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Study of the doubly charmed tetraquark $T_{cc}^{+}$

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Abstract

An exotic narrow state in the $D^0D^0\pi^+$ mass spectrum just below the $D^{*+}D^0$ mass threshold is studied using a data set corresponding to an integrated luminosity of 9 fb$^{-1}$ acquired with the LHCb detector in proton-proton collisions at centre-of-mass energies of 7, 8 and 13 TeV. The state is consistent with the ground isoscalar $T^+_{cc}$ tetraquark with a quark content of $cc\bar{u}\bar{d}$ and spin-parity quantum numbers $\mathrm{J}^{\mathrm{P}}=1^+$. Study of the $DD$ mass spectra disfavours interpretation of the resonance as the isovector state. The decay structure via intermediate off-shell $D^{*+}$ mesons is confirmed by the $D^0\pi^+$ mass distribution. The mass of the resonance and its coupling to the $D^{*}D$ system are analysed. Resonance parameters including the pole position, scattering length, effective range and compositeness are measured to reveal important information about the nature of the $T^+_{cc}$ state. In addition, an unexpected dependence of the production rate on track multiplicity is observed.

Figures and captions

{\bf Distribution of $ D ^0$ $ D ^0$ $\pi ^+$ mass}. Distribution of $ D ^0$ $ D ^0$ $\pi ^+$ mass where the contribution of the nondash-$ D ^0 $ background has been statistically subtracted. The result of the fit described in the text is overlaid. Uncertainties on the data points are statistical only and represent one standard deviation, calculated as a sum in quadrature of the assigned weights from the backgrounddash-subtraction procedure.

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{\bf Likelihood profile for the $\left|g\right|$ parameter.} Likelihood profile for the absolute value of the coupling constant $g$ from the fit to the backgrounddash-subtracted $ D ^0 D ^0 \pi ^+ $ mass spectrum with a model based on the $\mathfrak{F}^{\mathrm{U}}$ signal profile.

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{\bf Mass distribution for $ D ^0$ $\pi ^+$ pairs. } Mass distribution for $ D ^0$ $\pi ^+$ pairs from selected $ D ^0 D ^0 \pi ^+ $ candidates with a mass below the $ D ^{*+} D ^0 $ mass threshold with nondash- $ D ^0$ background subtracted. The overlaid fit result is described in the text. The background component vanishes in the fit. Uncertainties on the data points are statistical only and represent one standard deviation, calculated as a sum in quadrature of the assigned weights from the backgrounddash-subtraction procedure.

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{\bf Mass distributions for selected $ D ^0 D ^0 $, $ D ^+ D ^0 $ $ D ^+ D ^+ $ and $ D ^+ D ^0 \pi ^+ $ combinations. } (Top) $ D $ $ D $ and $ D D \pi ^+ $ mass distributions for selected (left) $ D ^0$ $ D ^0$ and (right) $ D ^+$ $ D ^0$ candidates with the nondash- $ D $ background subtracted. The overlaid fit results are described in the text. For visibility the $ { T _{ c c }^+} \rightarrow D ^+ D ^0 \pi ^0 $ is stacked on top of the $ { T _{ c c }^+} \rightarrow D ^+ D ^0 \gamma $ component. (Bottom) Mass distributions for selected (left) $ D ^+$ $ D ^+$ and (right) $ D ^+$ $ D ^0$ $\pi ^+$ candidates with the nondash- $ D $ background subtracted. The vertical coloured band indicates the expected mass for the hypothetical $\hat{ T }^{++}_{ c c }$ state. The overlaid fit results with backgrounddash-only functions are described in the text. Uncertainties on the data points are statistical only and represent one standard deviation, calculated as a sum in quadrature of the assigned weights from the backgrounddash-subtraction procedure.

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{\bf Mass distributions for selected $ D ^+$ $ D ^+$ and $ D ^+$ $ D ^0$ $\pi ^+$ candidates. } Mass distributions for selected (left) $ D ^+$ $ D ^+$ and (right) $ D ^+$ $ D ^0$ $\pi ^+$ candidates with the nondash- $ D $ background subtracted. The vertical coloured band indicates the expected mass for the hypothetical $\hat{ T }^{++}_{ c c }$ state. The overlaid fit results with backgrounddash-only functions are described in the text. Uncertainties on the data points are statistical only and represent one standard deviation, calculated as a sum in quadrature of the assigned weights from the backgrounddash-subtraction procedure.

