Investigation of $K^{+}{K}^{-}$ pairs in the effective mass region near $2m_K$

Abstract

The DIRAC experiment at CERN investigated in the reaction $\mathrm{p}(24\mathrm{GeV}/c)+\mathrm{Ni}$ the particle pairs $K^{+}{K}^{-},\ddot{I}{€}^{+}\ddot{I}{€}^{-}$ and $p\bar{p}$ with relative momentum $Q$ in the pair system less than 100 MeV/c. Because of background influence studies, DIRAC explored three subsamples of $K^{+}{K}^{-}$ pairs, obtained by subtracting -- using time-of-flight (TOF) technique -- background from initial $Q$ distributions with $K^{+}{K}^{-}$ sample fractions more than 70\%, 50\% and 30\%. The corresponding pair distributions in $Q$ and in its longitudinal projection $Q_L$ were analyzed first in a Coulomb model, which takes into account only Coulomb final state interaction (FSI) and assuming point-like pair production. This Coulomb model analysis leads to a $K^{+}{K}^{-}$ yield increase of about four at $Q_L=0.5$ MeV/c compared to 100 MeV/c. In order to study contributions from strong interaction, a second more sophisticated model was applied, considering besides Coulomb FSI also strong FSI via the resonances $f_0(980)$ and $a_0(980)$ and a variable distance $r^{\ast }$ between the produced $K$ mesons. This analysis was based on three different parameter sets for the pair production. For the 70\% subsample and with best parameters, $3680\pm 370$ $K^{+}{K}^{-}$ pairs was found to be compared to $3900\pm 410$ $K^{+}{K}^{-}$ extracted by means of the Coulomb model. Knowing the efficiency of the TOF cut for background suppression, the total number of detected $K^{+}{K}^{-}$ pairs was evaluated to be around $40000\pm 10\%$, which agrees with the result from the 30\% subsample. The $K^{+}{K}^{-}$ pair number in the 50\% subsample differs from the two other values by about three standard deviations, confirming -- as discussed in the paper -- that experimental data in this subsample is less reliable.