Central Production of Two-Pseudoscalar Meson Systems at the COMPASS Experiment at CERN

The question of the existence of glueballs is one of the unsolved problems in modern particle physics and can be regarded as a stringent test for quantum chromodynamics. Especially the supernumerous states in the light scalar meson spectrum are candidates for the observation of mixing effects between $q\bar q$ mesons and pure gluonic bound states. On the other hand, the existence and the properties of many resonances in this sector are disputed. The COMPASS experiment was proposed to make significant contributions to this field. COMPASS is a fixed-target experiment at the CERN SPS which focused on light-quark hadron spectroscopy during the data taking periods in 2008 and 2009. A world-leading data set was collected with a $190\,\mathrm{GeV}/c$ hadron beam impinging on a liquid hydrogen target in order to study, inter alia, the central production of glueball candidates in the light meson sector. Especially the double-Pomeron exchange mechanism is well suited for the production of mesons without valence-quark content. To this end, we select events with two protons and two pseudo-scalar mesons in the final state from the COMPASS data set recorded with an incident proton beam. Several selection criteria are compared in order to enhance the double-Pomeron component in the centrally produced sample. The angular distribution of the decay of these systems into $\pi^+\pi^-$ and $K^+K^-$ is decomposed in terms of partial-wave amplitudes, where particular attention is paid to the inherent mathematical ambiguities. They can be naturally resolved by using the information from the related $\pi^0\pi^0$ final state. The resulting distributions yield unprecedented precision, most notably on the relative phase between the partial-wave amplitudes. For the first time, an analysis in narrow bins of the squared four-momentum transfer is possible, which provides information about the dynamics of the production process. Furthermore, we show that a mass-dependent fit of the obtained $S$-wave intensity distribution alone, as it was done in the past, can be achieved by substantially different models. Only if the intensities of the $S$- and $D$-wave amplitudes as well as their relative phase are fitted simultaneously, resonant states can be distinguished from non-resonant background. With this method, we obtain realistic Breit-Wigner parameters for the scalar mesons above $1\,\mathrm{GeV}/c^2$, especially in the $K^+K^-$ channel. A combination of the results with precision data from elastic scattering experiments may be able to elucidate the entire sector of light scalar mesons.