Violated Symmetries

In 1956, in the course of a thorough review of the scientific literature, Chinese-American theorists Tsung-Dao Lee und Chen-Ning Yang realized that the conservation of parity symmetry by the weak interaction had never been tested experimentally – in contrast to the electromagnetic and the strong forces. Only a few months later, experimental physicist Chien-Shiung Wu, also of Chinese origin, managed to conduct such an experiment. At the centre of the setup was a sample of the radioactive metal ⁶⁰Co, which decays into the stable nuclide ⁶⁰Ni by emission of an electron and an antineutrino with a half-life of 5.27 years. Wu first cooled the material to 10 millikelvin and aligned the nuclear spin of the atoms to a preferred direction by means of an external magnetic field (polarization). Afterwards she used scintillators to observe the direction of the momentum of electrons released in the beta decay.

Let us first consider the significance of the experiment. The nuclear spin, like any other angular momentum, is the cross product of a position vector and a momentum vector. If the operator P is applied to the atomic nucleus, the signs of both basis vectors are reversed, whereas the magnitude and the orientation of the nuclear spin remain unchanged. The situation is different for the momentum of the emitted electrons, which reverses its direction under spatial inversion. If parity symmetry were conserved in beta decay, precisely the same number of electrons (on average) should be emitted in the direction of the nuclear spin as in the opposite direction, because otherwise the decay process would differ from its mirror image. Yet Wu indeed observed a large degree of correlation between the polarization of the cobalt nuclei and the momenta of the emitted electrons. In this way she proved that the weak interaction violates parity symmetry.Reference Wu, Ambler, Hayward, Hoppes and Hudson⁵ The same year (1957), Yang and Lee – but not Wu – received the Nobel Prize in Physics.

Subsequently, it was supposed that at least the combined CP symmetry was conserved by all interactions. In the wake of the surprising discovery of P violation, quite soon the CP symmetry of weak decay processes was also scrutinized. In 1964, American physicists James Cronin and Val Fitch studied the decay of the neutral kaons $$K^{0} =d\bar{s}$$ and their antiparticles $$\bar{K}^{0} =s\bar{d}$$ , which consist of pairs of down (d) and strange (s) quarks and their antiquarks. These short-lived kaons, which can be artificially produced only in an accelerator, usually decay into two or three pions. They can only decay via the weak force, because it is the only interaction that can change a particle’s quark type (flavour). By a combination of several such processes, $$K^{0} $$ and $$\bar{K}^{0} $$ can even transform into each other. In this way a mixing of quantum states can take place, resulting in the formation of states K ₁ und K ₂. These are eigenstates of the CP transformation, i.e., they are left unchanged (up to a sign) under CP.

If we initially assume that the decay of neutral kaons conserves CP symmetry, the state K ₁ should only decay into two pions, whereas K ₂ should only decay into three pions. Because of the lower decay energy, the second reaction proceeds much more slowly than the first. Indeed, two populations with half-lives of 9.0×10^–11 s and 5.1×10^–8 s are observed in the decay of neutral kaons. The experiment of Cronin and Fitch consisted of verifying the identity of the long-lived kaons with the state K ₂. For this purpose, they first let a beam of neutral kaons traverse a 15 m long flight path in order to select the long-lived component. Afterwards they searched the decay products for events with only two pions. Indeed they observed that about 0.2% of the long-lived kaons decayed in this way.Reference Christenson, Cronin, Fitch and Turlay⁶ Thus, it had been demonstrated that the weak interaction also violates CP symmetry. In today’s Standard Model, CP violation is incorporated by means of the so-called quark mixing matrix.

As in the case of the kaons, a mixing of quark eigenstates is also observed in the B and D mesons. In 2001, the experiments BaBar (SLAC National Accelerator Laboratory, USA) and Belle (KEK, Japan) almost simultaneously found a CP violation in the decay of the neutral B meson. The measurements were in agreement with the results from K decay and with the quark mixing formalism. The situation appears to be different for the newest results from the Large Hadron Collider (LHC) at CERN. At an accelerator conference that took place in the fall of 2011, members of the LHCb experiment led by Pierluigi Campana announced that there is mounting evidence for a strong CP violation in the decay of the D meson $$D^{0} =c\bar{u}$$ (c – charm quark, u – up quark). The scientists studied particle collisions in which pairs of D and anti-D mesons had been formed. By means of the LHCb detector, which is more than 10 m tall and 20 m long, they then identified decays of these short-lived particles into final states containing either two pions or two kaons, each CP eigenstates with an eigenvalue of +1.

