Antimatter tests of Lorentz violation

{{short description|Experiments testing the fundamental assumptions of physics}}

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.

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, 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 antineutrons

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.

{{cite journal

|first1=D. |last1=Colladay |first2=V.A. |last2=Kostelecky

|title=CPT Violation and the Standard Model

|date=1997

|arxiv=hep-ph/9703464|bibcode = 1997PhRvD..55.6760C |doi = 10.1103/PhysRevD.55.6760 |volume=55 |issue=11 |journal=Physical Review D |pages=6760–6774|s2cid=7651433 }}

{{cite journal

|first1=D. |last1=Colladay |first2=V.A. |last2=Kostelecky

|title=Lorentz-Violating Extension of the Standard Model

|date=1998

|arxiv=hep-ph/9809521|bibcode = 1998PhRvD..58k6002C |doi = 10.1103/PhysRevD.58.116002 |volume=58 |issue=11 |pages=116002 |journal=Physical Review D|s2cid=4013391 }}

{{cite journal

|first=V.A. |last=Kostelecky

|title=Gravity, Lorentz Violation, and the Standard Model

|date=2004

|pages=105009

|journal=Physical Review D|s2cid=55185765

}}

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.

Lorentz violation tests with Penning Traps

A Penning trap

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 (see {{section link|gyromagnetic ratio|gyromagnetic ratio for an isolated electron}}).

The first calculations of SME effects

in Penning traps

were published in 1997

and 1998.

{{cite journal

|title=Testing CPT with Anomalous Magnetic Moments

|date=1997

|arxiv=hep-ph/9707364|bibcode = 1997PhRvL..79.1432B |doi = 10.1103/PhysRevLett.79.1432 |volume=79 |issue=8 |journal=Physical Review Letters |pages=1432–1435|s2cid=119048753 }}

{{cite journal

|title=CPT and Lorentz Tests in Penning Traps

|date=1998

|arxiv=hep-ph/9809543|bibcode = 1998PhRvD..57.3932B |doi = 10.1103/PhysRevD.57.3932 |volume=57 |issue=7 |journal=Physical Review D |pages=3932–3943|s2cid=958994 }}

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 the physicist Gerald Gabrielse of Harvard University 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 1.0 Hz. The absence of Lorentz violating effects of this type

placed a limit on combinations of $c$ -type SME coefficients that had not been accessed in other experiments. The results{{cite journal | last1=Gabrielse | first1=G. | last2=Khabbaz | first2=A. | last3=Hall | first3=D. S. | last4=Heimann | first4=C. | last5=Kalinowsky | first5=H. | last6=Jhe | first6=W. | title=Precision Mass Spectroscopy of the Antiproton and Proton Using Simultaneously Trapped Particles | journal=Physical Review Letters | publisher=American Physical Society (APS) | volume=82 | issue=16 | date=19 April 1999 | issn=0031-9007 | doi=10.1103/physrevlett.82.3198 | pages=3198–3201 | bibcode=1999PhRvL..82.3198G}}

appeared in Physical Review Letters in 1999.

The Penning-trap group at the University of Washington, headed by the 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 $b$ -type electron coefficient.

This work{{cite journal | last1=Mittleman | first1=R. K. | last2=Ioannou | first2=I. I. | last3=Dehmelt | first3=H. G. | last4=Russell | first4=Neil | title=Bound onCPTand Lorentz Symmetry with a Trapped Electron | journal=Physical Review Letters | publisher=American Physical Society (APS) | volume=83 | issue=11 | date=13 September 1999 | issn=0031-9007 | doi=10.1103/physrevlett.83.2116 | pages=2116–2119| bibcode=1999PhRvL..83.2116M }}

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

$b$ -type coefficients at a level of about 10⁻²⁴ GeV.

In addition to being a limit on Lorentz violation,

this also limits the CPT violation.

This result{{cite journal | last1=Dehmelt | first1=H. | last2=Mittleman | first2=R. | last3=Van Dyck | first3=R. S. | last4=Schwinberg | first4=P. | title=Past Electron-Positrong−2Experiments Yielded Sharpest Bound onCPTViolation for Point Particles | journal=Physical Review Letters | volume=83 | issue=23 | date=6 December 1999 | issn=0031-9007 | doi=10.1103/physrevlett.83.4694 | pages=4694–4696| arxiv=hep-ph/9906262 | bibcode=1999PhRvL..83.4694D | s2cid=116195114 }}

appeared in Physical Review Letters in 1999.