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{\bf Complex plane of the $\updelta \sqrt{s}$ variable. } Complex plane of the $\updelta \sqrt{s}$ variable. The dashed red line shows the allowed region for large $\left| g\right|$ values. The filled red circle indicates the best estimate for the pole location and the filled regions show $1\upsigma$ and $2\upsigma$ confidence regions. Open blue and green circles show the branch points corresponding to the $ D ^{*+} D ^0 $ and $ D ^{*0} D ^+ $ channels, respectively, and the corresponding blue and green lines indicate branch cuts. Three other branch points at $\sqrt{s}$ of $m_{ D ^0 }+m_{ D ^+ }$, $m_{ D ^0 }+m_{ D ^+ }+m_{\pi ^0 }$ and $2m_{ D ^0 }+m_{\pi ^+ }$, corresponding to the openings of the $ D ^0 D ^+ \gamma$, $ D ^0 D ^+ \pi ^0 $ and $ D ^0 D ^0 \pi ^+ $ decay channels, are outside of the displayed region.

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{\bf Track multiplicity and transverse momentum distributions.} (left) Backgrounddash-subtracted distributions for the multiplicity of tracks reconstructed in the vertex detector for (red circles) $ { T _{ c c }^+} \rightarrow D ^0 D ^0 \pi ^+ $ signal, lowdash-mass (blue open squares) $ D ^0 \overline{ D } {}^0 $ and (green filled diamonds) $ D ^0 D ^0 $ pairs. The binning scheme is chosen to have an approximately uniform distribution for $ D ^0$ $\overline{ D } {}^0$ pairs. The distributions for the $ D ^0 \overline{ D } {}^0 $ and $ D ^0 D ^0 $ pairs are normalised to the same yields as the $ { T _{ c c }^+} \rightarrow D ^0 D ^0 \pi ^+ $ signal. (right) Background-subtracted transverse momentum spectra for (red circles) $ { T _{ c c }^+} \rightarrow D ^0 D ^0 \pi ^+ $ signal, (blue open squares) low-mass $ D ^0 \overline{ D } {}^0 $ and (green filled diamonds) $ D ^0 D ^0 $ pairs. The binning scheme is chosen to have an approximately uniform distribution for $ D ^0$ $\overline{ D } {}^0$ pairs. The distributions for the $ D ^0 \overline{ D } {}^0 $ and $ D ^0 D ^0 $ pairs are normalised to the same yields as $ { T _{ c c }^+} \rightarrow D ^0 D ^0 \pi ^+ $ signal. For better visualisation, the points are slightly displaced from the bin centres. For better visualisation, the points are slightly displaced from the bin centres. Uncertainties on the data points are statistical only and represent one standard deviation,

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{\bf Transverse momentum spectra.} Background-subtracted transverse momentum spectra for (red circles) $ { T _{ c c }^+} \rightarrow D ^0 D ^0 \pi ^+ $ signal, (blue open squares) low-mass $ D ^0 \overline{ D } {}^0 $ and (green filled diamonds) $ D ^0 D ^0 $ pairs. The binning scheme is chosen to have an approximately uniform distribution for $ D ^0$ $\overline{ D } {}^0$ pairs. The distributions for the $ D ^0 \overline{ D } {}^0 $ and $ D ^0 D ^0 $ pairs are normalised to the same yields as $ { T _{ c c }^+} \rightarrow D ^0 D ^0 \pi ^+ $ signal. For better visualisation, the points are slightly displaced from the bin centres. Uncertainties on the data points are statistical only and represent one standard deviation.

