or might be revealed in future ones.
Lorentz violation tests with Penning Traps
A Penning trapis a research apparatus
capable of trapping individual charged particles
and their antimatter counterparts.
The trapping mechanism is
a strong magnetic field that keeps the particles near a central axis,
and an electric field that turns the particles around
when they stray too far along the axis.
The motional frequencies of the trapped particle
can be monitored and measured with astonishing precision.
One of these frequencies is the anomaly frequency,
which has played an important role in the measurement
of the gyromagnetic ratio of the electron.
The first calculations of SME
Standard-Model Extension
Standard-Model Extension is an effective field theory that contains the Standard Model, General Relativity, and all possible operators that break Lorentz symmetry.Violations of this fundamental symmetry can be studied within this general framework...
effects
in Penning trap
Penning trap
Penning traps are devices for the storage of charged particles using a homogeneous static magnetic field and a spatially inhomogeneous static electric field. This kind of trap is particularly well suited to precision measurements of properties of ions and stable subatomic particles which have...
s
were published in 1997
and 1998.
They showed that,
in identical Penning traps,
if the
anomaly frequency of an electron
Electron
The electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...
was increased,
then the anomaly frequency of a positron
Positron
The positron or antielectron is the antiparticle or the antimatter counterpart of the electron. The positron has an electric charge of +1e, a spin of ½, and has the same mass as an electron...
would be decreased.
The size of the increase or decrease
in the frequency
would be a measure of
the strength of one of the SME
Standard-Model Extension
Standard-Model Extension is an effective field theory that contains the Standard Model, General Relativity, and all possible operators that break Lorentz symmetry.Violations of this fundamental symmetry can be studied within this general framework...
background fields.
More specifically,
it is a measure
of the component of the background field
along the direction of the axial magnetic field.
In tests of Lorentz symmetry,
the noninertial nature of the laboratory
due to the rotational and orbital motion of the Earth
has to be taken into account.
Each Penning-trap measurement
is the projection of the background SME
Standard-Model Extension
Standard-Model Extension is an effective field theory that contains the Standard Model, General Relativity, and all possible operators that break Lorentz symmetry.Violations of this fundamental symmetry can be studied within this general framework...
fields
along the axis of the experimental magnetic field
at the time of the experiment.
This is further complicated if the experiment takes
hours, days, or longer to perform.
One approach is to seek instantaneous differences,
by comparing anomaly frequencies
for a particle and an antiparticle
measured at the same time on different days.
Another approach is to seek
sidereal variations,
by continuously monitoring
the anomaly frequency for just one species of particle
over an extended time.
Each offers different challenges.
For example,
instantaneous comparisons
require the electric field in the trap to be
precisely reversed,
while sidereal tests are limited
by the stability of the magnetic field.
An experiment conducted by Harvard University
physicist Gerald Gabrielse
involved two particles confined in a Penning trap
Penning trap
Penning traps are devices for the storage of charged particles using a homogeneous static magnetic field and a spatially inhomogeneous static electric field. This kind of trap is particularly well suited to precision measurements of properties of ions and stable subatomic particles which have...
.
The idea was to compare a proton and an antiproton,
but to overcome the technicalities of having opposite charges,
a negatively charged hydrogen ion was used in place of the proton.
The ion, two electrons bound electrostatically with a proton
Proton
The proton is a subatomic particle with the symbol or and a positive electric charge of 1 elementary charge. One or more protons are present in the nucleus of each atom, along with neutrons. The number of protons in each atom is its atomic number....
,
and the antiproton have the same charge
and can therefore be simultaneously trapped.
This design allows for quick interchange
of the proton and the antiproton
and so an instantaneous-type Lorentz test can be performed.
The cyclotron frequencies of the two trapped particles
were about 90 MHz,
and the apparatus was capable of resolving differences
in these of about 1 Hz.
The absence of Lorentz violating effects of this type
placed a limit on
combinations of
-type SME coefficientsthat had not been accessed in other experiments.
The results
appeared in Physical Review Letters in 1999.
