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Amplitude analysis of the $D^+ \to \pi^-\pi^+\pi^+$ decay and measurement of the $\pi^-\pi^+$ S-wave amplitude

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Abstract

An amplitude analysis of the $D^+ \to \pi^- \pi^+ \pi^+$ decay is performed with a sample corresponding to $1.5\rm fb^{-1}$ of integrated luminosity of $pp$ collisions at a centre-of-mass energy $\sqrt{s}=8$ TeV collected by the LHCb detector in 2012. The sample contains approximately six hundred thousand candidates with a signal purity of $95\%$. The resonant structure is studied through a fit to the Dalitz plot where the $\pi^- \pi^+$ S-wave amplitude is extracted as a function of $\pi^-\pi^+$ mass, and spin-1 and spin-2 resonances are included coherently through an isobar model. The S-wave component is found to be dominant, followed by the $\rho(770)^0\pi^+$ and $f_2(1270)\pi^+$ components. A small contribution from the $\omega(782)\to\pi^-\pi^+$ decay is seen for the first time in the $D^+ \to \pi^- \pi^+ \pi^+$ decay.

Figures and captions

Leading diagram for the $ D ^+ \rightarrow \pi ^- \pi ^+ \pi ^+ $ decay. Possible rescattering effects are represented by the $a, b$ meson pair.

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Invariant-mass distribution of $ D ^+ \rightarrow \pi ^- \pi ^+ \pi ^+ $ candidates after final selection, with the fit result superimposed (blue solid line). The dashed red line and the solid gray line correspond to the signal and background components of the fit, respectively.

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Dalitz plot distribution of the final $ D ^+ \rightarrow \pi ^- \pi ^+ \pi ^+ $ sample. The lines in the interval $[0.235, 0.250]\text{ Ge V} ^2$ correspond to the veto applied to remove $ D ^+ \rightarrow K ^0_{\mathrm{S}} \pi ^+ $ decays.

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Models for (left) background distribution and (right) signal efficiency across the Dalitz plot, where the $z$-axis scale is arbitrary.

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Dalitz plot projections of (top left) $s_{\pi ^- \pi ^+ }$, (top right) $s_{23}$, (middle left) $s_{\rm low}$, and (middle right) $s_{\rm high}$ projections, where the (red) points are data and the (blue) line is the fit model result, with the fit normalised residuals displayed in the bottom plot.

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Fitted (left) magnitude and (right) phase of the $\pi ^-$ $\pi ^+$ S-wave amplitude with statistical uncertainties as the blue bars and the total uncertainties (combined statistical, experimental and model systematics) as the green bands.

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Animated gif made out of all figures.

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Tables and captions

Spin-dependent Blatt-Weisskopf barrier factors.

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Dalitz fit results for magnitudes, phases and fit fractions (%) of the spin-1 and spin-2 components, and the S-wave fit fraction. The uncertainties quoted are, in order, statistical, experimental systematics, and model systematics.

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Dalitz fit results for the interference fit fractions (%) (statistical uncertainties only).

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Fitted magnitude and phase of the S-wave amplitude at each $\pi ^-$ $\pi ^+$ mass knot, relative to the $\rho(770)^0\pi ^+ $ channel. The uncertainties quoted are, in order, statistical, experimental systematics and model systematics.

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Supplementary Material [file]

Supplementary material full pdf

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This ZIP file contains supplementary material for the publication LHCb-PAPER-2022-016. The files are: Supplementary.pdf : An overview of the extra figures *.pdf, *.png, *.eps : The figures in various formats

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Created on 20 April 2024.