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

The DIRAC experiment at CERN investigated in the reaction $p(24\mathrm{GeV}/\mathrm{c})+Ni$ the particle pairs $K^{+}{K}^{-},{\pi }^{+}{\pi }^{-}$, and $p\overline{p}$ with relative momentum $Q$ in the pair system less than $100\mathrm{MeV}/\mathrm{c}$. Because of background influence studies, DIRAC explored three subsamples of $K^{+}{K}^{-}$ pairs, obtained by subtracting-using the time-of-flight (TOF) technique-the 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 the Coulomb final-state interaction (FSI) and assuming pointlike pair production. This Coulomb model analysis leads to a $K^{+}{K}^{-}$ yield increase of about four at $Q_L=0.5\mathrm{MeV}/\mathrm{c}$ compared to $100\mathrm{MeV}/\mathrm{c}$. In order to study contributions from strong interaction, a second more sophisticated model was applied, considering also strong FSI via the resonances $f_0(980)$ and $a_0(980)$ and a variable distance $r^{*}$ between the produced $K$ mesons besides Coulomb FSI. This analysis was based on three different parameter sets for the pair production. For the 70% subsample and with the best parameters, $3680\pm 370$ $K^{+}{K}^{-}$ pairs were 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. In summary, the upgraded DIRAC experiment observed increased $K^{+}{K}^{-}$ production at small relative momentum $Q$. The pair distribution in $Q$ is well described by Coulomb FSI, whereas a potential influence from strong interaction in this $Q$ region is insignificant within experimental errors.

Figure 1

General view of the DIRAC setup (1—target station; 2—first shielding; 3—micro drift chambers (MDC); 4—scintillating fiber detector (SFD); 5—ionization hodoscope (IH); 6—second shielding; 7—vacuum tube; 8—spectrometer magnet; 9—vacuum chamber; 10—drift chambers (DC); 11—vertical hodoscope (VH); 12—horizontal hodoscope (HH); 13—aerogel Cherenkov (ChA); 14—heavy gas Cherenkov (ChF); 15—nitrogen Cherenkov (ChN); 16—preshower (PSh); 17—muon detector (Mu).

Figure 2

The schematic description of $K^{+}{K}^{-}$ production processes. (a) The black point presents the pair pointlike production; the wavy lines describe the Coulomb interaction in the final state. (b) The circle and square present the pair nonpointlike production and strong interaction in the final state, respectively.

Figure 3

$\mathrm{\Delta }{t}^K$ distribution of $K^{+}{K}^{-}$, ${\pi }^{+}{\pi }^{-}$, and $p\overline{p}$ pairs with momentum of about $3.5\mathrm{GeV}/\mathrm{c}$. The peak at zero corresponds to $K^{+}{K}^{-}$, the peak on the right to ${\pi }^{+}{\pi }^{-}$ and the small peak on the left to $p\overline{p}$ pairs.

Figure 4

$\mathrm{\Delta }{t}^e$ distribution of electron-positron pairs.

Figure 5

The $Q$ distribution of ${\pi }^{+}{\pi }^{-}$ (red), $p\overline{p}$ (black), and accidentals (green) pairs calculated as $K^{+}{K}^{-}$ pairs.

Figure 6

$Q_L$ distributions of the subsamples 30%, 50%, and 70% for DATA1 and DATA2. The experimental spectra in the interval $0<Q_L<100\mathrm{MeV}/\mathrm{c}$ are fitted by simulated $K^{+}{K}^{-}$ (pointlike Coulomb FSI) and residual ${\pi }^{+}{\pi }^{-}$ and $p\overline{p}$ background distributions. The red curve is the $K^{+}{K}^{-}$ distribution, the black one is the sum of $K^{+}{K}^{-}$ and residual background distributions. In the 70% and 30% subsamples, the residual background is small and these curves practically coincide. For $K^{+}{K}^{-}$ pairs in the region of $Q_L<10\mathrm{MeV}/\mathrm{c}$ the Coulomb enhancement is clearly visible, whereas the residual background is small.

Figure 7

$Q$ distributions of the 30%, 50%, and 70% subsamples for DATA1 and DATA2. Simulated distributions of $K^{+}{K}^{-}$ (ALICE parametrization) and residual background of ${\pi }^{+}{\pi }^{-}$, accidental and $p\overline{p}$ pairs are fitting the experimental spectrum in the interval $0<Q<100\mathrm{MeV}/\mathrm{c}$. The red line is the $K^{+}{K}^{-}$ distribution and the black line is the sum of $K^{+}{K}^{-}$ and the residual background. In the 70% and 30% subsamples the residual background is small and these lines practically coincide.

Figure 8

$Q$ distributions in the interval $0–100\mathrm{MeV}/\mathrm{c}$ of $K^{+}{K}^{-}$ (ALICE parametrization) of the 30%, 50%, and 70% subsamples for the DATA1 and DATA2 after residual background subtraction. The red and the blue fitting curves were evaluated from the analysis of experimental distributions with residual background in Coulomb and Martin parametrizations, respectively. It is seen that the difference between these curves is not significant and they describe “pure” experimental $K^{+}{K}^{-}$ distributions well.

Figure 9

$Q$ distributions in the interval $0–30\mathrm{MeV}/\mathrm{c}$ of $K^{+}{K}^{-}$ (ALICE parametrization) of the subsamples 30%, 50%, and 70% for DATA1 and DATA2 after residual background subtraction. The red and the blue fitting curves were evaluated from the analysis of experimental distributions with residual background in Coulomb and Martin parametrizations, respectively. It is seen that in this interval of $Q$ the difference between these curves is absent and they describe “pure” experimental $K^{+}{K}^{-}$ distributions well.