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{\bf Mass distributions for $ D ^0$ $ D ^0$ and $ D ^0$ $\overline{ D } {}^0$ candidates.} Backgrounddash-subtracted $ D ^0$ $ D ^0$ and $ D ^0$ $\overline{ D } {}^0$ mass distributions. The neardash-threshold enhancement in the $ D ^0 D ^0 $ channel corresponds to partially reconstructed ${{ T _{ c c }^+} \rightarrow D ^0 D ^0 \pi ^+ }$ decays, while in the $ D ^0 \overline{ D } {}^0 $ channel the threshold enhancement corresponds to partially reconstructed $\chi _{ c 1} (3872)\rightarrow D ^0 \overline{ D } {}^0 \pi ^0 $ decays. The $ D ^0 \overline{ D } {}^0 $ mass distribution is zerodash-suppressed for better visualisation. Uncertainties on the data points are statistical only and represent one standard deviation, calculated as a sum in quadrature of the assigned weights from the backgrounddash-subtraction procedure.

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Caption

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{\bf{Two-dimensional mass distributions for selected $ D ^0 D ^0 \pi ^+ $, $ D ^0 D ^0 $ and $ D ^0 D ^+ $ combinations.}} Twodash-dimensional mass distributions for $ D ^0 $ and $ D ^+ $ candidates from selected (a) $ D ^0 D ^0 \pi ^+ $, (b) $ D ^0 D ^0 $ and (c) $ D ^0 D ^+ $ combinations. $ K _{1/2}$ and $\pi _{1/2}$ correspond to daughters of the first/second $ D ^0$ candidate in $ D ^0 D ^0 $ and $ D ^0 D ^0 \pi ^+ $ final states.

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{\bf Mass distributions for $ D ^0 D ^0 \pi ^+ $ combinations with fake $ D ^0$ candidates.} Mass distributions for $ D ^0 D ^0 \pi ^+ $ combinations with (a) one true and one fake $ D ^0$ candidate, (b) two fake $ D ^0 $ candidates and (c) at least one fake $ D ^0 $ candidate. Results of the fits with backgrounddash-only functions are overlaid. Uncertainties on the data points are statistical only and represent one standard deviation, calculated as a sum in quadrature of the assigned weights from the backgrounddash-subtraction procedure.

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{\bf{Mass distributions for $ D ^0$ $ D ^0$ $\pi ^+$ and $ D ^0$ $\overline{ D } {}^0$ $\pi ^-$ candidates.}} Backgrounddash-subtracted $ D ^0$ $ D ^0$ $\pi ^+$ and $ D ^0$ $\overline{ D } {}^0$ $\pi ^-$ mass distributions. Uncertainties on the data points are statistical only and represent one standard deviation, calculated as a sum in quadrature of the assigned weights from the backgrounddash-subtraction procedure.

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{\bf{Mass distributions for $ D ^0$ $ D ^+$ and $ D ^0$ $ D ^-$ candidates.}} Backgrounddash-subtracted $ D ^0$ $ D ^+$ and $ D ^0$ $ D ^-$ mass distributions. Uncertainties on the data points are statistical only and represent one standard deviation, calculated as a sum in quadrature of the assigned weights from the backgrounddash-subtraction procedure.

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{\bf{Threedash-body phasedash-space functions $\varrho_f(s)$.}} Threedash-body phasedash-space functions $\varrho_f(s)$ with (left) linear and (right) logarithmic vertical-axis scale: (red) $ { T _{ c c }^+} \rightarrow D ^0 D ^0 \pi ^+ $, (blue) $ { T _{ c c }^+} \rightarrow D ^+ D ^0 \pi ^0 $ and (green) $ { T _{ c c }^+} \rightarrow D ^+ D ^0 \gamma $. The sum, $\varrho_{\mathrm{tot}}(s)$, is shown with a black line. The twodash-body $ D ^* D $ phase-space shapes are shown by the dashed lines and are different from the $\varrho_f(s)$ functions only in the vicinity of the thresholds or below them. Vertical dash-dotted line indicates $\sqrt{s^*}=3.9\text{ Ge V} $.

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{\bf{Function $\xi(s)$.}} Function $\xi(s)$ with (left) linear and (right) logarithmic vertical-axis scale is shown with a red line. The threedash-body phase-space function $\varrho_{\mathrm{tot}}(s)$ is shown for comparison with a dashed line.

