$\mathrm{K}^{*}(\mathrm{892})^{0}$ and $\mathrm{\phi(1020)}$ production in p-Pb collisions at $\sqrt{s_{\rm NN}}$ = 8.16 TeV

The ALICE collaboration Acharya, Shreyasi ; Adamova, Dagmar ; Adler, Alexander ; et al.
CERN-EP-2021-200, 2021.
Inspire Record 1946970 DOI 10.17182/hepdata.136309

The production of $\mathrm{K}^{*}(\mathrm{892})^{0}$ and $\mathrm{\phi(1020)}$ resonances has been measured in p-Pb collisions at $\sqrt{s_{\rm NN}}$ = 8.16 TeV using the ALICE detector. Resonances are reconstructed via their hadronic decay channels in the rapidity interval $-$0.5 $<$$y$$<$ 0 and the transverse momentum spectra are measured for various multiplicity classes up to $p_{\rm T}$ = 20 GeV/$c$ for $\mathrm{K}^{*}(\mathrm{892})^{0}$ and $p_{\rm T}$ = 16 GeV/$c$ for $\mathrm{\phi(1020)}$. The $p_{\rm T}$ -integrated yields and mean transverse momenta are reported and compared with previous results in pp, p-Pb and Pb-Pb collisions. The $x_{\mathrm{T}}$ scaling for $\mathrm{K}^{*}(\mathrm{892})^{0}$ and $\mathrm{\phi(1020)}$ resonance production is newly tested in p-Pb collisions and found to hold in the high-$p_{\rm T}$ region at LHC energies. The nuclear modification factors ($R_{\rm pPb}$) as a function of $p_{\rm T}$ for $\mathrm{K}^{*0}$ and $\mathrm{\phi}$ at $\sqrt{s_{NN}}$ = 8.16 TeV are presented along with the new $R_{\rm pPb}$ measurements of $\mathrm{K}^{*0}$, $\mathrm{\phi}$ , $\Xi$, and $\Omega$ at $\sqrt{s_{\rm NN}}$ = 5.02 TeV. At intermediate $p_{\rm T}$ (2-8 GeV/$c$), $R_{\rm pPb}$ of $\Xi$, $\Omega$ show a Cronin-like enhancement, while $\mathrm{K}^{*0}$ and $\mathrm{\phi}$ show no or little nuclear modification. At high $p_{\rm T}$ ($>$ 8 GeV/$c$), the $R_{\rm pPb}$ values of all hadrons are consistent with unity within uncertainties. The $R_{\rm pPb}$ of $\mathrm{K}^{*}(\mathrm{892})^{0}$ and $\mathrm{\phi(1020)}$ at $\sqrt{s_{\rm NN}}$ = 8.16 and 5.02 TeV show no significant energy dependence.

22 data tables

$p_{\mathrm T}$-differential yield of $\frac{\mathrm{K^{*0}} + \overline{\mathrm{K^{*0}}}}{2}$ in p-Pb collisions at $\sqrt{s_{\mathrm{NN}}}~=~$8.16 TeV (NSD).

$p_{\mathrm T}$-differential yield of $\frac{\mathrm{K^{*0}} + \overline{\mathrm{K^{*0}}}}{2}$ in p-Pb collisions at $\sqrt{s_{\mathrm{NN}}}~=~$8.16 TeV (Multiplicity class 0-5%).

$p_{\mathrm T}$-differential yield of $\frac{\mathrm{K^{*0}} + \overline{\mathrm{K^{*0}}}}{2}$ in p-Pb collisions at $\sqrt{s_{\mathrm{NN}}}~=~$8.16 TeV (Multiplicity class 5-10%).

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Version 2
Measurement of prompt $\rm{D_{s}^{+}}$-meson production and azimuthal anisotropy in Pb-Pb collisions at $\sqrt{s_{\rm NN}} = 5.02$ TeV

The ALICE collaboration Acharya, Shreyasi ; Adamova, Dagmar ; Adler, Alexander ; et al.
Phys.Lett.B 827 (2022) 136986, 2022.
Inspire Record 1946931 DOI 10.17182/hepdata.127980

