The study of nonstandard atoms has a long tradition in particle physics. Such exotic atoms include positronium, muonic atoms, antihydrogen and also hadronic atoms. In this last category, especially pionic hydrogen has been investigated in different experiments quite extensively, also in Switzerland at CERN and PSI. To the same category, the hadronic atoms [1], are belonging the dimeson atoms, the subject of this article.
Electromagnetically bound mesonic pairs like the atom pionium (A_2π), consisting of π⁺ and π^-, or the πK atom (A_πK) are an excellent tool to study the strong interaction theory QCD (quantum chromodynamics) at very low energy, i.e. in the confinement region. The strong interaction leads to a broadening and shift of atomic levels and dominates the lifetime of these exotic atoms.
Pion-pion interaction at low energy, constrained by the approximate chiral symmetry SU(2) for 2 flavours (u and d quarks), is the simplest and best known hadron-hadron process [2]. Since the bound state physics is well understood, a measurement of the A_2π lifetime provides basic low energy properties in the form of scattering lengths.
Moreover, low energy interaction between the pion and the next heavier and strange meson, the kaon, is a promising probe to learn about the more general 3-flavour SU(3) (u, d and s quark) structure of hadronic interactions – a matter not directly accessible in pion-pion interaction. Hence, data on πK atoms are very valuable, as they provide insights in the role played by the strange quarks in the QCD vacuum.

Method

A_2π [A_πK] atoms are produced by the Coulomb interaction in final states of oppositely charged ππ [πK] pairs, generated in proton–target interactions [3]. After production these atoms travel through the target and a part of them are broken up due to their interaction with matter: "atomic pairs" are produced, characterized by their small relative momenta in the centre of mass of the pair Q < 3 MeV/c. As shown in Fig. 1, these pairs are detected in the DIRAC setup. The rest of the atoms mainly annihilate into π⁰π⁰ [π⁰K⁰], which are not detected. The amount of broken up (ionised) atoms n_A depends on the lifetime τ which defines the decay rate. Therefore, the breakup probability P_br is a function of the A_2π [A_πK] lifetime τ.

In addition, proton–target interactions produce also oppositely charged ππ [πK] pairs with Coulomb ("Coulomb pairs") and without Coulomb final state interaction, depending on whether the pairs are produced close to each other or not. The latter category includes meson pairs with one meson from the decay of long-lived resonances ("non-Coulomb pairs") as well as two mesons from different interactions ("accidental pairs"). "Coulomb" and "non-Coulomb pairs" together are called "free pairs". The total number of produced atoms N_A is proportional to the number of "Coulomb pairs" N_C with low relative momenta: N_A = K · N_C. The coefficient K is precisely calculable. DIRAC measures the A_2π [A_πK] breakup probability: P_br(τ) is defined as ratio of the observed number n_A of "atomic pairs" to the number N_A of produced atoms A_2π [A_πK], calculated from the measured number of "Coulomb pairs" N_C.

Fig. 2: DIRAC double-arm spectrometer upgraded for K identification.
The microdrift gas chambers MDC, the scintillating fiber detector SFD and the scintillation ionisation hodoscope IH provide initial track data. Downstream of the spectrometer magnet, the drift chambers DC measure final tracks to determine momenta. The vertical VH and the horizontal scintillation hodoscopes HH are used for trigger purposes. The Cherenkov detectors containing nitrogen Ch or heavy gas (C₄F₁₀) or aerogel radiators as well as the preshower detectors PSh and the scintillation muon detectors Mu behiniron absorber help to distinguish pions and kaons from other particles like electrons, muons and protons.

Experimental setup

The purpose of the DIRAC setup (Fig. 2) at the CERN proton synchrotron is to record oppositely charged ππ [πK] pairs with small relative momenta Q. The 24 GeV/c proton beam hits a thin target (typically 100 μm thick Ni foil). Emerging charged π⁺π^- [πK] pairs travel in vacuum through the upstream spectrometer part with coordinate and ionisation detectors, before they are split by the 2.3 Tm bending magnet into the “positive” (T1) and “negative” (T2) arm. Both arms are equipped with high precision drift chambers, time of flight detectors, Cherenkov, preshower and muon counters. The relative time resolution between the two arms is around 200 ps.
The momentum reconstruction in the double-arm spectrometer makes use of the drift chamber information of the two arms as well as of the measured hits in the upstream coordinate detectors. The resolution on the components of the pair relative momentum Q is ~ 0.5 MeV/c. A system of fast trigger processors selects small Q events.

