Testing CPT Invariance with Antiprotonic Atoms 1

Testing CPT Invariance with Antiprotonic Atoms 1 Dezső Horváth KFKI Research Institute for Particle and Nuclear Physics, H 1525 Budapest, Hungary and Institute of Nuclear Research (ATOMKI), Debrecen, Hungary E-mail: horvath@rmki.kfki.hu ABSTRACT The structure of matter is related to symmetries on every level of study. CPT symmetry is one of the most important laws of 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 antiparticles by studying antihydrogen, the positron-antiproton bound system, and the antiprotonic helium atom. 1 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 interactions and even the masses of the particles. 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 differences 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. All fermions have antiparticles, anti-fermions which have identical properties but with opposite charges. The different abundance of particles and antiparticles in our Universe is one of the mysteries 1 Invited paper presented at 3rd Conference on the Elementary Processes in Atomic Systems, Miskolc, Hungary, 31 Aug 2 Sep 2005

of astrophysics: apparently there is no antimatter in the Universe in significant quantities, see, e.g., [1]. 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 [2]. It states that the following 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, T ψ(r,t) = ψ(r, t) when done together do 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: CPT ψ(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 spacetime. 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 parity 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 switching 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 impossible 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 [3 5]. As far as we know, the Standard Model is valid up to the Planck scale, 10 19 GeV. Above this energy scale we expect to have new physical laws which may allow for Lorentz and CPT violation as well [3]. Quantum gravity [4, 5] could cause fluctuations 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 [3]. 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 fact that most of us do not expect its violation. 2

CPT invariance is so far fully supported by the available experimental evidence and it is absolutely fundamental in field theory. Nevertheless, there are many experiments trying to test it. The simplest way to do that 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 which has so far been found to be less than 10 18 [2]. CERN has constructed its Antiproton Decelerator (AD) facility [6] 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. The aim of the present talk is to briefly summarize some of the results of the AD experiments, ASACUSA [7], ATHENA [8] and ATRAP [9]. 3 Antihydrogen Antihydrogen, the bound system of an antiproton and a positron, stands in the middle of attention 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 equivalence principle of gravity [10, 11]. 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 [10]. 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 [12]. 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 antihydrogen atom which then left the ring through a straight beam line. The antihydrogen atoms were stripped in thin Si detectors; the positron annihilations 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 [13]. In order to make spectroscopic studies one needs slow, confined, ground-state antihydrogen atoms. Several schemes have been proposed to produce trapped antihydrogen 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 [10]. 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 [10, 11]. 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 promising candidate for high precision measurements; 3

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 [14]. Recently, both antihydrogen experiments managed to produce cold antihydrogen atoms in large quantities at CERN [15, 16]. They used the same method for antihydrogen production: a nested Penning trap was loaded with positrons and then with antiprotons. The positron 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 [15] 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 [16] 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 [15]. Antihydrogen production could be driven by heating the positron cloud by a radiofrequency field [16]. 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. 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 n 0 = M/m 38 where M 0.8m p and m m e are the reduced masses of the phe ++ and e He ++ systems. A high n, naturally, involves orbital quantum numbers in the region 0 l n 1; and although experiments found deviations of the initial populations from a purely statistical 2l + 1 distribution, the states with higher l 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 radiation. 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 capture, de-excitation and nuclear absorption proceeds quite fast: theoretical calculations and experimental measurements agree upon total lifetimes below or around 1 ps (10 12 s). 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 l lose the energy degeneracy and so cannot undergo Stark transitions. The model and its experimental proof are 4

described in reviews [17 19]. The principle of the spectroscopy method is simple. We stop a bunch of antiprotons 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 antiproton at LEAR [20]. 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 our ASACUSA experiment is to supply additional data for facilitating the separation of charge and mass information. This is done via studying antiprotonic transition energies in the phe + system as those are proportional to m(p) q(p) 2 : E n m redc 2 (Zα) 2 2n 2. 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 [21] in order to make the comparison with the theoretical calculations for isolated atoms [22, 23]. 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 [24] (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% efficiency. 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 ) [25]. Further improvement is expected from a further improved laser system and from two-photon spectroscopy. 4.2 Level Splitting and Magnetic Moment As seen in Fig. 6 the (n = 37,l = 35) (38,34) line is split due to interaction 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 ν HF directly by emptying one of the split levels with a suitably 5

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 [26]. 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 important step towards supplying a large number of low-energy (10-100 kev) antiprotons at the AD of CERN. The ASACUSA Collaboration has developed a new facility called MUSASHI 2 (Monoenergetic Ultra Slow Antiproton Source for Spectroscopy and High-precision Investigations) which will consist of the RFQD, an electromagnetic trap and an extraction system [27]. The system is almost complete and under tests now: a large fraction of the 10 6 trapped and cooled antiprotons were extracted from the trap during the tests in 2004 [28]. The MUSASHI facility will be used measure atomic stopping power at low energies, to study single ionization of atoms, for nuclear studies, for further CPT tests with antiprotonic atoms and for measuring the magnetic moment of antihydrogen. 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 [29]. We expect to measure the hyperfine splitting, which may show a CPT -violating effect [30] with a ppm precision. 6 Acknowledgments The present work was supported by the Hungarian National Research Foundation (Contracts OTKA T042864 and T046095) and the Marie Curie Project TOK509252. References [1] Cohen, A.G., De Rujula, A., Glashow, S.L., Astrophys. J., 495, 539 (1998). [2] Particle Data Group, S. Eidelman et al., Review of Particle Physics, Physics Letters B 592, 1 (2004). (URL: http://pdg.lbl.gov). [3] V. A. Kostelecký: Phys.Rev.D 69, 105009 (2004). [4] N. E. Mavromatos: Lecture Notes in Physics (in press), E-print gr-qc/0407005. [5] F. R. Klinkhamer, Ch. Rupp: Phys.Rev.D 70, 045020 (2004). [6] The Antiproton Decelerator at CERN, http://psdoc.web.cern.ch/psdoc/acc/ad/index.html [7] ASACUSA (Atomic Spectroscopy And Collisions Using Slow Antiprotons) Collaboration 3, http://www.cern.ch/asacusa. 2 Musashi Miyamoto, 17th century samurai and philosopher 3 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 6