The production yield and angular anisotropy of prompt ${D_s^+}$ mesons were measured as a function of transverse momentum ($p_{ T}$) in Pb-Pb collisions at a centre-of-mass energy per nucleon pair $\sqrt{s_{ NN}} = 5.02$ TeV collected with the ALICE detector at the LHC. ${D_s^+}$ mesons and their charge conjugates were reconstructed at midrapidity ($|y|<0.5$) from their hadronic decay channel ${D_s^+ \to \phi \pi^+}$, with ${\phi \to K^-K^+}$, in the $p_{ T}$ intervals $2<p_{ T}<50$ GeV/$c$ and $2<p_{ T}<36$ GeV/$c$ for the 0-10% and 30-50% centrality intervals. For $p_{ T}>10$ GeV/$c$, the measured ${D_s^+}$-meson nuclear modification factor $R_{ AA}$ is consistent with the one of non-strange D mesons within uncertainties, while at lower $p_{ T}$ a hint for a ${D_s^+}$-meson $R_{ AA}$ larger than that of non-strange D mesons is seen. The enhanced production of ${D_s^+}$ relative to non-strange D mesons is also studied by comparing the $p_{ T}$-dependent ${D_s^+/D^0}$ production yield ratios in Pb-Pb and in pp collisions. The ratio measured in Pb-Pb collisions is found to be on average higher than that in pp collisions in the interval $2<p_{ T} <8$ GeV/$c$ with a significance of 2.3$\sigma$ and 2.4$\sigma$ for the 0-10% and 30-50% centrality intervals. The azimuthal anisotropy coefficient $v_2$ of prompt ${D_s^+}$ mesons was measured in Pb-Pb collisions in the 30-50% centrality interval and is found to be compatible with that of non-strange D mesons. The main features of the measured $R_{ AA}$, ${D_s^+/D^0}$ ratio, and $v_2$ as a function of $p_{ T}$ are described by theoretical calculations of charm-quark transport in a hydrodynamically expanding quark-gluon plasma including hadronisation via charm-quark recombination with light quarks from the medium. The $p_{ T}$-integrated production yield of ${D_s^+}$ mesons is compatible with the prediction of the statistical hadronisation model.

18 data tables

$p_\mathrm{T}$-differential production yield of prompt $\mathrm{D_s^+}$ mesons in the 0-10% centrality class in Pb-Pb collisions at $\sqrt{{s_\mathrm{NN}}}=5.02~\mathrm{{TeV}}$ in the rapidity interval $|y|<0.5$. Branching ratio of $\mathrm{D_s^+\to \phi\pi^+\to K^-K^+\pi^+}$: 0.0224

$p_\mathrm{T}$-differential production yield of prompt $\mathrm{D_s^+}$ mesons in the 0-10% centrality class in Pb-Pb collisions at $\sqrt{{s_\mathrm{NN}}}=5.02~\mathrm{{TeV}}$ in the rapidity interval $|y|<0.5$. Branching ratio of $\mathrm{D_s^+\to \phi\pi^+\to K^-K^+\pi^+}$: 0.0224

$p_\mathrm{T}$-differential production yield of prompt $\mathrm{D_s^+}$ mesons in the 30-50% centrality class in Pb-Pb collisions at $\sqrt{{s_\mathrm{NN}}}=5.02~\mathrm{{TeV}}$ in the rapidity interval $|y|<0.5$. Branching ratio of $\mathrm{D_s^+\to \phi\pi^+\to K^-K^+\pi^+}$: 0.0224

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Investigating charm production and fragmentation via azimuthal correlations of prompt D mesons with charged particles in pp collisions at $\sqrt{s} = 13$ TeV

The ALICE collaboration Acharya, Shreyasi ; Adamova, Dagmar ; Adler, Alexander ; et al.
Eur.Phys.J.C 82 (2022) 335, 2022.
Inspire Record 1946828 DOI 10.17182/hepdata.128823

Angular correlations of heavy-flavour and charged particles in high-energy proton-proton collisions are sensitive to the production mechanisms of heavy quarks and to their fragmentation as well as hadronisation processes. The measurement of the azimuthal-correlation function of prompt D mesons with charged particles in proton-proton collisions at a centre-of-mass energy of $\sqrt{s} = 13$ TeV with the ALICE detector is reported, considering D$^{0}$, D$^{+}$, and D$^{*+}$ mesons in the transverse-momentum interval $3 < p_{\rm T} < 36$ GeV/$c$ at midrapidity ($|y| < 0.5$), and charged particles with $p_{\rm T} > 0.3$ GeV/$c$ and pseudorapidity $|\eta| < 0.8$. This measurement has an improved precision and provides an extended transverse-momentum coverage compared to previous ALICE measurements at lower energies. The study is also performed as a function of the charged-particle multiplicity, showing no modifications of the correlation function with multiplicity within uncertainties. The properties and the transverse-momentum evolution of the near- and away-side correlation peaks are studied and compared with predictions from various Monte Carlo event generators. Among those considered, PYTHIA8 and POWHEG+PYTHIA8 provide the best description of the measured observables. The obtained results can provide guidance on tuning the generators.

