Testing CPT Invariance with Antiprotonic

Atoms

Dezso Horvath, a,b,∗

aKFKI Research Institute for Particle and Nuclear Physics of the Hungarian

Academy of Sciences (KFKI-RMKI),

H-1525 Budapest, PO Box 49, Hungary

bInstitute of Nuclear Research of the Hungarian Academy of Sciences (ATOMKI),

H-4001 Debrecen, PO Box 51, Hungary

Abstract

The structure of matter is related to symmetries on every level of study. CPT sym-

metry is one of the most important laws of the field theory: it states the invariance

of physical properties when one simultaneously changes the signs of the charge and

of the spatial and time coordinates of particles. Although in general opinion CPT

symmetry is not violated in Nature, there are theoretical attempts to develop CPT-

violating models. The Antiproton Decelerator at CERN has been built to test CPT

invariance. Its three experiments compare the properties of particles and antipar-

ticles by studying antihydrogen, the positron-antiproton bound system, and the

antiprotonic helium atom.

Key words: CPT invariance, antiproton, antihydrogen, antiprotonic helium;

PACS: 11.30.Er, 14.20.Dh, 36.10.-k

Preprint submitted to Radiation Physics and Chemistry 30 January 2006

1 Introduction: Symmetries in particle physics

Symmetries in particle physics are even more important than in chemistry or

solid state physics. Just like in any theory of matter, the inner structure of

the composite particles are described by symmetries, but in particle physics

everything is deduced from the symmetries (or invariance properties) of the

physical phenomena or from their violation: the conservation laws, the inter-

actions and even the masses of the particles (see (Halzen and Martin, 1984)

for all general references).

The conservation laws are related to symmetries: the Noether theorem states

that a global symmetry leads to a conserving quantity. The conservation of

momentum and energy are deduced from the translational invariance of space-

time: the physical laws do not depend upon where we place the zero point of

our coordinate system or time measurement; and the fact that we are free to

rotate the coordinate axes at any angle is the origin of angular momentum

conservation.

Spin is one of the most important properties of the particles: those having half-

integer spins are the fermions whereas the integer-spin particles are bosons.

The different symmetries of the fermions and bosons lead to dramatic differ-

ences in their behaviour, e.g. the numbers of fermions are conserved whereas

the numbers of bosons are not. The basic building blocks of the visible matter

of the Universe, the quarks and leptons are fermions and all known interactions

are mediated by bosons.

∗ corresponding author

Email address: horvath@rmki.kfki.hu (Dezso Horvath,).

2

All fermions have antiparticles, anti-fermions which have identical properties

but with opposite charges. The different abundance of particles and antiparti-

cles in our Universe is one of the mysteries of astrophysics: apparently there is

no antimatter in the Universe in significant quantities, see, e.g., (Cohen et al.,

1998). If there were antimatter galaxies they would radiate antiparticles and

we would see zones of strong radiation at their borders with matter galaxies,

but the astronomers do not see such a phenomenon anywhere.

An extremely interesting property of antiparticles is that they can be treated

mathematically as if they were particles of the same mass and of oppositely

signed charge of the same absolute value going backward in space and time.

This is the consequence of one of the most important symmetries of Nature:

CPT invariance (Eidelman et al., 2004). CPT reflection means the following

simultaneous operations:

• charge conjugation (i.e. changing particles into antiparticles), Cψ(r, t) =

ψ(r, t);

• parity change (i.e. mirror reflection), Pψ(r, t) = ψ(−r, t), and

• time reversal, Tψ(r, t) = ψ(r,−t).

The principle of CPT invariance states that this does not change the physical

properties (i.e., the wave function or in the language of field theory the field

function ψ(r, t)) of the system:

CPTψ(r, t) = ψ(−r,−t) ∼ ψ(r, t). (1)

This means that, e.g., the annihilation of a positron with an electron can be

described as if an electron came to the point of collision, irradiated two or

three photons and then went out backwards in space-time.

