CMS-HIN-17-001

CMS-HIN-17-001 ; CERN-EP-2017-193
Constraints on the chiral magnetic effect using charge-dependent azimuthal correlations in pPb and PbPb collisions at the LHC
CMS Collaboration
4 August 2017
Phys. Rev. C 97 (2018) 044912
Abstract: Charge-dependent azimuthal correlations of same- and opposite-sign pairs with respect to the second- and third-order event planes have been measured in pPb collisions at $\sqrt{s_{\mathrm{NN}}} =$ 8.16 TeV and PbPb collisions at 5.02 TeV with the CMS experiment at the LHC. The measurement is motivated by the search for the charge separation phenomenon predicted by the chiral magnetic effect (CME) in heavy ion collisions. Three- and two-particle azimuthal correlators are extracted as functions of the pseudorapidity difference, the transverse momentum ( $p_{\mathrm{T}}$ ) difference, and the $p_{\mathrm{T}}$ average of same- and opposite-charge pairs in various event multiplicity ranges. The data suggest that the charge-dependent three-particle correlators with respect to the second- and third-order event planes share a common origin, predominantly arising from charge-dependent two-particle azimuthal correlations coupled with an anisotropic flow. The CME is expected to lead to a $v_{2}$ -independent three-particle correlation when the magnetic field is fixed. Using an event shape engineering technique, upper limits on the $v_{2}$ -independent fraction of the three-particle correlator are estimated to be 6.6% for pPb and 3.8% for PbPb collisions at 95% confidence level. The results of this analysis, both the dominance of two-particle correlations as a source of the three-particle results and the similarities seen between PbPb and pPb, provide stringent constraints on the origin of charge-dependent three-particle azimuthal correlations and challenge their interpretation as arising from a chiral magnetic effect in heavy ion collisions.
Links: e-print arXiv:1708.01602 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; HepData record ; CADI line (restricted) ;

Figures & Tables	Summary	References	CMS Publications

Figures
png pdf	Figure 1: The $q_{2}$ classes are shown in different fractions with respect to the total number of events in multiplicity range 185 $\leq {N_\text {trk}^\text {offline}} <$ 250 in PbPb (left) and pPb (right) collisions at ${\sqrt {{s_{_{\mathrm {NN}}}}}}=$ 5.02 and 8.16 TeV, respectively.
png pdf	Figure 1-a: The $q_{2}$ classes are shown in different fractions with respect to the total number of events in multiplicity range 185 $\leq {N_\text {trk}^\text {offline}} <$ 250 in PbPb collisions at ${\sqrt {{s_{_{\mathrm {NN}}}}}}=$ 5.02 and 8.16 TeV, respectively.
png pdf	Figure 1-b: The $q_{2}$ classes are shown in different fractions with respect to the total number of events in multiplicity range 185 $\leq {N_\text {trk}^\text {offline}} <$ 250 in pPb collisions at ${\sqrt {{s_{_{\mathrm {NN}}}}}}=$ 5.02 and 8.16 TeV, respectively.
png pdf	Figure 2: The correlation between the tracker $v_{2}$ and the HF $q_{2}$ is shown for pPb and PbPb collisions at collisions at ${\sqrt {{s_{_{\mathrm {NN}}}}}} =$ 8.16 and 5.02 TeV, respectively.
png pdf	Figure 3: The SS and OS three-particle correlators, $\gamma _{112}$ (upper) and $\gamma _{123}$ (middle), and two-particle correlator, $\delta$ (lower), as a function of ${\| {\Delta \eta } \| }$ for 185 $\leq {N_\text {trk}^\text {offline}} <$ 250 in pPb collisions at ${\sqrt {{s_{_{\mathrm {NN}}}}}} =$ 8.16 TeV (left) and PbPb collisions at 5.02 TeV (right). The pPb results obtained with particle $c$ in Pb-going (solid markers) and p-going (open markers) sides are shown separately. The SS and OS two-particle correlators are denoted by different markers for both pPb and PbPb collisions. Statistical and systematic uncertainties are indicated by the error bars and shaded regions, respectively.
png pdf	Figure 4: The SS and OS three-particle correlators, $\gamma _{112}$ (upper) and $\gamma _{123}$ (middle), and two-particle correlator, $\delta$ (lower), as a function of ${\| \Delta {p_{\mathrm {T}}} \| }$ for 185 $\leq {N_\text {trk}^\text {offline}} <$ 250 in pPb collisions at ${\sqrt {{s_{_{\mathrm {NN}}}}}} =$ 8.16 TeV (left) and PbPb collisions at 5.02 TeV (right) collisions. The pPb results obtained with particle $c$ in Pb-going (solid markers) and p-going (open markers) sides are shown separately. The SS and OS two-particle correlators are denoted by different markers for both pPb and PbPb collisions. Statistical and systematic uncertainties are indicated by the error bars and shaded regions, respectively.
