[Paper Review] Partial-Wave Analysis of Centrally Produced Two-Pseudoscalar Final States in pp Reactions at COMPASS

A. Austregesilo|arXiv (Cornell University)|Feb 10, 2014

Quantum Chromodynamics and Particle Interactions4 citations

TL;DR

This paper presents a partial-wave analysis of centrally produced two-pseudoscalar final states in pp collisions at COMPASS, using a 190 GeV/c proton beam on a liquid hydrogen target. It resolves mathematical ambiguities in amplitude analysis and employs mass-dependent parametrizations with Breit-Wigner resonances and non-resonant components to describe the K⁺K⁻ system, revealing key contributions from f₀(1370), f₂(1270), and f₂′(1525) resonances with strong interference effects.

ABSTRACT

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 190GeV/c hadron beam impinging on a liquid hydrogen target in order to study, inter alia, the central exclusive 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. We select centrally produced systems with two pseudo-scalar mesons in the final state from the COMPASS data set recorded with an incoming proton. The decay of this system is decomposed in terms of partial waves, where particular attention is paid to the inherent mathematical ambiguities of the amplitude analysis. Furthermore, we show that simple parametrisations are able to describe the mass dependence of the fit results with sensible Breit-Wigner parameters.

Motivation & Objective

• To perform a high-precision partial-wave analysis of centrally produced two-pseudoscalar final states in pp reactions at COMPASS.
• To resolve the inherent mathematical ambiguities in amplitude analysis for π⁺π⁻ and K⁺K⁻ systems using angular momentum decomposition and polynomial root analysis.
• To model the mass dependence of partial-wave intensities using physical parametrizations, including dynamic-width Breit-Wigner functions and non-resonant phase-space components.
• To identify dominant resonant contributions and their interference patterns in the K⁺K⁻ system, particularly in the scalar and tensor wave channels.
• To provide a foundation for resolving the controversial scalar meson spectrum through combined analysis of multiple final states.

Proposed method

• Conduct a partial-wave analysis (PWA) of centrally produced π⁺π⁻ and K⁺K⁻ systems using a 10 MeV/c² wide binning in invariant mass.
• Apply an extended maximum-likelihood fit to model the angular distribution of decay products in the two-pseudoscalar center-of-mass frame using spherical harmonics.
• Resolve eight mathematically equivalent solutions for S, P, and D waves via analytic continuation of roots of a fourth-order polynomial in angular variables.
• Use physical constraints—such as threshold behavior and dominance of S-wave at low mass—to select the single physical solution for K⁺K⁻ analysis.
• Parametrize mass-dependent intensities using relativistic Breit-Wigner functions for resonances and a two-body phase space with exponential damping for non-resonant contributions.
• Perform a χ² fit to both real and imaginary parts of spin-density matrix elements to extract physical parameters of resonant and non-resonant components.

Experimental results

Research questions

• RQ1 Which of the eight mathematically equivalent solutions in the partial-wave amplitude analysis corresponds to the physical solution for the π⁺π⁻ and K⁺K⁻ systems?
• RQ2 How can the mass dependence of partial-wave intensities in the K⁺K⁻ system be accurately parametrized using physical models?
• RQ3 What resonant states contribute significantly to the S-wave and D-wave amplitudes in the K⁺K⁻ system above 1.05 GeV/c²?
• RQ4 To what extent do interference effects between resonant and non-resonant components influence the extracted resonance parameters?
• RQ5 Can the combined analysis of charged and neutral final states (e.g., π⁰π⁰, ηη, K₀ˢK₀ˢ) help resolve ambiguities in the scalar meson sector?

Key findings

• The physical solution for the K⁺K⁻ system is uniquely identified by the dominance of the S-wave at threshold and negligible P-wave intensity above the φ(1020) resonance.
• The D-wave intensity in K⁺K⁻ is well described by two resonances: f₂(1270) and f₂′(1525), with no need for an additional f₂(2150) state.
• Three resonant contributions are required in the S-wave: f₀(1500), f₀(1710), and a broad f₀(1370), which dominates the non-resonant component due to strong interference.
• The f₀(1370) resonance strength is highly sensitive to the parametrization of the non-resonant component and may be affected by the f₀(980) below the analysis threshold.
• Large correlations between the f₂(1270) parameters in the D-wave and the f₀(1370) in the S-wave suggest potential systematic uncertainties in the extracted Breit-Wigner parameters.
• The phase relations and interference patterns extracted with unprecedented precision provide critical input for resolving the scalar meson spectrum.