Observation of $\pi^- K^+$ and $\pi^+ K^-$ atoms

The observation of hydrogen-like $\pi K$ atoms, consisting of $\pi^- K^+$ or $\pi^+ K^-$ mesons, is presented. The atoms have been produced by 24 GeV/$c$ protons from the CERN PS accelerator, interacting with platinum or nickel foil targets. The breakup (ionisation) of $\pi K$ atoms in the same targets yields characteristic $\pi K$ pairs, called"atomic pairs", with small relative momenta in the pair centre-of-mass system. The upgraded DIRAC experiment has observed $349\pm62$ such atomic $\pi K$ pairs, corresponding to a signal of 5.6 standard deviations.


Introduction
Up to now, the DIRAC collaboration has published indications about the production of πK atoms 1 [1][2][3]. This time, DIRAC reports the first statistically significant observation of the strange dimesonic πK atom.
A method to produce and observe hadronic atoms has been developed [18]. In the DIRAC experiment, relativistic dimesonic bound states, formed by Coulomb final state interaction (FSI), are moving inside the target and can break up. Particle pairs from breakup (atomic pair in Fig. 1) are characterised by a small relative momentum Q < 3 MeV/c in the centre-of-mass (c.m.) system of the pair 2 . A first πK atom investigation has been performed with a platinum target at the CERN PS with 24 GeV/c protons in 2007 [1,2]. An enhancement of πK pairs at low relative momentum has been observed, corresponding to 173 ± 54 πK atomic pairs or a significance of 3.2 standard deviations (σ ). In the 1 The term πK atom or A Kπ refer to π − K + and π + K − atoms. 2 The quantity Q denotes the experimental c.m. relative momentum. The longitudinal (Q L ) and transverse components of the vector Q are defined with respect to the direction of the total laboratory pair momentum. experiment from 2008 to 2010, DIRAC has detected in a Ni target an excess of 178 ± 49 πK pairs, an effect of only 3.6 σ [3].
In the present paper, experimental data obtained in Ni and Pt targets have been analysed, using recorded informations from all detectors (see Fig. 2) and enhanced background description based on Monte Carlo (MC) simulations. Setup geometry correction, detector response simulation, background suppression and admixture evaluation have been significantly improved for all runs.
The above mentioned improvements allow a statistically reliable observation of πK atoms.

