CMS-FSQ-14-002 ; CERN-EP-2017-327 | ||
Study of Bose-Einstein correlations in pp, pPb, and PbPb collisions at the LHC | ||
CMS Collaboration | ||
20 December 2017 | ||
Phys. Rev. C 97 (2018) 064912 | ||
Abstract: Quantum statistical (Bose-Einstein) two-particle correlations are measured in pp collisions at $\sqrt{s}= $ 0.9, 2.76, and 7 TeV, as well as in pPb and peripheral PbPb collisions at nucleon-nucleon center-of-mass energies of 5.02 and 2.76 TeV, respectively, using the CMS detector at the LHC. Separate analyses are performed for same-sign unidentified charged particles as well as for same-sign pions and kaons identified via their energy loss in the silicon tracker. The characteristics of the one-, two-, and three-dimensional correlation functions are studied as functions of the pair average transverse momentum (${k_{\mathrm{T}}}$) and the charged-particle multiplicity in the event. For all systems, the extracted correlation radii steadily increase with the event multiplicity, and decrease with increasing ${k_{\mathrm{T}}}$. The radii are in the range 1-5 fm, the largest values corresponding to very high multiplicity pPb interactions and to peripheral PbPb collisions with multiplicities similar to those seen in pPb data. It is also observed that the dependencies of the radii on multiplicity and ${k_{\mathrm{T}}}$ largely factorize. At the same multiplicity, the radii are relatively independent of the colliding system and center-of-mass energy. | ||
Links: e-print arXiv:1712.07198 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; CADI line (restricted) ; |
Figures | |
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Figure 1:
Most probable logarithm of the energy loss rate $\varepsilon $ normalized at a reference path length $l_0 = $ 450 $\mu $m in pPb collisions at $ {\sqrt {\smash [b]{s_{_\text {NN}}}}} = $ 5.02 TeV. The distribution of $ \ln \varepsilon $ is shown as a function of total momentum $p$ for positively charged particles (left), as well as for identified charged particles (both charges) with high purity selection ($ > $99.5%, right). The linear $z$ axis scale is shown in arbitrary units. The curves show the expected $ \ln \varepsilon $ for electrons, pions, kaons, and protons (full theoretical calculation, Eq. (33.11) in Ref. [23]). |
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Figure 1-a:
Most probable logarithm of the energy loss rate $\varepsilon $ normalized at a reference path length $l_0 = $ 450 $\mu $m in pPb collisions at $ {\sqrt {\smash [b]{s_{_\text {NN}}}}} = $ 5.02 TeV. The distribution of $ \ln \varepsilon $ is shown as a function of total momentum $p$ for positively charged particles. The linear $z$ axis scale is shown in arbitrary units. The curves show the expected $ \ln \varepsilon $ for electrons, pions, kaons, and protons (full theoretical calculation, Eq. (33.11) in Ref. [23]). |
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Figure 1-b:
Most probable logarithm of the energy loss rate $\varepsilon $ normalized at a reference path length $l_0 = $ 450 $\mu $m in pPb collisions at $ {\sqrt {\smash [b]{s_{_\text {NN}}}}} = $ 5.02 TeV. The distribution of $ \ln \varepsilon $ is shown as a function of total momentum $p$ for identified charged particles (both charges) with high purity selection ($ > $99.5%). The linear $z$ axis scale is shown in arbitrary units. The curves show the expected $ \ln \varepsilon $ for electrons, pions, kaons, and protons (full theoretical calculation, Eq. (33.11) in Ref. [23]). |
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Figure 2:
Contribution of resonance decays to the measured Coulomb-corrected correlation function of $ {\pi ^+} {\pi ^-} $ (for 2 $ \le {N_\text {rec2}} < $ 10, left, blue squares) and $ {\mathrm {K^+}} {\mathrm {K^-}} $ (for 2 $ \le {N_\text {rec2}} < $ 60, right, blue squares). The $ {\phi \mathrm {(1020)}}$ peak (right panel) is off-scale. |
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Figure 2-a:
Contribution of resonance decays to the measured Coulomb-corrected correlation function of $ {\pi ^+} {\pi ^-} $ (for 2 $ \le {N_\text {rec2}} < $ 10, blue squares). |
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Figure 2-b:
Contribution of resonance decays to the measured Coulomb-corrected correlation function of $ {\mathrm {K^+}} {\mathrm {K^-}} $ (for 2 $ \le {N_\text {rec2}} < $ 60, blue squares). The $ {\phi \mathrm {(1020)}}$ peak is off-scale. |
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Figure 3:
Contribution of clusters (mini-jets and multi-body decays of resonances) to the measured Coulomb-corrected correlation function of ${\pi ^+} {\pi ^-}$ for pPb interactions at $ {\sqrt {\smash [b]{s_{_\text {NN}}}}} = $ 5.02 TeV in two bins of event multiplicity and $ {k_{\mathrm {T}}} $. The solid curves show fits according to Eq. 6. |
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Figure 3-a:
Contribution of clusters (mini-jets and multi-body decays of resonances) to the measured Coulomb-corrected correlation function of ${\pi ^+} {\pi ^-}$ for pPb interactions at $ {\sqrt {\smash [b]{s_{_\text {NN}}}}} = $ 5.02 TeV in a bin of event multiplicity and $ {k_{\mathrm {T}}} $. The solid curves show fits according to Eq. 6. |
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Figure 3-b:
Contribution of clusters (mini-jets and multi-body decays of resonances) to the measured Coulomb-corrected correlation function of ${\pi ^+} {\pi ^-}$ for pPb interactions at $ {\sqrt {\smash [b]{s_{_\text {NN}}}}} = $ 5.02 TeV in a bin of event multiplicity and $ {k_{\mathrm {T}}} $. The solid curves show fits according to Eq. 6. |
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Figure 4:
Dependence of the relative amplitude $z({N_\text {rec2}})$ of the cluster contribution (between SS and OS pairs), as a function of $ {N_\text {rec2}} $ for two $ {k_{\mathrm {T}}} $ bins. Fit results (points with error bars) from all collision types are plotted together with combinatorics-motivated fits (solid curves) and their estimated systematic uncertainties ($\pm $0.2 bands). |
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Figure 4-a:
Dependence of the relative amplitude $z({N_\text {rec2}})$ of the cluster contribution (between SS and OS pairs), as a function of $ {N_\text {rec2}} $ for a $ {k_{\mathrm {T}}} $ bin. Fit results (points with error bars) from all collision types are plotted together with combinatorics-motivated fits (solid curves) and their estimated systematic uncertainties ($\pm $0.2 bands). |
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Figure 4-b:
Dependence of the relative amplitude $z({N_\text {rec2}})$ of the cluster contribution (between SS and OS pairs), as a function of $ {N_\text {rec2}} $ for a $ {k_{\mathrm {T}}} $ bin. Fit results (points with error bars) from all collision types are plotted together with combinatorics-motivated fits (solid curves) and their estimated systematic uncertainties ($\pm $0.2 bands). |
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Figure 5:
Coulomb-corrected OS correlation function of pions (blue squares) as a function of a combination of $ {q_\text {L}} $ and $ {q_\text {T}} $, in two selected $ {N_\text {rec2}} $ bins for all $ {k_{\mathrm {T}}} $ values (left : 40 $ \le {N_\text {rec2}} < $ 50, right : 160 $ \le {N_\text {rec2}} < $ 170). For better visibility, only a randomly selected small fraction of the points is plotted. In addition, those with statistical uncertainty higher than 10% are plotted with light grey color. The solid curves indicate the prediction of the parametrized cluster contribution. |
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Figure 5-a:
Coulomb-corrected OS correlation function of pions (blue squares) as a function of a combination of $ {q_\text {L}} $ and $ {q_\text {T}} $, in a selected $ {N_\text {rec2}} $ bin for all $ {k_{\mathrm {T}}} $ values (40 $ \le {N_\text {rec2}} < $ 50). For better visibility, only a randomly selected small fraction of the points is plotted. In addition, those with statistical uncertainty higher than 10% are plotted with light grey color. The solid curves indicate the prediction of the parametrized cluster contribution. |
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Figure 5-b:
Coulomb-corrected OS correlation function of pions (blue squares) as a function of a combination of $ {q_\text {L}} $ and $ {q_\text {T}} $, in a selected $ {N_\text {rec2}} $ bin for all $ {k_{\mathrm {T}}} $ values (160 $ \le {N_\text {rec2}} < $ 170). For better visibility, only a randomly selected small fraction of the points is plotted. In addition, those with statistical uncertainty higher than 10% are plotted with light grey color. The solid curves indicate the prediction of the parametrized cluster contribution. |
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Figure 6:
Dependence on track multiplicity of the radius (left) and intercept parameter (right), from the exponential fits to the 1D correlation functions via Eq. I, obtained in the double ratio (filled markers) and the particle identification (for pions, empty squares) methods in pp collisions at 7 TeV, together with the results from Ref. [6]. The inner (outer) error bars correspond to statistical (systematic) uncertainties. |
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Figure 6-a:
Dependence on track multiplicity of the radius, from the exponential fits to the 1D correlation functions via Eq. I, obtained in the double ratio (filled markers) and the particle identification (for pions, empty squares) methods in pp collisions at 7 TeV, together with the results from Ref. [6]. The inner (outer) error bars correspond to statistical (systematic) uncertainties. |
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Figure 6-b:
Dependence on track multiplicity of the intercept parameter, from the exponential fits to the 1D correlation functions via Eq. I, obtained in the double ratio (filled markers) and the particle identification (for pions, empty squares) methods in pp collisions at 7 TeV, together with the results from Ref. [6]. The inner (outer) error bars correspond to statistical (systematic) uncertainties. |
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Figure 7:
Left : 1D single ratios as a function of $ {q_\text {inv}} $ for data and simulation (PYTHIA6 Z2 tune) in pp collisions at $\sqrt {s} = $ 2.76 TeV. Right : Corresponding 1D double ratio versus $ {q_\text {inv}} $ fitted to the superimposed exponential fit function. Only statistical uncertainties are included, commonly of the order or smaller than the marker size. |
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Figure 7-a:
1D single ratios as a function of $ {q_\text {inv}} $ for data and simulation (PYTHIA6 Z2 tune) in pp collisions at $\sqrt {s} = $ 2.76 TeV. Only statistical uncertainties are included, commonly of the order or smaller than the marker size. |
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Figure 7-b:
Corresponding 1D double ratio versus $ {q_\text {inv}} $ fitted to the superimposed exponential fit function. Only statistical uncertainties are included, commonly of the order or smaller than the marker size. |
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Figure 8:
Top: $ {R_\text {inv}} $ (left) and $\lambda $ (right) as a function of $ {k_{\mathrm {T}}} $ obtained from an exponential fit to BEC data in three multiplicity bins in pp collisions at 2.76 TeV (open symbols) and 7 TeV (filled symbols). The boxes indicate the systematic uncertainties. Bottom: Radius parameter $ {R_\text {inv}} $ as a function of $ {N_\text {trk0.4}} $ with statistical (inner error bars) and statistical plus systematic uncertainties added in quadrature (outer error bars) in pp collisions at 2.76 TeV (open squares) and 7 TeV (filled squares), together with previous results at 7 TeV (filled diamonds) [6]. The curves indicate the respective fits to a $ {N_\text {trk0.4}} ^{1/3}$ functional form. |
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Figure 8-a:
$ {R_\text {inv}} $ as a function of $ {k_{\mathrm {T}}} $ obtained from an exponential fit to BEC data in three multiplicity bins in pp collisions at 2.76 TeV (open symbols) and 7 TeV (filled symbols). The boxes indicate the systematic uncertainties. |
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Figure 8-b:
$\lambda $ as a function of $ {k_{\mathrm {T}}} $ obtained from an exponential fit to BEC data in three multiplicity bins in pp collisions at 2.76 TeV (open symbols) and 7 TeV (filled symbols). The boxes indicate the systematic uncertainties. |
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Figure 8-c:
Radius parameter $ {R_\text {inv}} $ as a function of $ {N_\text {trk0.4}} $ with statistical (inner error bars) and statistical plus systematic uncertainties added in quadrature (outer error bars) in pp collisions at 2.76 TeV (open squares) and 7 TeV (filled squares), together with previous results at 7 TeV (filled diamonds) [6]. The curves indicate the respective fits to a $ {N_\text {trk0.4}} ^{1/3}$ functional form. |
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Figure 9:
1D correlation functions (with the $y$-axis cut off at $\sim $1.1) versus $ {q_\text {inv}} $ obtained with the double ratio method in pp at 2.76 TeV for increasing ranges of $ {k_{\mathrm {T}}} $ (left to right) and of $ {N_\text {trk0.4}} $ (top to bottom). Data are fitted to the exponential (red curve) and the $\tau $ model (black curve) functions. The error bars show the statistical uncertainties. |
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Figure 10:
Left : Anticorrelation depth $\Delta $ as a function of $ {N_\text {trk0.4}} $ integrated over all $ {k_{\mathrm {T}}} $, in pp collisions at 2.76 TeV (open squares) and 7 TeV (filled squares), together with previous results at 7 TeV (filled diamonds) [6]. Inner (outer) error bars represent the statistical (plus systematic, added in quadrature) uncertainties. Right : Corresponding anticorrelation depth as a function of $ {k_{\mathrm {T}}} $ for various $ {N_\text {trk0.4}} $ ranges, in pp at 2.76 TeV (open symbols) and 7 TeV (filled symbols). The boxes indicate the systematic uncertainties. |
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Figure 10-a:
Anticorrelation depth $\Delta $ as a function of $ {N_\text {trk0.4}} $ integrated over all $ {k_{\mathrm {T}}} $, in pp collisions at 2.76 TeV (open squares) and 7 TeV (filled squares), together with previous results at 7 TeV (filled diamonds) [6]. Inner (outer) error bars represent the statistical (plus systematic, added in quadrature) uncertainties. |
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Figure 10-b:
Corresponding anticorrelation depth as a function of $ {k_{\mathrm {T}}} $ for various $ {N_\text {trk0.4}} $ ranges, in pp at 2.76 TeV (open symbols) and 7 TeV (filled symbols). The boxes indicate the systematic uncertainties. |
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Figure 11:
Double ratio results measured in the LCMS, integrated over all $ {N_\text {trk0.4}} $ and $ {k_{\mathrm {T}}} $ bins, in pp collisions at $\sqrt {s} = $ 2.76 TeV. Top: 2D correlation functions as a function of $({q_\text {T}}, {q_\text {L}})$ without (left) and with (right) the 2D L\'evy (with $a = 1$) fit function superimposed. Bottom: Corresponding 1D projections in terms of $ {q_\text {L}} $ (for $| {q_\text {T}} | < $ 0.05 GeV, left) and $ {q_\text {T}} $ (for $| {q_\text {L}} | < $ 0.05 GeV, right). The error bars indicate statistical uncertainties. |
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Figure 11-a:
Double ratio results measured in the LCMS, integrated over all $ {N_\text {trk0.4}} $ and $ {k_{\mathrm {T}}} $ bins, in pp collisions at $\sqrt {s} = $ 2.76 TeV. Top: 2D correlation functions as a function of $({q_\text {T}}, {q_\text {L}})$ without (left) and with (right) the 2D L\'evy (with $a = 1$) fit function superimposed. Bottom: Corresponding 1D projections in terms of $ {q_\text {L}} $ (for $| {q_\text {T}} | < $ 0.05 GeV, left) and $ {q_\text {T}} $ (for $| {q_\text {L}} | < $ 0.05 GeV, right). The error bars indicate statistical uncertainties. |
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Figure 11-b:
Double ratio results measured in the LCMS, integrated over all $ {N_\text {trk0.4}} $ and $ {k_{\mathrm {T}}} $ bins, in pp collisions at $\sqrt {s} = $ 2.76 TeV. Top: 2D correlation functions as a function of $({q_\text {T}}, {q_\text {L}})$ without (left) and with (right) the 2D L\'evy (with $a = 1$) fit function superimposed. Bottom: Corresponding 1D projections in terms of $ {q_\text {L}} $ (for $| {q_\text {T}} | < $ 0.05 GeV, left) and $ {q_\text {T}} $ (for $| {q_\text {L}} | < $ 0.05 GeV, right). The error bars indicate statistical uncertainties. |
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Figure 11-c:
Double ratio results measured in the LCMS, integrated over all $ {N_\text {trk0.4}} $ and $ {k_{\mathrm {T}}} $ bins, in pp collisions at $\sqrt {s} = $ 2.76 TeV. Top: 2D correlation functions as a function of $({q_\text {T}}, {q_\text {L}})$ without (left) and with (right) the 2D L\'evy (with $a = 1$) fit function superimposed. Bottom: Corresponding 1D projections in terms of $ {q_\text {L}} $ (for $| {q_\text {T}} | < $ 0.05 GeV, left) and $ {q_\text {T}} $ (for $| {q_\text {L}} | < $ 0.05 GeV, right). The error bars indicate statistical uncertainties. |
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Figure 11-d:
Double ratio results measured in the LCMS, integrated over all $ {N_\text {trk0.4}} $ and $ {k_{\mathrm {T}}} $ bins, in pp collisions at $\sqrt {s} = $ 2.76 TeV. Top: 2D correlation functions as a function of $({q_\text {T}}, {q_\text {L}})$ without (left) and with (right) the 2D L\'evy (with $a = 1$) fit function superimposed. Bottom: Corresponding 1D projections in terms of $ {q_\text {L}} $ (for $| {q_\text {T}} | < $ 0.05 GeV, left) and $ {q_\text {T}} $ (for $| {q_\text {L}} | < $ 0.05 GeV, right). The error bars indicate statistical uncertainties. |
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Figure 12:
Radius parameters as a function of $ {k_{\mathrm {T}}} $, for different $ {N_\text {trk0.4}} $ bins, obtained from data fitted to the stretched exponential function in pp collisions at $\sqrt {s} = $ 2.76 TeV (open symbols) and 7 TeV (filled symbols) in the CM frame (top) and in the LCMS (bottom). The boxes indicate the systematic uncertainties. |
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Figure 12-a:
Radius parameters as a function of $ {k_{\mathrm {T}}} $, for different $ {N_\text {trk0.4}} $ bins, obtained from data fitted to the stretched exponential function in pp collisions at $\sqrt {s} = $ 2.76 TeV (open symbols) and 7 TeV (filled symbols) in the CM frame (top) and in the LCMS (bottom). The boxes indicate the systematic uncertainties. |
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Figure 12-b:
Radius parameters as a function of $ {k_{\mathrm {T}}} $, for different $ {N_\text {trk0.4}} $ bins, obtained from data fitted to the stretched exponential function in pp collisions at $\sqrt {s} = $ 2.76 TeV (open symbols) and 7 TeV (filled symbols) in the CM frame (top) and in the LCMS (bottom). The boxes indicate the systematic uncertainties. |
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Figure 12-c:
Radius parameters as a function of $ {k_{\mathrm {T}}} $, for different $ {N_\text {trk0.4}} $ bins, obtained from data fitted to the stretched exponential function in pp collisions at $\sqrt {s} = $ 2.76 TeV (open symbols) and 7 TeV (filled symbols) in the CM frame (top) and in the LCMS (bottom). The boxes indicate the systematic uncertainties. |
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Figure 12-d:
Radius parameters as a function of $ {k_{\mathrm {T}}} $, for different $ {N_\text {trk0.4}} $ bins, obtained from data fitted to the stretched exponential function in pp collisions at $\sqrt {s} = $ 2.76 TeV (open symbols) and 7 TeV (filled symbols) in the CM frame (top) and in the LCMS (bottom). The boxes indicate the systematic uncertainties. |
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Figure 13:
Intercept parameter $\lambda $ as a function of $ {k_{\mathrm {T}}} $, for different $ {N_\text {trk0.4}} $ bins, obtained from data fitted to the stretched exponential function in pp collisions at $\sqrt {s} = $ 2.76 TeV (open symbols) and 7 TeV (filled symbols) in the CM frame (left) and in the LCMS (right). The boxes indicate the systematic uncertainties. |
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Figure 13-a:
Intercept parameter $\lambda $ as a function of $ {k_{\mathrm {T}}} $, for different $ {N_\text {trk0.4}} $ bins, obtained from data fitted to the stretched exponential function in pp collisions at $\sqrt {s} = $ 2.76 TeV (open symbols) and 7 TeV (filled symbols) in the CM frame (left) and in the LCMS (right). The boxes indicate the systematic uncertainties. |
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Figure 13-b:
Intercept parameter $\lambda $ as a function of $ {k_{\mathrm {T}}} $, for different $ {N_\text {trk0.4}} $ bins, obtained from data fitted to the stretched exponential function in pp collisions at $\sqrt {s} = $ 2.76 TeV (open symbols) and 7 TeV (filled symbols) in the CM frame (left) and in the LCMS (right). The boxes indicate the systematic uncertainties. |
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Figure 14:
Results obtained in the LCMS for the 2D double ratios in the $({q_\text {L}}, {q_\text {T}})$ plane, zoomed along the correlation function axis, for four charged multiplicity bins, $ {N_\text {trk0.4}} $ (integrated over all $ {k_{\mathrm {T}}} $), increasing from upper left to lower right. The BEC peak is cut off at $\sim $1.2 for a better visualization of the directional behavior. The 1D projections in $ {q_\text {L}} $ (for $ {| {q_\text {T}} |} < $ 0.05 GeV) and $ {q_\text {T}} $ (for $ {| {q_\text {L}} |} < $ 0.05 GeV) are shown to the right of the bidimensional plots, with error bars corresponding to statistical uncertainties. |
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Figure 14-a:
Results obtained in the LCMS for the 2D double ratios in the $({q_\text {L}}, {q_\text {T}})$ plane, zoomed along the correlation function axis, for four charged multiplicity bins, $ {N_\text {trk0.4}} $ (integrated over all $ {k_{\mathrm {T}}} $), increasing from upper left to lower right. The BEC peak is cut off at $\sim $1.2 for a better visualization of the directional behavior. The 1D projections in $ {q_\text {L}} $ (for $ {| {q_\text {T}} |} < $ 0.05 GeV) and $ {q_\text {T}} $ (for $ {| {q_\text {L}} |} < $ 0.05 GeV) are shown to the right of the bidimensional plots, with error bars corresponding to statistical uncertainties. |
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Figure 14-b:
Results obtained in the LCMS for the 2D double ratios in the $({q_\text {L}}, {q_\text {T}})$ plane, zoomed along the correlation function axis, for four charged multiplicity bins, $ {N_\text {trk0.4}} $ (integrated over all $ {k_{\mathrm {T}}} $), increasing from upper left to lower right. The BEC peak is cut off at $\sim $1.2 for a better visualization of the directional behavior. The 1D projections in $ {q_\text {L}} $ (for $ {| {q_\text {T}} |} < $ 0.05 GeV) and $ {q_\text {T}} $ (for $ {| {q_\text {L}} |} < $ 0.05 GeV) are shown to the right of the bidimensional plots, with error bars corresponding to statistical uncertainties. |
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Figure 14-c:
Results obtained in the LCMS for the 2D double ratios in the $({q_\text {L}}, {q_\text {T}})$ plane, zoomed along the correlation function axis, for four charged multiplicity bins, $ {N_\text {trk0.4}} $ (integrated over all $ {k_{\mathrm {T}}} $), increasing from upper left to lower right. The BEC peak is cut off at $\sim $1.2 for a better visualization of the directional behavior. The 1D projections in $ {q_\text {L}} $ (for $ {| {q_\text {T}} |} < $ 0.05 GeV) and $ {q_\text {T}} $ (for $ {| {q_\text {L}} |} < $ 0.05 GeV) are shown to the right of the bidimensional plots, with error bars corresponding to statistical uncertainties. |
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Figure 14-d:
Results obtained in the LCMS for the 2D double ratios in the $({q_\text {L}}, {q_\text {T}})$ plane, zoomed along the correlation function axis, for four charged multiplicity bins, $ {N_\text {trk0.4}} $ (integrated over all $ {k_{\mathrm {T}}} $), increasing from upper left to lower right. The BEC peak is cut off at $\sim $1.2 for a better visualization of the directional behavior. The 1D projections in $ {q_\text {L}} $ (for $ {| {q_\text {T}} |} < $ 0.05 GeV) and $ {q_\text {T}} $ (for $ {| {q_\text {L}} |} < $ 0.05 GeV) are shown to the right of the bidimensional plots, with error bars corresponding to statistical uncertainties. |
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Figure 15:
Results obtained in the LCMS for the 3D double ratios in pp collisions at 7 TeV, integrated over $ {N_\text {trk0.4}} $ and $ {k_{\mathrm {T}}} $. Top: 2D projections over the $({q_\text {L}}, {q_\text {S}})$, $({q_\text {O}}, {q_\text {S}})$, and $({q_\text {O}}, {q_\text {L}})$ planes, for $| {q_\text {O}} | < $ 0.05 GeV (left), $| {q_\text {L}} | < $ 0.05 GeV (middle), and $| {q_\text {S}} | < $ 0.05 GeV (right). Bottom: 1D projections of the same data, with the complementary two variables constrained to be within the first bin ($|q_{i,j}| < $ 0.05 GeV). The error bars show the corresponding statistical uncertainties. All plots are zoomed along the correlation function axis with the BEC peak cut off above 1.2. |
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Figure 15-a:
Results obtained in the LCMS for the 3D double ratios in pp collisions at 7 TeV, integrated over $ {N_\text {trk0.4}} $ and $ {k_{\mathrm {T}}} $. Top: 2D projections over the $({q_\text {L}}, {q_\text {S}})$, $({q_\text {O}}, {q_\text {S}})$, and $({q_\text {O}}, {q_\text {L}})$ planes, for $| {q_\text {O}} | < $ 0.05 GeV (left), $| {q_\text {L}} | < $ 0.05 GeV (middle), and $| {q_\text {S}} | < $ 0.05 GeV (right). Bottom: 1D projections of the same data, with the complementary two variables constrained to be within the first bin ($|q_{i,j}| < $ 0.05 GeV). The error bars show the corresponding statistical uncertainties. All plots are zoomed along the correlation function axis with the BEC peak cut off above 1.2. |
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Figure 15-b:
Results obtained in the LCMS for the 3D double ratios in pp collisions at 7 TeV, integrated over $ {N_\text {trk0.4}} $ and $ {k_{\mathrm {T}}} $. Top: 2D projections over the $({q_\text {L}}, {q_\text {S}})$, $({q_\text {O}}, {q_\text {S}})$, and $({q_\text {O}}, {q_\text {L}})$ planes, for $| {q_\text {O}} | < $ 0.05 GeV (left), $| {q_\text {L}} | < $ 0.05 GeV (middle), and $| {q_\text {S}} | < $ 0.05 GeV (right). Bottom: 1D projections of the same data, with the complementary two variables constrained to be within the first bin ($|q_{i,j}| < $ 0.05 GeV). The error bars show the corresponding statistical uncertainties. All plots are zoomed along the correlation function axis with the BEC peak cut off above 1.2. |
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Figure 15-c:
Results obtained in the LCMS for the 3D double ratios in pp collisions at 7 TeV, integrated over $ {N_\text {trk0.4}} $ and $ {k_{\mathrm {T}}} $. Top: 2D projections over the $({q_\text {L}}, {q_\text {S}})$, $({q_\text {O}}, {q_\text {S}})$, and $({q_\text {O}}, {q_\text {L}})$ planes, for $| {q_\text {O}} | < $ 0.05 GeV (left), $| {q_\text {L}} | < $ 0.05 GeV (middle), and $| {q_\text {S}} | < $ 0.05 GeV (right). Bottom: 1D projections of the same data, with the complementary two variables constrained to be within the first bin ($|q_{i,j}| < $ 0.05 GeV). The error bars show the corresponding statistical uncertainties. All plots are zoomed along the correlation function axis with the BEC peak cut off above 1.2. |
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Figure 15-d:
Results obtained in the LCMS for the 3D double ratios in pp collisions at 7 TeV, integrated over $ {N_\text {trk0.4}} $ and $ {k_{\mathrm {T}}} $. Top: 2D projections over the $({q_\text {L}}, {q_\text {S}})$, $({q_\text {O}}, {q_\text {S}})$, and $({q_\text {O}}, {q_\text {L}})$ planes, for $| {q_\text {O}} | < $ 0.05 GeV (left), $| {q_\text {L}} | < $ 0.05 GeV (middle), and $| {q_\text {S}} | < $ 0.05 GeV (right). Bottom: 1D projections of the same data, with the complementary two variables constrained to be within the first bin ($|q_{i,j}| < $ 0.05 GeV). The error bars show the corresponding statistical uncertainties. All plots are zoomed along the correlation function axis with the BEC peak cut off above 1.2. |
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Figure 15-e:
Results obtained in the LCMS for the 3D double ratios in pp collisions at 7 TeV, integrated over $ {N_\text {trk0.4}} $ and $ {k_{\mathrm {T}}} $. Top: 2D projections over the $({q_\text {L}}, {q_\text {S}})$, $({q_\text {O}}, {q_\text {S}})$, and $({q_\text {O}}, {q_\text {L}})$ planes, for $| {q_\text {O}} | < $ 0.05 GeV (left), $| {q_\text {L}} | < $ 0.05 GeV (middle), and $| {q_\text {S}} | < $ 0.05 GeV (right). Bottom: 1D projections of the same data, with the complementary two variables constrained to be within the first bin ($|q_{i,j}| < $ 0.05 GeV). The error bars show the corresponding statistical uncertainties. All plots are zoomed along the correlation function axis with the BEC peak cut off above 1.2. |
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Figure 15-f:
Results obtained in the LCMS for the 3D double ratios in pp collisions at 7 TeV, integrated over $ {N_\text {trk0.4}} $ and $ {k_{\mathrm {T}}} $. Top: 2D projections over the $({q_\text {L}}, {q_\text {S}})$, $({q_\text {O}}, {q_\text {S}})$, and $({q_\text {O}}, {q_\text {L}})$ planes, for $| {q_\text {O}} | < $ 0.05 GeV (left), $| {q_\text {L}} | < $ 0.05 GeV (middle), and $| {q_\text {S}} | < $ 0.05 GeV (right). Bottom: 1D projections of the same data, with the complementary two variables constrained to be within the first bin ($|q_{i,j}| < $ 0.05 GeV). The error bars show the corresponding statistical uncertainties. All plots are zoomed along the correlation function axis with the BEC peak cut off above 1.2. |
png pdf |
Figure 16:
3D radii parameters as a function of $ {k_{\mathrm {T}}} $ (integrated over all $ {N_\text {trk0.4}} $), obtained from double ratios fitted to the exponential (left) and L\'evy (with $a = 1$, right) functions for pp collisions at $\sqrt {s} = $ 7 TeV in the CM frame (top) and in the LCMS (bottom). The boxes indicate the systematic uncertainties. |
png pdf |
Figure 16-a:
3D radii parameters as a function of $ {k_{\mathrm {T}}} $ (integrated over all $ {N_\text {trk0.4}} $), obtained from double ratios fitted to the exponential (left) and L\'evy (with $a = 1$, right) functions for pp collisions at $\sqrt {s} = $ 7 TeV in the CM frame (top) and in the LCMS (bottom). The boxes indicate the systematic uncertainties. |
png pdf |
Figure 16-b:
3D radii parameters as a function of $ {k_{\mathrm {T}}} $ (integrated over all $ {N_\text {trk0.4}} $), obtained from double ratios fitted to the exponential (left) and L\'evy (with $a = 1$, right) functions for pp collisions at $\sqrt {s} = $ 7 TeV in the CM frame (top) and in the LCMS (bottom). The boxes indicate the systematic uncertainties. |
png pdf |
Figure 16-c:
3D radii parameters as a function of $ {k_{\mathrm {T}}} $ (integrated over all $ {N_\text {trk0.4}} $), obtained from double ratios fitted to the exponential (left) and L\'evy (with $a = 1$, right) functions for pp collisions at $\sqrt {s} = $ 7 TeV in the CM frame (top) and in the LCMS (bottom). The boxes indicate the systematic uncertainties. |
png pdf |
Figure 16-d:
3D radii parameters as a function of $ {k_{\mathrm {T}}} $ (integrated over all $ {N_\text {trk0.4}} $), obtained from double ratios fitted to the exponential (left) and L\'evy (with $a = 1$, right) functions for pp collisions at $\sqrt {s} = $ 7 TeV in the CM frame (top) and in the LCMS (bottom). The boxes indicate the systematic uncertainties. |
png pdf |
Figure 17:
3D radii parameters as a function of $ {N_\text {trk0.4}} $ (integrated over all $ {k_{\mathrm {T}}} $), obtained from double ratios fitted to the exponential (left) and Levy (with $a = $ 1, right) functions for pp collisions at $\sqrt {s} = $ 7 TeV in the CM frame (top) and in the LCMS (bottom). The boxes indicate the systematic uncertainties. |
png pdf |
Figure 17-a:
3D radii parameters as a function of $ {N_\text {trk0.4}} $ (integrated over all $ {k_{\mathrm {T}}} $), obtained from double ratios fitted to the exponential (left) and Levy (with $a = $ 1, right) functions for pp collisions at $\sqrt {s} = $ 7 TeV in the CM frame (top) and in the LCMS (bottom). The boxes indicate the systematic uncertainties. |
png pdf |
Figure 17-b:
3D radii parameters as a function of $ {N_\text {trk0.4}} $ (integrated over all $ {k_{\mathrm {T}}} $), obtained from double ratios fitted to the exponential (left) and Levy (with $a = $ 1, right) functions for pp collisions at $\sqrt {s} = $ 7 TeV in the CM frame (top) and in the LCMS (bottom). The boxes indicate the systematic uncertainties. |
png pdf |
Figure 17-c:
3D radii parameters as a function of $ {N_\text {trk0.4}} $ (integrated over all $ {k_{\mathrm {T}}} $), obtained from double ratios fitted to the exponential (left) and Levy (with $a = $ 1, right) functions for pp collisions at $\sqrt {s} = $ 7 TeV in the CM frame (top) and in the LCMS (bottom). The boxes indicate the systematic uncertainties. |
png pdf |
Figure 17-d:
3D radii parameters as a function of $ {N_\text {trk0.4}} $ (integrated over all $ {k_{\mathrm {T}}} $), obtained from double ratios fitted to the exponential (left) and Levy (with $a = $ 1, right) functions for pp collisions at $\sqrt {s} = $ 7 TeV in the CM frame (top) and in the LCMS (bottom). The boxes indicate the systematic uncertainties. |
png pdf |
Figure 18:
Intercept parameter $\lambda ^{(*)}$ in the CM frame (left) and in the LCMS (right) as functions of $ {k_{\mathrm {T}}} $ (integrated over $ {N_\text {trk0.4}} $, top) and of $ {N_\text {trk0.4}} $ (integrated over $ {k_{\mathrm {T}}} $, bottom), obtained from fits to the double ratios with the exponential and the Levy (with $a = $ 1) functions in pp collisions at 7 TeV. The boxes indicate the systematic uncertainties. |
png pdf |
Figure 18-a:
Intercept parameter $\lambda ^{(*)}$ in the CM frame (left) and in the LCMS (right) as functions of $ {k_{\mathrm {T}}} $ (integrated over $ {N_\text {trk0.4}} $, top) and of $ {N_\text {trk0.4}} $ (integrated over $ {k_{\mathrm {T}}} $, bottom), obtained from fits to the double ratios with the exponential and the Levy (with $a = $ 1) functions in pp collisions at 7 TeV. The boxes indicate the systematic uncertainties. |
png pdf |
Figure 18-b:
Intercept parameter $\lambda ^{(*)}$ in the CM frame (left) and in the LCMS (right) as functions of $ {k_{\mathrm {T}}} $ (integrated over $ {N_\text {trk0.4}} $, top) and of $ {N_\text {trk0.4}} $ (integrated over $ {k_{\mathrm {T}}} $, bottom), obtained from fits to the double ratios with the exponential and the Levy (with $a = $ 1) functions in pp collisions at 7 TeV. The boxes indicate the systematic uncertainties. |
png pdf |
Figure 18-c:
Intercept parameter $\lambda ^{(*)}$ in the CM frame (left) and in the LCMS (right) as functions of $ {k_{\mathrm {T}}} $ (integrated over $ {N_\text {trk0.4}} $, top) and of $ {N_\text {trk0.4}} $ (integrated over $ {k_{\mathrm {T}}} $, bottom), obtained from fits to the double ratios with the exponential and the Levy (with $a = $ 1) functions in pp collisions at 7 TeV. The boxes indicate the systematic uncertainties. |
png pdf |
Figure 18-d:
Intercept parameter $\lambda ^{(*)}$ in the CM frame (left) and in the LCMS (right) as functions of $ {k_{\mathrm {T}}} $ (integrated over $ {N_\text {trk0.4}} $, top) and of $ {N_\text {trk0.4}} $ (integrated over $ {k_{\mathrm {T}}} $, bottom), obtained from fits to the double ratios with the exponential and the Levy (with $a = $ 1) functions in pp collisions at 7 TeV. The boxes indicate the systematic uncertainties. |
png pdf |
Figure 19:
Longitudinal radius parameter as a function of $ {N_\text {trk0.4}} $ (integrated over all $ {k_{\mathrm {T}}} $) in the CM frame ($ {R_\text {L}} ^*$, left) and in the LCMS ($ {R_\text {L}} $, right), obtained from 2D correlation functions fitted as functions of $ {q_\text {T}} $ and $ {q_\text {L}} $, compared to the values obtained in the 3D case (fits as a function of $ {q_\text {S}} $, $ {q_\text {L}} $, and $ {q_\text {S}} $), in pp collisions at $\sqrt {s} = $ 2.76 TeV (open symbols) and 7 TeV (closed symbols). The boxes indicate the systematic uncertainties. |
png pdf |
Figure 19-a:
Longitudinal radius parameter as a function of $ {N_\text {trk0.4}} $ (integrated over all $ {k_{\mathrm {T}}} $) in the CM frame ($ {R_\text {L}} ^*$, left) and in the LCMS ($ {R_\text {L}} $, right), obtained from 2D correlation functions fitted as functions of $ {q_\text {T}} $ and $ {q_\text {L}} $, compared to the values obtained in the 3D case (fits as a function of $ {q_\text {S}} $, $ {q_\text {L}} $, and $ {q_\text {S}} $), in pp collisions at $\sqrt {s} = $ 2.76 TeV (open symbols) and 7 TeV (closed symbols). The boxes indicate the systematic uncertainties. |
png pdf |
Figure 19-b:
Longitudinal radius parameter as a function of $ {N_\text {trk0.4}} $ (integrated over all $ {k_{\mathrm {T}}} $) in the CM frame ($ {R_\text {L}} ^*$, left) and in the LCMS ($ {R_\text {L}} $, right), obtained from 2D correlation functions fitted as functions of $ {q_\text {T}} $ and $ {q_\text {L}} $, compared to the values obtained in the 3D case (fits as a function of $ {q_\text {S}} $, $ {q_\text {L}} $, and $ {q_\text {S}} $), in pp collisions at $\sqrt {s} = $ 2.76 TeV (open symbols) and 7 TeV (closed symbols). The boxes indicate the systematic uncertainties. |
png pdf |
Figure 20:
SS correlation function (integrated over all $ {k_{\mathrm {T}}} $) measured in pPb collisions at 5.02 TeV as a function of $ {q_\text {inv}} $ or of the combined momentum, in two selected $ {N_\text {rec2}} $ bins (left and right), for pion pairs (red triangles) in one (top), two (middle), and three (bottom) dimensions, corrected for Coulomb interaction and cluster contributions (mini-jets and multi-body resonance decays). For better visibility, only a fraction of the points is plotted, and those with statistical uncertainty higher than 10% are in light-grey color. The solid curves indicate fits with the stretched exponential parametrization. |
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Figure 20-a:
SS correlation function (integrated over all $ {k_{\mathrm {T}}} $) measured in pPb collisions at 5.02 TeV as a function of $ {q_\text {inv}} $ or of the combined momentum, in two selected $ {N_\text {rec2}} $ bins (left and right), for pion pairs (red triangles) in one (top), two (middle), and three (bottom) dimensions, corrected for Coulomb interaction and cluster contributions (mini-jets and multi-body resonance decays). For better visibility, only a fraction of the points is plotted, and those with statistical uncertainty higher than 10% are in light-grey color. The solid curves indicate fits with the stretched exponential parametrization. |
png pdf |
Figure 20-b:
SS correlation function (integrated over all $ {k_{\mathrm {T}}} $) measured in pPb collisions at 5.02 TeV as a function of $ {q_\text {inv}} $ or of the combined momentum, in two selected $ {N_\text {rec2}} $ bins (left and right), for pion pairs (red triangles) in one (top), two (middle), and three (bottom) dimensions, corrected for Coulomb interaction and cluster contributions (mini-jets and multi-body resonance decays). For better visibility, only a fraction of the points is plotted, and those with statistical uncertainty higher than 10% are in light-grey color. The solid curves indicate fits with the stretched exponential parametrization. |
png pdf |
Figure 20-c:
SS correlation function (integrated over all $ {k_{\mathrm {T}}} $) measured in pPb collisions at 5.02 TeV as a function of $ {q_\text {inv}} $ or of the combined momentum, in two selected $ {N_\text {rec2}} $ bins (left and right), for pion pairs (red triangles) in one (top), two (middle), and three (bottom) dimensions, corrected for Coulomb interaction and cluster contributions (mini-jets and multi-body resonance decays). For better visibility, only a fraction of the points is plotted, and those with statistical uncertainty higher than 10% are in light-grey color. The solid curves indicate fits with the stretched exponential parametrization. |
png pdf |
Figure 20-d:
SS correlation function (integrated over all $ {k_{\mathrm {T}}} $) measured in pPb collisions at 5.02 TeV as a function of $ {q_\text {inv}} $ or of the combined momentum, in two selected $ {N_\text {rec2}} $ bins (left and right), for pion pairs (red triangles) in one (top), two (middle), and three (bottom) dimensions, corrected for Coulomb interaction and cluster contributions (mini-jets and multi-body resonance decays). For better visibility, only a fraction of the points is plotted, and those with statistical uncertainty higher than 10% are in light-grey color. The solid curves indicate fits with the stretched exponential parametrization. |
png pdf |
Figure 20-e:
SS correlation function (integrated over all $ {k_{\mathrm {T}}} $) measured in pPb collisions at 5.02 TeV as a function of $ {q_\text {inv}} $ or of the combined momentum, in two selected $ {N_\text {rec2}} $ bins (left and right), for pion pairs (red triangles) in one (top), two (middle), and three (bottom) dimensions, corrected for Coulomb interaction and cluster contributions (mini-jets and multi-body resonance decays). For better visibility, only a fraction of the points is plotted, and those with statistical uncertainty higher than 10% are in light-grey color. The solid curves indicate fits with the stretched exponential parametrization. |
png pdf |
Figure 20-f:
SS correlation function (integrated over all $ {k_{\mathrm {T}}} $) measured in pPb collisions at 5.02 TeV as a function of $ {q_\text {inv}} $ or of the combined momentum, in two selected $ {N_\text {rec2}} $ bins (left and right), for pion pairs (red triangles) in one (top), two (middle), and three (bottom) dimensions, corrected for Coulomb interaction and cluster contributions (mini-jets and multi-body resonance decays). For better visibility, only a fraction of the points is plotted, and those with statistical uncertainty higher than 10% are in light-grey color. The solid curves indicate fits with the stretched exponential parametrization. |
png pdf |
Figure 21:
SS correlation function (integrated over all $ {k_{\mathrm {T}}} $) measured in pPb collisions at 5.02 TeV as a function of $ {q_\text {inv}} $ or of the combined momentum, in two selected $ {N_\text {rec2}} $ bins (left and right), for kaon pairs (red triangles) in one (top) and two (bottom) dimensions, corrected for Coulomb interaction and cluster contributions (mini-jets and multi-body resonance decays). For better visibility, only a fraction of the points is plotted, and those with statistical uncertainty higher than 10% are in light-grey color. The solid curves indicate fits with the stretched exponential parametrization. |
png pdf |
Figure 21-a:
SS correlation function (integrated over all $ {k_{\mathrm {T}}} $) measured in pPb collisions at 5.02 TeV as a function of $ {q_\text {inv}} $ or of the combined momentum, in two selected $ {N_\text {rec2}} $ bins (left and right), for kaon pairs (red triangles) in one (top) and two (bottom) dimensions, corrected for Coulomb interaction and cluster contributions (mini-jets and multi-body resonance decays). For better visibility, only a fraction of the points is plotted, and those with statistical uncertainty higher than 10% are in light-grey color. The solid curves indicate fits with the stretched exponential parametrization. |
png pdf |
Figure 21-b:
SS correlation function (integrated over all $ {k_{\mathrm {T}}} $) measured in pPb collisions at 5.02 TeV as a function of $ {q_\text {inv}} $ or of the combined momentum, in two selected $ {N_\text {rec2}} $ bins (left and right), for kaon pairs (red triangles) in one (top) and two (bottom) dimensions, corrected for Coulomb interaction and cluster contributions (mini-jets and multi-body resonance decays). For better visibility, only a fraction of the points is plotted, and those with statistical uncertainty higher than 10% are in light-grey color. The solid curves indicate fits with the stretched exponential parametrization. |
png pdf |
Figure 21-c:
SS correlation function (integrated over all $ {k_{\mathrm {T}}} $) measured in pPb collisions at 5.02 TeV as a function of $ {q_\text {inv}} $ or of the combined momentum, in two selected $ {N_\text {rec2}} $ bins (left and right), for kaon pairs (red triangles) in one (top) and two (bottom) dimensions, corrected for Coulomb interaction and cluster contributions (mini-jets and multi-body resonance decays). For better visibility, only a fraction of the points is plotted, and those with statistical uncertainty higher than 10% are in light-grey color. The solid curves indicate fits with the stretched exponential parametrization. |
png pdf |
Figure 21-d:
SS correlation function (integrated over all $ {k_{\mathrm {T}}} $) measured in pPb collisions at 5.02 TeV as a function of $ {q_\text {inv}} $ or of the combined momentum, in two selected $ {N_\text {rec2}} $ bins (left and right), for kaon pairs (red triangles) in one (top) and two (bottom) dimensions, corrected for Coulomb interaction and cluster contributions (mini-jets and multi-body resonance decays). For better visibility, only a fraction of the points is plotted, and those with statistical uncertainty higher than 10% are in light-grey color. The solid curves indicate fits with the stretched exponential parametrization. |
png pdf |
Figure 22:
Track-multiplicity ($ {N_\text {trk}} $) dependence of the 1D pion radius parameter $ {R_\text {inv}} $ (left) and intercept parameter $\lambda $ (right), obtained from 1D fits (integrated over all $ {k_{\mathrm {T}}} $) for all collision systems studied. For better visibility, only every second measurement is plotted. Lines are drawn to guide the eye. |
png pdf |
Figure 22-a:
Track-multiplicity ($ {N_\text {trk}} $) dependence of the 1D pion radius parameter $ {R_\text {inv}} $ (left) and intercept parameter $\lambda $ (right), obtained from 1D fits (integrated over all $ {k_{\mathrm {T}}} $) for all collision systems studied. For better visibility, only every second measurement is plotted. Lines are drawn to guide the eye. |
png pdf |
Figure 22-b:
Track-multiplicity ($ {N_\text {trk}} $) dependence of the 1D pion radius parameter $ {R_\text {inv}} $ (left) and intercept parameter $\lambda $ (right), obtained from 1D fits (integrated over all $ {k_{\mathrm {T}}} $) for all collision systems studied. For better visibility, only every second measurement is plotted. Lines are drawn to guide the eye. |
png pdf |
Figure 23:
Track-multiplicity ($ {N_\text {trk}} $) dependence of the 1D kaon radius parameter $ {R_\text {inv}} $ (left) and intercept parameter $\lambda $ (right), obtained from 1D fits (integrated over all $ {k_{\mathrm {T}}} $) for all collision systems studied. For better visibility, only every second measurement is plotted. Lines are drawn to guide the eye. |
png pdf |
Figure 23-a:
Track-multiplicity ($ {N_\text {trk}} $) dependence of the 1D kaon radius parameter $ {R_\text {inv}} $ (left) and intercept parameter $\lambda $ (right), obtained from 1D fits (integrated over all $ {k_{\mathrm {T}}} $) for all collision systems studied. For better visibility, only every second measurement is plotted. Lines are drawn to guide the eye. |
png pdf |
Figure 23-b:
Track-multiplicity ($ {N_\text {trk}} $) dependence of the 1D kaon radius parameter $ {R_\text {inv}} $ (left) and intercept parameter $\lambda $ (right), obtained from 1D fits (integrated over all $ {k_{\mathrm {T}}} $) for all collision systems studied. For better visibility, only every second measurement is plotted. Lines are drawn to guide the eye. |
png pdf |
Figure 24:
$ {k_{\mathrm {T}}} $-dependence of the 1D pion radius $ {R_\text {inv}} $, for several $ {N_\text {trk}} $ bins, extracted for the pp and pPb systems. Lines are drawn to guide the eye. |
png pdf |
Figure 24-a:
$ {k_{\mathrm {T}}} $-dependence of the 1D pion radius $ {R_\text {inv}} $, for several $ {N_\text {trk}} $ bins, extracted for the pp and pPb systems. Lines are drawn to guide the eye. |
png pdf |
Figure 24-b:
$ {k_{\mathrm {T}}} $-dependence of the 1D pion radius $ {R_\text {inv}} $, for several $ {N_\text {trk}} $ bins, extracted for the pp and pPb systems. Lines are drawn to guide the eye. |
png pdf |
Figure 24-c:
$ {k_{\mathrm {T}}} $-dependence of the 1D pion radius $ {R_\text {inv}} $, for several $ {N_\text {trk}} $ bins, extracted for the pp and pPb systems. Lines are drawn to guide the eye. |
png pdf |
Figure 24-d:
$ {k_{\mathrm {T}}} $-dependence of the 1D pion radius $ {R_\text {inv}} $, for several $ {N_\text {trk}} $ bins, extracted for the pp and pPb systems. Lines are drawn to guide the eye. |
png pdf |
Figure 25:
Track-multiplicity ($ {N_\text {trk}} $) dependence of the 2D pion radius parameters $ {R_\text {L}} $ and $ {R_\text {T}} $ (top), and intercept parameter $\lambda $ (bottom), obtained from fits (integrated over all $ {k_{\mathrm {T}}} $) for all collision systems studied. For better visibility, only every second measurement is plotted. Lines are drawn to guide the eye. |
png pdf |
Figure 25-a:
Track-multiplicity ($ {N_\text {trk}} $) dependence of the 2D pion radius parameters $ {R_\text {L}} $ and $ {R_\text {T}} $ (top), and intercept parameter $\lambda $ (bottom), obtained from fits (integrated over all $ {k_{\mathrm {T}}} $) for all collision systems studied. For better visibility, only every second measurement is plotted. Lines are drawn to guide the eye. |
png pdf |
Figure 25-b:
Track-multiplicity ($ {N_\text {trk}} $) dependence of the 2D pion radius parameters $ {R_\text {L}} $ and $ {R_\text {T}} $ (top), and intercept parameter $\lambda $ (bottom), obtained from fits (integrated over all $ {k_{\mathrm {T}}} $) for all collision systems studied. For better visibility, only every second measurement is plotted. Lines are drawn to guide the eye. |
png pdf |
Figure 25-c:
Track-multiplicity ($ {N_\text {trk}} $) dependence of the 2D pion radius parameters $ {R_\text {L}} $ and $ {R_\text {T}} $ (top), and intercept parameter $\lambda $ (bottom), obtained from fits (integrated over all $ {k_{\mathrm {T}}} $) for all collision systems studied. For better visibility, only every second measurement is plotted. Lines are drawn to guide the eye. |
png pdf |
Figure 26:
Track-multiplicity ($ {N_\text {trk}} $) dependence of the 2D kaon radius parameters (left; $ {R_\text {L}} $ - open symbols, $ {R_\text {T}} $ - closed symbols) and intercept parameter $\lambda $ (right), obtained from fits (integrated over all $ {k_{\mathrm {T}}} $) for all collision systems studied. For better visibility, only every second measurement is plotted. Lines are drawn to guide the eye. |
png pdf |
Figure 26-a:
Track-multiplicity ($ {N_\text {trk}} $) dependence of the 2D kaon radius parameters (left; $ {R_\text {L}} $ - open symbols, $ {R_\text {T}} $ - closed symbols) and intercept parameter $\lambda $ (right), obtained from fits (integrated over all $ {k_{\mathrm {T}}} $) for all collision systems studied. For better visibility, only every second measurement is plotted. Lines are drawn to guide the eye. |
png pdf |
Figure 26-b:
Track-multiplicity ($ {N_\text {trk}} $) dependence of the 2D kaon radius parameters (left; $ {R_\text {L}} $ - open symbols, $ {R_\text {T}} $ - closed symbols) and intercept parameter $\lambda $ (right), obtained from fits (integrated over all $ {k_{\mathrm {T}}} $) for all collision systems studied. For better visibility, only every second measurement is plotted. Lines are drawn to guide the eye. |
png pdf |
Figure 27:
Track-multiplicity ($ {N_\text {trk}} $) dependence of the 3D pion radius parameters $ {R_\text {L}} $ (top left), $ {R_\text {O}} $ (top right), $ {R_\text {S}} $ (bottom left), and the intercept parameter $\lambda $ (bottom right), obtained from fits (integrated over all $ {k_{\mathrm {T}}} $) for all collision systems studied. For better visibility, only every second measurement is plotted. Lines are drawn to guide the eye. |
png pdf |
Figure 27-a:
Track-multiplicity ($ {N_\text {trk}} $) dependence of the 3D pion radius parameters $ {R_\text {L}} $ (top left), $ {R_\text {O}} $ (top right), $ {R_\text {S}} $ (bottom left), and the intercept parameter $\lambda $ (bottom right), obtained from fits (integrated over all $ {k_{\mathrm {T}}} $) for all collision systems studied. For better visibility, only every second measurement is plotted. Lines are drawn to guide the eye. |
png pdf |
Figure 27-b:
Track-multiplicity ($ {N_\text {trk}} $) dependence of the 3D pion radius parameters $ {R_\text {L}} $ (top left), $ {R_\text {O}} $ (top right), $ {R_\text {S}} $ (bottom left), and the intercept parameter $\lambda $ (bottom right), obtained from fits (integrated over all $ {k_{\mathrm {T}}} $) for all collision systems studied. For better visibility, only every second measurement is plotted. Lines are drawn to guide the eye. |
png pdf |
Figure 27-c:
Track-multiplicity ($ {N_\text {trk}} $) dependence of the 3D pion radius parameters $ {R_\text {L}} $ (top left), $ {R_\text {O}} $ (top right), $ {R_\text {S}} $ (bottom left), and the intercept parameter $\lambda $ (bottom right), obtained from fits (integrated over all $ {k_{\mathrm {T}}} $) for all collision systems studied. For better visibility, only every second measurement is plotted. Lines are drawn to guide the eye. |
png pdf |
Figure 27-d:
Track-multiplicity ($ {N_\text {trk}} $) dependence of the 3D pion radius parameters $ {R_\text {L}} $ (top left), $ {R_\text {O}} $ (top right), $ {R_\text {S}} $ (bottom left), and the intercept parameter $\lambda $ (bottom right), obtained from fits (integrated over all $ {k_{\mathrm {T}}} $) for all collision systems studied. For better visibility, only every second measurement is plotted. Lines are drawn to guide the eye. |
png pdf |
Figure 28:
Radius parameters for pions as a function of $ {N_\text {trk}} $ scaled to $ {k_{\mathrm {T}}} = $ 0.45 GeV with help of the parametrization, as $R ({k_{\mathrm {T}}} /0.45 GeV)^\gamma $ (Eq. 15) for pp collisions. (For better visibility, systematic uncertainties are indicated with shaded boxes, only for a fraction of the points.) Left column, from upper to lower: $ {R_\text {inv}} $ from the 1D ($ {q_\text {inv}} $) analysis, $ {R_\text {L}} $ and $ {R_\text {T}} $ from the 2D $({q_\text {L}}, {q_\text {T}})$ analysis. Right column, from upper to lower: $ {R_\text {L}} $, $ {R_\text {O}} $, and $ {R_\text {S}} $ from the 3D $({q_\text {L}}$, ${q_\text {O}}$, ${q_\text {S}})$ analysis. Fit results are indicated in the figures, see text for details. |
png pdf |
Figure 28-a:
Radius parameters for pions as a function of $ {N_\text {trk}} $ scaled to $ {k_{\mathrm {T}}} = $ 0.45 GeV with help of the parametrization, as $R ({k_{\mathrm {T}}} /0.45 GeV)^\gamma $ (Eq. 15) for pp collisions. (For better visibility, systematic uncertainties are indicated with shaded boxes, only for a fraction of the points.) Left column, from upper to lower: $ {R_\text {inv}} $ from the 1D ($ {q_\text {inv}} $) analysis, $ {R_\text {L}} $ and $ {R_\text {T}} $ from the 2D $({q_\text {L}}, {q_\text {T}})$ analysis. Right column, from upper to lower: $ {R_\text {L}} $, $ {R_\text {O}} $, and $ {R_\text {S}} $ from the 3D $({q_\text {L}}$, ${q_\text {O}}$, ${q_\text {S}})$ analysis. Fit results are indicated in the figures, see text for details. |
png pdf |
Figure 28-b:
Radius parameters for pions as a function of $ {N_\text {trk}} $ scaled to $ {k_{\mathrm {T}}} = $ 0.45 GeV with help of the parametrization, as $R ({k_{\mathrm {T}}} /0.45 GeV)^\gamma $ (Eq. 15) for pp collisions. (For better visibility, systematic uncertainties are indicated with shaded boxes, only for a fraction of the points.) Left column, from upper to lower: $ {R_\text {inv}} $ from the 1D ($ {q_\text {inv}} $) analysis, $ {R_\text {L}} $ and $ {R_\text {T}} $ from the 2D $({q_\text {L}}, {q_\text {T}})$ analysis. Right column, from upper to lower: $ {R_\text {L}} $, $ {R_\text {O}} $, and $ {R_\text {S}} $ from the 3D $({q_\text {L}}$, ${q_\text {O}}$, ${q_\text {S}})$ analysis. Fit results are indicated in the figures, see text for details. |
png pdf |
Figure 28-c:
Radius parameters for pions as a function of $ {N_\text {trk}} $ scaled to $ {k_{\mathrm {T}}} = $ 0.45 GeV with help of the parametrization, as $R ({k_{\mathrm {T}}} /0.45 GeV)^\gamma $ (Eq. 15) for pp collisions. (For better visibility, systematic uncertainties are indicated with shaded boxes, only for a fraction of the points.) Left column, from upper to lower: $ {R_\text {inv}} $ from the 1D ($ {q_\text {inv}} $) analysis, $ {R_\text {L}} $ and $ {R_\text {T}} $ from the 2D $({q_\text {L}}, {q_\text {T}})$ analysis. Right column, from upper to lower: $ {R_\text {L}} $, $ {R_\text {O}} $, and $ {R_\text {S}} $ from the 3D $({q_\text {L}}$, ${q_\text {O}}$, ${q_\text {S}})$ analysis. Fit results are indicated in the figures, see text for details. |
png pdf |
Figure 28-d:
Radius parameters for pions as a function of $ {N_\text {trk}} $ scaled to $ {k_{\mathrm {T}}} = $ 0.45 GeV with help of the parametrization, as $R ({k_{\mathrm {T}}} /0.45 GeV)^\gamma $ (Eq. 15) for pp collisions. (For better visibility, systematic uncertainties are indicated with shaded boxes, only for a fraction of the points.) Left column, from upper to lower: $ {R_\text {inv}} $ from the 1D ($ {q_\text {inv}} $) analysis, $ {R_\text {L}} $ and $ {R_\text {T}} $ from the 2D $({q_\text {L}}, {q_\text {T}})$ analysis. Right column, from upper to lower: $ {R_\text {L}} $, $ {R_\text {O}} $, and $ {R_\text {S}} $ from the 3D $({q_\text {L}}$, ${q_\text {O}}$, ${q_\text {S}})$ analysis. Fit results are indicated in the figures, see text for details. |
png pdf |
Figure 28-e:
Radius parameters for pions as a function of $ {N_\text {trk}} $ scaled to $ {k_{\mathrm {T}}} = $ 0.45 GeV with help of the parametrization, as $R ({k_{\mathrm {T}}} /0.45 GeV)^\gamma $ (Eq. 15) for pp collisions. (For better visibility, systematic uncertainties are indicated with shaded boxes, only for a fraction of the points.) Left column, from upper to lower: $ {R_\text {inv}} $ from the 1D ($ {q_\text {inv}} $) analysis, $ {R_\text {L}} $ and $ {R_\text {T}} $ from the 2D $({q_\text {L}}, {q_\text {T}})$ analysis. Right column, from upper to lower: $ {R_\text {L}} $, $ {R_\text {O}} $, and $ {R_\text {S}} $ from the 3D $({q_\text {L}}$, ${q_\text {O}}$, ${q_\text {S}})$ analysis. Fit results are indicated in the figures, see text for details. |
png pdf |
Figure 28-f:
Radius parameters for pions as a function of $ {N_\text {trk}} $ scaled to $ {k_{\mathrm {T}}} = $ 0.45 GeV with help of the parametrization, as $R ({k_{\mathrm {T}}} /0.45 GeV)^\gamma $ (Eq. 15) for pp collisions. (For better visibility, systematic uncertainties are indicated with shaded boxes, only for a fraction of the points.) Left column, from upper to lower: $ {R_\text {inv}} $ from the 1D ($ {q_\text {inv}} $) analysis, $ {R_\text {L}} $ and $ {R_\text {T}} $ from the 2D $({q_\text {L}}, {q_\text {T}})$ analysis. Right column, from upper to lower: $ {R_\text {L}} $, $ {R_\text {O}} $, and $ {R_\text {S}} $ from the 3D $({q_\text {L}}$, ${q_\text {O}}$, ${q_\text {S}})$ analysis. Fit results are indicated in the figures, see text for details. |
png pdf |
Figure 29:
Left: Radius parameters for pions as a function of $ {N_\text {trk}} $ scaled to $ {k_{\mathrm {T}}} = $ 0.45 GeV with help of the parametrization, as $R ({k_{\mathrm {T}}} /0.45 GeV)^\gamma $ (Eq. 15). Right: Ratio of the radius parameter and the value of the parametrization $ {R_\text {param}}$ (Eq. 15) at $ {k_{\mathrm {T}}} = $ 0.45 GeV as a function $ {k_{\mathrm {T}}} $. (For better visibility, points are shifted to left and to right with respect to the center of the $ {k_{\mathrm {T}}} $ bin. Systematic uncertainties are indicated with shaded boxes, only for a fraction of the points.) Upper row: $ {R_\text {inv}} $ from the 1D ($ {q_\text {inv}} $) analysis. Middle row: $ {R_\text {L}} $ from the 2D $({q_\text {L}}, {q_\text {T}})$ analysis. Lower row: $ {R_\text {T}} $ from the 2D $({q_\text {L}}, {q_\text {T}})$ analysis. Fit results are indicated in the figures, see text for details. |
png pdf |
Figure 29-a:
Left: Radius parameters for pions as a function of $ {N_\text {trk}} $ scaled to $ {k_{\mathrm {T}}} = $ 0.45 GeV with help of the parametrization, as $R ({k_{\mathrm {T}}} /0.45 GeV)^\gamma $ (Eq. 15). Right: Ratio of the radius parameter and the value of the parametrization $ {R_\text {param}}$ (Eq. 15) at $ {k_{\mathrm {T}}} = $ 0.45 GeV as a function $ {k_{\mathrm {T}}} $. (For better visibility, points are shifted to left and to right with respect to the center of the $ {k_{\mathrm {T}}} $ bin. Systematic uncertainties are indicated with shaded boxes, only for a fraction of the points.) Upper row: $ {R_\text {inv}} $ from the 1D ($ {q_\text {inv}} $) analysis. Middle row: $ {R_\text {L}} $ from the 2D $({q_\text {L}}, {q_\text {T}})$ analysis. Lower row: $ {R_\text {T}} $ from the 2D $({q_\text {L}}, {q_\text {T}})$ analysis. Fit results are indicated in the figures, see text for details. |
png pdf |
Figure 29-b:
Left: Radius parameters for pions as a function of $ {N_\text {trk}} $ scaled to $ {k_{\mathrm {T}}} = $ 0.45 GeV with help of the parametrization, as $R ({k_{\mathrm {T}}} /0.45 GeV)^\gamma $ (Eq. 15). Right: Ratio of the radius parameter and the value of the parametrization $ {R_\text {param}}$ (Eq. 15) at $ {k_{\mathrm {T}}} = $ 0.45 GeV as a function $ {k_{\mathrm {T}}} $. (For better visibility, points are shifted to left and to right with respect to the center of the $ {k_{\mathrm {T}}} $ bin. Systematic uncertainties are indicated with shaded boxes, only for a fraction of the points.) Upper row: $ {R_\text {inv}} $ from the 1D ($ {q_\text {inv}} $) analysis. Middle row: $ {R_\text {L}} $ from the 2D $({q_\text {L}}, {q_\text {T}})$ analysis. Lower row: $ {R_\text {T}} $ from the 2D $({q_\text {L}}, {q_\text {T}})$ analysis. Fit results are indicated in the figures, see text for details. |
png pdf |
Figure 29-c:
Left: Radius parameters for pions as a function of $ {N_\text {trk}} $ scaled to $ {k_{\mathrm {T}}} = $ 0.45 GeV with help of the parametrization, as $R ({k_{\mathrm {T}}} /0.45 GeV)^\gamma $ (Eq. 15). Right: Ratio of the radius parameter and the value of the parametrization $ {R_\text {param}}$ (Eq. 15) at $ {k_{\mathrm {T}}} = $ 0.45 GeV as a function $ {k_{\mathrm {T}}} $. (For better visibility, points are shifted to left and to right with respect to the center of the $ {k_{\mathrm {T}}} $ bin. Systematic uncertainties are indicated with shaded boxes, only for a fraction of the points.) Upper row: $ {R_\text {inv}} $ from the 1D ($ {q_\text {inv}} $) analysis. Middle row: $ {R_\text {L}} $ from the 2D $({q_\text {L}}, {q_\text {T}})$ analysis. Lower row: $ {R_\text {T}} $ from the 2D $({q_\text {L}}, {q_\text {T}})$ analysis. Fit results are indicated in the figures, see text for details. |
png pdf |
Figure 29-d:
Left: Radius parameters for pions as a function of $ {N_\text {trk}} $ scaled to $ {k_{\mathrm {T}}} = $ 0.45 GeV with help of the parametrization, as $R ({k_{\mathrm {T}}} /0.45 GeV)^\gamma $ (Eq. 15). Right: Ratio of the radius parameter and the value of the parametrization $ {R_\text {param}}$ (Eq. 15) at $ {k_{\mathrm {T}}} = $ 0.45 GeV as a function $ {k_{\mathrm {T}}} $. (For better visibility, points are shifted to left and to right with respect to the center of the $ {k_{\mathrm {T}}} $ bin. Systematic uncertainties are indicated with shaded boxes, only for a fraction of the points.) Upper row: $ {R_\text {inv}} $ from the 1D ($ {q_\text {inv}} $) analysis. Middle row: $ {R_\text {L}} $ from the 2D $({q_\text {L}}, {q_\text {T}})$ analysis. Lower row: $ {R_\text {T}} $ from the 2D $({q_\text {L}}, {q_\text {T}})$ analysis. Fit results are indicated in the figures, see text for details. |
png pdf |
Figure 29-e:
Left: Radius parameters for pions as a function of $ {N_\text {trk}} $ scaled to $ {k_{\mathrm {T}}} = $ 0.45 GeV with help of the parametrization, as $R ({k_{\mathrm {T}}} /0.45 GeV)^\gamma $ (Eq. 15). Right: Ratio of the radius parameter and the value of the parametrization $ {R_\text {param}}$ (Eq. 15) at $ {k_{\mathrm {T}}} = $ 0.45 GeV as a function $ {k_{\mathrm {T}}} $. (For better visibility, points are shifted to left and to right with respect to the center of the $ {k_{\mathrm {T}}} $ bin. Systematic uncertainties are indicated with shaded boxes, only for a fraction of the points.) Upper row: $ {R_\text {inv}} $ from the 1D ($ {q_\text {inv}} $) analysis. Middle row: $ {R_\text {L}} $ from the 2D $({q_\text {L}}, {q_\text {T}})$ analysis. Lower row: $ {R_\text {T}} $ from the 2D $({q_\text {L}}, {q_\text {T}})$ analysis. Fit results are indicated in the figures, see text for details. |
png pdf |
Figure 29-f:
Left: Radius parameters for pions as a function of $ {N_\text {trk}} $ scaled to $ {k_{\mathrm {T}}} = $ 0.45 GeV with help of the parametrization, as $R ({k_{\mathrm {T}}} /0.45 GeV)^\gamma $ (Eq. 15). Right: Ratio of the radius parameter and the value of the parametrization $ {R_\text {param}}$ (Eq. 15) at $ {k_{\mathrm {T}}} = $ 0.45 GeV as a function $ {k_{\mathrm {T}}} $. (For better visibility, points are shifted to left and to right with respect to the center of the $ {k_{\mathrm {T}}} $ bin. Systematic uncertainties are indicated with shaded boxes, only for a fraction of the points.) Upper row: $ {R_\text {inv}} $ from the 1D ($ {q_\text {inv}} $) analysis. Middle row: $ {R_\text {L}} $ from the 2D $({q_\text {L}}, {q_\text {T}})$ analysis. Lower row: $ {R_\text {T}} $ from the 2D $({q_\text {L}}, {q_\text {T}})$ analysis. Fit results are indicated in the figures, see text for details. |
png pdf |
Figure 30:
Left: Radius parameters for pions as a function of $ {N_\text {trk}} $ scaled to $ {k_{\mathrm {T}}} = $ 0.45 GeV with help of the parametrization as $R ({k_{\mathrm {T}}} /0.45 GeV)^\gamma $ (Eq. 15). Right: Ratio of the radius parameter and the value of the parametrization $ {R_\text {param}}$ (Eq. 15) at $ {k_{\mathrm {T}}} = $ 0.45 GeV as a function $ {k_{\mathrm {T}}} $. (For better visibility, points are shifted to left and to right with respect to the center of the $ {k_{\mathrm {T}}} $ bin. Systematic uncertainties are indicated with shaded boxes, only for a fraction of the points.) Radii from the 3D $({q_\text {L}}$, ${q_\text {O}}$, ${q_\text {S}})$ analysis are shown, from upper to lower: $ {R_\text {L}} $, $ {R_\text {O}} $, $ {R_\text {S}} $. Fit results are indicated in the figures, see text for details. |
png pdf |
Figure 30-a:
Left: Radius parameters for pions as a function of $ {N_\text {trk}} $ scaled to $ {k_{\mathrm {T}}} = $ 0.45 GeV with help of the parametrization as $R ({k_{\mathrm {T}}} /0.45 GeV)^\gamma $ (Eq. 15). Right: Ratio of the radius parameter and the value of the parametrization $ {R_\text {param}}$ (Eq. 15) at $ {k_{\mathrm {T}}} = $ 0.45 GeV as a function $ {k_{\mathrm {T}}} $. (For better visibility, points are shifted to left and to right with respect to the center of the $ {k_{\mathrm {T}}} $ bin. Systematic uncertainties are indicated with shaded boxes, only for a fraction of the points.) Radii from the 3D $({q_\text {L}}$, ${q_\text {O}}$, ${q_\text {S}})$ analysis are shown, from upper to lower: $ {R_\text {L}} $, $ {R_\text {O}} $, $ {R_\text {S}} $. Fit results are indicated in the figures, see text for details. |
png pdf |
Figure 30-b:
Left: Radius parameters for pions as a function of $ {N_\text {trk}} $ scaled to $ {k_{\mathrm {T}}} = $ 0.45 GeV with help of the parametrization as $R ({k_{\mathrm {T}}} /0.45 GeV)^\gamma $ (Eq. 15). Right: Ratio of the radius parameter and the value of the parametrization $ {R_\text {param}}$ (Eq. 15) at $ {k_{\mathrm {T}}} = $ 0.45 GeV as a function $ {k_{\mathrm {T}}} $. (For better visibility, points are shifted to left and to right with respect to the center of the $ {k_{\mathrm {T}}} $ bin. Systematic uncertainties are indicated with shaded boxes, only for a fraction of the points.) Radii from the 3D $({q_\text {L}}$, ${q_\text {O}}$, ${q_\text {S}})$ analysis are shown, from upper to lower: $ {R_\text {L}} $, $ {R_\text {O}} $, $ {R_\text {S}} $. Fit results are indicated in the figures, see text for details. |
png pdf |
Figure 30-c:
Left: Radius parameters for pions as a function of $ {N_\text {trk}} $ scaled to $ {k_{\mathrm {T}}} = $ 0.45 GeV with help of the parametrization as $R ({k_{\mathrm {T}}} /0.45 GeV)^\gamma $ (Eq. 15). Right: Ratio of the radius parameter and the value of the parametrization $ {R_\text {param}}$ (Eq. 15) at $ {k_{\mathrm {T}}} = $ 0.45 GeV as a function $ {k_{\mathrm {T}}} $. (For better visibility, points are shifted to left and to right with respect to the center of the $ {k_{\mathrm {T}}} $ bin. Systematic uncertainties are indicated with shaded boxes, only for a fraction of the points.) Radii from the 3D $({q_\text {L}}$, ${q_\text {O}}$, ${q_\text {S}})$ analysis are shown, from upper to lower: $ {R_\text {L}} $, $ {R_\text {O}} $, $ {R_\text {S}} $. Fit results are indicated in the figures, see text for details. |
png pdf |
Figure 30-d:
Left: Radius parameters for pions as a function of $ {N_\text {trk}} $ scaled to $ {k_{\mathrm {T}}} = $ 0.45 GeV with help of the parametrization as $R ({k_{\mathrm {T}}} /0.45 GeV)^\gamma $ (Eq. 15). Right: Ratio of the radius parameter and the value of the parametrization $ {R_\text {param}}$ (Eq. 15) at $ {k_{\mathrm {T}}} = $ 0.45 GeV as a function $ {k_{\mathrm {T}}} $. (For better visibility, points are shifted to left and to right with respect to the center of the $ {k_{\mathrm {T}}} $ bin. Systematic uncertainties are indicated with shaded boxes, only for a fraction of the points.) Radii from the 3D $({q_\text {L}}$, ${q_\text {O}}$, ${q_\text {S}})$ analysis are shown, from upper to lower: $ {R_\text {L}} $, $ {R_\text {O}} $, $ {R_\text {S}} $. Fit results are indicated in the figures, see text for details. |
png pdf |
Figure 30-e:
Left: Radius parameters for pions as a function of $ {N_\text {trk}} $ scaled to $ {k_{\mathrm {T}}} = $ 0.45 GeV with help of the parametrization as $R ({k_{\mathrm {T}}} /0.45 GeV)^\gamma $ (Eq. 15). Right: Ratio of the radius parameter and the value of the parametrization $ {R_\text {param}}$ (Eq. 15) at $ {k_{\mathrm {T}}} = $ 0.45 GeV as a function $ {k_{\mathrm {T}}} $. (For better visibility, points are shifted to left and to right with respect to the center of the $ {k_{\mathrm {T}}} $ bin. Systematic uncertainties are indicated with shaded boxes, only for a fraction of the points.) Radii from the 3D $({q_\text {L}}$, ${q_\text {O}}$, ${q_\text {S}})$ analysis are shown, from upper to lower: $ {R_\text {L}} $, $ {R_\text {O}} $, $ {R_\text {S}} $. Fit results are indicated in the figures, see text for details. |
png pdf |
Figure 30-f:
Left: Radius parameters for pions as a function of $ {N_\text {trk}} $ scaled to $ {k_{\mathrm {T}}} = $ 0.45 GeV with help of the parametrization as $R ({k_{\mathrm {T}}} /0.45 GeV)^\gamma $ (Eq. 15). Right: Ratio of the radius parameter and the value of the parametrization $ {R_\text {param}}$ (Eq. 15) at $ {k_{\mathrm {T}}} = $ 0.45 GeV as a function $ {k_{\mathrm {T}}} $. (For better visibility, points are shifted to left and to right with respect to the center of the $ {k_{\mathrm {T}}} $ bin. Systematic uncertainties are indicated with shaded boxes, only for a fraction of the points.) Radii from the 3D $({q_\text {L}}$, ${q_\text {O}}$, ${q_\text {S}})$ analysis are shown, from upper to lower: $ {R_\text {L}} $, $ {R_\text {O}} $, $ {R_\text {S}} $. Fit results are indicated in the figures, see text for details. |
Tables | |
png pdf |
Table 1:
Ranges in charged-particle multiplicity over $ {| \eta |} < $ 2.4, $ {N_\text {rec1}} $, and corresponding average corrected number of tracks with $ {p_{\mathrm {T}}} > $ 0.4 GeV, $< {N_\text {trk0.4}} > $, in pp collisions at 2.76 and 7 TeV considered in the double ratio method. The $< {N_\text {trk0.4}} > $ values are rounded off to the nearest integer. A dash indicates that there is not enough data to allow for a good-quality measurement. |
png pdf |
Table 2:
Relation between the number of reconstructed tracks ($ {N_\text {rec2}} $, $ {p_{\mathrm {T}}} > $ 0.1 GeV) and the average number of corrected tracks ($< {N_\text {trk}} > $, $ {p_{\mathrm {T}}} > $ 0) in the region $ {| \eta |} < $ 2.4 for the 24 multiplicity classes considered in the particle identification and cluster subtraction method. The values are rounded off to the nearest integer. The corrected $< {N_\text {trk}} > $ values listed for pp collisions are common to all three measured energies. A dash indicates that there is not enough data to allow for a good-quality measurement. |
png pdf |
Table 3:
Bin widths chosen for the various variables studied with the double ratio method. |
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Table 4:
Chosen bin widths for the various variables studied for pions and kaons in the particle identification and cluster subtraction method. |
png pdf |
Table 5:
Fit parameters of the 1D BEC function in pp collisions at $\sqrt {s} = $ 2.76 and 7 TeV. |
png pdf |
Table 6:
Fit parameters of the 2D BEC function in pp collisions at $\sqrt {s} = $ 2.76 and 7 TeV in the LCMS. |
png pdf |
Table 7:
Parameters of the 3D BEC function, obtained from a stretched exponential fit, in pp collisions at $\sqrt {s} = $ 2.76 and 7 TeV in the LCMS. |
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Table 8:
Values of the 1D, 2D, and 3D fit parameters for pions using Eq. 15 in pp, pPb and PbPb collisions. The estimated uncertainty in the parameters is about 10%. |
Summary |
Detailed studies have been presented on femtoscopic correlations between pairs of same-sign hadrons produced in pp collisions at $\sqrt{s} = $ 0.9, 2.76, and 7 TeV, as well as in pPb collisions at ${\sqrt{\smash[b]{s_{_\text{NN}}}}} = $ 5.02 TeV and peripheral PbPb collisions at ${\sqrt{\smash[b]{s_{_\text{NN}}}}} = $ 2.76 TeV. The characteristics of two-particle Bose-Einstein correlations are investigated in one (${R_\text{inv}} $), two (${R_\text{T}} $ and ${R_\text{L}} $), and three (${R_\text{L}} $, ${R_\text{S}} $, and ${R_\text{O}} $) dimensions, as functions of charged multiplicity ${N_\text{trk}} $ and pair average transverse momentum ${k_{\mathrm{T}}}$. Two different analysis techniques are employed. The first "double ratio'' technique is used to study Bose-Einstein correlations of pairs of charged hadrons emitted in pp collisions at $\sqrt{s} = $ 2.76 and 7 TeV, both in the collision center-of-mass frame and in the local co-moving system. The second "particle identification and cluster subtraction'' method is used to study the characteristics of two-particle correlation functions of identical charged pions and kaons, identified via their energy loss in the CMS silicon tracker, in collisions of pp, pPb, and peripheral PbPb collisions at various center-of-mass energies. The similarities and differences between the three colliding systems have been investigated. The quantum correlations are well described by an exponential parametrization as a function of the relative momentum of the particle pair, both in one and in multiple dimensions, consistent with a Cauchy-Lorentz spatial source distribution. The fitted radius parameters of the emitting source, obtained for inclusive charged hadrons as well as for identified pions, increase along with charged-particle multiplicity for all colliding systems and center-of-mass energies, for one, two, and three dimensions alike. The radii are in the range 1-5 fm, reaching the largest values for very high multiplicity pPb collisions, close to those observed in peripheral PbPb collisions with similar multiplicity. In the one-dimensional case, ${R_\text{inv}} $ in pp collisions steadily increases with the charged multiplicity following a ${N_\text{trk}} ^{1/3}$ dependence, as well as showing an approximate independence of the center-of-mass energy. This behavior is also observed for the longitudinal radius parameter (${R_\text{L}} ^*$ in the center-of-mass frame, and ${R_\text{L}} $ in the local co-moving system) in the two-dimensional case. The multiplicity dependence of ${R_\text{L}} $ and ${R_\text{T}} $ is similar for pp and pPb collisions in all ${k_{\mathrm{T}}}$ bins, and that similarity also applies to peripheral PbPb collisions for ${k_{\mathrm{T}}} > $ 0.4 GeV. In general, the observed orderings, ${R_\text{L}} > {R_\text{T}} $ and ${R_\text{L}} \ge {R_\text{S}} > {R_\text{O}} $, indicate that the pp and pPb sources are elongated in the beam direction. For peripheral PbPb collisions, the source is quite symmetric, and shows a slightly different ${N_\text{trk}} $ dependence, with the largest differences between the systems for ${R_\text{T}} $ and ${R_\text{O}} $, while ${R_\text{L}} $ and ${R_\text{S}} $ are approximately equal. The most visible differences between pp, pPb, and PbPb collisions are seen in ${R_\text{O}} $, which could point to a different lifetime of the emitting systems in the three cases. The kaon radius parameters show a smaller increase with ${N_\text{trk}} $ than observed for pions. The radius parameters of charged hadrons and pions decrease with increasing ${k_{\mathrm{T}}}$, an observation compatible with expanding emitting sources. The ${k_{\mathrm{T}}}$- and ${N_\text{trk}} $-dependences of the radius parameters factorize, and are largely independent of beam energy and colliding system for lower multiplicities, although some system dependence appears at higher values of ${N_\text{trk}} $. A shallow anticorrelation (a region where the correlation function falls below one) observed using the double ratio technique in a previous analysis of pp collisions, is also seen in the present data. The depth of this dip in the one-dimensional correlation functions decreases with increasing particle multiplicity and also decreases slightly with increasing ${k_{\mathrm{T}}}$. Finally, the similar multiplicity dependencies of the radii extracted for pp, pPb, and peripheral PbPb collisions suggest a common freeze-out density of hadrons for all collision systems, since the correlation techniques measure the characteristic size of the system near the time of the last interactions. In the case of pp collisions, extending the investigation of these similarities to higher multiplicities than those accessible with the current data can provide new information on final state collective effects in such events. |
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Compact Muon Solenoid LHC, CERN |