High statistics measurement of the underground muon pair separation at Gran Sasso

We present a measurement of the underground decoherence function using multi-muon events observed in the MACRO detector at Gran Sasso at an average depth of $3800 \mathrm{hg}/{\mathrm{cm}}^{2}.$ Muon pair separations up to 70 m have been measured, corresponding to parent mesons with ${P}_{\ensuremath{\perp}}l~1$--$2 \mathrm{GeV}/c.$ Improved selection criteria are used to reduce detector effects mainly in the low distance separation region of muon pairs. Special care is given to a new unfolding procedure designed to minimize systematic errors in the numerical algorithm. The accuracy of the measurement is such that the possible contribution of rare processes, such as ${\ensuremath{\mu}}^{\ifmmode\pm\else\textpm\fi{}}+\stackrel{\ensuremath{\rightarrow}}{N}{\ensuremath{\mu}}^{\ifmmode\pm\else\textpm\fi{}}+N+{\ensuremath{\mu}}^{+}+{\ensuremath{\mu}}^{\ensuremath{-}},$ can be experimentally studied. The measured decoherence function is compared with the predictions of the hadronic interaction model of the HEMAS Monte Carlo code. Good agreement is obtained. We interpret this agreement to indicate that no anomalous ${P}_{\ensuremath{\perp}}$ components in soft hadron-nucleus and nucleus-nucleus collisions are required by the MACRO experimental data. Preliminary comparisons with other Monte Carlo codes point out that the uncertainties associated with the hadronic interaction model may be as large as 20%, depending on the energy. MACRO data can be used as a benchmark for future work on the discrimination of shower models in the primary energy region around and below the knee of the spectrum.