A possible CP violation would manifest itself by a difference between the decay probabilities of the initial particles $$D^{0} $$ and $$\bar{D}^{0} $$ into these states. Over the past 15 years, comparable measurements at other accelerators did not show any deviations beyond their experimental uncertainties. The LHCb collaboration measured the probabilities for all four possible decays. But instead of considering the differences in the decay rates of $$D^{0} $$ and $$\bar{D}^{0} $$ particles into pions and the corresponding quantity for kaons separately, the scientists subtracted the two differences. In this way they were able to minimize systematic errors. In the course of these measurements, they found an asymmetry of 0.8%, about a factor of ten larger than the CP violation predicted by the quark mixing matrix of the Standard Model.Reference Aaij⁷ For the time being, the results are based on about half the data from 2011. The results have a statistical significance of 3.5σ; this means that the observed asymmetry is non-zero with a probability greater than 99.7%. If this observation were corroborated, it would be a clear indication of new physics outside the Standard Model. However, the LHCb results have so far not been confirmed and can therefore not yet been considered as positive proof.Reference Stahl⁸

The observed violations of the discrete symmetries are relevant for our initial question. In the middle of the 1960s, Soviet physicist and future Nobel Prize laureate Andrei Sakharov studied the reason behind the observed dominance of ordinary baryonic matter. He realized that baryon asymmetry could have arisen immediately after the Big Bang during a period of thermal non-equilibrium. In addition to the obvious non-conservation of baryon number, this scenario would have required the violation of both C and CP symmetry.Reference Sakharov⁹ The CP violation experimentally observed in kaon decay was however much too weak to be responsible for baryon asymmetry. It was realized only 30 years later that the matter–antimatter imbalance could also have come about by a violation of CPT symmetry in connection with a non-conservation of baryon number.Reference Bertolami, Colladay, Kostelecký and Potting¹⁰ However, it remains to be determined which of the two processes is the dominant one.

A violation of CPT symmetry is inconceivable within the current Standard Model of particle physics. However, recent theoretical advances, which pursue a unification of the fundamental interactions into a ‘Theory of Everything,’ call into question some of the premises on which the CPT theorem is based. Take superstring theory, for example: In this approach, the principle of locality (the prohibition against action-at-a-distance) is no longer valid at the smallest length scales – and this contradicts Pauli’s CPT theorem, which only applies to local and causal theories. It is possible to test CPT symmetry by comparing the properties of antiparticles with those of their ordinary-matter partners and looking for deviations. Over the past few decades a large number of such measurements have been carried out. In this way, for instance, the g factors (i.e. the magnetic moments) of the electron and the positron have been compared to a relative precision of 2×10^–12 and the masses of the proton and the antiproton to 9×10^–11. Until now, no evidence of CPT violation has been found in any of these experiments.

Antihydrogen in a Trap

With a relative uncertainty of 4×10⁻¹⁵, the transition frequency between the ground state (1S) and the metastable excited state (2S) of the hydrogen atom is currently the most precisely known physical quantity.Reference Parthey¹¹ The measurements by the group of Theodor Hänsch are based on so-called Doppler-free spectroscopy, in which two photons impinging on the atom from opposite directions collectively contribute to the excitation. In this way, the shift of the transition frequency due to the thermal motion of the atoms (the Doppler effect) is reduced. The measured frequency is related to a caesium atomic clock by means of a frequency comb. It would stand to reason to perform the same measurement on antihydrogen in order to test CPT symmetry with the highest possible precision. For this reason the production of antihydrogen from its constituents, antiprotons and positrons, has been fervently pursued since the beginning of the 1990s. However, there is no primary antimatter in the Universe. So how can it be produced in order to examine it in the laboratory?

Again, the key lies in the equivalence of energy and matter. Pairs of matter and antimatter particles can be created from a large amount of energy. For this purpose, highly energetic protons are fired onto a metallic target, giving rise to pairs of protons and antiprotons. The antiprotons are selected with a magnetic filter and are then injected into the Antiproton Decelerator (AD), a storage ring with a circumference of 190 m. In the AD, they first circulate near the speed of light before being decelerated to an energy of 5 MeV within about 100 s by inverted accelerator cavities. Simultaneously, the beam is radially cooled and collimated. Afterwards, bunches containing roughly 3×10⁷ antiprotons are distributed to the antimatter experiments located at the AD.

