Resonance Production and $\pi\pi$ S-wave in $\pi^- + p \rightarrow \pi^- \pi^- \pi^+ + p_{recoil}$ at 190 GeV/c
- Adolph, C et al
- arXiv:1509.00992CERN-PH-EP-2015-233
| Diffractive dissociation of a beam pion on a target proton into the three-pion final state. The figure shows the excitation of an intermediate resonance $X^-$ via Pomeron exchange and its subsequent decay into $3\pi$. |
| \colorPlot Simplified scheme of the diffractive trigger. The main components are the beam trigger, which selects beam particles, and the RPD, which triggers on slow charged particles leaving the target. The veto system (red) rejects uninteresting events and consists of three parts: The veto hodoscopes, the sandwich, and the beam veto. |
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| The decay of $X^-$, as described in the isobar model, is assumed to proceed via an intermediate \twoPi state $\xi$, the so-called isobar. |
| \colorPlot Definition of the Gottfried-Jackson reference frame~(GJ) in the $X$ rest system and of the helicity reference frame~(HF) in the $\xi^0$ rest system as they are used to analyze the angular distributions of the decays $X^- \to \xi^0 + \pi^-$ and $\xi^0 \to \pi^- + \pi^+$, respectively. Unit vectors are indicated by a circumflex. |
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| width=0.37\textwidth\colorPlot Example of a $3\pi$ angular distribution observed in the mass region \SIvalRange{1.6}{\mThreePi}{1.7}{\GeVcc} around the \PpiTwo indicated by vertical red lines in the upper left panel. The main decay of this resonance is through the \PfTwo isobar, which is a $\JPC = 2^{++}$ state, decaying into \twoPi in a $D$-wave. The \PfTwo and the bachelor pion are in a relative $S$ or $D$-wave.Caption not extracted |
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| Parametrization of the \pipiS isobar amplitude based on the $M$~solution described in \refCite{au:1986vs}. Panel~(a) shows the intensity, (b)~the phase, and (c)~the corresponding \Argand. The open circles in the latter are evenly spaced in \mTwoPi in \SI{20}{\MeVcc} intervals. Arbitrary units are denoted by \enquote{a.~u.}. |
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| \colorPlot Correlation of the reduced four-momentum transfer squared \tpr and the invariant mass \mThreePi of the $3\pi$ system in the analyzed kinematic region. The partial-wave analysis is performed independently in 100~equidistant \mThreePi bins with a width of \SI{20}{\MeVcc}, each of which is subdivided into eleven non-equidistant \tpr bins. The latter are indicated by the dashed horizontal lines. The numerical values for the \tpr bins are listed in \cref{tab:t-bins}. |
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| Example for a nonresonant production process for the $3\pi$ final state as proposed by Deck~\cite{Deck:1964hm}. |
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| Intensity of the coherent sum of all $\PfZero[980]\,\pi$ waves with positive reflectivity, summed over all \tpr bins. |
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| \colorPlot Distributions of the five phase-space variables used to calculate the decay amplitudes shown for different $3\pi$ mass bins in the region \SIvalRange{0.127}{\tpr}{0.144}{\GeVcsq}. Each distribution is shown for real data (blue points) and for weighted Monte Carlo events (red bands), which are generated according to the fit result. Each distribution is normalized to its maximum deviation from its average $y$~value. Along the ordinate, the average $y$~values for the distributions (indicated by gray lines) are shifted equidistantly with respect to one another. The $3\pi$ mass ranges from \SIrange{1.0}{2.4}{\GeVcc} and is subdivided into \SI{40}{\MeVcc} wide bins. The central values of selected $3\pi$ mass bins are given as labels in the \cosThetaGJ distribution. |
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| \colorPlot Same as \cref{fig:wMC_low_t_overview}, but for the high-\tpr region \SIvalRange{0.449}{\tpr}{0.724}{\GeVcsq}. |
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| captionskip=4pt\mThreePi spectrum for high values of \tpr. |
| captionskip=4pt\tpr spectrum for medium values of \mThreePi. |
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| \colorPlot Detection efficiency for \threePi phase-space events in different regions of \mThreePi and \tpr. Each graph shows the detection efficiency as a function of the angles, \cosThetaGJ (abscissa, from $-1$ to $+1$) and \phiGJ (ordinate, from \SI{-180}{\degree} to $+\SI{180}{\degree}$), of the isobar in the Gottfried-Jackson frame. |
| \colorPlot Same as \cref{fig:acceptance_phase_space_GJ}, but for the detection efficiency as a function of the angles, \cosThetaHF and \phiHF, of the $\pi^-$ in the helicity frame. |
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| The \tpr-summed intensities of partial waves with $\JPC = 0^{-+}$ and positive reflectivity. |
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| The \tpr-summed intensities of partial waves with $\JPC = 1^{++}$ and positive reflectivity. |
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| The \tpr-summed intensities of partial waves with $\JPC = 1^{++}$ and positive reflectivity. |
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| The \tpr-summed intensity of the partial wave with spin-exotic $\JPC = 1^{-+}$ and positive reflectivity. |
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| The \tpr-summed intensities of partial waves with $\JPC = 2^{-+}$ and positive reflectivity. |
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| The \tpr-summed intensities of partial waves with $\JPC = 3^{++}$ and positive reflectivity. |
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| The \tpr-summed intensities of partial waves with $\JPC = 4^{++}$ and positive reflectivity. |
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| The \tpr-summed intensities of partial waves with $\JPC = 5^{++}$ and positive reflectivity. |
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| The \tpr-summed intensities of partial waves with negative reflectivity. |
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