# Current News

*g*-factor measurements

The high-precision comparison of basic properties of matter/antimatter counterparts provides stringent tests of charge-parity-time
(CPT) invariance of the Standard Model. The experiments of the
BASE collaboration
target comparisons of the fundamental properties
of protons and antiprotons by determining and comparing their charge-to-mass ratios and magnetic moments in Penning traps.

In 2014 the collaboration directly measured the magnetic moment of the proton with 3.3 parts per billion (p.p.b.) precision at
the Johannes Gutenberg University Mainz using a challenging double Penning-trap technique (see our
news of 28.05.14). In a recent
experiment at Mainz the collaboration improved the precision of the proton magnetic moment by a factor of eleven using an optimized
double Penning-trap technique (see our news of 24.11.17).
Last year the BASE collaboration also measured the antiproton magnetic
moment with an unprecedented fractional precision of 1.5 p.p.b. (see our news of 18.10.17).

The precision of these experiments is, however, largely limited by the particle mode energy in the Penning trap. A reduction of
the particle preparation times using sympathetically cooled protons/antiprotons is expected to significantly further improve the
measurement precision.

In a recent article published in the *Journal of Modern Optics*, M. Bohman *et al.* present an upcoming experiment
to sympathetically cool single protons and antiprotons in a Penning trap by resonantly coupling the particles to laser-cooled
beryllium ions using a common endcap technique.

The measurement of the magnetic moment of a single proton or antiproton in a Penning trap is based on the measurement
of the frequency ratio of the Larmor frequency and the cyclotron frequency (ν_{L}/ν_{c}). The Larmor
frequency ν_{L} is determined by detection of spin transitions, which can only be observed at very low temperatures
(cyclotron energies *E*_{+}/*k*_{B} < 0.6 K), where the axial frequency ν_{z} is
stable enough.

In the previous proton/antiproton experiments time consuming selective resistive cooling techniques have been used to prepare the
particles below a threshold *E*_{+}/*k*_{B} < 1 K. The successful application of sympathetic cooling of protons and antiprotons to
deterministically low temperatures by coupling the particles to laser-cooled beryllium ions drastically reduces the cycle time of
the experiments.

An analysis of the energy exchange in the complete system leads to cyclotron energies below 30 mK/*k*_{B}.
Thus, a reduction of the ion preparation time from nearly an hour or more to just a few minutes can be expected.

To apply sympathetic cooling not only to protons but also to the negatively charged antiprotons, the BASE collaboration decided to
use one trap for the proton (or antiproton) and a second trap for the beryllium ion cloud and connect the two with a common endcap.
Each Penning trap has an outer endcap electrode, two inner correction electrodes, a central ring electrode and one shared endcap.

To realize the new sympathetic cooling scheme a heavily modified version of the double Penning-trap setup used for the proton
measurements in 2014 at Mainz has been built. The new apparatus for an improved upcoming proton *g*-factor measurement consists of
five traps: the new source trap (ST) for particle preparation, the analysis trap (AT) for spin state analysis, the precision
trap (PT) for high precision frequency measurements, the coupling trap (CT) for common endcap coupling, and the beryllium trap (BT)
for storage of laser cooled beryllium ions.

The upcoming application of sympathetic cooling with the common endcap technique on protons and antiprotons using the improved five Penning trap system will provide a direct CPT test at more than an order of magnitude improved precision and allow the most precise direct CPT comparison of single baryons.

Please read more in the article ... >

The proton is one of the central building blocks of stable matter. For that reason the precise knowledge of its fundamental properties
such as its mass (see our news of 18.07.17), lifetime, charge radius and magnetic moment is of great importance and thus the subject
of many contemporary physics research programs. The mass, for example, is an input parameter for precise quantum electrodynamics
calculations and the lower bound of the proton lifetime sets constraints on possible baryon number violation.

Apart from its fundamental nature, the proton is one of the few particles, which is comparable to its antiparticle – the antiproton.
This allows for a test of the Charge, Parity, and Time Reversal (CPT) symmetry of the Standard Model of particle physics and Big Bang
cosmology, which postulates that the fundamental properties of a particle and its antiparticle are exactly equal. Therefore,
particles and antiparticles should have been created with same amounts. The lack of antimatter in our Universe, however, is in
contradiction with this assumed matter-antimatter symmetry of the Standard Model. One possible explanation of the baryon asymmetry
of the Universe is a violation of CPT invariance. Therefore, the measurement of minutest differences between the properties of a
proton and its corresponding antiparticle, the antiproton, provides a precise test of the particle-antiparticle equality in the
baryonic sector and of the CPT symmetry of the Standard Model.

