This work reports femtoscopic correlations of p$-$p ($\bar{\rm p}-\bar{\rm p}$) and p$-$d ($\bar{\rm p}-\bar{\rm d}$) pairs measured in Pb$-$Pb collisions at center-of-mass energy $\sqrt{s_{\rm NN}}$ = 5.02 TeV by the ALICE Collaboration. A fit to the measured proton-proton correlation functions allows one to extract the dependence of the nucleon femtoscopic radius of the particle-emitting source on the pair transverse mass ($m_\text{T}$) and on the average charge particle multiplicity $\langle\text{dN}_\text{ch}/\text{d}\eta\rangle^{1/3}$ for three centrality intervals (0$-$10$\%$, 10$-$30$\%$, 30$-$50$\%$). In both cases, the expected power-law and linear scalings are observed, respectively. The measured p$-$d correlations can be described by both two- and three-body calculations, indicating that the femtoscopy observable is not sensitive to the short-distance features of the dynamics of the p$-$(p$-$n) system, due to the large inter-particle distances in Pb$-$Pb collisions at the LHC. Indeed, in this study, the minimum measured femtoscopic source sizes for protons and deuterons have a minimum value at $2.73^{+0.05}_{-0.05}$ and $3.10^{+1.04}_{-0.86}$ fm, respectively, for the 30$-$50$\%$ centrality collisions. Moreover, the $m_{\rm{T}}$-scaling obtained for the p$-$p and p$-$d systems is compatible within 1$\sigma$ of the uncertainties. These findings provide new input for fundamental studies on the production of light (anti)nuclei under extreme conditions.
proton-proton (same charge) correlation function for centrality 0-10% from Pb-Pb collisions at 5020 GeV
proton-proton (same charge) correlation function for centrality 10-30% from Pb-Pb collisions at 5020 GeV
proton-proton (same charge) correlation function for centrality 30-50% from Pb-Pb collisions at 5020 GeV
Event-by-event fluctuations of the event-wise mean transverse momentum, $\langle p_{\mathrm{T}}\rangle$, of charged particles produced in proton$-$proton (pp) collisions at $\sqrt{s}$ = 5.02 TeV, Xe$-$Xe collisions at $\sqrt{s_{\mathrm{NN}}} =$ 5.44 TeV, and Pb$-$Pb collisions at $\sqrt{s_{\mathrm{NN}}} =$ 5.0 TeV are studied using the ALICE detector based on the integral correlator $\langle\langle Δp_{\rm T}Δp_{\rm T}\rangle\rangle $. The correlator strength is found to decrease monotonically with increasing produced charged-particle multiplicity measured at midrapidity in all three systems. In Xe$-$Xe and Pb$-$Pb collisions, the multiplicity dependence of the correlator deviates significantly from a simple power-law scaling as well as from the predictions of the HIJING and AMPT models. The observed deviation from power-law scaling is expected from transverse radial flow in semicentral to central Xe$-$Xe and Pb$-$Pb collisions. In pp collisions, the correlation strength is also studied by classifying the events based on the transverse spherocity, $S_0$, of the particle production at midrapidity, used as a proxy for the presence of a pronounced back-to-back jet topology. Low-spherocity (jetty) events feature a larger correlation strength than those with high spherocity (isotropic). The strength and multiplicity dependence of jetty and isotropic events are well reproduced by calculations with the PYTHIA 8 and EPOS LHC models.
Normalized transverse momentum correlator, $\sqrt{ \langle\langle \Delta p_{{\rm T}1}\Delta p_{{\rm T}2} \rangle\rangle }$$/\langle\langle p_{\rm T} \rangle\rangle $, as a function of the charged-particle multiplicity density, $\langle{\rm d}N_{\rm ch}/{\rm d}\eta \rangle$, in pp collisions at $\sqrt{s}$ = 5.02 TeV.
Normalized transverse momentum correlator, $\sqrt{ \langle\langle \Delta p_{{\rm T}1}\Delta p_{{\rm T}2} \rangle\rangle }$$/\langle\langle p_{\rm T} \rangle\rangle $, as a function of the charged-particle multiplicity density, $\langle{\rm d}N_{\rm ch}/{\rm d}\eta \rangle$, in Pb--Pb collisions at $\sqrt{s_{\rm NN}}$ = 5.02 TeV.