png pdf	Figure 5: The SS and OS three-particle correlators, $\gamma _{112}$ (upper) and $\gamma _{123}$ (middle), and two-particle correlator, $\delta$ (lower), as a function of ${\overline {p}_\mathrm {T}}$ for 185 $\leq {N_\text {trk}^\text {offline}} <$ 250 in pPb collisions at ${\sqrt {{s_{_{\mathrm {NN}}}}}} =$ 8.16 TeV (left) and PbPb collisions at 5.02 TeV (right). The pPb results obtained with particle $c$ in Pb-going (solid markers) and p-going (open markers) sides are shown separately. The SS and OS two-particle correlators are denoted by different markers for both pPb and PbPb collisions. Statistical and systematic uncertainties are indicated by the error bars and shaded regions, respectively.
png pdf	Figure 6: The SS and OS three-particle correlators, $\gamma _{112}$ (upper) and $\gamma _{123}$ (middle), and two-particle correlator, $\delta$ (lower), averaged over ${\| {\Delta \eta } \| }<$ 1.6 as a function of ${N_\text {trk}^\text {offline}}$ in pPb collisions at ${\sqrt {{s_{_{\mathrm {NN}}}}}} =$ 8.16 TeV and PbPb collisions at 5.02 TeV. The SS and OS two-particle correlators are denoted by different markers for pPb collisions. The results of $\gamma _{112}$ for pPb collisions at 5.02 TeV from Ref. [21], are also shown for comparison. Statistical and systematic uncertainties are indicated by the error bars and shaded regions, respectively.
png pdf	Figure 7: The difference of the OS and SS three-particle correlators, $\gamma _{112}$ (upper) and $\gamma _{123}$ (middle), and two-particle correlator, $\delta$ (lower) as functions of $\Delta \eta$ (left), $\Delta {p_{\mathrm {T}}}$ (middle), and ${\overline {p}_\mathrm {T}}$ (right) for 185 $\leq {N_\text {trk}^\text {offline}} <$ 250 in pPb collisions at ${\sqrt {{s_{_{\mathrm {NN}}}}}} =$ 8.16 TeV and PbPb collisions at 5.02 TeV. The $\Delta \delta$ correlator is denoted by a different marker for pPb collisions. The pPb results are obtained with particle $c$ from Pb- and p-going sides separately. Statistical and systematic uncertainties are indicated by the error bars and shaded regions, respectively.
png pdf	Figure 8: The difference of the OS and SS three-particle correlators, $\gamma _{112}$ (upper) and $\gamma _{123}$ (middle), and two-particle correlator, $\delta$ (lower), averaged over ${\| {\Delta \eta } \| }<$ 1.6 as a function of ${N_\text {trk}^\text {offline}}$ in pPb collisions at ${\sqrt {{s_{_{\mathrm {NN}}}}}} =$ 8.16 TeV and PbPb collisions at 5.02 TeV. The pPb results are obtained with particle $c$ from Pb- and p-going sides separately. The $\Delta \delta$ correlator is denoted by a different marker for pPb collisions. The results of $\gamma _{112}$ for pPb collisions at 5.02 TeV from Ref. [21], are also shown for comparison. Statistical and systematic uncertainties are indicated by the error bars and shaded regions, respectively.
png pdf	Figure 9: The ratio of $\Delta \gamma _{112}$ and $\Delta \gamma _{123}$ to the product of $v_{n}$ and $\delta$ , averaged over ${\| {\Delta \eta } \| }<$ 1.6, in pPb collisions for the Pb-going direction at ${\sqrt {{s_{_{\mathrm {NN}}}}}} =$ 8.16 TeV (upper) and PbPb collisions at 5.02 TeV (lower). Statistical and systematic uncertainties are indicated by the error bars and shaded regions, respectively.
png pdf	Figure 10: The ratio of $\Delta \gamma _{112}$ and $\Delta \gamma _{123}$ to the product of $v_{n}$ and $\delta$ , as functions of $\Delta \eta$ (left), $\Delta {p_{\mathrm {T}}}$ (middle), and ${\overline {p}_\mathrm {T}}$ (right) for 185 $\leq {N_\text {trk}^\text {offline}} <$ 250 in pPb collisions at ${\sqrt {{s_{_{\mathrm {NN}}}}}} =$ 8.16 TeV (upper) and PbPb collisions at 5.02 TeV (lower). Statistical and systematic uncertainties are indicated by the error bars and shaded regions, respectively.