The proton magnetic moment *μ*_{p} was directly measured in 2014 at the University of Mainz with a unprecedented fractional precision
of 3.3 parts per billion (see our news of 28.05.14) using a novel double Penning-trap technique. Since then, the researchers at
Mainz have developed techniques that enabled them to improve the measurement of the proton magnetic moment by more than one order
of magnitude.

In a recent article published in "*Science*", G. Schneider *et al.* report on a direct high-precision measurement of the magnetic
moment of the proton *μ*_{p} in units of the nuclear magneton *μ*_{N}. The measurement has been carried out in an improved double Penning-trap
system at the University of Mainz, Germany.

A Penning trap is formed by a superposition of an electrostatic quadrupole potential and a homogeneous magnetic field *B*_{0}, which was at
1.9 T in the described proton experiment.

The measurement of the frequency ratio *ν*_{L}/*ν*_{c} of the Larmor frequency and the cyclotron frequency allows the determination of the
magnetic moment of a single proton in the Penning trap independent from the magnetic field *B*_{0}. The cyclotron frequency *ν*_{c} can be
determined from the three harmonic components *ν*_{z}, *ν*_{+}, and *ν*_{-} of the proton motion in the Penning trap using the
invariance theorem: *ν*_{c}^{2} = *ν*_{+}^{2} + *ν*_{z}^{2} + *ν*_{-}^{2}.
The axial frequency *ν*_{z} of the stored proton is directly observed by non-destructive
image current detection. The modified cyclotron frequency *ν*_{+} and the magnetron frequency *ν*_{-} are measured by sideband coupling.

Since the Larmor frequency *ν*_{L} is not accompanied by an oscillating charge it cannot be determined by image current detection but by
means of spin-transition spectroscopy. The superimposition of an inhomogeneous magnetic field, called a "magnetic bottle", couples
the spin-magnetic moment of the proton to its axial oscillation frequency and thus allows to apply non-destructive detection of
spin transitions (spin flips) using the continuous Stern-Gerlach effect.

However, the strong magnetic bottle broadens the Larmor resonance line significantly and limits the measurement to a relative precision
of order 10^{-6} (p.p.m.). The application of a double Penning-trap technique overcomes this problem by using two separate Penning traps
which are interconnected by a transport section. A precision trap (PT) with a nearly homogenous magnetic field is used for high-precision
measurements of *ν*_{c} and *ν*_{L} and an analysis trap (AT) with the magnetic bottle is deployed for spin state detection of the proton.
By applying this method, the proton *g*-factor measurement in 2014 at Mainz reached a relative precision of 3.3 p.p.b..

With respect to the proton measurements in 2014 the recent proton experiment at Mainz used an optimized double Penning-trap technique.
The trap geometry was optimized to reach a higher magnetic homogeneity in the precision trap. Together with a superconducting
self-shielding coil this allowed to improve the cyclotron stability by one order of magnitude. The width of the *g*-factor resonance,
a major limitation in the previous measurement, was reduced by carefully optimizing the Larmor rf drive to probe the resonance. The
particle preparation time for each individual measurement cycle could be reduced by applying a significantly improved superconducting
detector for the modified cyclotron frequency *ν*_{+}. This enabled a twice as high data acquisition rate which greatly increased statistics.
Furthermore, the simultaneous measurement of *ν*_{L} and *ν*_{+} instead of a sequential determination
ensured that *ν*_{L} and *ν*_{+} were measured at
the same energies and times which eliminated many systematic shift contributions.

The final result of the determined proton magnetic moment in units of the nuclear magneton has a fractional precision of
0.3 p.p.b. (3·10^{-10}): *μ*_{p} = 2.792 847 344 62(75)(34) *μ*_{N}. The first
value in parentheses is the statistical uncertainty and
the second one the systematic uncertainty. The new value of *μ*_{p} is in agreement with the currently accepted CODATA
(Committee on Data for Science and Technology) value, but a factor of ten more precise. It improves the 3.3 p.p.b. precision
of the *μ*_{p} measurement in 2014 at Mainz by a factor of eleven.

The BASE collaboration
recently measured the antiproton magnetic moment with a fractional precision of 1.5 p.p.b.
(see our news of 18.10.17).