56 data tables

Comparison of the azimuthal-correlation distributions of D mesons (average of D$^{0}$, D$^{+}$, and D$^{*+}$) with $3 < p_{\rm T} < 5$ GeV/$c$ and charged particles with $0.3 < p_{\rm T} < 1$ GeV/$c$, in pp collisions at $\sqrt{s} = $5, 7, and 13 TeV, after baseline subtraction. Rapidity range for the D mesons is $|y^{\rm D}_{\rm cms}| < 0.5$. Correlations are integrated for $|\Delta\eta|=|\eta_{\rm ch}-\eta_{\rm D}| < 1$. The azimuthal-correlation distributions are reported in the range $0 < \Delta\varphi < \pi$.

Comparison of the azimuthal-correlation distributions of D mesons (average of D$^{0}$, D$^{+}$, and D$^{*+}$) with $8 < p_{\rm T} < 16$ GeV/$c$ and charged particles with $0.3 < p_{\rm T} < 1$ GeV/$c$, in pp collisions at $\sqrt{s} = $5, 7, and 13 TeV, after baseline subtraction. Rapidity range for the D mesons is $|y^{\rm D}_{\rm cms}| < 0.5$. Correlations are integrated for $|\Delta\eta|=|\eta_{\rm ch}-\eta_{\rm D}| < 1$. The azimuthal-correlation distributions are reported in the range $0 < \Delta\varphi < \pi$.

Comparison of the azimuthal-correlation distributions of D mesons (average of D$^{0}$, D$^{+}$, and D$^{*+}$) with $16 < p_{\rm T} < 24$ GeV/$c$ and charged particles with $0.3 < p_{\rm T} < 1$ GeV/$c$, in pp collisions at $\sqrt{s} = $5, 7, and 13 TeV, after baseline subtraction. Rapidity range for the D mesons is $|y^{\rm D}_{\rm cms}| < 0.5$. Correlations are integrated for $|\Delta\eta|=|\eta_{\rm ch}-\eta_{\rm D}| < 1$. The azimuthal-correlation distributions are reported in the range $0 < \Delta\varphi < \pi$.

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Characterizing the initial conditions of heavy-ion collisions at the LHC with mean transverse momentum and anisotropic flow correlations

The ALICE collaboration Acharya, Shreyasi ; Adamova, Dagmar ; Adler, Alexander ; et al.
Phys.Lett.B 834 (2022) 137393, 2022.
Inspire Record 1966120 DOI 10.17182/hepdata.133026

Correlations between mean transverse momentum $[p_{\rm T}]$ and anisotropic flow coefficients $v_{\rm 2}$ or $v_{\rm 3}$ are measured as a function of centrality in Pb$-$Pb and Xe$-$Xe collisions at $\sqrt{s_{\rm NN}} = 5.02$ TeV and 5.44 TeV, respectively, with ALICE. In addition, the recently proposed higher-order correlation between $[p_{\rm T}]$, $v_{\rm 2}$, and $v_{\rm 3}$ is measured for the first time, which shows an anticorrelation for the presented centrality ranges. These measurements are compared with hydrodynamic calculations using IP-Glasma and $\rm T_{R}ENTo$ initial-state shapes, the former based on the Color Glass Condensate effective theory with gluon saturation, and the latter a parameterized model with nucleons as the relevant degrees of freedom. The data are better described by the IP-Glasma rather than the $\rm T_{R}ENTo$ based calculations. In particular, Trajectum and JETSCAPE predictions, both based on the $\rm T_{R}ENTo$ initial state model but with different parameter settings, fail to describe the measurements. As the correlations between $[p_{\rm T}]$ and $v_{\rm n}$ are mainly driven by the correlations of the size and the shape of the system in the initial state, these new studies pave a novel way to characterize the initial state and help pin down the uncertainty of the extracted properties of the quark$-$gluon plasma recreated in relativistic heavy-ion collisions.

