Peak Locations and Relative Phase of Different Decay Modes of the a_{1} Axial Vector Resonance in Diffractive Production.
We show that a single I=1 spin-parity J^{PC}=1^{++} a_{1} resonance can manifest itself as two separated mass peaks, one decaying into an S-wave ρπ system and the second decaying into a P-wave f_{0}(980)π system, with a rapid increase of the phase difference between their amplitudes arising mainly from the structure of the diffractive production process. This study clarifies questions related to the mass, width, and decay rates of the a_{1} resonance raised by the recent high statistics data of the COMPASS Collaboration on a_{1} production in πN→πππN at high energies.
Meson Spectroscopy at COMPASS
The goal of the COMPASS experiment at CERN is to study the structure and dynamics of hadrons. The two-stage spectrometer used by the experiment has large acceptance and covers a wide kinematic range for charged as well as neutral particles and can therefore measure a wide range of reactions. The spectroscopy of light mesons is performed with negative (mostly $\pi^-$) and positive ($p$, $\pi^+$) hadron beams with a momentum of 190 GeV/$c$. The light-meson spectrum is measured in different final states produced in diffractive dissociation reactions with squared four-momentum transfer $t$ to the target between 0.1 and 1.0 $(\text{GeV}/c)^2$. The flagship channel is the $\pi^-\pi^-\pi^+$ final state, for which COMPASS has recorded the currently world's largest data sample. These data not only allow to measure the properties of known resonances with high precision, but also to observe new states. Among these is a new axial-vector signal, the $a_1(1420)$, with unusual properties. Novel analysis techniques have been developed to extract also the amplitude of the $\pi^-\pi^+$ subsystem as a function of $3\pi$ mass from the data. The findings are confirmed by the analysis of the $\pi^-\pi^0\pi^0$ final state.
Positivity conditions on the spin density matrix: A simple parametrization
A simple parametrization of the spin density matrix $\ensuremath{\rho}$ is given which ensures that $\ensuremath{\rho}$ is a positive, Hermitian matrix which satisfies the parity symmetry conditions. There is a minimal number of parameters and they can vary independently; no complicated constraints on their allowed region of variation are required. A similar parametrization is given for the real part of $\ensuremath{\rho}$. Rank conditions, polarized targets, and angular distributions are also discussed.