The recent results for the magnetic moments of the proton and the antiproton enable a test of the
fundamental symmetry between matter and antimatter in the baryonic sector at the 10^{-9} - 10^{-10} level. The researchers expect that
proton/antiproton magnetic moment measurements on the parts per trillion level (10^{-12}) will become possible by reducing the particle
preparation times by more than two orders of magnitude using sympathetically cooled protons/antiprotons by coupling them to laser
cooled beryllium ions.

Please read more in the "*Science*" article ... >

A radio report on the most precise measurement of the proton magnetic moment (start at 2:15 min.).

Further press releases:

In atomic nuclei the protons and neutrons occupy quantum levels that are separated by energy gaps. This leads to the
ordering of the energy levels of the nucleons in the simple nuclear shell model. It successfully describes the nuclear
structure near the valley of stability and explains the exceptional stability of nuclei with completely filled proton or neutron shells
(i.e. magic proton or neutron numbers). However, over the years studies of exotic neutron-rich nuclei have shown that the postulated
stability of nuclei with magic numbers can disappear. Today it is known that the shell-model magic numbers *N* = 8, 20, 28, and 40
are broken at the so called islands of inversion. Improved shell-model calculations predict a fifth island of inversion for
*Z* < 28. Thus, the *Z* = 28, *N* = 50 region of the nuclear chart is a focus of today’s experimental and theoretical nuclear structure
research. The doubly magic exotic nuclide ^{78}Ni is of special interest and it is an open question, whether it retains the
exceptional stability of the classic closed-shell nuclides. Furthermore, recent studies by laser spectroscopy offered strong
evidence, that normal near-spherical and deformed structures coexist (so called shape coexistence) close to ^{78}Ni.
Copper isotopes in the vicinity of ^{78}Ni provide an excellent proxy for probing the structure of ^{78}Ni.

In a recently in Physical Review Letters published article A. Welker *et al.* report on high-precision mass measurements of the
*Z* = 29 copper isotopes ^{75–79}Cu (*N* = 46-50). The measurements were performed using the high-resolution multi-reflection
time-of-flight mass spectrometer/separator (MR-TOF MS) ISOLTRAP at CERN, Geneva.

A purified copper-ion ensemble was injected in a precision Penning trap, where the high-precision mass measurements were carried
out by time-of-flight ion-cyclotron resonance (TOF-ICR). The TOF-ICR yields the atomic masses of the copper ions of interest by determination
of the cyclotron-frequency ratio between the reference ^{85}Rb^{+} ions and the copper ions. The use of the MR-TOF MS allowed measuring
at a lower yield than would have been possible solely by Penning-trap mass spectrometry.

From the determined mass excesses the two-neutron separation energies *S _{2n}* of the nuclides in the

^{78}Ni region were deduced. The

*S*values allow to probe the evolution of nuclear structure with neutron number. The

_{2n}*S*value is theoretically expected to drop between

_{2n}*N*= 50 and

*N*= 52, which would be a well-known sign for magicity. Since the new masses do not extend beyond

*N*= 50, it is not possible to observe the expected

*S*drop. However, the new data differ significantly from that of previous results and the effect of the magic number is already noticeable in the

_{2n}*S*difference between

_{2n}*N*= 48 and

*N*= 50. Thus, the high-precision mass measurements on

^{75–79}Cu allow to define the mass surface above

^{78}Ni and offer evidence for its doubly magic nature.

In addition to the mass experiments, large-scale shell-model calculations with the recently developed PFSDG-U interaction were performed.
The new calculations predict shape coexistence in a doubly magic ^{78}Ni and a new island of inversion for Z < 28. The calculated *S _{2n}* values
are in excellent agreement with the experimental results for Ni and Cu isotopes. This gives confidence in the underlying shell-model
description of these exotic nuclides.

Please read more in the article ... >

The article has been selected for a Viewpoint in Physics. Please read also the viewpoint on the article by Daniel Bazin.

Further information also in the press releases of the idw and CERN .

The Charge, Parity, and Time Reversal (CPT) symmetry of the Standard Model of particle physics implies the exact equality between the properties of a particle and its antiparticle. Thus, precise comparisons of the fundamental properties of matter/antimatter conjugates provide sensitive tests of CPT invariance. They provide data for Standard Model Extensions and contribute to a better understanding of the matter-antimatter imbalance of our universe.

Since the magnetic moment of the antiproton is 660 times smaller than the one of the positron, it is very difficult to measure
its magnetic moment with high precision. Therefore, the antiproton magnetic moment is so far only known to a fractional uncertainty
at the parts per million (p.p.m.) level (see our news of 18.01.17), whereas other matter/antimatter properties have been compared
on the parts per billion (p.p.b.) level or better.