3

If we build a clock looking at its design in a mirror, it should work properly

except that its hands will rotate the opposite way and the lettering will be

inverted. The laws governing the work of the clock are invariant under space

inversion, i.e. conserve parity. As we know, the weak interaction violates par-

ity conservation, unlike the other interactions. The weak forces violate the

conservation of CP as well. CPT invariance, however, is still assumed to be

absolute. Returning to the example of the clock, a P reflection means switch-

ing left to right, a C transformation means changing the matter of the clock

to antimatter, and the time reversal T means that we play the video recording

of the movement of the clock backward.

2 Testing CPT invariance

This principle requires, e.g., that particles and antiparticles have the same

mass and have additive quantum numbers (like charge) of the same absolute

value but opposite sign. Thus a straightforward CPT test is measuring the

mass and charge of particles and antiparticles (the best candidates being the

proton and the antiproton as the heaviest stable particles).

All such laws have to be and are checked experimentally. CPT invariance is

so deeply embedded in field theory that many theorists claim it is impossi-

ble to test within the framework of present-day physics. Indeed, in order to

develop CPT -violating models one has to reject such fundamental axioms as

Lorentz invariance or the locality of interactions (i.e. causality) or unitarity

(Kostelecky, 2004; Mavromatos, 2005; Klinkhamer and Rupp, 2004).

As far as we know, the Standard Model is valid up to the Planck scale, ∼ 1019

4

GeV. Above this energy scale we expect to have new physical laws which may

allow for Lorentz and CPT violation as well (Kostelecky, 2004). Quantum

gravity (Mavromatos, 2005; Klinkhamer and Rupp, 2004) could cause fluctu-

ations leading to Lorentz violation, or loss of information in black holes which

would mean unitarity violation. Also, a quantitative expression of Lorentz

and CPT invariance needs a Lorentz and CPT violating theory (Kostelecky,

2004). On the other hand, testing CPT invariance at low energy should be

able to limit possible high energy violation. This makes experimental CPT

tests physically valuable in spite of the fact that most of us do not expect its

violation.

CPT invariance is so far fully supported by the available experimental evi-

dence and it is absolutely fundamental in field theory. Nevertheless, there are

many experiments trying to test it. The simplest way is to compare the mass

or charge of particles and antiparticles. The most precise such measurement is

that of the relative mass difference of the neutral K meson and its antiparticle:

it is less than 10−18 (Eidelman et al., 2004).

CERN has constructed its Antiproton Decelerator (AD) facility (The Antipro-

ton Decelerator) in 1999 in order to test the CPT invariance by comparing the

properties of proton and antiproton and those of hydrogen and antihydrogen

(Fig. 1).The AD was constructed mainly using outside funds and started to

operate at the end of 1999. By the end of 2000 it was brought to specifications.

25 GeV/c protons from the Proton Synchrotron are shot in an iridium target

where they produce particle–antiparticle pairs. Antiprotons are collected at

3.5 GeV/c momentum and slowed down in the AD ring in three steps to 100

MeV/c using stochastic and electron cooling.

5

The aim of the present work is to briefly summarize some of the results of the

AD experiments, ASACUSA (The ASACUSA Collaboration), ATHENA (The

ATHENA Collaboration) and ATRAP (The ATRAP Collaboration).

3 Antihydrogen

Antihydrogen, the bound system of an antiproton and a positron, stands in

the centre of interest of the low–energy antiproton community. The reason is

that antihydrogen spectroscopy offers to test several fundamental principles of

physics, the most important ones being CPT symmetry and the weak equiv-

alence principle of gravity (Charlton et al., 1994; Holzscheiter et al., 2004).

According to CPT invariance an antiproton should accelerate the same way in

the gravitational field of an Anti-earth as protons in that of Earth. The weak

equivalence principle states the same for an antiproton in the field of Earth.

