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    Multiplicity dependence of (multi-)strange hadron production in proton-proton collisions at √s = 13 TeV
    (Springer, 2020-02-01)
    Abstract The production rates and the transverse momentum distribution of strange hadrons at mid-rapidity ( $$\left| y\right| < 0.5$$ y < 0.5 ) are measured in proton-proton collisions at $$\sqrt{s}$$ s = 13 TeV as a function of the charged particle multiplicity, using the ALICE detector at the LHC. The production rates of $$\mathrm{K}^{0}_{S}$$ K S 0 , $$\Lambda $$ Λ , $$\Xi $$ Ξ , and $$\Omega $$ Ω increase with the multiplicity faster than what is reported for inclusive charged particles. The increase is found to be more pronounced for hadrons with a larger strangeness content. Possible auto-correlations between the charged particles and the strange hadrons are evaluated by measuring the event-activity with charged particle multiplicity estimators covering different pseudorapidity regions. When comparing to lower energy results, the yields of strange hadrons are found to depend only on the mid-rapidity charged particle multiplicity. Several features of the data are reproduced qualitatively by general purpose QCD Monte Carlo models that take into account the effect of densely-packed QCD strings in high multiplicity collisions. However, none of the tested models reproduce the data quantitatively. This work corroborates and extends the ALICE findings on strangeness production in proton-proton collisions at 7 TeV.
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    Multiplicity dependence of π, K, and p production in pp collisions at √s=13 TeV
    (Institute for Ionics, 2020-08-01)
    Abstract This paper presents the measurements of $$\pi ^{\pm }$$ π± , $$\mathrm {K}^{\pm }$$ K± , $$\text {p}$$ p and $$\overline{\mathrm{p}} $$ p¯ transverse momentum ( $$p_{\text {T}}$$ pT ) spectra as a function of charged-particle multiplicity density in proton–proton (pp) collisions at $$\sqrt{s}\ =\ 13\ \text {TeV}$$ s=13TeV with the ALICE detector at the LHC. Such study allows us to isolate the center-of-mass energy dependence of light-flavour particle production. The measurements reported here cover a $$p_{\text {T}}$$ pT range from 0.1 to 20 $$\text {GeV}/c$$ GeV/c and are done in the rapidity interval $$|y|<0.5$$ |y|<0.5 . The $$p_{\text {T}}$$ pT -differential particle ratios exhibit an evolution with multiplicity, similar to that observed in pp collisions at $$\sqrt{s}\ =\ 7\ \text {TeV}$$ s=7TeV , which is qualitatively described by some of the hydrodynamical and pQCD-inspired models discussed in this paper. Furthermore, the $$p_{\text {T}}$$ pT -integrated hadron-to-pion yield ratios measured in pp collisions at two different center-of-mass energies are consistent when compared at similar multiplicities. This also extends to strange and multi-strange hadrons, suggesting that, at LHC energies, particle hadrochemistry scales with particle multiplicity the same way under different collision energies and colliding systems.
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    Measurement of electrons from heavy-flavour hadron decays as a function of multiplicity in p-Pb collisions at √sNN = 5.02 TeV
    (Springer, 2020-02-01)
    Abstract The multiplicity dependence of electron production from heavy-flavour hadron decays as a function of transverse momentum was measured in p-Pb collisions at $$ \sqrt{s_{\mathrm{NN}}} $$ s NN = 5.02 TeV using the ALICE detector at the LHC. The measurement was performed in the centre-of-mass rapidity interval −1.07 < ycms< 0.14 and transverse momentum interval 2 < pT< 16 GeV/c. The multiplicity dependence of the production of electrons from heavy-flavour hadron decays was studied by comparing the pT spectra measured for different multiplicity classes with those measured in pp collisions (QpPb) and in peripheral p-Pb collisions (Qcp). The QpPb results obtained are consistent with unity within uncertainties in the measured pT interval and event classes. This indicates that heavy-flavour decay electron production is consistent with binary scaling and independent of the geometry of the collision system. Additionally, the results suggest that cold nuclear matter effects are negligible within uncertainties, in the production of heavy-flavour decay electrons at midrapidity in p-Pb collisions.
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    J/ψ production as a function of charged-particle multiplicity in p-Pb collisions at √sNN = 8.16 TeV
    (Springer, 2020-09-01)
    Abstract Inclusive J/ψ yields and average transverse momenta in p-Pb collisions at a center-of-mass energy per nucleon pair $$ \sqrt{s_{\mathrm{NN}}} $$ s NN = 8.16 TeV are measured as a function of the charged-particle pseudorapidity density with ALICE. The J/ψ mesons are reconstructed at forward (2.03 < ycms< 3.53) and backward (−4.46 < ycms< −2.96) center-of-mass rapidity in their dimuon decay channel while the charged-particle pseudorapidity density is measured around midrapidity. The J/ψ yields at forward and backward rapidity normalized to their respective average values increase with the normalized charged-particle pseudorapidity density, the former showing a weaker increase than the latter. The normalized average transverse momenta at forward and backward rapidity manifest a steady increase from low to high charged-particle pseudorapidity density with a saturation beyond the average value.
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    Pseudorapidity distributions of charged particles as a function of mid- and forward rapidity multiplicities in pp collisions at √s = 5.02, 7 and 13 TeV
    (Springer Science and Business Media Deutschland GmbH, 2021-07-01)
    The multiplicity dependence of the pseudorapidity density of charged particles in proton–proton (pp) collisions at centre-of-mass energies $$\sqrt{s}~=~5.02$$ s = 5.02 , 7 and 13 TeV measured by ALICE is reported. The analysis relies on track segments measured in the midrapidity range ( $$|\eta | < 1.5$$ | η | < 1.5 ). Results are presented for inelastic events having at least one charged particle produced in the pseudorapidity interval $$|\eta |<1$$ | η | < 1 . The multiplicity dependence of the pseudorapidity density of charged particles is measured with mid- and forward rapidity multiplicity estimators, the latter being less affected by autocorrelations. A detailed comparison with predictions from the PYTHIA 8 and EPOS LHC event generators is also presented. The results can be used to constrain models for particle production as a function of multiplicity in pp collisions.