Lorentz violation in antihydrogen

The antihydrogen atom is

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

{{cite journal

|title=CPT and Lorentz Tests in Hydrogen and Antihydrogen

|date=1999

|arxiv=hep-ph/9810269|bibcode = 1999PhRvL..82.2254B |doi = 10.1103/PhysRevLett.82.2254 |volume=82 |issue=11 |journal=Physical Review Letters |pages=2254–2257|s2cid=10398057 }}

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: AEGIS, ALPHA, ASACUSA, ATRAP, and GBAR.

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

In October 2017, the BASE experiment at CERN reported a measurement of the antiproton magnetic moment to a precision of 1.5 parts per billion.{{cite web |last=Adamson |first=Allan |title=Universe Should Not Actually Exist: Big Bang Produced Equal Amounts Of Matter And Antimatter |url=http://www.techtimes.com/articles/214821/20171025/universe-should-not-actually-exist-big-bang-produced-equal-amounts-of-matter-and-antimatter.htm |date=19 October 2017 |work=TechTimes.com |accessdate=26 October 2017 }}{{cite journal |author=Smorra C.|display-authors=et al |title=A parts-per-billion measurement of the antiproton magnetic moment |date=20 October 2017 |journal=Nature |volume=550 |issue=7676 |pages=371–374 |doi=10.1038/nature24048 |bibcode=2017Natur.550..371S |pmid=29052625|doi-access=free |url=http://cds.cern.ch/record/2291601/files/nature24048.pdf }} It is consistent with the most precise measurement of the proton magnetic moment (also made by BASE in 2014), which supports the hypothesis of CPT symmetry. This measurement represents the first time that a property of antimatter is known more precisely than the equivalent property in matter.

Lorentz violation with muons

The muon 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 the year 2000.

{{cite journal

|title=CPT and Lorentz Tests with Muons

|date=2000

|arxiv=hep-ph/9912451|bibcode = 2000PhRvL..84.1098B |doi = 10.1103/PhysRevLett.84.1098 |volume=84 |issue=6 |journal=Physical Review Letters |pages=1098–1101|pmid=11017453 |s2cid=11593326 }}

In the year 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 a 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 $b$ -type coefficients in the SME,

published in Physical Review Letters.

{{cite journal

|author= V.W. Hughes

|title=Test of CPT and Lorentz Invariance from Muonium Spectroscopy, Phys. Rev. Lett. 87, 111804 (2001)

|date=2001

|display-authors=etal}}

In 2008,

the Muon $g-2$ Collaboration at the Brookhaven National Laboratory 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 antiparticle. 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,

{{cite journal

|collaboration= BNL g-2 collaboration

|author=G.W. Bennett

|journal=Physical Review Letters |pmid=18352695 |pages=091602|year=2008

|s2cid=26270066

}}

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.

{{cite journal

|first1=V.A. |last1=Kostelecky |first2=N. |last2=Russell

|title=Data Tables for Lorentz and CPT Violation

|date=2010

|arxiv=0801.0287|bibcode = 2011RvMP...83...11K |doi=10.1103/RevModPhys.83.11 |volume=83 |issue=1 |journal=Reviews of Modern Physics |pages=11–31|s2cid=3236027 }}

References

External links

[http://www.physics.indiana.edu/~kostelec/faq.html Background information on Lorentz and CPT violation]
[https://arxiv.org/abs/0801.0287 Data Tables for Lorentz and CPT Violation]
[https://web.archive.org/web/20110811045124/http://aegis.web.cern.ch/aegis/home.html AEGIS Experiment]
[http://alpha.web.cern.ch ALPHA Experiment]
[http://asacusa.web.cern.ch ASACUSA Experiment]
[https://web.archive.org/web/20100627174211/http://hussle.harvard.edu/~atrap/ ATRAP Experiment]
[http://www.g-2.bnl.gov/ Muon $g-2$ Experiment]

Category:Antimatter

Antimatter tests of Lorentz violation

Introduction

Lorentz violation tests with Penning Traps

Lorentz violation in antihydrogen

Lorentz violation with muons

See also

References

External links