Amplitude analysis of the $D_s^+ \to \pi^- \pi^+ \pi^+$ decay

Information

LHCb-PAPER-2022-030
CERN-EP-2022-173
arXiv:2209.09840 [PDF]

(Submitted on 20 Sep 2022)
JHEP 07 (2023) 204
Inspire 2154232

Tools

Abstract

A Dalitz plot analysis of the $D_s^+ \to \pi^- \pi^+ \pi^+$ decay is presented. The analysis is based on proton-proton collision data recorded by the LHCb experiment at a centre-of-mass energy of $8$ TeV and corresponding to an integrated luminosity of $1.5 fb^{-1}$. The resonant structure of the decay is obtained using a quasi-model-independent partial-wave analysis, in which the $\pi^+\pi^-$ S-wave amplitude is parameterised as a generic complex function determined by a fit to the data. The S-wave component is found to be dominant, followed by the contribution from spin-2 resonances and a small contribution from spin-1 resonances. The latter includes the first observation of the $D_s^+ \to \omega(782) \pi^+$ channel in the $D_s^+ \to \pi^- \pi^+ \pi^+$ decay. The resonant structures of the $D_s^+ \to \pi^- \pi^+ \pi^+$ and $D^+ \to \pi^- \pi^+ \pi^+$ decays are compared, providing information about the mechanisms for the hadron formation in these decays.

Figures and captions

Dominant tree-level diagrams leading to the (left) $D^+_s\rightarrow \pi^-\pi^+\pi^+$ and (right) $ D ^+ \rightarrow \pi ^- \pi ^+ \pi ^+ $ decays. The resonances are produced from an $s\bar s$ pair in the $D^+_s\rightarrow \pi^-\pi^+\pi^+$ decay and from a $d\bar d$ pair in the $ D ^+ \rightarrow \pi ^- \pi ^+ \pi ^+ $ decay. For both decays, the annihilation diagram is suppressed.	Fig1.pdf [296 KiB] HiDef png [194 KiB] Thumbnail [102 KiB] *.C file
Invariant-mass distribution of $ D ^+_ s \rightarrow \pi ^- \pi ^+ \pi ^+ $ candidates after the final selection, with the fit result superimposed.	Fig2.pdf [36 KiB] HiDef png [197 KiB] Thumbnail [160 KiB] *.C file
(Top) Dalitz plot from selected $ D ^+_ s \rightarrow \pi ^- \pi ^+ \pi ^+ $ candidates in the signal region. The colour scale indicates the density of candidates. (Bottom) Perspective view of the Dalitz plot.	Fig3a.pdf [102 KiB] HiDef png [652 KiB] Thumbnail [324 KiB] *.C file
	Fig3b.pdf [1 MiB] HiDef png [872 KiB] Thumbnail [353 KiB] *.C file
(Left) efficiency variation over the Dalitz plot and (right) background model for $ D ^+_ s \rightarrow \pi ^- \pi ^+ \pi ^+ $ decays.	Fig4a.pdf [217 KiB] HiDef png [503 KiB] Thumbnail [269 KiB] *.C file
	Fig4b.pdf [213 KiB] HiDef png [522 KiB] Thumbnail [266 KiB] *.C file
{The folded Dalitz plot projections (left) $s_{high}$ and (right) $s_{low}$}.	Fig5a.pdf [18 KiB] HiDef png [143 KiB] Thumbnail [127 KiB] *.C file
	Fig5b.pdf [19 KiB] HiDef png [150 KiB] Thumbnail [134 KiB] *.C file
(Left) The unfolded Dalitz plot projection $s_{13}$; (right) the folded distribution of the normalised residuals across the Dalitz plot.	Fig6a.pdf [19 KiB] HiDef png [143 KiB] Thumbnail [124 KiB] *.C file
(Left) Magnitude and (right) phase of the S-wave amplitude as a function of $m(\pi^+\pi^-)$. The uncertainties are statistical.	Fig7a.pdf [15 KiB] HiDef png [100 KiB] Thumbnail [97 KiB] *.C file
	Fig7b.pdf [15 KiB] HiDef png [99 KiB] Thumbnail [93 KiB] *.C file
Argand plot of the $\pi^+\pi^-$ S-wave amplitude. The values of $m(\pi^+\pi^-)$ at the edge of each interval are indicated next to the corresponding experimental point. The amplitude starts at the point circled in red and undergoes two counterclockwise circles.	Fig8.pdf [18 KiB] HiDef png [224 KiB] Thumbnail [184 KiB] *.C file
(Left) Dalitz plot of the $ D ^+_ s \rightarrow \pi ^- \pi ^+ \pi ^+ $ and (right) $ D ^+ \rightarrow \pi ^- \pi ^+ \pi ^+ $ decays [4]. The colour scale indicates the density of candidates.	Fig3a.pdf [102 KiB] HiDef png [652 KiB] Thumbnail [324 KiB] *.C file
	Fig9b.pdf [98 KiB] HiDef png [1 MiB] Thumbnail [421 KiB] *.C file
Dominant amplitudes for the $ D ^+ \rightarrow \pi ^- \pi ^+ \pi ^+ $ and $ D ^+_ s \rightarrow \pi ^- \pi ^+ \pi ^+ $ decays. The scalar resonances are produced from rescattering of the two pseudoscalar mesons $ab$ ($a'b'$) formed by a $q\bar q$ pair from the vacuum and the $d\bar d$ ($s\bar s$) pair from the decay of the $c$ quark.	Fig10.pdf [301 KiB] HiDef png [163 KiB] Thumbnail [86 KiB] *.C file
(Left) Magnitude and (right) phase of the $\pi ^-$ $\pi ^+$ S-wave amplitude for the $ D ^+ \rightarrow \pi ^- \pi ^+ \pi ^+ $ (black line) and $ D ^+_ s \rightarrow \pi ^- \pi ^+ \pi ^+ $ decays (blue dot).	Fig11a.pdf [18 KiB] HiDef png [169 KiB] Thumbnail [160 KiB] *.C file
	Fig11b.pdf [17 KiB] HiDef png [144 KiB] Thumbnail [132 KiB] *.C file
(Left) Comparison of the $\pi^+\pi^-$ S-wave phase from $ D ^+_ s \rightarrow \pi ^- \pi ^+ \pi ^+ $ decays and the phase from $\pi^+\pi^-\rightarrow \pi^+\pi^-$ scattering. Data on $\pi^+\pi^-\rightarrow \pi^+\pi^-$ scattering above 0.6 $\text{ Ge V}$ are from a re-analysis [5] of original data from [34], and below 0.4 $\text{ Ge V}$ are from $K_{e4}$ decays [35]. (Right) The S-wave phase from the $ D ^+_ s \rightarrow \pi ^- \pi ^+ \pi ^+ $ decay is shifted by 210$^{\circ}$.	Fig12a.pdf [18 KiB] HiDef png [119 KiB] Thumbnail [116 KiB] *.C file
	Fig12b.pdf [18 KiB] HiDef png [138 KiB] Thumbnail [140 KiB] *.C file
Comparison of $\pi ^+$ $\pi ^-$ S-wave amplitude from the $ D ^+_ s \rightarrow \pi ^- \pi ^+ \pi ^+ $ decay with previous results from BaBar [6] and BESIII [7].	Fig13.pdf [28 KiB] HiDef png [298 KiB] Thumbnail [152 KiB] *.C file
Animated gif made out of all figures.	PAPER-2022-030.gif Thumbnail