Normalized transverse momentum correlator, $\sqrt{ \langle\langle \Delta p_{{\rm T}1}\Delta p_{{\rm T}2} \rangle\rangle }$$/\langle\langle p_{\rm T} \rangle\rangle $, as a function of the charged-particle multiplicity density, $\langle{\rm d}N_{\rm ch}/{\rm d}\eta \rangle$, in Xe--Xe collisions at $\sqrt{s_{\rm NN}}$ = 5.44 TeV.
Differential two-particle normalized cumulants ($R_2$) and transverse momentum correlations ($P_2$) are measured as a function of the relative pseudorapidity and azimuthal angle difference $( \Delta \eta, \Delta \varphi )$ of charged particle pairs in minimum bias pp collisions at $\sqrt{\textit{s}}$ = 13 TeV. The measurements use charged hadrons in the pseudorapidity region of $|\eta| < 0.8$ and the transverse momentum range 0.2 $< \textit{p}_{\mathrm T} < $ 2.0 $\mathrm{GeV}/\textit{c}$ in order to focus on soft multiparticle interactions and to complement prior measurements of these correlation functions in p-Pb and Pb-Pb collisions. The correlation functions are reported for both unlike-sign and like-sign pairs and their charge-independent and charge-dependent combinations. Both the $R_2$ and $P_2$ measured in pp collisions exhibit features qualitatively similar to those observed in p-Pb and Pb-Pb collisions. The $\Delta\eta$ and $\Delta\varphi$ root mean square widths of the near-side peak of the correlation functions are evaluated and compared with those observed in p-Pb and Pb-Pb collisions and show smooth evolution with the multiplicity of charged particles produced in the collision. The comparison of the measured correlation functions with predictions from PYTHIA8 shows that this model qualitatively captures their basic structure and characteristics but feature important differences. In addition, the $R_2^{\rm CD}$ is used to determine the charge balance function of hadrons produced within the detector acceptance of the measurements. The integral of the balance function is found to be compatible with those reported by a previous measurement in Pb-Pb collisions. These results, which are sensitive to the interplay between the underlying event and mini-jets in pp collisions, establish a baseline for heavy-ion collisions.
Correlation functions $R_2^{\rm US}$ of charged hadrons measured in minimum bias pp collisions at $\sqrt{s}=13\;\text{TeV}$. Charged hadrons are selected in the range $0.2 < p_{\rm T} < 2.0$ GeV/$c$ and with pseudorapidity $|\eta| < 0.8$.
Correlation functions $R_2^{\rm LS}$ of charged hadrons measured in minimum bias pp collisions at $\sqrt{s}=13\;\text{TeV}$. Charged hadrons are selected in the range $0.2 < p_{\rm T} < 2.0$ GeV/$c$ and with pseudorapidity $|\eta| < 0.8$.
Correlation functions $P_2^{\rm US}$ of charged hadrons measured in minimum bias pp collisions at $\sqrt{s}=13\;\text{TeV}$. Charged hadrons are selected in the range $0.2 < p_{\rm T} < 2.0$ GeV/$c$ and with pseudorapidity $|\eta| < 0.8$.