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{\bf{Scaling behaviour of the $\mathfrak{F}^{\mathrm{U}}$ profile.}} The full width at half maximum $\mathfrak{w}$ as a function of the $\left|g\right|$ parameter for a fixed value of the $\updelta m_{\mathrm{U}}$ parameter $\updelta m_{\mathrm{U}}=-359\text{ ke V /}c^2 $. The horizontal dashed blue line indicates the value of $\mathfrak{w}$ corresponding to the best fit parameters.

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{\bf{Unitarised three-body Breitdash--Wigner function $\mathfrak{F}^{\mathrm{U}}$.}} Unitarised threedash-body Breitdash--Wigner function $\mathfrak{F}^{\mathrm{U}}$ for ${ { T _{ c c }^+} \rightarrow D ^0 D ^0 \pi ^+ }$ decays (red line) for a large value of the $\left|g\right|$ parameter and $\updelta m_{\mathrm{U}}=-359\text{ ke V /}c^2 $, normalized to unity for $\updelta m_{ D ^0 D ^0 \pi ^+ }=\updelta m_{\mathrm{U}}$. Top inset shows a zoomed region with overlaid (blue dashed line) { {singledash-pole}} profile with $\sqrt{\hat{s}}=\mathfrak{m}-\tfrac{i}{2}\mathfrak{w}$, and (thin green line) threedash-body Breitdash--Wigner profile with $\left|g\right|=5.1\text{ Ge V} $. Bottom inset shows the $\mathfrak{F}^{\mathrm{U}}$ profile in log-scale. Vertical dashed lines indicate (leftdash-todash-right) $ D ^{*+} D ^0 $ and $ D ^{*0} D ^+ $ mass thresholds.

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{\bf{Comparison of the $\mathcal{A}_{\mathrm{U}}$ and $\mathcal{A}_{\mathrm{NR}}$ amplitudes.}} The real and imaginary parts of the inverse $\mathcal{A}_{\mathrm{U}}$ and $\mathcal{A}_{\mathrm{NR}}$ amplitudes. The yellow band correspond to the pole position and vertical dashed lines show the $ D ^{*+} D ^0 $ and $ D ^{*0} D ^+ $ mass thresholds.

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{\bf{Two-dimensional $ D ^0 \pi ^+ $ mass distribution.}} Backgrounddash-sub\-tracted twodash-dimensional $ D ^0 \pi ^+ $ mass distribution for the $ D ^0 D ^0 \pi ^+ $ events with $\updelta m_{ D ^0 D ^0 \pi ^+ }\le0$. Dashed vertical and horizontal lines indicate the known $ D ^{*+} $ mass. Red and dashed blue lines show the boundary corresponding to $\updelta m_{ D ^0 D ^0 \pi ^+ }=0$ and $\updelta m_{ D ^0 D ^0 \pi ^+ }=-359\text{ ke V /}c^2 $, respectively.

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Animated gif made out of all figures.

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Tables and captions

Tetra- and pentaquark candidates and their plausible valence quark content.

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Signal yield, $N$, and the resonance mass parameter with respect to the $ D ^{*+} D ^0 $ mass threshold, $\updelta m_{\mathrm{U}}$, obtained from the fit with a model based on the $\mathfrak{F}^{\mathrm{U}}$ signal profile. Uncertainties are statistical only.

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Mode relative to the $ D ^{*+}$ $ D ^0$ mass threshold, $\updelta\mathfrak{m}$, and FWHM, $\mathfrak{w}$, for the $\mathfrak{F}^{\mathrm{U}}$ and $\mathfrak{F}^{\mathrm{BW}}$ signal profiles. Uncertainties are statistical only.

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Mean and root mean square (RMS) values for the $\updelta m_{\mathrm{BW}}$, $\Gamma_{\mathrm{BW}}$ and $\updelta m_{\mathrm{U}}$ parameters obtained from pseudoexperiments produced as a consistency check.

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Systematic uncertainties for the $\updelta m_{\mathrm{U}}$ parameter. The total uncertainty is calculated as the sum in quadrature of all components.

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Signal and background yields, $N_S$ and $N_B$, from the fits to $ D D $ mass spectra. The uncertainties are statistical only.

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Supplementary Material [file]

Supplementary material full pdf

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Created on 22 March 2024.