In 2002, scientists working on the ATHENA experiment headed by Rolf Landua managed for the first time to create cold antihydrogen in an ion trap.Reference Amoretti¹² For this purpose, they captured the antiprotons delivered by the AD in a Penning trap and further decelerated them to a few kelvin. Then they brought them into contact with equally cold positrons from a radioactive source. In this way, antihydrogen atoms spontaneously formed but, due to the fact that they are electrically neutral, they no longer remained confined. When these particles impinged on the trap electrodes, they gave rise to a characteristic annihilation signal, by means of which it was possible to elegantly demonstrate the formation of antihydrogen. At the same time, however, the created anti-atoms were lost for further measurements. Thus, the ATRAP and ALPHA collaborations further enhanced their apparatuses such that they allowed the capture and study of neutral antihydrogen.

In 2011, ALPHA, one of the successor experiments of ATHENA, announced that they had for the first time succeeded in the capture of antihydrogen. How was this achieved? A Penning trap is needed to confine the constituents, antiprotons and positrons. It consists of a homogeneous magnetic field along the trap axis and an electrical quadrupole field, which is applied to the cylindrical trap electrodes. The neutral antihydrogen atom is confined in a magnetic trap. The gradient of an inhomogeneous magnetic field B exerts a force

(2) $${\bf F}=\,\pm\mu \;\nabla B$$

on the magnetic moment μ of the atom. In the ground state the magnetic moment has the magnitude of the Bohr magneton

(3) $$\mu =\mu _{{\rm B}} ={{e\hbar } \over {2m_{{\rm e}} }}$$

where e and m _e designate the charge and the mass of the electron and ħ is Planck’s constant. The sign of the direction of the force – towards the minimum or the maximum of the magnetic field – depends on the (arbitrary) alignment of the positron spin relative to the external magnetic field. Therefore, in the best of cases half of the atoms are trapped.

The difficulty lies in combining the two types of traps in such a way that their fields do not disturb each other. The radial component of the magnetic trap is problematic, in particular, because it breaks the cylindrical symmetry of the Penning trap. This can compromise the storage time of the ions. The problem is alleviated by the fact that ALPHA uses a radial trap with a high multipole order, because in this way the field magnitude rapidly decreases towards the trap axis. The trap configuration used by ALPHA is shown in Figure 3(a). The radial trap consists of so-called race track coils (red in the figure), which create an octupole field with a magnitude of about 1.7 tesla. Two circular mirror coils (green) ensure the confinement in axial direction. The solenoid magnet (not shown in the figure) has a field of 1 T. This results in a magnetic trap depth of just under 1 T, which corresponds to 0.6 K in temperature units (Figure 3(b)).

Figure 3 Combined ion and atom trap. (a) Configuration of the magnet coils and electrodes of ALPHA’s combined ion and atom trap: Octupole coils (red), mirror coils (green), trap electrodes (yellow). The solenoid used to generate the strong axial magnetic field is not shown. (b) False-colour image of the magnetic-field magnitude in the radial and axial projection (top) and on the axis (bottom) as a function of the radial and axial coordinates. (Images: (a) CERN, (b) courtesy Nature Publishing Group.)

In summer 2011, ALPHA managed to store single antihydrogen atoms in the magnetic trap for many hundreds of seconds.Reference Andresen^13, Reference Andresen¹⁴ As was the case in ATHENA, antiprotons and positrons were confined in a nested electric potential (Figure 4). Their temperature is a few 10 K. The two clouds of particles are brought into overlap by a weak high-frequency excitation of the antiprotons, such that antihydrogen is spontaneously produced. A small part of the antihydrogen atoms, those whose temperature is below 0.6 K, remains trapped in the magnetic trap. After waiting up to 1000 s, the magnetic field of the octupole coils is ramped down within a few hundredths of a second. The anti-atoms then leave the trap and annihilate on the electrodes. This signal is recorded with a silicon strip detector, which surrounds the entire trap in three layers (light blue in Figure 3(a)). The storage of neutral antihydrogen has thus been demonstrated.

Figure 4 Ions in the Penning trap. Nested electric potential applied to the trap electrodes for the simultaneous confinement of positively charged positrons and negatively charged antiprotons in the Penning trap. (Image: CERN.)

In a further experiment, the ALPHA group even managed to take a first step towards antihydrogen spectroscopy: by means of a microwave signal, the scientists changed the alignment of the positron’s spin within antihydrogen with respect to the external magnetic field.Reference Amole¹⁵ This caused the direction of the force due to the magnetic trap to be reversed for these particles and they were thus accelerated out of the trap. The observed correlation between the familiar annihilation signal with the resonant microwave excitation demonstrates that the hyperfine structure of antihydrogen coincides at least roughly with that of hydrogen.

Does the Anti-apple Fall Up?