png pdf	Figure 11: The SS and OS three-particle correlators, $\gamma _{112}$ , averaged over ${\| {\Delta \eta } \| }<$ 1.6 as a function of $v_2$ evaluated in each $q_2$ class, for the multiplicity range 185 $\leq {N_\text {trk}^\text {offline}} <$ 250 in pPb collisions at ${\sqrt {{s_{_{\mathrm {NN}}}}}} =$ 8.16 TeV (left) and PbPb collisions at 5.02 TeV (right). The pPb results are obtained with particle $c$ from Pb- and p-going sides separately. Statistical and systematic uncertainties are indicated by the error bars and shaded regions, respectively.
png pdf	Figure 12: The difference of the OS and SS three-particle correlators, $\gamma _{112}$ , averaged over ${\| {\Delta \eta } \| }<$ 1.6 as a function of $v_2$ evaluated in each $q_2$ class, for the multiplicity range 185 $\leq {N_\text {trk}^\text {offline}} <$ 250 in pPb collisions at ${\sqrt {{s_{_{\mathrm {NN}}}}}} =$ 8.16 TeV and PbPb collisions at 5.02 TeV (upper), and for different centrality classes in PbPb collisions at 5.02 TeV (lower). Statistical and systematic uncertainties are indicated by the error bars and shaded regions, respectively. A one standard deviation uncertainty from the fit is also shown.
png pdf	Figure 12-a: The difference of the OS and SS three-particle correlators, $\gamma _{112}$ , averaged over ${\| {\Delta \eta } \| }<$ 1.6 as a function of $v_2$ evaluated in each $q_2$ class, for the multiplicity range 185 $\leq {N_\text {trk}^\text {offline}} <$ 250 in pPb collisions at ${\sqrt {{s_{_{\mathrm {NN}}}}}} =$ 8.16 TeV and PbPb collisions at 5.02 TeV. Statistical and systematic uncertainties are indicated by the error bars and shaded regions, respectively. A one standard deviation uncertainty from the fit is also shown.
png pdf	Figure 12-b: The difference of the OS and SS three-particle correlators, $\gamma _{112}$ , averaged over ${\| {\Delta \eta } \| }<$ 1.6 as a function of $v_2$ evaluated in each $q_2$ class, for different centrality classes in PbPb collisions at 5.02 TeV. Statistical and systematic uncertainties are indicated by the error bars and shaded regions, respectively. A one standard deviation uncertainty from the fit is also shown.
png pdf	Figure 13: The difference of the OS and SS two-particle correlators, $\delta$ , averaged over ${\| {\Delta \eta } \| }<$ 1.6 as a function of $v_2$ evaluated in each $q_2$ class, for different multiplicity ranges in pPb collisions at ${\sqrt {{s_{_{\mathrm {NN}}}}}} =$ 8.16 TeV (upper), and for different centrality classes in PbPb collisions at 5.02 TeV (lower). Statistical and systematic uncertainties are indicated by the error bars and shaded regions, respectively.
png pdf	Figure 13-a: The difference of the OS and SS two-particle correlators, $\delta$ , averaged over ${\| {\Delta \eta } \| }<$ 1.6 as a function of $v_2$ evaluated in each $q_2$ class, for different multiplicity ranges in pPb collisions at ${\sqrt {{s_{_{\mathrm {NN}}}}}} =$ 8.16 TeV. Statistical and systematic uncertainties are indicated by the error bars and shaded regions, respectively.
png pdf	Figure 13-b: The difference of the OS and SS two-particle correlators, $\delta$ , averaged over ${\| {\Delta \eta } \| }<$ 1.6 as a function of $v_2$ evaluated in each $q_2$ class, for different centrality classes in PbPb collisions at 5.02 TeV. Statistical and systematic uncertainties are indicated by the error bars and shaded regions, respectively.
png pdf	Figure 14: The ratio between the difference of the OS and SS three-particle correlators and the difference of OS and SS in $\delta$ correlators, $\Delta \gamma _{112}/\Delta \delta$ , averaged over ${\| {\Delta \eta } \| }<$ 1.6 as a function of $v_2$ evaluated in each $q_2$ class, for the multiplicity range 185 $\leq {N_\text {trk}^\text {offline}} <$ 250 in pPb collisions at ${\sqrt {{s_{_{\mathrm {NN}}}}}} =$ 8.16 TeV and PbPb collisions at 5.02 TeV (upper), and for different centrality classes in PbPb collisions at 5.02 TeV (lower). Statistical and systematic uncertainties are indicated by the error bars and shaded regions, respectively. A one standard deviation uncertainty from the fit is also shown.
png pdf	Figure 14-a: The ratio between the difference of the OS and SS three-particle correlators and the difference of OS and SS in $\delta$ correlators, $\Delta \gamma _{112}/\Delta \delta$ , averaged over ${\| {\Delta \eta } \| }<$ 1.6 as a function of $v_2$ evaluated in each $q_2$ class, for the multiplicity range 185 $\leq {N_\text {trk}^\text {offline}} <$ 250 in pPb collisions at ${\sqrt {{s_{_{\mathrm {NN}}}}}} =$ 8.16 TeV and PbPb collisions at 5.02 TeV. Statistical and systematic uncertainties are indicated by the error bars and shaded regions, respectively. A one standard deviation uncertainty from the fit is also shown.
