International Conference on Exotic Atoms and Related Topics - EXA2014

Theory, using Low Energy QCD, calculated with high precision the $\pi \pi$ and $\pi K$ scattering length. Because these calculations are using the chiral symmetry that describe quarks, gluons, and the QCD vacuum property, the experimental check of these predictions is important. To check the theoretical calculations for the process including also $s$ quarks we must measure the $\pi K$ atom lifetime that is connected to the $\pi K$ scattering lengths by a precise relation. The results of the search for hydrogen-like atoms consisting of ${\pi }^{-}{K}^{+}$ and ${\pi }^{+}K-$ mesons are presented. Evidence for $\pi K$ atoms production, using a 24 GeV/c protons beam from CERN PS interacting with a nickel target, is reported here. From the analysis of Coulomb final state interaction $\pi K$ pairs was evaluated the number of produced $\pi K$ atoms $N_A=653\pm 42$ together with the value of the $\pi K$ pairs from atoms that breakup in the same target $N_a=178\pm 49$. Using these results the analysis yields to a first value for the $\pi K$ atom lifetime of $t={2.5}_{-1.8}^{+3.0}$ fs and a first model-independent measurement of the S-wave isospin-odd $\pi K$ scattering length $|a0-|=1/3|a_{1/2}-a_{3/2}|={0.11}_{-0.04}^{+0.09}$ $1/M_{\pi }$ (the I in $a_I$ stands for isospin).