[8] ATHENA (ApparaTus for High precision Experiments on Neutral Antimatter) Collaboration, http://athena.web.cern.ch/athena. [9] ATRAP (Antimatter TRAP) Collaboration, http://hussle.harvard.edu/ atrap/. [10] M. Charlton, J. Eades, D. Horváth, R. J. Hughes, C. Zimmermann, Physics Reports 241 (1994) 65 117. [11] M. H. Holzscheiter, M. Charlton and M. M. Nieto, Physics Reports 402 (2004) 1 101. [12] G. Baur et al., Phys. Lett., B368 (1996) 251. [13] G. Blanford et al., Phys. Rev. Lett., 80 (1998) 3037. [14] M. Niering et al., Phys. Rev. Lett. 84 (2000) 5496-5499. [15] M. Amoretti et al., Nature 419 (2002) 456; Phys. Lett. B, 583 (2004) 59. [16] G. Gabrielse et al., Phys. Rev. Lett. 89 (2002) 213401. [17] D. Horváth, D., Radiochimica Acta 77 (1997) 75. [18] J. Eades, J.F. Hartmann, Rev. Mod. Phys. 71 (1999) 373. [19] T. Yamazaki, N. Morita, R.S. Hayano, E. Widmann, J. Eades, Physics Reports, 366 (2002) 183. [20] G. Gabrielse et al., Phys. Rev. Lett. 82 (1999) 3198. [21] H. A. Torii et al., Phys. Rev. A 59 (1999) 223. [22] V.I. Korobov, Phys. Rev. A 54 (1996) R1749. [23] V.I. Korobov, D.D. Bakalov, Phys. Rev. Lett. 79 (1997) 3379. [24] M. Hori et al., Phys. Rev. Lett., 87 (2001) 093401. [25] M. Hori et al., Phys. Rev. Lett. 91 (2003) 123401. [26] E. Widmann et al., Phys. Rev. Lett., 89 (2002) 243402. [27] K. Y. Franzen et al., Rev. Sci. Instrum. 74 (2003) 3305. [28] N. Kuroda et al., Phys. Rev. Lett. 94 (2005) 023401. [29] E. Widmann et al., Nucl. Instr. Meth. 214 (2004) 31. [30] R. Bluhm et al., Phys. Rev. Lett. 82 (1999) 2254. 7

Figure 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. 8

1 2 3 Bohr Dirac Lamb HFS 1S 2P 1/2 1/2 2S 1/2 2P 3/2 ANTIHYDROGEN F=0 F=1 HYDROGEN 3 2 2P 3/2 2S 1/2 2P1/2 1 1S1/2 F=1 F=0 Bohr Dirac Lamb HFS Figure 2: Atomic levels in hydrogen and antihydrogen. CPT symmetry requires them to be exactly equivalent. 9

Figure 3: An antihydrogen annihilation event detected by ATHENA [15]. 10

counts / 10 ns analog amplitude (arb. units) 4000 3500 3000 2500 2000 1500 1000 500 0 0-2.5-5 -7.5-10 -12.5-15 -17.5-20 event-by-event λ = 470.724 nm 0 0.5 1 1.5 2 2.5 3 3.5 4 Annihilation time (µs) analog method λ = 470.724 nm 0 0.5 1 1.5 2 2.5 3 3.5 4 Annihilation time (µs) Figure 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. 11

2 1.5 0.5 + phe LEAR δm M p p 2 1.5 [10 6 ] Q p / M p 1 1 0.5 allowed region 0.5 1 1.5 2 δq Q p p [10 6 ] 0.5 p + He AD 1 1.5 2 Figure 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 [20] whereas M Q 2 by ASACUSA [21, 24, 25]. With the improvement of the experimental technique the allowed region was step-by-step reduced: the present limit is 10 ppb (10 8 ) [25]. 12

Figure 6: Collisional effects on three favoured, (n, l) (n 1, l 1), and three unfavored, (n, l) (n+ 1,l 1) antiprotonic transitions in the phe + system [24]: 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. 13

F =L 1/2 f (n,l ) ν HF F =L 1/2 J + =L ν SHF J =L 1 F + =L +1/2 (n,l) ν HF ν HF + f + F + =L+1/2 ν HF J ++ = L+1 ν SHF + J + =L 1.15 1.10 + ν HF ν HF R ++ /R ++ off 1.05 1.00 0.95 12.86 12.88 12.90 12.92 12.94 12.96 ν MW (GHz) Figure 7: The scheme of a split transition line in the p- 4 He + atom as studied using the laser microwave laser resonance method in order to measure the magnetic moment of the antiproton [26] in the atomic bound state: splitting of the (n = 37,l = 35) (38,34) transition (above); the measured spectrum (below): number of forced antiproton annihilations against the microwave frequency. 14