First observation of $\pi^{-}K^+$ and $\pi^{+}K^-$ atoms, their lifetime measurement and $\pi K$ scattering lengths evaluation

The Low Energy QCD allows to calculate the ππ and π K scattering lengths with high precision. There are accurate relations between these scattering lengths and π + π − , π − K + , π + K − atoms lifetimes. The experiment on the first observation of π − K + and π + K − atoms is described. The atoms were generated in Nickel and Platinum targets hit by the PS CERN proton beam with momentum of 24 GeV/ c . Moving in the target, part of atoms break up producing characteristic π K pairs (atomic pairs) with small relative momentum Q in their c.m.s. In the experiment, we detected n A = 349 ± 62 (5.6 standard deviations) π − K + and π + K − atomic pairs. The main part of π K pairs are produced in free state. The majority of such particles are generated directly or from short-lived sources as ρ , ω and similar resonances. The electromagnetic interactions in the final state create Coulomb pairs with a known sharp dependence on Q . This effect allows to evaluate the number of these Coulomb pairs. There is a precise ratio ( ∼ 1%) between the number of π − K + ( π + K − ) Coulomb pairs with small Q and the number of produced π − K + ( π + K − ) atoms. Using this ratio, we obtained the numbers of generated π − K + and π + K − atoms. The atom breakup probability in a target P br = n A / N A depends on the atom lifetime. Using such dependences for the Ni and Pt targets, known with a precision about 1%, the π K atom lifetime was measured and from this value the π K scattering lengths were evaluated. The presented analysis shows that the π − K + and π + K − atoms production in the p-nucleus inter- actions increases by 16 and 38 times respectively if the proton momentum is increased from 24 GeV/ c up to 450 GeV/ c .