Experimental setup
The setup [19], sketched in Fig. 2, detects and identifies π + π − , π − K + and π + K − pairs with small Q. The structure of these pairs after the magnet is approximately symmetric for π + π − and asymmetric for πK. Originating from a bound system, these particles travel with the nearly same velocity, and hence for πK atomic pairs, the kaon momentum is by a factor of about M K M π ≈ 3.5 larger than the pion momentum (M K is the charged kaon mass and M π the charged π mass). The 2-arm vacuum magnetic spectrometer presented is optimized for simultaneous detection of these pairs [20,21].
The 24 GeV/c primary proton beam, extracted from the CERN PS, hits a (26 ± 1) µm thick Pt target in 2007 3 and Ni targets with thicknesses (98 ± 1) µm in 2008 and (108 ± 1) µm in 2009 and 2010 4 . The radiation thickness of the 98 (108) µm Ni target amounts to about 7 · 10 −3 X 0 (radiation length). The secondary channel (solid angle Ω = 1.2 · 10 −3 sr) together with the whole setup is vertically inclined relative to the proton beam by 5.7 • upward. Secondary particles are confined by the rectangular beam collimator inside of the second steel shielding wall, and the angular divergence in the horizontal (X) and vertical (Y) planes is ±1 • . With a spill duration of 450 ms, the beam intensity has been (10.5-12)·10 10 protons/spill and, correspondingly, the single counting rate in one plane of the ionisation hodoscope (IH) (5-6)·10 6 particles/spill. Secondary particles propagate mainly in vacuum up to the Al foil at the exit of the vacuum chamber, which is located between the poles of the dipole magnet (B max = 1.65 T and BL = 2.2 T·m). In the vacuum gap, MicroDrift Chambers (MDC) with 18 planes and a Scintillating Fiber Detector (SFD) with 3 planes X, Y and U, inclined by 45 • , have been installed to measure particle coordinates (σ SFDx = σ SFDy = 60 µm, σ SFDu = 120 µm) and particle time (σ tSFDx = 380 ps, σ tSFDy = σ tSFDu = 520 ps). The four IH planes serve to identify unresolved double track events with only one hit in SFD.
Each spectrometer arm is equipped with the following subdetectors: drift chambers (DC) to measure particle coordinates with about 85 µm precision; vertical hodoscope (VH) to measure time with 110 ps accuracy for particle identification via time-of-flight determination; horizontal hodoscope (HH) to select pairs with vertical separation less than 75 mm between the arms (Q Y less than 15 MeV/c); aerogel Cherenkov counter (ChA) to distinguish kaons from protons; heavy gas (C 4 F 10 ) Cherenkov counter (ChF) to distinguish pions from kaons; nitrogen Cherenkov (ChN) and preshower (PSh) detector to identify e + e − pairs; iron absorber and two-layer scintillation counter (Mu) to identify muons. In the "negative" arm, an aerogel counter has not been installed, because the number of antiprotons is small compared to K − .
Pairs of oppositely charged time-correlated particles (prompt pairs) and accidentals in the time interval ±20 ns are selected by requiring a 2-arm coincidence (ChN in anticoincidence) with a coplanarity restriction (HH) in the first-level trigger. The second-level trigger selects events with at least one track in each arm by exploiting DC-wire information (track finder). Using track information, the online trigger selects ππ and πK pairs with relative momenta |Q X | < 12 MeV/c and |Q L | < 30 MeV/c. The trigger efficiency is about 98% for pairs with |Q X | < 6 MeV/c, |Q Y | < 4 MeV/c and |Q L | < 28 MeV/c. Particle pairs π − p (π +p ) from Λ (Λ) decay have been used for spectrometer calibration and e + e − pairs for general detector calibration.
3 Production of bound and free π − K + and π + K − pairs Prompt π ∓ K ± pairs from proton-nucleus collisions are produced either directly or originate from shortlived (e.g. ∆, ρ), medium-lived (e.g. ω, φ ) or long-lived (e.g. η , η) sources. Pion-kaon pairs produced directly, from short-or medium-lived sources, undergo Coulomb FSI resulting in unbound states (Coulomb pair in Fig. 1) or forming bound states (A Kπ in Fig. 1). Pairs from long-lived sources are practically not affected by Coulomb interaction (non-Coulomb pair in Fig. 1). The accidental pairs are generated via different proton-nucleus interactions.
The cross-section of πK atom production is given by the expression [18]: where p A , E A and M A are the momentum, total energy and mass of the πK atom in the laboratory (lab) system, respectively, and p K and p π the momenta of the charged kaon and pion with equal velocities. Therefore, these momenta obey in good approximation the relations p K = M K M A p A and p π = M π M A p A . The inclusive production cross-section of πK pairs from short-lived sources without FSI is denoted by σ 0 s , and ψ n (0) is the S-state Coulomb atom wave function at the origin with principal quantum number n. According to (1), πK atoms are only produced in S-states with probabilities W n = W 1 n 3 : W 1 = 83.2%, In complete analogy, the π ∓ K ± Coulomb pair production is described in the point-like production ap-proximation, depending on the relative momentum q in the production point 5 : The Coulomb enhancement function A C (q) is the well-known Sommerfeld-Gamov-Sakharov factor [22][23][24], µ = 109 MeV/c 2 the reduced mass of the π ∓ K ± system and α the fine structure constant. The relative production yield of atoms to Coulomb pairs [25] is calculated from the ratio (1) to (2).
For π and K production from non-pointlike medium-lived sources, corrections at the percent level have been applied to the production cross-sections [26]. Strong final state elastic and inelastic interactions are negligible [26].

Data processing
Recorded events have been reconstructed with the DIRAC ππ analysis software (ARIANE) modified for analysing πK data.