Observation and lifetime measurement of pionium

Already in 1993 the observation of A_2π was reported in [4] from an experiment at Serpukhov and ten years later a measurement of the A_2π lifetime at DIRAC in [5]. Fig. 3 shows a characteristic accumulation of low Q_L events, which are due to π⁺π^- atoms (breakup). In summer 2009 DIRAC presented the most recent value for the A_2π lifetime τ_2π = (2.82 ± 0.31)·10^-15 s [6], based on the statistics of 13300 "atomic pairs" collected in 2001-2003 on the Ni target. Using the relation between lifetime and scattering length [7], the above lifetime corresponds to the scattering length difference |a₀ - a₂| = 0.268 ± 0.015 (m_π^-1), where a₀ and a₂ are the S-wave ππ scattering lengths for isospin 0 and 2, respectively. The corresponding theoretical values are 0.265 ± 0.004 (m_π^-1) for the scattering length [8] and (2.9 ± 0.1)·10^-15 s for the lifetime [7]. These results show the high precision that can be reached in low energy hadronic interactions both in experiments and theory.

Fig. 3: Q_L distribution measured with DIRAC for signal π⁺π^- pair [5].
The peak at low QL corresponds to the residuals, the "atomic pairs", after background subtraction of the "free pairs" ("Coulomb" and "non-Coulomb pairs"): the red line represents the expected atomic signal shape.

Observation and lifetime measurement of πK atoms

First evidence for the observation of the atom A_πK was published in [9]: πK atoms were produced in a 26 μm thin Pt target, and the oppositely charged πK "atomic pairs" from the atom breakup were analysed in the upgraded DIRAC double-arm spectrometer (Fig. 2). The observed enhancement at low relative momentum corresponds to a production of 173 ± 54 "atomic pairs". From this first data sample DIRAC derives a lower limit on the πK atom lifetime of τ_πK > 0.8·10^-15 s (90% CL), to be compared with the theoretical prediction of (3.7 ± 0.4)·10^-15 s [10].

Future investigations with DIRAC

In addition to the activities above, DIRAC proposes to measure the pionium energy splitting between np and ns states („Lamb shift“) in 2011 and later. The energy shift for the levels with the principal quantum number n and orbital quantum number l includes electromagnetic as well as a strong contribution depending on the same scattering lengths a₀ and a₂ as above. Therefore, the observation of such long-lived states would open a novel possibility to measure level splittings and to determine another comscattering lengths, hence allowing a determination of a₀ and a₂ individually.

References

[1] J. Gasser, V. E. Lyubovitskij, A. Rusetzky, Physics Report 456 (2008) 167
[2] S. Weinberg, Phys. Rev. Lett. 17 (1966) 616; G. Colangelo, J. Gasser, H. Leutwyler, Nucl. Phys. B 603 (2001) 125.
[3] L. Nemenov, Sov. J. Nucl. Phys. 41 (1985) 629.
[4] L. G. Afanasyev, et al., Phys. Lett. B 308 (1993) 200.
[5] B. Adeva, et al., Phys. Lett. B 619 (2005) 50.
[6] V. Yazkov, "Investigation of π⁺π⁻ and πK atoms at DIRAC", 6th International Workshop on Chiral Dynamics, Bern 2009.
[7] J. Gasser, et al., Phys. Rev. D 64 (2001) 016008.
[8] G. Colangelo, J. Gasser, H. Leutwyler, Phys. Lett. B 488 (2000) 261.
[9] B. Adeva, et al., Phys. Lett. B 674 (2009) 11[10] J. Schweizer, Phys. Lett. B 587 (2004) 33.

[Released: July 2010]