A study of strange hadron production associated with hard scattering processes and with the underlying event is conducted to investigate the origin of the enhanced production of strange hadrons in small collision systems characterised by large charged-particle multiplicities. For this purpose, the production of the single-strange meson ${\rm K^0_S}$ and the double-strange baryon $\Xi^{\pm}$ is measured, in each event, in the azimuthal direction of the highest-$p_{\rm T}$ particle (``trigger" particle), related to hard scattering processes, and in the direction transverse to it in azimuth, associated with the underlying event, in pp collisions at $\sqrt{s}=5.02$ TeV and $\sqrt{s}=13$ TeV using the ALICE detector at the LHC. The per-trigger yields of ${\rm K^0_S}$ and $\Xi^{\pm}$ are dominated by the transverse-to-leading production (i.e., in the direction transverse to the trigger particle), whose contribution relative to the toward-leading production is observed to increase with the event charged-particle multiplicity. The transverse-to-leading and the toward-leading $\Xi^{\pm}$/${\rm K^0_S}$ yield ratios increase with the multiplicity of charged particles, suggesting that strangeness enhancement with multiplicity is associated with both hard scattering processes and the underlying event. The relative production of $\Xi^{\pm}$ with respect to ${\rm K^0_S}$ is higher in transverse-to-leading processes over the whole multiplicity interval covered by the measurement. The ${\rm K}^{0}_{\rm{S}}$ and $\Xi^{\pm}$ per-trigger yields and yield ratios are compared with predictions of three different phenomenological models, namely PYTHIA 8.2 with the Monash tune, PYTHIA 8.2 with ropes and EPOS LHC. The comparison shows that none of them can quantitatively describe either the transverse-to-leading or the toward-leading yields of ${\rm K}^{0}_{\rm{S}}$ and $\Xi^{\pm}$.
Yields of $\rm K^{0}_\rm{S}$ per trigger particle per unit $\Delta\eta\Delta\varphi$ area in pp collisions at $\sqrt{s}=13$ TeV, as a function of the $\rm K^{0}_\rm{S}$ $p_\rm{T}$. Trigger particles are charged particles with $p_\rm{T}>3$ GeV/c. The trigger-particle-$\rm K^{0}_\rm{S}$ correlation is integrated in the ranges $-1.2<\Delta\eta<1.2$ and $-\pi/2<\Delta\varphi<3/2\pi$.
Transverse-to-leading yields of $\rm K^{0}_\rm{S}$ per trigger particle per unit $\Delta\eta\Delta\varphi$ area in pp collisions at $\sqrt{s}=13$ TeV, as a function of the $\rm K^{0}_\rm{S}$ $p_\rm{T}$. Trigger particles are charged particles with $p_\rm{T}>3$ GeV/c. The trigger-particle-$\rm K^{0}_\rm{S}$ correlation is integrated in the ranges $0.86<|\Delta\eta|<1.2$ and $0.96<\Delta\varphi<1.8$.
Toward-leading yields of $\rm K^{0}_\rm{S}$ per trigger particle per unit $\Delta\eta\Delta\varphi$ area in pp collisions at $\sqrt{s}=13$ TeV, as a function of the $\rm K^{0}_\rm{S}$ $p_\rm{T}$. Trigger particles are charged particles with $p_\rm{T}>3$ GeV/c. The trigger-particle-$\rm K^{0}_\rm{S}$ correlation is integrated in the ranges $|\Delta\eta|<0.86$ and $|\Delta\varphi|<1.1$.
Two-particle correlations are presented for K$^0_\mathrm{S}$, $\Lambda$, and $\overline\Lambda$ strange hadrons as a function of relative momentum in lead-lead collisions at a nucleon-nucleon center-of-mass energy of 5.02 TeV. The dataset corresponds to an integrated luminosity of 0.607 nb$^{-1}$ and was collected using the CMS detector at the CERN LHC. These correlations are sensitive to quantum statistics and to final-state interactions between the particles. The source size extracted from the K$^0_\mathrm{S}$K$^0_\mathrm{S}$ correlations is found to decrease from 4.6 to 1.6 fm in going from central to peripheral collisions. Strong interaction scattering parameters (i.e., scattering length and effective range) are determined from the $\Lambda$K$^0_\mathrm{S}$ and $\Lambda\Lambda$ (including their charge conjugates) correlations using the Lednick$\'y$-Lyuboshitz model and are compared to theoretical and other experimental results.
The $K^{0}_{S}$ Invariant mass in $0-80\%$ centrality,
The $\Lambda (\overline{\Lambda})$ Invariant mass in $0-80\%$ centrality.
$K^{0}_{S} K^{0}_{S}$ correlation meassurement in $0-10\%$ centrality.