The Penning-trap group
at the University of Washington in Seattle,
headed by Nobel Laureate Hans Dehmelt,
conducted a search for sidereal variations
in the anomaly frequency of a trapped electron.
The results were extracted from
an experiment that ran for several weeks,
and the analysis required splitting the data
into bins according to the orientation of the apparatus
in the inertial reference frame of the Sun.
At a resolution of 0.20 Hz,
they were unable to discern any sidereal variations
in the anomaly frequency,
which runs around 185,000,000 Hz.
Translating this into an upper bound on the relevant
SME
Standard-Model Extension
Standard-Model Extension is an effective field theory that contains the Standard Model, General Relativity, and all possible operators that break Lorentz symmetry.Violations of this fundamental symmetry can be studied within this general framework...
background field,
places a
bound of about
10−24 GeV
on a
-type electron coefficient.This work
was published in Physical Review Letters in 1999.
Another experimental result from the Dehmelt group
involved a comparison of the instantaneous
type.
Using data from a single trapped electron
and a single trapped positron,
they again found no difference
between the two anomaly frequencies
at a resolution of about 0.2 Hz.
This result placed a bound on a simpler combination of
-type coefficients at a level of about10−24 GeV.
In addition to being a limit on Lorentz violation
Standard-Model Extension
Standard-Model Extension is an effective field theory that contains the Standard Model, General Relativity, and all possible operators that break Lorentz symmetry.Violations of this fundamental symmetry can be studied within this general framework...
,
this also limits CPT violation.
This result
appeared in
Physical Review Letters in 1999.
Lorentz violation in antihydrogen
The antihydrogen atom isthe antimatter counterpart of the hydrogen atom.
It has a negatively charged antiproton
at the nucleus
that attracts a positively charged positron
orbiting around it.
The spectral lines of hydrogen have frequencies
determined by the energy differences
between the quantum-mechanical orbital states
of the electron.
These lines
have been studied in thousands of spectroscopic experiments
and are understood in great detail.
The quantum mechanics of the positron orbiting an antiproton
in the antihydrogen atom is expected to be very similar
to that of the hydrogen atom.
In fact,
conventional physics predicts that the spectrum of antihydrogen
is identical to that of regular hydrogen.
In the presence of the background fields of the SME
Standard-Model Extension
Standard-Model Extension is an effective field theory that contains the Standard Model, General Relativity, and all possible operators that break Lorentz symmetry.Violations of this fundamental symmetry can be studied within this general framework...
,
the spectra of hydrogen and antihydrogen
are expected to show tiny differences
in some lines,
and no differences in others.
Calculations of these SME
Standard-Model Extension
Standard-Model Extension is an effective field theory that contains the Standard Model, General Relativity, and all possible operators that break Lorentz symmetry.Violations of this fundamental symmetry can be studied within this general framework...
effects
in antihydrogen and hydrogen
were published
in Physical Review Letters
in 1999.
One of the main results found
is that hyperfine transitions
are sensitive to Lorentz breaking effects.
Several experimental groups at CERN
CERN
The European Organization for Nuclear Research , known as CERN , is an international organization whose purpose is to operate the world's largest particle physics laboratory, which is situated in the northwest suburbs of Geneva on the Franco–Swiss border...
are working on producing antihydrogen.
They are:
- AEGIS
- ALPHA
- ASACUSA
- ATRAP
Creating trapped antihydrogen
in sufficient quantities
to do spectroscopy
is an enormous experimental challenge.
Signatures of Lorentz violation
Standard-Model Extension
Standard-Model Extension is an effective field theory that contains the Standard Model, General Relativity, and all possible operators that break Lorentz symmetry.Violations of this fundamental symmetry can be studied within this general framework...
are similar to those expected in Penning traps.
There would be sidereal effects
causing variations in the spectral frequencies
as the experimental laboratory turns with the Earth.
There would also be the possibility of finding instantaneous
Lorentz breaking signals
when antihydrogen spectra are compared directly with conventional hydrogen spectra
Lorentz violation with muons
The muonMuon
The muon |mu]] used to represent it) is an elementary particle similar to the electron, with a unitary negative electric charge and a spin of ½. Together with the electron, the tau, and the three neutrinos, it is classified as a lepton...
and its positively charged antiparticle
have been used to perform tests of Lorentz symmetry.