Tracking and setup tuning
Only events with one or two particle tracks in the DC detector of each arm are processed. Event reconstruction is performed according to the following steps: 1) One or two hadron tracks are identified in the DC of each arm with hits in VH, HH and PSh slabs and no signal in ChN and Mu ( Fig. 2 and related text). The earliest track in each arm is used for further analysis, because these tracks induce the trigger signal starting the readout procedure.
2) Track segments, reconstructed in DC, are extrapolated backward to the incident proton beam position in the target, using the transfer function of the DIRAC dipole magnet. This procedure provides approximate particle momenta and corresponding intersection points in MDC, SFD and IH.
3) Hits are searched for around the expected SFD coordinates in the region ±1 cm, corresponding to 3-5 σ defined by the position accuracy, taking into account particle momenta. This way, events are selected with low and medium background defined by the following criteria: the number of hits around the two tracks is ≤ 4 in each SFD plane and ≤ 9 in all three SFD planes. The case of only one hit in the region ±1 cm can occur because of detector inefficiency (two crossing particles, but one is not detected) or if two particles cross the same SFD column. The latter event type can be regained by double ionisation selection in the corresponding slab of the IH. For data collected in 2007 with the Pt target, criteria are different: the number of hits is two in the Y -and U-plane (SFD X-plane and IH, which may resolve crossing of only one SFD column by two particles, have not been used in 2007). The momentum of the positively or negatively charged particle is refined to match the X-coordinates of the tracks in DC as well as the SFD hits in the Xor U-plane, depending on presence of hits. In order to find the best two-track combination, the two tracks may not use a common SFD hit in case of more than one hit in the proper region. In the final analysis, the combination with the best χ 2 in the other SFD planes is kept.
In order to improve the mechanical alignment and general description of the setup geometry, the Λ andΛ particle decays into pπ − and π +p are exploited [27][28][29]. By requiring the mass equality M exp Λ = M exp Λ , the angles of the DC axes are modified. In the next step, the obtained angle between the DC axes is tuned to get the PDG (Particle Data group) reference Λ mass: the survey value of this angle needs to be increased by a few 10 −4 rad. For the data set 2007-2010, the weighted average of the experimental Λ mass values is M exp Λ = (1.115680 ± 2.9 · 10 −6 )GeV/c 2 , in agreement with the PDG value M PDG Λ = (1.115683 ± 6 · 10 −6 )GeV/c 2 [30]. This confirms consistency of the setup alignment. The Λ mass width in the simulated distribution tests how well the MC simulation reproduces the momentum and angle resolution of the setup. Data of each year has been investigated which simulated distribution -with different widths -fits best the experimental Λ distribution. Simulated Λ distributions providing a better χ 2 fit to the data are created with a width increased by the following factors: 1.027 ± 0.003 in 2007 (two SFD planes), while this increase in the subsequent years (three SFD planes) is not significant: 1.002 ± 0.004 (2008), 1.001 ± 0.003 (2009) and 1.003 ± 0.003 (2010). The difference between data and MC width could be the consequence of an imperfect description of the setup downstream part and can be removed by introducing a Gaussian smearing of the reconstructed momenta [3]. This technique is also used to evaluate the systematic error connected with reconstructed momentum smearing. Taking into account momentum smearing, the momentum resolution has been evaluated as d p p = p gen −p rec p gen with p gen and p rec the generated and reconstructed momenta, respectively. Between 1.5 and 8 GeV/c, particle momenta are reconstructed with a relative precision from 2.8 · 10 −3 to 4.4 · 10 −3 [27]. Relative momentum resolutions after the target are: σ QX ≈ σ QY ≈ 0.36 MeV/c, σ QL ≈ 0.94 MeV/c for p πK = p π + p K = 5 GeV/c and about 6% worse values for p πK = 7.5 GeV/c.

Event selection
Selected events are classified into three categories: π − K + , π + K − and π − π + . The last category is used for calibration purposes. Pairs of πK are cleaned of π − π + and π − p background by the Cherenkov counters ChF and ChA. In the momentum range from 3.8 to 7 GeV/c, pions are detected by ChF with (95-97)% efficiency [31], whereas kaons and protons (antiprotons) do not produce a signal. The admixture of π − p pairs is suppressed by the aerogel Cherenkov detector (ChA), which records kaons but not protons [32]. By requiring a signal in ChA and selecting compatible time-of-flights (TOF) between the target and VH, π − p and π − π + pairs, contaminating π − K + , can be substantially suppressed. Correspondingly, the admixture of π + π − pairs to π + K − has also been taken into account. Fig. 3 shows, after applying the selection criteria, the well-defined π − K + Coulomb peak at Q L = 0 and the strongly suppressed peak from Λ decays at Q L = −30 MeV/c. The Q L distribution of π + K − pairs is similar [3].
The final analysis sample contains only events which fulfil the following criteria: Due to finite detector efficiency, a certain admixture of misidentified pairs still remains in the experimental distributions. Their contribution has been estimated by TOF investigation and accordingly been subtracted [33]. Under the assumption that all positively charged particles are K + , Fig. 4 compares the experimental with the simulated TOF difference distribution for π − K + , π − π + and π − p pairs. Two ranges for positively charged particle momenta, (4.4-4.5) and (5.4-5.5) GeV/c, have been investigated.