Femtoscopic correlations of non-identical charged kaons ($\rm K^+ K^-$) are studied in Pb$-$Pb collisions at a center-of-mass energy per nucleon$-$nucleon collision $\sqrt{s_{\mathrm{NN}}} =2.76$ TeV by ALICE at the LHC. One-dimensional $\rm K^+ K^-$ correlation functions are analyzed in three centrality classes and eight intervals of particle-pair transverse momentum. The Lednický and Luboshitz interaction model used in the $\rm K^+ K^-$ analysis includes the final-state Coulomb interactions between kaons and the final-state interaction through $a_{0}$(980) and $f_{0}$(980) resonances. The mass of $f_{0}$(980) and coupling were extracted from the fit to $\rm K^+ K^-$ correlation functions using the femtoscopic technique for the first time. The measured mass and width of the $f_{0}$(980) resonance are consistent with other published measurements. The height of the $\phi$(1020) meson peak present in the $\rm K^+ K^-$ correlation function rapidly decreases with increasing source radius, qualitatively in agreement with an inverse volume dependence. A phenomenological fit to this trend suggests that the $\phi$(1020) meson yield is dominated by particles produced directly from the hadronization of the system. The small fraction subsequently produced by FSI could not be precisely quantified with data presented in this paper and will be assessed in future work.
K+K- correlation function for 0.3<kT<0.4 GeV/c and centrality class 0-10%
K+K- correlation function for 0.5<kT<0.6 GeV/c and centrality class 0-10%
K+K- correlation function for 0.8<kT<1.0 GeV/c and centrality class 0-10%
Two-particle transverse momentum differential correlators, recently measured in Pb--Pb collisions at energies available at the CERN Large Hadron Collider (LHC), provide an additional tool to gain insights into particle production mechanisms and infer transport properties, such as the ratio of shear viscosity to entropy density, of the medium created in Pb-Pb collisions. The longitudinal long-range correlations and the large azimuthal anisotropy measured at low transverse momenta in small collision systems, namely pp and p-Pb, at LHC energies resemble manifestations of collective behaviour. This suggests that locally equilibrated matter may be produced in these small collision systems, similar to what is observed in Pb-Pb collisions. In this work, the same two-particle transverse momentum differential correlators are exploited in pp and p-Pb collisions at $\sqrt{s} = 7$ TeV and $\sqrt{s_{\rm NN}} = 5.02$ TeV, respectively, to seek evidence for viscous effects. Specifically, the strength and shape of the correlators are studied as a function of the produced particle multiplicity to identify evidence for longitudinal broadening that might reveal the presence of viscous effects in these smaller systems. The measured correlators and their evolution from pp and p--Pb to Pb--Pb collisions are additionally compared to predictions from Monte Carlo event generators, and the potential presence of viscous effects is discussed.
Two-particle transverse momentum correlation $G_{2}^{\rm CD}$ for 0$-$5% multiplicity class pp collisions at $\sqrt{s}=7\;\text{TeV}$.
Two-particle transverse momentum correlation $G_{2}^{\rm CD}$ for 30$-$40% multiplicity class pp collisions at $\sqrt{s}=7\;\text{TeV}$.
Two-particle transverse momentum correlation $G_{2}^{\rm CD}$ for 70$-$80% multiplicity class pp collisions at $\sqrt{s}=7\;\text{TeV}$.
The interaction of $\rm{K}^{-}$ with protons is characterised by the presence of several coupled channels, systems like ${\rm \overline{K}^0}$n and $\pi\Sigma$ with a similar mass and the same quantum numbers as the $\rm{K}^{-}$p state. The strengths of these couplings to the $\rm{K}^{-}$p system are of crucial importance for the understanding of the nature of the $\Lambda(1405)$ resonance and of the attractive $\rm{K}^{-}$p strong interaction. In this article, we present measurements of the $\rm{K}^{-}$p correlation functions in relative momentum space obtained in pp collisions at $\sqrt{s}~=~13$ TeV, in p-Pb collisions at $\sqrt{s_{\mathrm{NN}}}~=~5.02$ TeV, and (semi)peripheral Pb-Pb collisions at $\sqrt{s_{\mathrm{NN}}}~=~5.02$ TeV. The emitting source size, composed of a core radius anchored to the $\rm{K}^{+}$p correlation and of a resonance halo specific to each particle pair, varies between 1 and 2 fm in these collision systems. The strength and the effects of the ${\rm \overline{K}^0}$n and $\pi\Sigma$ inelastic channels on the measured $\rm{K}^{-}$p correlation function are investigated in the different colliding systems by comparing the data with state-of-the-art models of chiral potentials. A novel approach to determine the conversion weights $\omega$, necessary to quantify the amount of produced inelastic channels in the correlation function, is presented. In this method, particle yields are estimated from thermal model predictions, and their kinematic distribution from blast-wave fits to measured data. The comparison of chiral potentials to the measured $\rm{K}^{-}$p interaction indicates that, while the $\pi\Sigma-\rm{K}^{-}$p dynamics is well reproduced by the model, the coupling to the ${\rm \overline{K}^0}$n channel in the model is currently underestimated.
