First πK atom lifetime measurement and recent results from the DIRAC experiment

We report evidence for πK atoms production, using 24 GeV/c proton beam from CERN PS interacting with a thin Ni target. We have identified (178 ± 49) πK pairs, which were produced in a bound state — πK atom, which was subsequently brokenup (ionized) in the Ni target. Our analysis yields a first measurement of the πK atom lifetime ( 2.5+3.0 −1.8 ) fs [1]. This lifetime is connected in a model-independent way to the S-wave isospin-odd πK scattering length |a0 | = 3 |a1/2 − a3/2| = ( 0.11+0.09 −0.04 ) M−1 π (aI for isospin I).


Introduction
Low-energy QCD and specifically Chiral Perturbation Theory (ChPT) [2] predict ππ and πK scattering lengths with high precision [3,4]. For processes involving u-and d-quarks theoretical predictions have been experimentally checked by π + π − atom lifetime measurement [5] and by analysis of Kdecays [6,7]. Detection and lifetime measurement of πK atom cast a look into processes which involve s-quark as well.
A πK (πK atom) is an exotic atom -a hydrogen-like bound system of oppositely charged π and K mesons. Its ground state binding energy is 2.9 keV, Bohr radius a B = 249 fm and Bohr momentum is 0.79 MeV/c. Lifetime of πK atoms is limited by strong interaction through the decay into a pair of neutral pion and kaon, π 0 K 0 or π 0 K 0 , other decay channels contribution is of the order 10 −3 . The A πK decay width Γ πK in the ground state (1S) is directly related to the S-wave isospin-odd πK scattering length a − 0 = 1 3 (a 1/2 − a 3/2 ) [8,9]: Here τ is the lifetime in the ground state, a I is the scattering length for isospin I, α is the fine structure constant, μ is the reduced mass of π ± K ∓ pair, p * is the outgoing π 0 momentum in the atomic rest frame, and δ K summarizes corrections due to isospin breaking. Inserting in (1) the value M π a − 0 = 0.090 ± 0.005 calculated with the dispersion analysis [10] and using δ K = 0.040 ± 0.022 [9] predicts the πK atom lifetime τ = (3.5 ± 0.4) · 10 −15 s.

Experimental method
The method of A πK lifetime measurement [11] used by DIRAC experiment is as follows. A πK originate from collisions of 24 GeV/c protons with Ni atoms. Atoms are produced in nS-states, depending on the principal quantum number as n −3 [11]: where p A , E A and M A are the momentum, total energy and mass of the πK atom in the laboratory system, respectively, and p K and p π the momenta of the charged kaon and pion with equal velocities. The inclusive production cross section from short-lived sources without final state interaction is denoted as σ 0 s , ψ(0) stands for the atomic wave function at the origin. On a similar way, free π ± K ∓ pair production from short-lived sources is enhanced by a Gamow-Sommerfeld-Sakharov factor [12] as a function of their relative momentum q: Thus the total number N A of produced atoms is proportional to the number N C of Coulomb pairs generated with small relative momentum: While crossing the target, πK atoms can be excited or even ionized (break-up) due to Coulomb interaction with target atoms. Pairs of π ± K ∓ mesons from πK atom break-up, called atomic pairs later in the text, are characterized by low relative momenta q in their center of mass system. Thanks to their distinct shape, atomic pairs can be revealed in a reconstructed Q distribution (Q stands for experimental relative momentum) by an experiment with sufficiently high momentum resolution. Thus a number n A of atomic pairs can be identified from the experimental Q-spectra over background of free πK pairs. Ionization of πK atoms in the target is in competition with their annihilation. Therefore the probability P br = n A /N A of A πK ionization in the target is a unique function of its lifetime τ, which is calculated with sufficient precision [13,14] (Fig. 1). Earlier this method was successfully applied to measure the lifetime of exotic π + π − atoms [5]. First evidence for πK atoms through the observation of (173 ± 54) πK atomic pairs produced on 26 μm Pt target in 2007 has been published [15]. In the current work data from Ni targets is analysed, as for Ni a function P br (τ) provides better sensitivity to the lifetime τ.

Experimental setup
The DIRAC Collaboration constructed the double arm magnetic spectrometer which is optimized to detect and identify π + π − , π + K − and π − K + pairs with small relative momenta Q. The sketch of the apparatus is shown on Fig. 2. The experiment uses a 24 GeV/c primary proton beam from the CERN PS. Protons are directed onto a pure Ni thin foil with a radiation thickness of ∼ 7 · 10 −3 X 0 . The DIRAC apparatus with its secondary channel is inclined by 5.7 • with respect to the primary proton beam. Tracking detectors are positioned in two groups: between the target station and the spectrometer magnet (BL = 2.2T·m), and downstream the magnet. The resolution of the setup on components of pair relative momenta in c.m.s. σ Q x ≈ σ Q y ≈ 0.2 MeV/c and σ Q L ≈ 0.85 MeV/c is comparable to A πK Bohr momentum. Particle identification (e/μ/π/K/p) is performed through a combination of time-of-flight technique, threshold Cherenkov detectors and muon veto.

Experimental results
The data sample was collected on two Ni targets with thickness (98 ± 1) μm in 2008 and (108 ± 1) μm in 2009 and 2010. Events containing π ± K ∓ pairs with low relative momenta Q in their centreof-mass system were selected. Then the reconstructed 2-dimensional (Q T , Q L ) distribution of πK pairs was fitted by a sum of simulated distributions of atomic, Coulomb and non-Coulomb pairs with abundances of each component as free fit parameters. Here Q L corresponds to a component of the relative momentum parallel to the direction of pair total momentum, while Q T comprises the transverse component. In the low Q L region (Fig. 3), where atomic pairs are expected, there is an excess of events over the background of free pairs. Fit results for all data periods are summarized in   Year The lifetime dependence P br,i (τ) for each period i of data taking was calculated, which takes into account the target thickness and experimental spectrum on π + K − or π − K + laboratory momenta. The maximum likelihood method has been applied EPJ Web of C onferences 01019-p.4  where U i = Π i − P br,i (τ) is a vector of differences between measured Π i (P br in Table 1) and theoretical breakup probability P br,i (τ) for data sample i. The error matrix G includes both statistical and systematic uncertainties [16]. The combined likelihood function L(τ) for both charge combinations is shown on Fig. 4. Its maximum yields the following estimation of πK atom lifetime in the ground state: −0.1 syst fs = 2.5 +3.0 −1.8 tot fs.

Conclusions
The analysis of πK data collected by DIRAC experiment in 2008-2010 leads to the observation of n A (π − K + +π + K − ) = 178±49 (3.6 sigma) characteristic atomic pairs of both charge combinations. The probability of A πK ionization (break-up) has been measured. Combined with the known dependence of break-up probability on atom lifetime, this results in a first measurement of the πK atom lifetime in the ground state τ = 2.5 +3.0 −1.8 tot fs. As the atom lifetime is related to a scattering length, a measurement of the S-wave isospin-odd πK scattering length a − 0 = 0.11 +0.09 −0.04 M −1 π has been presented.