*Jürg Schacher, University of Bern and CERN, on behalf of the DIRAC collaboration*

* **DI**meson **R**elativistic **A**tom **C**omplex

**Introduction**

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 π^{0}π^{0} [π^{0}K^{0}], 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}.

**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 |a_{0} - a_{2}| = 0.268 ± 0.015 (m_{π}^{-1}), where a_{0} and a_{2} 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.

**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 a_{0} and a_{2} 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 a_{0} and a_{2} 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]*