png pdf	Figure 14-b: The ratio between the difference of the OS and SS three-particle correlators and the difference of OS and SS in $\delta$ correlators, $\Delta \gamma _{112}/\Delta \delta$ , averaged over ${\| {\Delta \eta } \| }<$ 1.6 as a function of $v_2$ evaluated in each $q_2$ class, for different centrality classes in PbPb collisions at 5.02 TeV. Statistical and systematic uncertainties are indicated by the error bars and shaded regions, respectively. A one standard deviation uncertainty from the fit is also shown.
png pdf	Figure 15: Extracted intercept parameter $b_{\text {norm}}$ (upper) and corresponding upper limit of the fraction of $v_2$ -independent $\gamma _{112}$ correlator component (lower), averaged over ${\| {\Delta \eta } \| }<$ 1.6, as a function of ${N_\text {trk}^\text {offline}}$ in pPb collisions at ${\sqrt {{s_{_{\mathrm {NN}}}}}} =$ 8.16 TeV and PbPb collisions at 5.02 TeV. Statistical and systematic uncertainties are indicated by the error bars and shaded regions in the top panel, respectively.
png pdf	Figure 15-a: Extracted intercept parameter $b_{\text {norm}}$ , averaged over ${\| {\Delta \eta } \| }<$ 1.6, as a function of ${N_\text {trk}^\text {offline}}$ in pPb collisions at ${\sqrt {{s_{_{\mathrm {NN}}}}}} =$ 8.16 TeV and PbPb collisions at 5.02 TeV. Statistical and systematic uncertainties are indicated by the error bars and shaded regions in the top panel, respectively.
png pdf	Figure 15-b: Upper limit of the fraction of $v_2$ -independent $\gamma _{112}$ correlator component, averaged over ${\| {\Delta \eta } \| }<$ 1.6, as a function of ${N_\text {trk}^\text {offline}}$ in pPb collisions at ${\sqrt {{s_{_{\mathrm {NN}}}}}} =$ 8.16 TeV and PbPb collisions at 5.02 TeV. Statistical and systematic uncertainties are indicated by the error bars and shaded regions in the top panel, respectively.
png pdf	Figure 16: The intercepts $b_{\text {norm}}$ of $v_2$ -independent $\gamma _{112}$ correlator component using particle $c$ from HF $+$ and HF $-$ data, averaged over $\|\Delta \eta \|<$ 1.6, are shown as a function of ${N_\text {trk}^\text {offline}}$ in PbPb collisions at ${\sqrt {{s_{_{\mathrm {NN}}}}}}=$ 5.02 TeV. Statistical and systematic uncertainties are indicated by the error bars and shaded regions, respectively.
png pdf	Figure 17: The $v_{2,c}$ using particle $c$ from HF $+$ and HF $-$ data are shown as a function of $v_{2}$ in the tracker region ( $\|\eta \|<2.4$ ) in PbPb collisions at ${\sqrt {{s_{_{\mathrm {NN}}}}}}=$ 5.02 TeV.
png pdf	Figure 18: The $v_{2,c}$ using particle $c$ from the Pb-going side of the HF (4.4 $< \eta <$ 5.0) data are shown as a function of $v_{2}$ in the tracker region ( $\|\eta \|<$ 2.4) in pPb collisions at ${\sqrt {{s_{_{\mathrm {NN}}}}}} =$ 8.16 TeV.
png pdf	Figure 19: The average multiplicity ${N_\text {trk}^\text {offline}}$ as a function of $v_2$ evaluated in each $q_2$ class, for different multiplicity ranges in pPb collisions at ${\sqrt {{s_{_{\mathrm {NN}}}}}} =$ 8.16 TeV (upper), and for different centrality classes in PbPb collisions at 5.02 TeV (lower). Statistical uncertainties are invisible on the current scale.
png pdf	Figure 19-a: The average multiplicity ${N_\text {trk}^\text {offline}}$ as a function of $v_2$ evaluated in each $q_2$ class, for different multiplicity ranges in pPb collisions at ${\sqrt {{s_{_{\mathrm {NN}}}}}} =$ 8.16 TeV. Statistical uncertainties are invisible on the current scale.
png pdf	Figure 19-b: The average multiplicity ${N_\text {trk}^\text {offline}}$ as a function of $v_2$ evaluated in each $q_2$ class, for different centrality classes in PbPb collisions at 5.02 TeV. Statistical uncertainties are invisible on the current scale.