4 data tables

Centrality dependence of $\rho\left(v_{2}^{2}, [p_{\rm T}] \right)$ and $\rho\left(v_{3}^{2}, [p_{\rm T}] \right)$ in Pb--Pb collisions at $\sqrt{s_{\rm NN}}$ = 5.02 TeV

Centrality dependence of $\rho\left(v_{2}^{2}, [p_{\rm T}] \right)$ in Xe--Xe collisions at $\sqrt{s_{\rm NN}}$ = 5.44 TeV

Centrality dependence of $\rho\left(v_{3}^{2}, [p_{\rm T}] \right)$ in Xe--Xe collisions at $\sqrt{s_{\rm NN}}$ = 5.44 TeV

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Observation of a multiplicity dependence in the $p_{\rm T}$-differential charm baryon-to-meson ratios in proton-proton collisions at $\sqrt{s} = 13$ TeV

The ALICE collaboration Acharya, Shreyasi ; Adamova, Dagmar ; Adler, Alexander ; et al.
Phys.Lett.B 829 (2022) 137065, 2022.
Inspire Record 1973854 DOI 10.17182/hepdata.128718

The production of prompt $D^{0}$, $D^{+}_{\rm s}$, and $\Lambda_{\rm c}^{+}$ hadrons, and their ratios, $D^{+}_{\rm s}$/$D^{0}$ and $\Lambda_{\rm c}^{+}$/$D^{0}$, are measured in proton-proton collisions at $\sqrt{s}$ = 13 TeV at midrapidity ($|y| <0.5$) with the ALICE detector at the LHC. The measurements are performed as a function of the charm-hadron transverse momentum ($p_{\rm T}$) in intervals of charged-particle multiplicity, measured with two multiplicity estimators covering different pseudorapidity regions. While the strange to non-strange $D^{+}_{\rm s}$/$D^{0}$ ratio indicates no significant multiplicity dependence, the baryon-to-meson $p_{\rm T}$-differential $\Lambda_{\rm c}^{+}$/$D^{0}$ ratio shows a multiplicity-dependent enhancement, with a significance of 5.3$\sigma$ for $1< p_{\rm T} < 12$ GeV/$c$, comparing the highest multiplicity interval with respect to the lowest one. The measurements are compared with a theoretical model that explains the multiplicity dependence by a canonical treatment of quantum charges in the statistical hadronisation approach, and with predictions from event generators that implement colour reconnection mechanisms beyond the leading colour approximation to model the hadronisation process. The $\Lambda_{\rm c}^{+}$/$D^{0}$ ratios as a function of $p_{\rm T}$ present a similar shape and magnitude as the $\Lambda/K^{0}_{s}$ ratios in comparable multiplicity intervals, suggesting a potential common mechanism for light- and charm-hadron formation, with analogous multiplicity dependence. The $p_{\rm T}$-integrated ratios, extrapolated down to $p_{\rm T}$=0, do not show a significant dependence on multiplicity within the uncertainties.

20 data tables

Transverse-momentum spectra of $\mathrm{D^0}$ hadrons measured in pp collisions at $\sqrt{{s}} = 13$~TeV for different multiplicity classes selected with the $N_\mathrm{trkl}$ estimator at midrapidity.

Transverse-momentum spectra of $\mathrm{D_s^+}$ hadrons measured in pp collisions at $\sqrt{{s}} = 13$~TeV for different multiplicity classes selected with the $N_\mathrm{trkl}$ estimator at midrapidity.

Transverse-momentum spectra of $\mathrm{\Lambda_c^+}$ hadrons measured in pp collisions at $\sqrt{{s}} = 13$~TeV for different multiplicity classes selected with the $N_\mathrm{trkl}$ estimator at midrapidity.

