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

The DIRAC experiment at CERN investigated in the reaction <math display="inline"><mi>p</mi><mo stretchy="false">(</mo><mn>24</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi><mo>/</mo><mi mathvariant="normal">c</mi><mo stretchy="false">)</mo><mo>+</mo><mi>N</mi><mi>i</mi></math> the particle pairs <math display="inline"><msup><mi>K</mi><mo>+</mo></msup><msup><mi>K</mi><mo>-</mo></msup><mo>,</mo><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>-</mo></msup></math>, and <math display="inline"><mi>p</mi><mover accent="true"><mi>p</mi><mo stretchy="false">¯</mo></mover></math> with relative momentum <math display="inline"><mi>Q</mi></math> in the pair system less than <math display="inline"><mn>100</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi><mo>/</mo><mi mathvariant="normal">c</mi></math>. Because of background influence studies, DIRAC explored three subsamples of <math display="inline"><msup><mi>K</mi><mo>+</mo></msup><msup><mi>K</mi><mo>-</mo></msup></math> pairs, obtained by subtracting-using the time-of-flight (TOF) technique-the background from initial <math display="inline"><mi>Q</mi></math> distributions with <math display="inline"><msup><mi>K</mi><mo>+</mo></msup><msup><mi>K</mi><mo>-</mo></msup></math> sample fractions more than 70%, 50%, and 30%. The corresponding pair distributions in <math display="inline"><mi>Q</mi></math> and in its longitudinal projection <math display="inline"><msub><mi>Q</mi><mi>L</mi></msub></math> 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 <math display="inline"><msup><mi>K</mi><mo>+</mo></msup><msup><mi>K</mi><mo>-</mo></msup></math> yield increase of about four at <math display="inline"><msub><mi>Q</mi><mi>L</mi></msub><mo>=</mo><mn>0.5</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi><mo>/</mo><mi mathvariant="normal">c</mi></math> compared to <math display="inline"><mn>100</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi><mo>/</mo><mi mathvariant="normal">c</mi></math>. In order to study contributions from strong interaction, a second more sophisticated model was applied, considering also strong FSI via the resonances <math display="inline"><msub><mi>f</mi><mn>0</mn></msub><mo stretchy="false">(</mo><mn>980</mn><mo stretchy="false">)</mo></math> and <math display="inline"><msub><mi>a</mi><mn>0</mn></msub><mo stretchy="false">(</mo><mn>980</mn><mo stretchy="false">)</mo></math> and a variable distance <math display="inline"><msup><mi>r</mi><mo>*</mo></msup></math> between the produced <math display="inline"><mi>K</mi></math> 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, <math display="inline"><mn>3680</mn><mo>±</mo><mn>370</mn></math> <math display="inline"><msup><mi>K</mi><mo>+</mo></msup><msup><mi>K</mi><mo>-</mo></msup></math> pairs were found to be compared to <math display="inline"><mn>3900</mn><mo>±</mo><mn>410</mn></math> <math display="inline"><msup><mi>K</mi><mo>+</mo></msup><msup><mi>K</mi><mo>-</mo></msup></math> extracted by means of the Coulomb model. Knowing the efficiency of the TOF cut for background suppression, the total number of detected <math display="inline"><msup><mi>K</mi><mo>+</mo></msup><msup><mi>K</mi><mo>-</mo></msup></math> pairs was evaluated to be around <math display="inline"><mn>40000</mn><mo>±</mo><mn>10</mn><mo>%</mo></math>, which agrees with the result from the 30% subsample. The <math display="inline"><msup><mi>K</mi><mo>+</mo></msup><msup><mi>K</mi><mo>-</mo></msup></math> 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 <math display="inline"><msup><mi>K</mi><mo>+</mo></msup><msup><mi>K</mi><mo>-</mo></msup></math> production at small relative momentum <math display="inline"><mi>Q</mi></math>. The pair distribution in <math display="inline"><mi>Q</mi></math> is well described by Coulomb FSI, whereas a potential influence from strong interaction in this <math display="inline"><mi>Q</mi></math> region is insignificant within experimental errors.