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    Long- and short-range correlations and their event-scale dependence in high-multiplicity pp collisions at √s = 13 TeV
    (Springer Science and Business Media Deutschland GmbH, 2021-05-01)
    Two-particle angular correlations are measured in high-multiplicity proton-proton collisions at s = 13 TeV by the ALICE Collaboration. The yields of particle pairs at short-(∆η ∼ 0) and long-range (1.6 < |∆η| < 1.8) in pseudorapidity are extracted on the near-side (∆φ ∼ 0). They are reported as a function of transverse momentum (pT) in the range 1 < pT< 4 GeV/c. Furthermore, the event-scale dependence is studied for the first time by requiring the presence of high-pT leading particles or jets for varying pT thresholds. The results demonstrate that the long-range “ridge” yield, possibly related to the collective behavior of the system, is present in events with high-pT processes as well. The magnitudes of the short- and long-range yields are found to grow with the event scale. The results are compared to EPOS LHC and PYTHIA 8 calculations, with and without string-shoving interactions. It is found that while both models describe the qualitative trends in the data, calculations from EPOS LHC show a better quantitative agreement for the pT dependency, while overestimating the event-scale dependency. [Figure not available: see fulltext.]
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    First study of the two-body scattering involving charm hadrons
    (American Physical Society, 2022-09-01)
    This article presents the first measurement of the interaction between charm hadrons and nucleons. The two-particle momentum correlations of $\mathrm{p}{\mathrm{D}}^{\ensuremath{-}}$ and ${\overline{\mathrm{p}}\mathrm{D}}^{+}$ pairs are measured by the ALICE Collaboration in high-multiplicity pp collisions at $\sqrt{s}=13\text{ }\text{ }\mathrm{TeV}$. The data are compatible with the Coulomb-only interaction hypothesis within $(1.1--1.5)\ensuremath{\sigma}$. The level of agreement slightly improves if an attractive nucleon $(\mathrm{N})\overline{\mathrm{D}}$ 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 $\mathrm{N}\overline{\mathrm{D}}$ state ${f}_{0,\mathrm{I}=0}^{\ensuremath{-}1}\ensuremath{\in}[\ensuremath{-}0.4,0.9]\text{ }\text{ }{\mathrm{fm}}^{\ensuremath{-}1}$, assuming negligible interaction for the isospin $\mathrm{I}=1$ channel.
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    Complete transversal and formal normal forms of germs of vector fields
    (Sociedade Brasileira de Matemática, 2022-12-26)
    In this work, inspired by the technique of the complete transversal, used for the classification of plane branches, developed by Hefez, A. and Hernandes, M., as well as Bruce, J.W., Kirk, N.P. and du Plesis, A.A., study the singularities of applications, we establish a classification of vector fields through their normal forms. In the case of vector fields with non zero linear part in $(\mathbb{C}^{2}, 0) $ and nilpotent fields in $(\mathbb {C}^{n}, 0), n\geq 2$ we recover the classical normal forms for those fields, and we provide a formal normal form different from Takens in dimension 2. Likewise, we obtain the normal form for the vector fields in $(\mathbb{C},0)$ of any multiplicity.
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    On some indices of foliations and applications
    (Springer Science and Business Media Deutschland GmbH, 2026-03-01)
    In this paper, we establish a relationship between the Milnor number, the χ-number and the Tjurina number of a foliation with respect to an effective balanced divisor of separatrices. Moreover, using the Gómez-Mont–Seade–Verjovsky index, we prove that the difference between the multiplicity and the Tjurina number of a foliation with respect to a reduced curve is independent of the foliation. We also derive a local formula for the Tjurina number of a foliation with respect to a reduced curve. From a global point of view, these results lead to the following consequences: We provide a new proof of a global result regarding the multiplicity of a foliation due to Cerveau–Lins Neto and a new proof of a Soares’s inequality for the sum of the Milnor number of an invariant curve of a foliation. Additionally, we obtain bounds for the global Tjurina number of a foliation on the complex projective plane. Finally, we provide an answer to the conjecture posed by Alcántara and Mozo-Fernández about foliations on the complex projective plane having a unique singularity.
      1
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    Charged-particle multiplicity distributions over a wide pseudorapidity range in p–Pb collisions at √ˢɴɴ=5.02 TeV
    (Springer Nature, 2025)
    This paper presents the primary charged-particle multiplicity distributions in proton–lead collisions at a centre-of-mass energy per nucleon–nucleon collision of √ˢɴɴ = 5.02 TeV. The distributions are reported for non-single diffractive collisions in different pseudorapidity ranges. The measurements are performed using the combined information from the Silicon Pixel Detector and the Forward Multiplicity Detector of ALICE. The multiplicity distributions are parametrised with a double negative binomial distribution function which provides satisfactory descriptions of the distributions for all the studied pseudorapidity intervals. The data are compared to models and analysed quantitatively, evaluating the first four moments (mean, standard deviation, skewness, and kurtosis). The shape evolution of the measured multiplicity distributions is studied in terms of KNO variables and it is found that none of the considered models reproduces the measurements. This paper also reports on the average charged-particle multiplicity, normalised by the average number of participating nucleon pairs, as a function of the collision energy. The multiplicity results are then compared to measurements made in proton–proton and nucleus–nucleus collisions across a wide range of collision energies.
      9