Unfortunately, it is very hard to test experimentally as the gravitational force

on an antiproton at the surface of Earth is about the same as the electric force

of a point charge from a distance of 10 cm. Such a test is proposed using the

effect of the different gravitational force of the Sun in winter and summer on

the atomic transitions of antihydrogen (Charlton et al., 1994).

Antihydrogen atoms were created the first time at CERN in 1995 via crossing

a relativistic antiproton beam with a xenon jet target in the LEAR ring (Baur

et al., 1996). The antiproton created electron–positron pairs in the field of the

Xe nucleus and if the direction of the positron momentum coincided with that

of the antiproton, having the same velocity near c, they could form an antihy-

drogen atom which then left the ring through a straight beam line. The anti-

hydrogen atoms were stripped in thin Si detectors; the positron annihilations

6

were detected in NaI X–ray detectors whereas the freed antiprotons were led

to a magnetic spectrometer for identification. 11 antihydrogen atoms were

detected with a possible background of 2±1 events. A similar experiment was

performed at Fermilab two years later (Blanford et al.,1998 ).

In order to make spectroscopic studies we need slow, confined, ground-state an-

tihydrogen atoms. Several schemes have been proposed to produce trapped an-

tihydrogen atoms for spectroscopy. In order to take the excess momentum away

and increase the production rate most of them involve a third colliding partner:

another positron, an electron, a resonant photon or an external radio-frequency

field (Charlton et al., 1994). Spontaneous radiative two-body recombination

is generally considered to be slow. The antihydrogen atoms are to be formed

in a quadrupole (or combined quadrupole–octupole) magnetic field in order to

confine half of them: those with the correct orientation of the positron spin.

Such traps can confine cold hydrogen atoms of temperatures below 1 K thus

they have to be cooled after formation, for which optical (laser) cooling seems

to be feasible (Charlton et al., 1994; Holzscheiter et al., 2004).

The extremely small line width (1 Hz) corresponding to the long lifetime of the

metastable 2S state makes the 2S − 1S transition (Fig. 2) the most promis-

ing candidate for high–precision measurements; a Doppler–free excitation is

possible in the case of absorption of two photons from opposite directions.

This transition has been recently measured in hydrogen with a precision of

1.8 × 10−14 (Niering et al., 2000).

Recently, both antihydrogen experiments managed to produce cold antihydro-

gen atoms in large quantities at CERN (Amoretti et al., 2002; Gabrielse et

al., 2002). They used the same method for antihydrogen production: a nested

7

Penning trap was loaded with positrons and then with antiprotons. The posi-

tron cloud cooled itself with synchrotron radiation in the magnetic field of the

trap, and the antiprotons, in turn, cooled in collisions with the cold positrons.

Antihydrogen was most probably produced in triple collisions of an antiproton

with two psitrons. The ATHENA collaboration (Amoretti et al., 2002) proved

the creation of antihydrogen by reconstructing the space-time coordinates of

the annihilation of positrons and antiprotons (Fig. 3) for cold and hot mixing

of the constituents – in a hot mix the recombination was suppressed and most

of the annihilations happened in the residual gas whereas in the cold mix the

neutral antihydrogen drifted out of the magnetic filed and annihilated in the

walls. The ATRAP group (Gabrielse et al., 2002) re-ionized the freshly formed

antihydrogen atoms, deducing thereby their quantum states as well. Further

studies have shown that antihydrogen production slows down if the particles

are overcooled: they sink in their respective potential wells and do not overlap

any more (Amoretti et al., 2002). Antihydrogen production could be driven by

heating the positron cloud by a radiofrequency field (Gabrielse et al., 2002).

The way to spectroscopy is still long as the antihydrogen atoms have to be

confined in a quadrupole trap and brought to ground state. In the case of

single-atom spectroscopy one has to make sure that the studied system is not

ordinary hydrogen from the residual gas whereas in the case of a system of

many atoms one can rely on annihilation following the forced spectroscopic

transition for tagging the antihydrogen.