png pdf	Figure 20: The SS and OS three-particle correlators, $\gamma _{112}$ (upper) and $\gamma _{123}$ (middle), and two-particle correlator, $\delta$ (lower), as a function of ${\| {\Delta \eta } \| }$ for four multiplicity ranges in pPb collisions at ${\sqrt {{s_{_{\mathrm {NN}}}}}} =$ 8.16 TeV (left) and PbPb collisions at 5.02 TeV (right). The pPb results obtained with particle $c$ in Pb-going (solid markers) and p-going (open markers) sides are shown separately. The SS and OS two-particle correlators are denoted by different markers for both pPb and PbPb collisions. Statistical and systematic uncertainties are indicated by the error bars and shaded regions, respectively.
png pdf	Figure 20-a: The SS and OS three-particle correlators, $\gamma _{112}$ (upper) and $\gamma _{123}$ (middle), and two-particle correlator, $\delta$ (lower), as a function of ${\| {\Delta \eta } \| }$ for 120 $\leq {N_\text {trk}^\text {offline}} <$ 150 in pPb collisions at ${\sqrt {{s_{_{\mathrm {NN}}}}}} =$ 8.16 TeV (left) and PbPb collisions at 5.02 TeV (right). The pPb results obtained with particle $c$ in Pb-going (solid markers) and p-going (open markers) sides are shown separately. The SS and OS two-particle correlators are denoted by different markers for both pPb and PbPb collisions. Statistical and systematic uncertainties are indicated by the error bars and shaded regions, respectively.
png pdf	Figure 20-b: The SS and OS three-particle correlators, $\gamma _{112}$ (upper) and $\gamma _{123}$ (middle), and two-particle correlator, $\delta$ (lower), as a function of ${\| {\Delta \eta } \| }$ for 150 $\leq {N_\text {trk}^\text {offline}} <$ 185 in pPb collisions at ${\sqrt {{s_{_{\mathrm {NN}}}}}} =$ 8.16 TeV (left) and PbPb collisions at 5.02 TeV (right). The pPb results obtained with particle $c$ in Pb-going (solid markers) and p-going (open markers) sides are shown separately. The SS and OS two-particle correlators are denoted by different markers for both pPb and PbPb collisions. Statistical and systematic uncertainties are indicated by the error bars and shaded regions, respectively.
png pdf	Figure 20-c: The SS and OS three-particle correlators, $\gamma _{112}$ (upper) and $\gamma _{123}$ (middle), and two-particle correlator, $\delta$ (lower), as a function of ${\| {\Delta \eta } \| }$ for 185 $\leq {N_\text {trk}^\text {offline}} <$ 250 in pPb collisions at ${\sqrt {{s_{_{\mathrm {NN}}}}}} =$ 8.16 TeV (left) and PbPb collisions at 5.02 TeV (right). The pPb results obtained with particle $c$ in Pb-going (solid markers) and p-going (open markers) sides are shown separately. The SS and OS two-particle correlators are denoted by different markers for both pPb and PbPb collisions. Statistical and systematic uncertainties are indicated by the error bars and shaded regions, respectively.
png pdf	Figure 20-d: The SS and OS three-particle correlators, $\gamma _{112}$ (upper) and $\gamma _{123}$ (middle), and two-particle correlator, $\delta$ (lower), as a function of ${\| {\Delta \eta } \| }$ for 250 $\leq {N_\text {trk}^\text {offline}} <$ 300 in pPb collisions at ${\sqrt {{s_{_{\mathrm {NN}}}}}} =$ 8.16 TeV (left) and PbPb collisions at 5.02 TeV (right). The pPb results obtained with particle $c$ in Pb-going (solid markers) and p-going (open markers) sides are shown separately. The SS and OS two-particle correlators are denoted by different markers for both pPb and PbPb collisions. Statistical and systematic uncertainties are indicated by the error bars and shaded regions, respectively.
png pdf	Figure 21: The SS and OS three-particle correlators, $\gamma _{112}$ (upper) and $\gamma _{123}$ (middle), and two-particle correlator, $\delta$ (lower), as a function of ${\| \Delta {p_{\mathrm {T}}} \| }$ for four multiplicity ranges in pPb collisions at ${\sqrt {{s_{_{\mathrm {NN}}}}}} =$ 8.16 TeV (left) and PbPb collisions at 5.02 TeV (right). The pPb results obtained with particle $c$ in Pb-going (solid markers) and p-going (open markers) sides are shown separately. The SS and OS two-particle correlators are denoted by different markers for both pPb and PbPb collisions. Statistical and systematic uncertainties are indicated by the error bars and shaded regions, respectively.