Data simulation
Since the πK data samples consist of Coulomb, non-Coulomb and atomic pairs, these event types have been generated by MC (DIPGEN [34], GEANT-DIRAC (setup simulator)). The MC sample exceeds ten times the number of experimental events. The events are characterised by different q distributions: the non-Coulomb pairs are distributed in accordance with phase space, while the q distribution of Coulomb pairs is modified by the factor A C (q) (2). For atomic pairs, one needs to know the breakup position and the lab momentum of each pair. In practice, lab momenta for MC events are generated in accordance with analytic formulae, resembling the experimental momentum distributions of such pairs [34,35]. After comparing experimental momentum spectra [33] with MC distributions reconstructed by the analysis software, their ratio is used as event-by-event weight function for MC events in order to provide the same lab momentum spectra for simulated as for experimental data. The breakup point, from which the ionisation occurred, the quantum numbers of the atomic state and the corresponding q distribution of the atomic pair are obtained by solving numerically transport equations [36] using total and transition cross-sections [37]. The lab momenta of the atoms are assumed, in accordance with equation (1), to be the same as for Coulomb pairs. The description of the charged particle propagation through the setup takes into account: a) multiple scattering in the target, detector planes and setup partitions, b) response of all detectors, c) additional momentum smearing and d) results of the SFD response analysis [33,38,39] with influence on the Q T resolution.

Data analysis
In the analysis of πK data, the experimental 1-dimensional distributions of relative momentum Q and |Q L | and the 2-dimensional distributions (|Q L |, Q T ) have been fitted for each year and each πK charge combination by simulated distributions of atomic, Coulomb and non-Coulomb pairs. Their corresponding numbers n A , N C and N nC are free fit parameters. The sum of these parameters is equal to the number of analysed events.
In the 2-dimensional (|Q L |,Q T ) analysis, all experimental data in the same |Q L | and Q T intervals have been analysed using simulated 2-dimensional distributions. The evaluated atomic pair number, n A = 314 ± 59 (χ 2 /n = 237/157), corresponds to 5.3 standard deviations and coincides with the previous analysis result.
In Table 1, the results of the three analysis types (Ni and Pt target together) are presented for each atom type and combined. There is a good agreement between the results of the Q and (|Q L |,Q T ) analyses. The 1-dimensional |Q L | analysis for all πK data yields n A = 230 ± 92 (χ 2 /n = 52/37), which does not contradict the values obtained in the other two statistically more precise analyses.
Compared to the previous investigation [1], in the present work the Pt data has been analysed including upstream detectors. The consequence is a decrease of the statistics, but on the other hand an increase of the Q T resolution. This better resolution improves the data quality. Concerning the Ni target, the increase of n A , compared to [3], is caused by optimizing the time-of-flight criteria, which decreases atomic pair losses for the same fraction of background in the final distributions.

Systematic errors
The evaluation of the atomic pair number n A is affected by several sources of systematic errors [29,33]. Most of them are induced by imperfections in the simulation of the different πK pairs (atomic, Coulomb, non-Coulomb) and misidentified pairs. Shape differences of experimental and simulated distributions in the fit procedure (section 6) lead to biases of parameters, including atomic pair contribution, and finally on n A . The influence of systematic error sources is different for the analyses of Q, (|Q L |, Q T ) and Q L distributions. Table 2 shows systematic errors induced by different sources.

Conclusion
In the dedicated experiment DIRAC at CERN, the dimesonic Coulomb bound states involving strangeness, π − K + and π + K − atoms, have been observed for the first time with reliable statistics. These atoms are generated by a 24 GeV/c proton beam, hitting Pt and Ni targets. In the same targets, a fraction of the produced atoms breaks up, leading to π − K + and π + K − atomic pairs with small relative c.m. momenta Q. The 1-dimensional π ∓ K ± analysis in Q yields 349 ± 61(stat) ± 9(syst) = 349 ± 62(tot) atomic pairs (5.6 standard deviations) for both charge combinations. Analogously, a 2-dimensional analysis in (|Q L |,Q T ) has been performed with the result of 314 ± 59(stat) ± 10(syst) = 314 ± 60(tot) atomic pairs (5.2 standard deviations), in agreement with the former number.
The resulting πK atom lifetime and πK scattering length from the ongoing analysis will be presented in a separate paper.