8

4 Antiprotonic Helium Atoms

An exotic atom is formed when a fast negative particle — muon, pion, kaon

or antiproton — penetrates matter: it first slows down in atomic collisions

(mostly via ionization), then gets captured in an atomic orbit replacing the

last knocked–out electron. The capture cross–section is related to the overlap

between the wave functions of the particle and the atomic electron so the

heavy particle will initially populate atomic states with radii close to that of

the electrons. Thus an antiproton captured, e.g., in a helium atom will initially

populate the pHe+ states with principal quantum numbers n0 =√

M/m ≈ 38

where M ≈ 0.8mp and m ≈ me are the reduced masses of the pHe++ and

e−He++ systems(Tokesi et al., 2005). A high n, naturally, involves orbital

quantum numbers in the region 0 ≤ ` ≤ n − 1; and although experiments

found deviations of the initial populations from a purely statistical 2` + 1

distribution, the states with higher ` will be populated with higher probability.

The freshly formed, highly excited exotic atom has two basic ways to step

down. Between high-n states, where the energy spacing is low, the Auger

mechanism dominates whereas lower lying levels will preferably decay via ra-

diation. Approaching the ground state a strongly interacting hadron like the

antiproton gets absorbed by the nucleus from higher nS levels and it hardly

reaches ground state in heavier atoms. Both in condensed media and in gases

at higher pressures (about standard conditions) slowing down, atomic cap-

ture, de-excitation and nuclear absorption proceeds quite fast: theoretical cal-

culations and experimental measurements agree upon total lifetimes below or

around 1 ps (10−12 s).

9

The only exception is helium: while 97% of the antiprotons stopped in a dense

helium target annihilate with the usual short lifetimes, 3% live as long as

several microseconds, sufficiently long to use laser spectroscopy. They form a

pHe+ 3–body system where the antiproton orbit is protected against collisions

by the electron, and the antiprotonic states of the same n but different ` lose

the energy degeneracy and so cannot undergo Stark transitions. The model

and its experimental proof are described in reviews (Horvath, 1997; Eades and

Hartmann, 1999; Yamazaki et al., 2002).

The principle of the spectroscopy method is simple. We stop a bunch of an-

tiprotons in helium, wait until the promptly annihilating states disappear and

then stimulate the transition from a long–living state to a short–lived one

with a tunable laser system. At the resonant frequency corresponding to the

transition energy the laser shot will be followed by immediate annihilation as

shown in Fig. 4.

4.1 The Mass and Charge of the Antiproton

The TRAP group measured the charge/mass ratio of the proton and the anti-

proton at LEAR (Gabrielse et al., 1999). They kept a single antiproton and a

single H− ion in the same Penning–trap simultaneously at different orbits and

measured their cyclotron frequencies. After having made corrections for the

H− — p deviation they limited the relative difference to 9 · 10−11. Achieving

this precision took 10 years’ work.

The aim of the ASACUSA experiment is to supply additional data for facilitat-

ing the separation of charge and mass information. This is done via studying

10

antiprotonic transition energies in the pHe+ system as those are proportional

to m(p) · q(p)2:

En ≈ −mredc

2(Zα)2

2n2

.

The precision of determining the transition frequencies is limited among others

by the laser bandwidth, the density shift of the lines and the Doppler effect.

Our first measurement was performed at LEAR for different helium densities

and we extrapolated to zero (Torii et al., 1999) in order to make the comparison

with the theoretical calculations for isolated atoms (Korobov, 1996; Korobov

and Bakalov, 1997). The way to obtain a limit on the antiprotonic mass and

charge is illustrated in Fig. 5: the intersection of the regions allowed by the

two measurements constitutes the limit. The result was [m(p)−m(p)]/m(p) <

5 · 10−7 and similarly [q(p) − q(p)]/q(p) < 5 · 10−7.