In 2014 the magnetic moment of the proton was measured directly at Mainz with 3.3 parts per billion (p.p.b.) precision
(see our news of 28.05.14). These high-precision proton measurements were
based on the application of the challenging double Penning-trap technique. The implementation of this method promised an improvement
of the precision in antiproton magnetic moment measurements to the level of a few parts per billion.

In a recent article published in "*Nature*" C. Smorra and the BASE collaboration
reports on a measurement of the magnetic moment of the antiproton with a fractional precision of 1.5 p.p.b.. The measurement was
performed at the Antiproton Decelerator (AD)
of CERN, Geneva, utilizing a novel two-particle spectroscopy method in an advanced cryogenic multi-Penning trap system.

The determination of the magnetic moment of a single particle in a Penning trap is based on the measurement of the frequency ratio of the
Larmor frequency (*ν*_{L}) and the cyclotron frequency (*ν*_{c}). The measurement was mainly performed in
two separate Penning traps, an analysis trap (AT) with an inhomogeneous magnetic field and a precision trap (PT) with a factor
~10^{5} more homogeneous magnetic field *B*_{0} = 1.945 T.

In contrast to the double-Penning trap technique used in the measurement of the proton magnetic moment in 2014 at Mainz, the novel
two-particle technique utilized a hot cyclotron antiproton for measurements of the cyclotron frequency *ν*_{c},
and a cold Larmor antiproton to determine the Larmor frequency *ν*_{L}. Thus, the new method eliminated the need
of cyclotron cooling in each measurement cycle, and increased the sampling rate.

The Larmor frequency measurement is based on spin-transition spectroscopy. To this end, the spin-state of the antiproton is non-destructively
determined in the magnetic bottle of the analysis trap, which couples the spin magnetic moment of the antiproton to its axial oscillation
frequency *ν*_{z}. After the initial spin state is defined, the Larmor antiproton is moved into the precision trap where a spin transition for
the spin-flip resonance is induced. The final state of the spin transition is analyzed by moving the Larmor antiproton back to the analysis trap.

The cyclotron antiproton is used to determine the magnetic field before and after each spin-flip attempt of the Larmor particle in
the precision trap. It is moved to a park electrode before the Larmor antiproton is transported to the precision trap. The cyclotron
frequency measurement is also based on image current detection. The three oscillation frequencies of the trapped antiproton are measured
and the cyclotron frequency is obtained using the invariance theorem:
*ν*_{c}^{2} = *ν*_{+}^{2} + *ν*_{z}^{2} + *ν*_{-}^{2}.

The axial frequency *ν*_{z} of the stored antiprotons is directly observed by the image current detector. The modified
cyclotron frequency *ν*_{+} and the magnetron frequency *ν*_{-} were measured by coupling the axial
and the radial modes using radio frequency drives on the motional sidebands at *ν*_{+} - *ν*_{z}
resp. *ν*_{z} + *ν*_{-}.

The novel two-particle spectroscopy method yielded a highly improved value for the magnetic moment of the antiproton in units of the
nuclear magneton *μ*_{N}: *μ*_{p} = -2.792 847 344 1 (42) *μ*_{N}.
This new value is about 350 times more precise than the result of the previous best *μ*_{p}
measurement. It is consistent with the proton magnetic moment measured at Mainz in 2014, *μ*_{p} = 2.792 847 350 (9) *μ*_{N},
and is at the reached level of precision in agreement with CPT invariance.

The BASE collaboration expects that with a technically revised apparatus, including an improved magnetic shielding, an improved resistive cooling system for the cyclotron mode with lower temperature, and a precision trap with a 10-fold more homogeneous magnetic field, a ten-fold improved limit on CPT-odd interactions from proton/antiproton magnetic moment comparisons can be obtained in the future.

Please read more in the "*Nature*" article ... >

Further information also in the press release of the MPIK .

Further press releases:

- idw - Informationsdienst Wissenschaft
- Johannes Gutenberg University Mainz
- CERN
- RIKEN
- Ulmer Fundamental Symmetries Laboratory
- AlphaGalileo | AlphaGalileo (in French)
- EurekAlert!
- pro-physik.de
- Phys.org
- ScienceDaily
- Sci-News.com
- Science Newsline
- APA-SCIENCE
- ZEIT ONLINE
- Süddeutsche.de
- WELT
- SPIEGEL ONLINE
- FOCUS Online
- derStandard.de
- innovations-report
- Le Matin (in French)
- 24heures (in French)