png pdf	Figure 21-a: The SS and OS three-particle correlators, $\gamma _{112}$ (upper) and $\gamma _{123}$ (middle), and two-particle correlator, $\delta$ (lower), as a function of ${\| \Delta {p_{\mathrm {T}}} \| }$ for 120 $\leq {N_\text {trk}^\text {offline}} <$ 150 in pPb collisions at ${\sqrt {{s_{_{\mathrm {NN}}}}}} =$ 8.16 TeV (left) and PbPb collisions at 5.02 TeV (right). The pPb results obtained with particle $c$ in Pb-going (solid markers) and p-going (open markers) sides are shown separately. The SS and OS two-particle correlators are denoted by different markers for both pPb and PbPb collisions. Statistical and systematic uncertainties are indicated by the error bars and shaded regions, respectively.
png pdf	Figure 21-b: The SS and OS three-particle correlators, $\gamma _{112}$ (upper) and $\gamma _{123}$ (middle), and two-particle correlator, $\delta$ (lower), as a function of ${\| \Delta {p_{\mathrm {T}}} \| }$ for 150 $\leq {N_\text {trk}^\text {offline}} <$ 185 in pPb collisions at ${\sqrt {{s_{_{\mathrm {NN}}}}}} =$ 8.16 TeV (left) and PbPb collisions at 5.02 TeV (right). The pPb results obtained with particle $c$ in Pb-going (solid markers) and p-going (open markers) sides are shown separately. The SS and OS two-particle correlators are denoted by different markers for both pPb and PbPb collisions. Statistical and systematic uncertainties are indicated by the error bars and shaded regions, respectively.
png pdf	Figure 21-c: The SS and OS three-particle correlators, $\gamma _{112}$ (upper) and $\gamma _{123}$ (middle), and two-particle correlator, $\delta$ (lower), as a function of ${\| \Delta {p_{\mathrm {T}}} \| }$ for 185 $\leq {N_\text {trk}^\text {offline}} <$ 250 in pPb collisions at ${\sqrt {{s_{_{\mathrm {NN}}}}}} =$ 8.16 TeV (left) and PbPb collisions at 5.02 TeV (right). The pPb results obtained with particle $c$ in Pb-going (solid markers) and p-going (open markers) sides are shown separately. The SS and OS two-particle correlators are denoted by different markers for both pPb and PbPb collisions. Statistical and systematic uncertainties are indicated by the error bars and shaded regions, respectively.
png pdf	Figure 21-d: The SS and OS three-particle correlators, $\gamma _{112}$ (upper) and $\gamma _{123}$ (middle), and two-particle correlator, $\delta$ (lower), as a function of ${\| \Delta {p_{\mathrm {T}}} \| }$ for 250 $\leq {N_\text {trk}^\text {offline}} <$ 300 in pPb collisions at ${\sqrt {{s_{_{\mathrm {NN}}}}}} =$ 8.16 TeV (left) and PbPb collisions at 5.02 TeV (right). The pPb results obtained with particle $c$ in Pb-going (solid markers) and p-going (open markers) sides are shown separately. The SS and OS two-particle correlators are denoted by different markers for both pPb and PbPb collisions. Statistical and systematic uncertainties are indicated by the error bars and shaded regions, respectively.
png pdf	Figure 22: The SS and OS three-particle correlators, $\gamma _{112}$ (upper) and $\gamma _{123}$ (middle), and two-particle correlator, $\delta$ (lower), as a function of ${\overline {p}_\mathrm {T}}$ for four multiplicity ranges in pPb collisions at ${\sqrt {{s_{_{\mathrm {NN}}}}}} =$ 8.16 TeV (left) and PbPb collisions at ${\sqrt {{s_{_{\mathrm {NN}}}}}}=$ 5.02 TeV (right). The pPb results obtained with particle $c$ in Pb-going (solid markers) and p-going (open markers) sides are shown separately. The SS and OS two-particle correlators are denoted by different markers for both pPb and PbPb collisions. Statistical and systematic uncertainties are indicated by the error bars and shaded regions, respectively.
png pdf	Figure 22-a: The SS and OS three-particle correlators, $\gamma _{112}$ (upper) and $\gamma _{123}$ (middle), and two-particle correlator, $\delta$ (lower), as a function of ${\overline {p}_\mathrm {T}}$ for 120 $\leq {N_\text {trk}^\text {offline}} <$ 150 in pPb collisions at ${\sqrt {{s_{_{\mathrm {NN}}}}}} =$ 8.16 TeV (left) and PbPb collisions at ${\sqrt {{s_{_{\mathrm {NN}}}}}}=$ 5.02 TeV (right). The pPb results obtained with particle $c$ in Pb-going (solid markers) and p-going (open markers) sides are shown separately. The SS and OS two-particle correlators are denoted by different markers for both pPb and PbPb collisions. Statistical and systematic uncertainties are indicated by the error bars and shaded regions, respectively.