K$^+$p (K$^+$p $\oplus$ K$^-\overline{\mathrm p}$) correlation function in pp collisions at $\sqrt{s}=13$ TeV.
K$^+$p (K$^+$p $\oplus$ K$^-\overline{\mathrm p}$) correlation function in p-Pb collisions at $\sqrt{s_{\mathrm {NN}}}=5.02 $ TeV (0-20%).
K$^+$p (K$^+$p $\oplus$ K$^-\overline{\mathrm p}$) correlation function in p-Pb collisions at $\sqrt{s_{\mathrm{NN}}}=5.02$ TeV (20-40%).
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.
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 $0 < \Delta\varphi < \pi$.
First measurements of balance functions (BFs) of all combinations of identified charged hadron $(\pi,\rm K,\rm p)$ pairs in Pb$-$Pb collisions at $\sqrt{s_{\rm NN}} = 2.76$ TeV recorded by the ALICE detector are presented. The BF measurements are carried out as two-dimensional differential correlators versus the relative rapidity ($\Delta y$) and azimuthal angle ($\Delta\varphi$) of hadron pairs, and studied as a function of collision centrality. The $\Delta\varphi$ dependence of BFs is expected to be sensitive to the light quark diffusivity in the quark$-$gluon plasma. While the BF azimuthal widths of all pairs substantially decrease from peripheral to central collisions, the longitudinal widths exhibit mixed behaviors: BFs of $\pi\pi$ and cross-species pairs narrow significantly in more central collisions, whereas those of $\rm KK$ and $\rm pp$ are found to be independent of collision centrality. This dichotomy is qualitatively consistent with the presence of strong radial flow effects and the existence of two stages of quark production in relativistic heavy-ion collisions. Finally, the first measurements of the collision centrality evolution of BF integrals are presented, with the observation that charge balancing fractions are nearly independent of collision centrality in Pb$-$Pb collisions. Overall, the results presented provide new and challenging constraints for theoretical models of hadron production and transport in relativistic heavy-ion collisions.
Balance function $B^{\pi\pi}$ measured in semicentral Pb--Pb collisions at $\sqrt{s_{\rm NN}}=2.76\;\text{TeV}$ ($\pi,{\rm K}: 0.2 \leq p_{\rm T} \leq 2.0\;{\rm GeV}/c$; ${\rm p}: 0.5 \leq p_{\rm T} \leq 2.5\;{\rm GeV}/c$).
Balance function $B^{{\rm KK}}$ measured in semicentral Pb--Pb collisions at $\sqrt{s_{\rm NN}}=2.76\;\text{TeV}$ ($\pi,{\rm K}: 0.2 \leq p_{\rm T} \leq 2.0\;{\rm GeV}/c$; ${\rm p}: 0.5 \leq p_{\rm T} \leq 2.5\;{\rm GeV}/c$).
Balance function $B^{{\rm p\bar{p}}}$ measured in semicentral Pb--Pb collisions at $\sqrt{s_{\rm NN}}=2.76\;\text{TeV}$ ($\pi,{\rm K}: 0.2 \leq p_{\rm T} \leq 2.0\;{\rm GeV}/c$; ${\rm p}: 0.5 \leq p_{\rm T} \leq 2.5\;{\rm GeV}/c$).
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