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Observation of a resonant structure near the $D_s^+ D_s^-$ threshold in the $B^+\to D_s^+ D_s^- K^+$ decay

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Abstract

An amplitude analysis of the $B^+\to D_s^+ D_s^- K^+$ decay is carried out to study for the first time its intermediate resonant contributions, using proton-proton collision data collected with the LHCb detector at centre-of-mass energies of 7, 8 and 13 TeV. A near-threshold peaking structure, referred to as $X(3960)$, is observed in the $D_s^+ D_s^-$ invariant-mass spectrum with significance greater than 12 standard deviations. The mass, width and the quantum numbers of the structure are measured to be $3956\pm5\pm10$ MeV, $43\pm13\pm8$ MeV and $J^{PC}=0^{++}$, respectively, where the first uncertainties are statistical and the second systematic. The properties of the new structure are consistent with recent theoretical predictions for a state composed of $c\bar{c}s\bar{s}$ quarks. Evidence for an additional structure is found around 4140 MeV in the $D_s^+ D_s^-$ invariant mass, which might be caused either by a new resonance with the $0^{++}$ assignment or by a $J/\psi \phi\leftrightarrow D_s^+ D_s^-$ coupled-channel effect.

Figures and captions

Dalitz-plot distribution for the $ B ^+ \rightarrow D ^+_ s D ^-_ s K ^+ $ decay after background subtraction.

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Background-subtracted invariant-mass distributions (top left) $ m( D ^+_ s D ^-_ s )$ , (top right) $m( D ^+_ s K ^+ )$ and (bottom) $ m( D ^-_ s K ^+ )$ for the $ B ^+ \rightarrow D ^+_ s D ^-_ s K ^+ $ signal. The projections of the fit with the baseline amplitude model are also shown.

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Background-subtracted distributions of the $ D ^+_ s D ^-_ s $ invariant mass of $ B ^+ \rightarrow D ^+_ s D ^-_ s K ^+ $ decays with fit results obtained from (left) two-channel Flatt\'{e}-like and (right) $K$-matrix parameterisations. The fit projections for the $ D ^-_ s $ $ K ^+$ and $ D ^+_ s $ $ K ^+$ invariant-mass spectra look very similar to the baseline model.

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Animated gif made out of all figures.

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Tables and captions

Summary of the main results obtained with the baseline model, where the first uncertainty is statistical and the second systematic. The last column shows the signal significance with (without) the systematic uncertainty included.

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Summary of the systematic uncertainties on the parameters measured in the amplitude analysis. Mass ($M_0$) and width ($\Gamma_0$) are in units of MeV, while fit fraction ($\mathcal{F}$) is in %.

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Main results found in two-channel Flatt\'{e}-like parameterisation, where the coupling strength of the $X(3960)$ state to $ D ^+_ s D ^-_ s $ ($ D ^+ D ^- $) is obtained to be $0.33\pm1.18$ ($0.15\pm0.33$) $\text{ Ge V}$ . Uncertainties are statistical only. The large uncertainty on $\Gamma_0$ for the $X(3960)$ state is due to the large uncertainty on the coupling strengths.

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Main results found from the $K$-matrix fit. Uncertainties are statistical only.

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Created on 09 August 2024.