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Production of light (anti)nuclei in pp collisions at $\sqrt{s}~=~5.02$ TeV

The ALICE collaboration Acharya, Shreyasi ; Adamova, Dagmar ; Adler, Alexander ; et al.
Eur.Phys.J.C 82 (2022) 289, 2022.
Inspire Record 1981685 DOI 10.17182/hepdata.128684

The study of the production of nuclei and antinuclei in pp collisions has proven to be a powerful tool to investigate the formation mechanism of loosely bound states in high-energy hadronic collisions. In this paper, the production of protons, deuterons and $^3$He and their charge conjugates at midrapidity is studied as a function of the charged-particle multiplicity in inelastic pp collisions at $\sqrt{s}=5.02$ TeV using the ALICE detector. Within the uncertainties, the yields of nuclei in pp collisions at $\sqrt{s}=5.02$ TeV are compatible with those in pp collisions at different energies and to those in p-Pb collisions when compared at similar multiplicities. The measurements are compared with the expectations of coalescence and Statistical Hadronisation Models. The results suggest a common formation mechanism behind the production of light nuclei in hadronic interactions and confirm that they do not depend on the collision energy but on the number of produced particles.

43 data tables

(Anti)proton spectrum in V0M multiplicity class I

(Anti)proton spectrum in V0M multiplicity class II

(Anti)proton spectrum in V0M multiplicity class III

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Version 2
Constraining hadronization mechanisms with $\rm \Lambda_{\rm c}^{+}$/D$^0$ production ratios in Pb-Pb collisions at $\sqrt{s_{\rm NN}} = 5.02$ TeV

The ALICE collaboration Acharya, Shreyasi ; Adamova, Dagmar ; Adler, Alexander ; et al.
Phys.Lett.B 839 (2023) 137796, 2023.
Inspire Record 1990765 DOI 10.17182/hepdata.138404

The production of prompt $\rm \Lambda_{\rm c}^{+}$ baryons at midrapidity ($|y|<0.5$) was measured in central (0-10%) and mid-central (30-50%) Pb-Pb collisions at the center-of-mass energy per nucleon-nucleon pair $\sqrt{s_{\rm NN}} = 5.02$ TeV with the ALICE detector. The results are more precise, more differential in centrality, and reach much lower transverse momentum ($p_{\rm T}=1$ GeV/$c$) with respect to previous measurements performed by the ALICE, STAR, and CMS Collaborations in nucleus-nucleus collisions, allowing for an extrapolation down to $p_{\rm T}=0$. The $p_{\rm T}$-differential $\rm \Lambda_{\rm c}^{+}$/D$^0$ production ratio is enhanced with respect to the pp measurement for $4<p_{\rm T}<8$ GeV/$c$ by 3.7 standard deviations ($\sigma$), while the $p_{\rm T}$-integrated ratios are compatible within 1$\sigma$. The observed trend is similar to that observed in the strange sector for the $\Lambda/$K$^0_{\rm S}$ ratio. Model calculations including coalescence or statistical hadronization for charm-hadron formation are compared with the data.

6 data tables

Transverse-momentum-differential production yields of prompt $\mathrm{\Lambda_c^+}$ in central (0--10\%) and mid-central (30--50\%) Pb--Pb collisions at $\sqrt{s_{\mathrm{NN}}}=5.02$ TeV.

Transverse-momentum-differential production yields of prompt $\mathrm{\Lambda_c^+}$ in central (0--10\%) and mid-central (30--50\%) Pb--Pb collisions at $\sqrt{s_{\mathrm{NN}}}=5.02$ TeV.

The $\mathrm{\Lambda_c^+ / D^0}$ production yield ratio in central (0--10\%) and mid-central (30--50\%) Pb--Pb collisions at $\sqrt{s_{\mathrm{NN}}}=5.02$ TeV.

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Neutral to charged kaon yield fluctuations in Pb$-$Pb collisions at $\sqrt{s_{\rm NN}}$ = 2.76TeV

The ALICE collaboration Acharya, Shreyasi ; Adamova, Dagmar ; Adler, Alexander ; et al.
Phys.Lett.B 832 (2022) 137242, 2022.
Inspire Record 1993200 DOI 10.17182/hepdata.131260

We present the first measurement of event-by-event fluctuations in the kaon sector in Pb-Pb collisions at $\sqrt {s_{\rm NN}}=$ 2.76 TeV with the ALICE detector at the LHC. The robust fluctuation correlator $\nu_{\rm dyn}$ is used to evaluate the magnitude of fluctuations of the relative yields of neutral and charged kaons, as well as the relative yields of charged kaons, as a function of collision centrality and selected kinematic ranges. While the correlator $\nu_{\rm dyn}[\rm K^+,\rm K^-]$ exhibits a scaling approximately in inverse proportion of the charged particle multiplicity, $\nu_{\rm dyn}[\rm K_S^0,\rm K^{\pm}]$ features a significant deviation from such scaling. Within uncertainties, the value of $\nu_{\rm dyn}[\rm K_S^0,\rm K^{\pm}]$ is independent of the selected transverse momentum interval, while it exhibits a pseudorapidity dependence. The results are compared with HIJING, AMPT and EPOS-LHC predictions, and are further discussed in the context of the possible production of disoriented chiral condensates in central Pb-Pb collisions.

