Investigation of the Resonance-like <em>a₁</em>(1420) Signal and First Partial-Wave Decomposition of the <nobr><em>π^-K_S⁰K_S⁰</em></nobr> Final State at COMPASS

Abstract

In 2014, a supernumerous light-meson state was found by the COMPASS collaboration. This discovery bore similarities to some of the <em>XYZ</em> states in the heavy-meson sector, discovered at <nobr><em>e⁺e^-</em></nobr> colliders, that did not fit the expectations from the quark model and hence were called exotic states. The partial-wave decomposition of the COMPASS data for the <nobr><em>π^-π⁺π^-</em></nobr> final state, which is employing an isobar model, revealed a narrow signal with axial-vector quantum numbers in the <nobr><em>f₀</em>(980)<em>π</em> P-wave</nobr>. Since it was found at an energy of <nobr>1.4 GeV</nobr> by a resonance-model fit with a relativistic Breit-Wigner model, it was called <em>a₁</em>(1420). This thesis investigates the nature of the signal, following two avenues.<br/>

In the first part, it is shown how a rescattering of final-state particles can produce such a signal by explicitly performing a projection of a <em>K^*K</em> intermediate state to the <em>f₀</em>(980)<em>π</em> final state. The resulting theoretical model is fitted to the COMPASS data and the quality is compared to a fit using a conventional relativistic Breit-Wigner model. Several systematic studies are performed. This includes a fit to each of the systematic studies of the underlying partial-wave decomposition, as well as a bootstrap analysis and modifications of the theoretical model. In all cases except one, the rescattering interpretation shows a better compatibility with the data.<br/>

In the second part, an event selection of the complementary <nobr><em>π^-K_S⁰K_S⁰</em></nobr> final state is performed, where the optimal vertex separation for the <em>K_S⁰</em> mesons is determined by means of a significance study to reduce background coming from a possible 5<em>π</em> final state. A total of ~240000 exclusive events are selected, superseding the statistics of previous experiments of diffractive <nobr><em>π^-K_S⁰K_S⁰</em></nobr> production by a factor of ~240. Based on the selected data set, a first partial-wave decomposition is performed, revealing strong evidence for the <em>a₁</em>(1420) signal in the <nobr><em>f₀</em>(980)<em>π</em> P-wave</nobr> of the <nobr><em>π^-K_S⁰K_S⁰</em></nobr> final state in form of an enhancement in the intensity and a phase motion in the relative phase to other waves, even for both resonance-spin projections <em>M=0</em> and <em>M=1</em>. At the same time, no resonance-like signal is visible at <nobr>~1.4 GeV</nobr> in the <nobr><em>K^*</em>(892)<em>K_S⁰</em> S-wave,</nobr> which agrees well with the interpretation of a rescattering effect. The spin-exotic <em>π₁</em>(1600), a candidate for the lightest hybrid meson, manifests itself as a broad peak in the <nobr><em>K^*</em>(892)<em>K_S⁰</em> P-wave,</nobr> however, no significant evidence for a relative phase motion with other partial waves is observed. Another hybrid candidate with ordinary quantum numbers, the pseudoscalar <em>π</em>(1800), shows up as a clean narrow peak in the <nobr><em>f₀</em>(980)<em>π</em> S-wave.</nobr> It is accompanied by a narrow resonance-like signal at <nobr>1.4 GeV</nobr>, i.e. an enhancement in the intensity together with phase motion in the relative phase to other partial waves. This could be the first observation of a "<em>π</em>(1420)" rescattering effect, similar to the <em>a₁</em>(1420), but with pseudoscalar resonance quantum numbers.