png pdf	Figure 22-b: The SS and OS three-particle correlators, $\gamma _{112}$ (upper) and $\gamma _{123}$ (middle), and two-particle correlator, $\delta$ (lower), as a function of ${\overline {p}_\mathrm {T}}$ for 150 $\leq {N_\text {trk}^\text {offline}} <$ 185 in pPb collisions at ${\sqrt {{s_{_{\mathrm {NN}}}}}} =$ 8.16 TeV (left) and PbPb collisions at ${\sqrt {{s_{_{\mathrm {NN}}}}}}=$ 5.02 TeV (right). The pPb results obtained with particle $c$ in Pb-going (solid markers) and p-going (open markers) sides are shown separately. The SS and OS two-particle correlators are denoted by different markers for both pPb and PbPb collisions. Statistical and systematic uncertainties are indicated by the error bars and shaded regions, respectively.
png pdf	Figure 22-c: The SS and OS three-particle correlators, $\gamma _{112}$ (upper) and $\gamma _{123}$ (middle), and two-particle correlator, $\delta$ (lower), as a function of ${\overline {p}_\mathrm {T}}$ for 185 $\leq {N_\text {trk}^\text {offline}} <$ 250 in pPb collisions at ${\sqrt {{s_{_{\mathrm {NN}}}}}} =$ 8.16 TeV (left) and PbPb collisions at ${\sqrt {{s_{_{\mathrm {NN}}}}}}=$ 5.02 TeV (right). The pPb results obtained with particle $c$ in Pb-going (solid markers) and p-going (open markers) sides are shown separately. The SS and OS two-particle correlators are denoted by different markers for both pPb and PbPb collisions. Statistical and systematic uncertainties are indicated by the error bars and shaded regions, respectively.
png pdf	Figure 22-d: The SS and OS three-particle correlators, $\gamma _{112}$ (upper) and $\gamma _{123}$ (middle), and two-particle correlator, $\delta$ (lower), as a function of ${\overline {p}_\mathrm {T}}$ for 250 $\leq {N_\text {trk}^\text {offline}} <$ 300 in pPb collisions at ${\sqrt {{s_{_{\mathrm {NN}}}}}} =$ 8.16 TeV (left) and PbPb collisions at ${\sqrt {{s_{_{\mathrm {NN}}}}}}=$ 5.02 TeV (right). The pPb results obtained with particle $c$ in Pb-going (solid markers) and p-going (open markers) sides are shown separately. The SS and OS two-particle correlators are denoted by different markers for both pPb and PbPb collisions. Statistical and systematic uncertainties are indicated by the error bars and shaded regions, respectively.
png pdf	Figure 23: The SS and OS three-particle correlators, $\gamma _{112}$ (upper) and $\gamma _{123}$ (middle), and two-particle correlator, $\delta$ (lower), as a function of ${\| {\Delta \eta } \| }$ for five centrality classes in PbPb collisions at 5.02 TeV. The SS and OS two-particle correlators are denoted by different markers. Statistical and systematic uncertainties are indicated by the error bars and shaded regions, respectively.
png pdf	Figure 23-a: The SS and OS three-particle correlators, $\gamma _{112}$ (upper) and $\gamma _{123}$ (middle), and two-particle correlator, $\delta$ (lower), as a function of ${\| {\Delta \eta } \| }$ for centrality class 30-40% in PbPb collisions at 5.02 TeV. The SS and OS two-particle correlators are denoted by different markers. Statistical and systematic uncertainties are indicated by the error bars and shaded regions, respectively.
png pdf	Figure 23-b: The SS and OS three-particle correlators, $\gamma _{112}$ (upper) and $\gamma _{123}$ (middle), and two-particle correlator, $\delta$ (lower), as a function of ${\| {\Delta \eta } \| }$ for centrality class 40-50% in PbPb collisions at 5.02 TeV. The SS and OS two-particle correlators are denoted by different markers. Statistical and systematic uncertainties are indicated by the error bars and shaded regions, respectively.
png pdf	Figure 23-c: The SS and OS three-particle correlators, $\gamma _{112}$ (upper) and $\gamma _{123}$ (middle), and two-particle correlator, $\delta$ (lower), as a function of ${\| {\Delta \eta } \| }$ for centrality class 50-60% in PbPb collisions at 5.02 TeV. The SS and OS two-particle correlators are denoted by different markers. Statistical and systematic uncertainties are indicated by the error bars and shaded regions, respectively.
png pdf	Figure 23-d: The SS and OS three-particle correlators, $\gamma _{112}$ (upper) and $\gamma _{123}$ (middle), and two-particle correlator, $\delta$ (lower), as a function of ${\| {\Delta \eta } \| }$ for centrality class 60-70% in PbPb collisions at 5.02 TeV. The SS and OS two-particle correlators are denoted by different markers. Statistical and systematic uncertainties are indicated by the error bars and shaded regions, respectively.