14 data tables
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Forward rapidity J/$\psi$ production as a function of charged-particle multiplicity in pp collisions at $\sqrt{s} =$ 5.02 and 13 TeV

The ALICE collaboration Acharya, Shreyasi ; Adamova, Dagmar ; Adler, Alexander ; et al.
JHEP 06 (2022) 015, 2022.
Inspire Record 1992719 DOI 10.17182/hepdata.129601

The production of J/$\psi$ is measured as a function of charged-particle multiplicity at forward rapidity in proton$-$proton (pp) collisions at center-of-mass energies $\sqrt{s} =$ 5.02 and 13 TeV. The J/$\psi$ mesons are reconstructed via their decay into dimuons in the rapidity interval (2.5 $< y <$ 4.0), whereas the charged-particle multiplicity density (${\rm d}N_{\rm{ch}}/{\rm d}\eta$) is measured at midrapidity $(|\eta| < 1)$. The production rate as a function of multiplicity is reported as the ratio of the yield in a given multiplicity interval to the multiplicity-integrated one. This observable shows a linear increase with charged-particle multiplicity normalized to the corresponding average value for inelastic events (${{\rm d}N_{\rm ch}/{\rm d}\eta}/{\langle {\rm d}N_{\rm ch}/{\rm d}\eta \rangle}$), at both the colliding energies. Measurements are compared with available ALICE results at midrapidity and theoretical model calculations. First measurement of the mean transverse momentum ($\langle p_{\mathrm{T}}\rangle$) of J/$\psi$ in pp collisions exhibits an increasing trend as a function of ${{\rm d}N_{\rm ch}/{\rm d}\eta}/{\langle {\rm d}N_{\rm ch}/{\rm d}\eta \rangle}$ showing a saturation towards high charged-particle multiplicities.

4 data tables
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First study of the two-body scattering involving charm hadrons

The ALICE collaboration Acharya, Shreyasi ; Adamova, Dagmar ; Adler, Alexander ; et al.
Phys.Rev.D 106 (2022) 052010, 2022.
Inspire Record 2011222 DOI 10.17182/hepdata.133153

This article presents the first measurement of the interaction between charm hadrons and nucleons. The two-particle momentum correlations of $\mathrm{pD^-}$ and $\mathrm{\overline{p}D}^+$ pairs are measured by the ALICE Collaboration in high-multiplicity pp collisions at $\sqrt{s} = 13~\mathrm{TeV}$. The data are compatible with the Coulomb-only interaction hypothesis within (1.1-1.5)$\sigma$. The level of agreement slightly improves if an attractive nucleon(N)$\overline{\mathrm{D}}$ strong interaction is considered, in contrast to most model predictions which suggest an overall repulsive interaction. This measurement allows for the first time an estimation of the 68% confidence level interval for the isospin $\mathrm{I}=0$ inverse scattering length of the $\mathrm{N\overline{D}}$ state ${f_{0,~\mathrm{I}=0}^{-1} \in [-0.4,0.9]~\mathrm{fm^{-1}}}$, assuming negligible interaction for the isospin $\mathrm{I}=1$ channel.

3 data tables

$\mathrm{pD^-}$ $\oplus$ $\mathrm{\overline{p}D^+}$ momentum correlation function as a function of the relative momentum in the particle-pair rest frame $k^*$ in high-multiplicity (0-0.17%) pp collisions at $\sqrt{s}=13$ TeV.

$1\sigma$ confidence interval for the $\mathrm{N\overline{D}}$ inverse scattering length for the isospin $\mathrm{I}=0$ channel, $f_{0,~\mathrm{I}=0}^{-1}$, as a function of the effective source radius $R_\mathrm{eff}$.

Best fit for the $\mathrm{N\overline{D}}$ inverse scattering length for the isospin $\mathrm{I}=0$ channel, $f_{0,~\mathrm{I}=0}^{-1}$, as a function of the effective source radius $R_\mathrm{eff}$.