The AEGIS group headed by Michael Doser, which is another successor of the ATHENA collaboration, is pursuing a completely different approach. As mentioned before, gravity is a special case among the interactions. It is the only one not described by a quantum field theory. Within General Relativity, gravity is a geometric phenomenon. Test bodies move along geodesics, the shortest paths between two points in four-dimensional spacetime. Matter causes spacetime to become distorted. The Weak Equivalence Principle (WEP), which states that all bodies fall with the same acceleration independent of their composition, directly follows from this notion. For bodies consisting of ordinary matter, measurements have confirmed the WEP to high precision. In a hypothetical quantum theory of gravity, however, both negative mass charges and exotic gravitons are conceivable, which could both result in a deviation from the equivalence principle for antimatter.

The principle of the AEGIS experiment is to study the deviation of a horizontal antihydrogen beam in the gravitational field of the earth.¹⁶Figure 5 shows an overview sketch of the apparatus. For the creation of antihydrogen, AEGIS makes use of a charge exchange reaction via the detour of positronium (Ps):

(4) $${\rm Ps}{\plus}\bar{p}\to{\rm \bar{H}}{\plus}e^{{\minus}} $$

Positronium is the bound state of an electron and a positron and has a structure very similar to that of the hydrogen atom. It can be produced with high efficiency from the bombardment of a nanoporous material with positrons. The advantage of this reaction is the fact that the formed antihydrogen has the same temperature as the pre-cooled antiprotons from which it was made. A low temperature is crucial for the measurement precision of the experiment. Afterwards, the antihydrogen atoms are accelerated into a beam by means of an inhomogeneous electric field. Its horizontal velocity v _hor is between 400 and 700 m s^–1.

Figure 5 Principle of the AEGIS experiment (overview sketch). Antiprotons and positrons are stored in two parallel Penning traps within the same magnet. Positrons are converted into positronium in a nanoporous material. The positronium atoms pass through the pre-cooled antiprotons (yellow cloud), and cold antihydrogen is formed (pink cloud). The antihydrogen atoms are accelerated by means of an inhomogeneous electric field in the direction of the deflectometer, where the gravity measurement takes place. (Image: courtesy of Asimmetrie/INFN.)

The effect of gravity is determined via the vertical deflection of the beam over a flight path of about 80 cm. Assuming a local gravitation due to earth of g=9.81 m s^–2, a shift of less than 0.01 mm is to be expected. Since the beam spot on the detector is much larger, such a small deviation cannot be measured directly. Therefore, AEGIS uses a measurement setup whose principle is loosely based on the matter wave interferometer developed by Ludwig Mach and Ludwig Zehnder. A Mach–Zehnder interferometer consists of three gratings with fine horizontal slits, mounted at equal distances L. As the beam passes through the first two gratings, a diffraction pattern is generated at the location of the third. The third grating functions as an analyser. A detector placed behind it records a maximal signal when the grating is brought into overlap with the interference pattern. Finally, the vertical displacement of the pattern is recorded as a function of the flight time.

However, at a temperature of 100 mK, the opening angle of the antihydrogen beam is larger than the expected diffraction angle. Furthermore, decoherence effects, for example atomic transitions or annihilations on the grating, can further wash out the diffraction pattern. For this reason, AEGIS makes use of a moiré deflectometer, which is the classical counterpart of the Mach–Zehnder apparatus based on matter wave interference. Instead of diffraction maxima, the first two gratings cast a classical shadow pattern on the third one. Nevertheless, the vertical drop of the pattern is the same in both cases and amounts to

(5) $$\delta x={\minus}gT^{2} $$

where T=L/v _hor is the time of flight between a pair of gratings. The gravitational acceleration g is obtained from a fit of equation (5) to a large number of measurements with different beam velocities v _hor. Simulations have shown that about 10⁵ antihydrogen atoms at a temperature of 100 mK are required to carry out a measurement of the earth’s gravitational acceleration to a relative precision of 1%. Such a measurement would take a few weeks of beam time.

After more than ten years of research work, the experiments located at the Antiproton Decelerator have reached significant milestones towards precision measurements with antimatter. With the successful capture of neutral antihydrogen, all of the prerequisites for laser spectroscopy on antimatter atoms are now satisfied. The two collaborations ALPHA and ATRAP are in the process of modifying their apparatuses such that a laser beam can reach the confined particles. In this way, a first test of CPT symmetry in an atomic system is finally coming within reach. It will bring us closer to answering the question of whether the already established CP violation or a still hypothetical CPT violation is responsible for baryon asymmetry. Meanwhile, AEGIS is making great strides towards a test of the Weak Equivalence Principle with antimatter. However, some parts of the AEGIS experiment, in particular the moiré deflectometer, are still being developed. Therefore, first results should not be expected before the beginning of 2015.