Since the lifetime of the muon
Muon
The muon |mu]] used to represent it) is an elementary particle similar to the electron, with a unitary negative electric charge and a spin of ½. Together with the electron, the tau, and the three neutrinos, it is classified as a lepton...
is only a few microseconds,
the experiments are quite different
from ones with electrons and positrons.
Calculations for muon
Muon
The muon |mu]] used to represent it) is an elementary particle similar to the electron, with a unitary negative electric charge and a spin of ½. Together with the electron, the tau, and the three neutrinos, it is classified as a lepton...
experiments
aimed at probing Lorentz violation
Standard-Model Extension
Standard-Model Extension is an effective field theory that contains the Standard Model, General Relativity, and all possible operators that break Lorentz symmetry.Violations of this fundamental symmetry can be studied within this general framework...
in the SME
Standard-Model Extension
Standard-Model Extension is an effective field theory that contains the Standard Model, General Relativity, and all possible operators that break Lorentz symmetry.Violations of this fundamental symmetry can be studied within this general framework...
were first published in 2000.
In 2001,
Hughes and collaborators published their results
from a search for sidereal signals in the spectrum
of muonium,
an atom consisting of an electron bound to an negatively-charged muon.
Their data,
taken over a two-year period,
showed no evidence for Lorentz violation
Standard-Model Extension
Standard-Model Extension is an effective field theory that contains the Standard Model, General Relativity, and all possible operators that break Lorentz symmetry.Violations of this fundamental symmetry can be studied within this general framework...
.
This placed a stringent constraint on
a combination of
-type coefficients in the SMEStandard-Model Extension
Standard-Model Extension is an effective field theory that contains the Standard Model, General Relativity, and all possible operators that break Lorentz symmetry.Violations of this fundamental symmetry can be studied within this general framework...
,
published in Physical Review Letters.
In 2008,
the Muon
Collaboration at Brookhaven National LaboratoryBrookhaven National Laboratory
Brookhaven National Laboratory , is a United States national laboratory located in Upton, New York on Long Island, and was formally established in 1947 at the site of Camp Upton, a former U.S. Army base...
in New York state
published results
after searching for signals of Lorentz violation
Standard-Model Extension
Standard-Model Extension is an effective field theory that contains the Standard Model, General Relativity, and all possible operators that break Lorentz symmetry.Violations of this fundamental symmetry can be studied within this general framework...
with muons and antimuons.
In one type of analysis, they compared the anomaly frequencies
for the muon and its antiparicle.
In another,
they looked for sidereal variations
by allocating their data into one-hour bins
according to the orientation of the Earth
relative to the Sun-centered inertial reference frame.
Their results,
published in Physical Review Letters in 2008,
show no signatures of Lorentz violation
Standard-Model Extension
Standard-Model Extension is an effective field theory that contains the Standard Model, General Relativity, and all possible operators that break Lorentz symmetry.Violations of this fundamental symmetry can be studied within this general framework...
at the resolution of the Brookhaven experiment.
Experimental results in all sectors of the
SME
Standard-Model Extension
Standard-Model Extension is an effective field theory that contains the Standard Model, General Relativity, and all possible operators that break Lorentz symmetry.Violations of this fundamental symmetry can be studied within this general framework...
are summarized in the Data Tables for Lorentz and CPT violation.
See also
- Standard-Model ExtensionStandard-Model ExtensionStandard-Model Extension is an effective field theory that contains the Standard Model, General Relativity, and all possible operators that break Lorentz symmetry.Violations of this fundamental symmetry can be studied within this general framework...
- Lorentz-violating neutrino oscillationsLorentz-violating neutrino oscillationsLorentz-violating neutrino oscillation refers to the quantum phenomenon of neutrino oscillations described in a framework that allows the breakdown of Lorentz invariance...
- AEGIS Experiment
- ALPHA Experiment
- ASACUSA Experiment
- ATRAP Experiment
Experiment