In 2000, the first year of the AD we lowered the deteriorating effects of the laser

bandwidth and gained almost an order of magnitude in precision (Hori et al.,

2001) (Fig. 5), but the collisional effects were still significant. Fig. 6 presents

the density dependence of 6 antiprotonic transitions in pHe+ together with

the corresponding resonance line shapes.

In 2002 we have installed a radio-frequency quadrupole post-decelerator (RFQD)

which decelerated the AD beam from 5.6 MeV to 100 keV with a ∼ 30% effi-

ciency. The RFQD made it possible to substantially reduce the density effect

by using a low-pressure (< 1 mbar), cryogenic (T = 6 − 10 K) target. Our

latest limit of possible CPT-violation on the antiproton charge and mass is

10 ppb (< 10−8) (Hori et al., 2003). Further improvement is expected from a

11

further improved laser system and from two-photon spectroscopy.

4.2 Level Splitting and Magnetic Moment

As seen in Fig. 6 the (n = 37, ` = 35)→(38, 34) line is split due to inter-

action between the antiproton magnetic moment and the electron spin. This

resonance was used by the ASACUSA Collaboration to measure the magnetic

moment of the antiproton: of course, as that is in a highly excited state, the

measured momentum is mostly orbital.

The level scheme is presented in Fig. 7. Both levels involved in the transition

(n′, L′)→(n, L) are split, scanning the laser frequency will show the difference

between the transition frequencies f− and f+. We have measured the splitting

νHF directly by emptying one of the split levels with a suitably tuned laser

pulse, irradiating the system with a variable microwave pulse and again with a

laser pulse of the same frequency as before. When the microwave was correctly

tuned to the resonance, the second resonance had a reduced amplitude. The

result is presented in Fig. 7b (Widmann et al., 2002). It agrees within 6×10−5

with the recent theoretical calculations performed with the properties of the

proton assumed. We also checked the possible effect of collisions on the result

by studying its density dependence and found it was negligible.

5 Outlook

The radio-frequency quadrupole decelerator (RFQD) proved to be a very im-

portant step towards supplying a large number of low-energy (10-100 keV)

antiprotons at the AD of CERN. The ASACUSA Collaboration has devel-

12

oped a new facility called MUSASHI 1 (Monoenergetic Ultra Slow Antiproton

Source for Spectroscopy and High-precision Investigations) which will consist

of the RFQD, an electromagnetic trap and an extraction system (Franzen et

al., 2003). The system is almost complete and and recently in the test phase:

a large fraction of the 106 trapped and cooled antiprotons were extracted from

the trap during the tests in 2004 (Kuroda et al., 2005). The MUSASHI fa-

cility will be used to perform various basic studies: to measure the atomic

stopping power at low energies, to study single ionization of atoms, to study

the nuclear absorption of very slow antiprotons, to make more precise CPT

tests with antiprotonic atoms and to measuring the magnetic moment of an-

tihydrogen. For the latter slowly moving (v ∼ 350 m/s) antihydrogen atoms

will be flying through two sextupole magnets (polarizer and analyzer) with

a tunable microwave cavity in between, which, in case of resonance, will flip

the spin of the positron (Widmann et al., 2004). We expect to measure the

hyperfine splitting, which may show a CPT -violating effect (Bluhm et al.,

1999) with a ppm precision.

6 Acknowledgments

The present work was supported by the Hungarian National Research Foun-

dation (Contracts OTKA T042864 and T046095) and the Marie Curie Project

TOK509252.