Tables and captions

Masses and widths of the resonances used in the fit [2]. Quoted uncertainties are used to estimate systematic uncertainties.	Table_1.pdf [60 KiB] HiDef png [111 KiB] Thumbnail [40 KiB] tex code
Spin-dependent Blatt--Weisskopf barrier factors. The normalisation ensures that the barrier factors are equal to unity at the resonance mass.	Table_2.pdf [66 KiB] HiDef png [27 KiB] Thumbnail [13 KiB] tex code
Results from the default fit. The row "combined" has the combined fit fractions of the $\rho(1450)^0$ and $\rho(1700)^0$ contributions, including the interference between them. The uncertainties are statistical.	Table_3.pdf [65 KiB] HiDef png [87 KiB] Thumbnail [41 KiB] tex code
Results from the default fit. Interference fit fractions (%) between the resonant amplitudes. The uncertainties are statistical.	Table_4.pdf [59 KiB] HiDef png [98 KiB] Thumbnail [44 KiB] tex code
Summary of the systematic uncertainties on the magnitudes and phases of the complex coefficients from the P- and D-wave amplitudes. The column "total exp." is the sum in quadrature of the first four columns. For comparison, the statistical uncertainties are included in the last column.	Table_5.pdf [55 KiB] HiDef png [97 KiB] Thumbnail [42 KiB] tex code
Systematic uncertainties on the fit fractions (%). The combined fit fractions of the $\rho(1450)^{0}\pi^+$ and $\rho(1700)^{0}\pi^+$ are quoted in the row "combined".	Table_6.pdf [56 KiB] HiDef png [98 KiB] Thumbnail [47 KiB] tex code
Final results of the $ D ^+_ s \rightarrow \pi ^- \pi ^+ \pi ^+ $ Dalitz plot fit. The uncertainties are statistical, experimental systematic and associated to the decay amplitude model, respectively.	Table_7.pdf [64 KiB] HiDef png [132 KiB] Thumbnail [65 KiB] tex code
Resonant structure of the $ D ^+_ s \rightarrow \pi ^- \pi ^+ \pi ^+ $ decay from this analysis compared to previous determinations from BaBar [6] and BESIII [7]. The fit fractions are given in per cent. The statistical and systematic uncertainties are added in quadrature.	Table_8.pdf [62 KiB] HiDef png [90 KiB] Thumbnail [46 KiB] tex code
Magnitude and phase of the S-wave amplitude as a function of $\pi ^-$ $\pi ^+$ invariant mass. The uncertainties are statistical, experimental and model, respectively. The $\pi^+\pi^-$ invariant mass is expressed in $\text{ Ge V}$ .	Table_9.pdf [60 KiB] HiDef png [528 KiB] Thumbnail [288 KiB] tex code
Resonant structures of the $ D ^+_ s \rightarrow \pi ^- \pi ^+ \pi ^+ $ and $ D ^+ \rightarrow \pi ^- \pi ^+ \pi ^+ $ [4] decays, expressed fit fractions (%). Uncertainties are only statistical.	Table_10.pdf [66 KiB] HiDef png [50 KiB] Thumbnail [25 KiB] tex code