High-precision experiments could revealsmall previously unseen differences between the behaviorof matter and antimatter.This prospect is appealing to physicists because it mayshow that nature is not Lorentz symmetric.
Ordinary matter is made up of protons, electrons, and neutrons.The quantum behavior of these particles can be predicted with excellent accuracyusing the Dirac equation, named after P.A.M. Dirac.One of the triumphs of the Dirac equation isits prediction of the existence of antimatter particles.Antiprotons, positrons, and antineutronsare now well understood,and can be created and studied in experiments.
High-precision experiments have been unable todetect any difference between the massesof particles andthose of the corresponding antiparticles.They also have been unable to detect any difference between the magnitudes ofthe charges,or between the lifetimes,of particles and antiparticles.These mass, charge, and lifetime symmetriesare required in a Lorentz and CPT symmetric universe,but are only a small number of the properties that need to matchif the universe is Lorentz and CPT symmetric.
The Standard-Model Extension (SME),a comprehensive theoretical framework for Lorentz and CPT violation,makes specific predictionsabout how particles and antiparticleswould behave differently in a universethat is very close to,but not exactly,Lorentz symmetric.[1] [2] [3] In loose terms,the SME can be visualizedas being constructed fromfixed background fieldsthat interact weakly, but differently,with particles and antiparticles.
The behavioral differences betweenmatter and antimatterare specific to each individual experiment.Factors that determine the behavior includethe 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 craftis an important factor in determining the signalsof Lorentz violation that might arise.To harness the predictive power of the SME in any specific system,a calculation has to be performedso that all these factors can be accounted for.These calculations are facilitated by the reasonable assumption that Lorentzviolations, if they exist,are small. This makes it possible to use perturbation theory to obtain resultsthat would otherwise be extremely difficult to find.
The SME generates a modified Dirac equationthat breaks Lorentz symmetryfor some types of particle motions, but not others.It therefore holds important informationabout how Lorentz violations might have been hiddenin past experiments,or might be revealed in future ones.
A Penning trapis a research apparatuscapable of trapping individual charged particlesand their antimatter counterparts.The trapping mechanism isa strong magnetic field that keeps the particles near a central axis,and an electric field that turns the particles aroundwhen they stray too far along the axis.The motional frequencies of the trapped particlecan be monitored and measured with astonishing precision.One of these frequencies is the anomaly frequency,which has played an important role in the measurementof the gyromagnetic ratio of the electron (see).
The first calculations of SME effectsin Penning trapswere published in 1997and 1998.[4] [5] They showed that,in identical Penning traps,if theanomaly frequency of an electron was increased,then the anomaly frequency of a positronwould be decreased.The size of the increase or decreasein the frequencywould be a measure ofthe strength of one of the SME background fields.More specifically,it is a measureof the component of the background fieldalong the direction of the axial magnetic field.
In tests of Lorentz symmetry,the noninertial nature of the laboratorydue to the rotational and orbital motion of the Earthhas to be taken into account.Each Penning-trap measurementis the projection of the background SME fieldsalong the axis of the experimental magnetic fieldat the time of the experiment.This is further complicated if the experiment takeshours, days, or longer to perform.
One approach is to seek instantaneous differences,by comparing anomaly frequenciesfor a particle and an antiparticlemeasured at the same time on different days.Another approach is to seeksidereal variations,by continuously monitoringthe anomaly frequency for just one species of particleover an extended time.Each offers different challenges.For example,instantaneous comparisonsrequire the electric field in the trap to beprecisely reversed,while sidereal tests are limitedby 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 particleswere about 90 MHz, and the apparatus was capable of resolving differencesin these of about 1.0 Hz. The absence of Lorentz violating effects of this typeplaced a limit on combinations of
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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 relevantSME background field, places a bound of about10−24 GeV on a
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Another experimental result from the Dehmelt group involved a comparison of the instantaneous type. Using data from a single trapped electronand a single trapped positron, they again found no differencebetween the two anomaly frequencies at a resolution of about 0.2 Hz.This result placed a bound on a simpler combination of
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The antihydrogen atom isthe antimatter counterpart of the hydrogen atom.It has a negatively charged antiprotonat the nucleusthat attracts a positively charged positronorbiting around it.
The spectral lines of hydrogen have frequenciesdetermined by the energy differencesbetween the quantum-mechanical orbital statesof the electron.These lineshave been studied in thousands of spectroscopic experimentsand are understood in great detail.The quantum mechanics of the positron orbiting an antiprotonin the antihydrogen atom is expected to be very similarto that of the hydrogen atom.In fact,conventional physics predicts that the spectrum of antihydrogenis identical to that of regular hydrogen.
In the presence of the background fields of the SME,the spectra of hydrogen and antihydrogenare expected to show tiny differencesin some lines,and no differences in others.Calculations of these SME effectsin antihydrogen and hydrogenwere published[9] in Physical Review Lettersin 1999.One of the main results foundis that hyperfine transitionsare sensitive to Lorentz breaking effects.
Several experimental groups at CERN are working on producing antihydrogen: AEGIS, ALPHA, ASACUSA, ATRAP, and GBAR.
Creating trapped antihydrogenin sufficient quantitiesto do spectroscopyis an enormous experimental challenge.Signatures of Lorentz violationare similar to those expected in Penning traps.There would be sidereal effectscausing variations in the spectral frequenciesas the experimental laboratory turns with the Earth.There would also be the possibility of finding instantaneousLorentz breaking signalswhen 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.[10] [11] 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.
The muon and its positively charged antiparticlehave been used to perform tests of Lorentz symmetry.Since the lifetime of the muon is only a few microseconds,the experiments are quite differentfrom ones with electrons and positrons.Calculations for muon experimentsaimed at probing Lorentz violationin the SMEwere first published in the year 2000.[12]
In the year 2001,Hughes and collaborators published their resultsfrom a search for sidereal signals in the spectrumof 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 ona combination of
b
In 2008,the Muon
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Experimental results in all sectors of theSME are summarized in the Data Tables for Lorentz and CPT violation.[15]
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