1 Musashi Miyamoto, 17th century samurai and philosopher

13

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14

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2 Asakusa is one of the oldest districts of Tokyo; the name was proposed by our

non–Japanese collaborators to honour the dominant Japanese contribution to the

experiment

15

Fig. 1. The accelerator complex of CERN. The LINAC2 linear accelerator and the

PSB booster feed protons into the PS proton synchrotron, which accelerates them

to 25 GeV/c and passes them to the experiments in the East Area or to the SPS

super proton synchrotron for further acceleration and once every 100 seconds into an

iridium target to produce antiprotons. The antiprotons are collected at 3.5 GeV/c

by the AD where they are decelerated in three steps to 100 MeV/c. The PS also

accelerates heavy ions for the SPS North Area experiments and until 2000 it did

accelerate electrons and positrons for the LEP Large Electron Positron collider

which was dismounted to be replaced by the LHC Large Hadron Collider in 2007.

16

1

2

3

BohrDiracLambHFS

1S

2P

1/2

1/2

2S1/2

2P3/2

F=0

F=1

ANTIHYDROGEN

1

2

3

Bohr Dirac Lamb HFS

1S

2P

1/2

1/2

2S1/2

2P3/2

F=0

F=1

HYDROGEN

Fig. 2. Atomic levels in hydrogen and antihydrogen. CPT symmetry requires them

to be exactly equivalent.

17

Fig. 3. An antihydrogen annihilation event detected by ATHENA (Amoretti et al.,

2002).

18

0500

1000150020002500300035004000

0 0.5 1 1.5 2 2.5 3 3.5 4

event-by-eventλ = 470.724 nm

Annihilation time (µs)

coun

ts /

10 n

s

analog method

λ = 470.724 nm

Annihilation time (µs)

anal

og a

mpl

itude

(ar

b. u

nits

)

-20-17.5

-15-12.5

-10-7.5

-5-2.5

0

0 0.5 1 1.5 2 2.5 3 3.5 4

Fig. 4. Laser stimulated resonances as detected at LEAR in the regime with singly

stopped antiprotons (above) and at the AD with an antiproton pulse (below). The

analog method gives higher background, but its laser resonance is timed by the

extraction signal of the AD and not the stop of the antiproton.

19

p

p

δQ

Qp

p

[10� 6]

δM

Mp

p

[10� 6]

Q p

M p/He L

EAR+

He AD+

allowed region

1 2

1

2

� 1

� 2

� 1� 2 � 1.5 � 0.5 0.5 1.5

� 0.5

� 1.5

0.5

1.5

Fig. 5. Limits on the difference of mass and charge between proton and antiproton.

The charge/mass (Q/M) ratio was measured by the TRAP group (Gabrielse et al.,

1999) whereas M · Q2 by ASACUSA (Torii et al., 1999; Hori et al., 2001; Hori et

al., 2003). With the improvement of the experimental technique the allowed region

was step-by-step reduced: the present limit is 10 ppb (10−8) (Hori et al., 2003).

20

Fig. 6. Collisional effects on three favoured, (n, `)→(n−1, `−1), and three unfavored,

(n, `)→(n+1, `−1) antiprotonic transitions in the pHe+ system (Hori et al., 2001):

resonance shapes (left) and density dependence (right). In order to compare the

measured and calculated values we extrapolated to zero density. The splitting in

the (37,35) → (38,34) line is due to interaction between the antiproton magnetic

moment and the electron spin.

21

(n,L)νHF

F+=L+1/2

F−=L−1/2 J−+=L

J−−=L−1

νSHF−

J++= L+1

J+−=L

νSHF+

νHF−

νHF+

(n’,L’)νHF

’

F+’=L’+1/2

F−’=L’−1/2

f−

f+

12.86 12.88 12.90 12.92 12.94 12.96

0.95

1.00

1.05

1.10

1.15+HFν −

HFν

R+

+/R

++

off

νMW (GHz)

Fig. 7. The scheme of a split transition line in the p-4He+ atom as studied using the

laser–microwave–laser resonance method in order to measure the magnetic moment

of the antiproton (Widmann et al., 2002) in the atomic bound state: splitting of

the (n = 37, ` = 35)→(38, 34) transition (above); the measured spectrum (below):

number of forced antiproton annihilations against the microwave frequency.

22