png pdf	Figure 23-e: The SS and OS three-particle correlators, $\gamma _{112}$ (upper) and $\gamma _{123}$ (middle), and two-particle correlator, $\delta$ (lower), as a function of ${\| {\Delta \eta } \| }$ for centrality class 70-80% in PbPb collisions at 5.02 TeV. The SS and OS two-particle correlators are denoted by different markers. Statistical and systematic uncertainties are indicated by the error bars and shaded regions, respectively.
png pdf	Figure 24: The SS and OS three-particle correlators, $\gamma _{112}$ (upper) and $\gamma _{123}$ (middle), and two-particle correlator, $\delta$ (lower), as a function of ${\| \Delta {p_{\mathrm {T}}} \| }$ for five centrality classes in PbPb collisions at ${\sqrt {{s_{_{\mathrm {NN}}}}}}=$ 5.02 TeV. The SS and OS two-particle correlators are denoted by different markers. Statistical and systematic uncertainties are indicated by the error bars and shaded regions, respectively.
png pdf	Figure 24-a: The SS and OS three-particle correlators, $\gamma _{112}$ (upper) and $\gamma _{123}$ (middle), and two-particle correlator, $\delta$ (lower), as a function of ${\| \Delta {p_{\mathrm {T}}} \| }$ for centrality class 30-40% in PbPb collisions at ${\sqrt {{s_{_{\mathrm {NN}}}}}}=$ 5.02 TeV. The SS and OS two-particle correlators are denoted by different markers. Statistical and systematic uncertainties are indicated by the error bars and shaded regions, respectively.
png pdf	Figure 24-b: The SS and OS three-particle correlators, $\gamma _{112}$ (upper) and $\gamma _{123}$ (middle), and two-particle correlator, $\delta$ (lower), as a function of ${\| \Delta {p_{\mathrm {T}}} \| }$ for centrality class 40-50% in PbPb collisions at ${\sqrt {{s_{_{\mathrm {NN}}}}}}=$ 5.02 TeV. The SS and OS two-particle correlators are denoted by different markers. Statistical and systematic uncertainties are indicated by the error bars and shaded regions, respectively.
png pdf	Figure 24-c: The SS and OS three-particle correlators, $\gamma _{112}$ (upper) and $\gamma _{123}$ (middle), and two-particle correlator, $\delta$ (lower), as a function of ${\| \Delta {p_{\mathrm {T}}} \| }$ for centrality class 50-60% in PbPb collisions at ${\sqrt {{s_{_{\mathrm {NN}}}}}}=$ 5.02 TeV. The SS and OS two-particle correlators are denoted by different markers. Statistical and systematic uncertainties are indicated by the error bars and shaded regions, respectively.
png pdf	Figure 24-d: The SS and OS three-particle correlators, $\gamma _{112}$ (upper) and $\gamma _{123}$ (middle), and two-particle correlator, $\delta$ (lower), as a function of ${\| \Delta {p_{\mathrm {T}}} \| }$ for centrality class 60-70% in PbPb collisions at ${\sqrt {{s_{_{\mathrm {NN}}}}}}=$ 5.02 TeV. The SS and OS two-particle correlators are denoted by different markers. Statistical and systematic uncertainties are indicated by the error bars and shaded regions, respectively.
png pdf	Figure 24-e: The SS and OS three-particle correlators, $\gamma _{112}$ (upper) and $\gamma _{123}$ (middle), and two-particle correlator, $\delta$ (lower), as a function of ${\| \Delta {p_{\mathrm {T}}} \| }$ for centrality class 70-80% in PbPb collisions at ${\sqrt {{s_{_{\mathrm {NN}}}}}}=$ 5.02 TeV. The SS and OS two-particle correlators are denoted by different markers. Statistical and systematic uncertainties are indicated by the error bars and shaded regions, respectively.
png pdf	Figure 25: The SS and OS three-particle correlators, $\gamma _{112}$ (upper) and $\gamma _{123}$ (middle), and two-particle correlator, $\delta$ (lower), as a function of ${\overline {p}_\mathrm {T}}$ for five centrality classes in PbPb collisions at ${\sqrt {{s_{_{\mathrm {NN}}}}}}=$ 5.02 TeV. The SS and OS two-particle correlators are denoted by different markers. Statistical and systematic uncertainties are indicated by the error bars and shaded regions, respectively.
png pdf	Figure 25-a: The SS and OS three-particle correlators, $\gamma _{112}$ (upper) and $\gamma _{123}$ (middle), and two-particle correlator, $\delta$ (lower), as a function of ${\overline {p}_\mathrm {T}}$ for centrality class 30-40% in PbPb collisions at ${\sqrt {{s_{_{\mathrm {NN}}}}}}=$ 5.02 TeV. The SS and OS two-particle correlators are denoted by different markers. Statistical and systematic uncertainties are indicated by the error bars and shaded regions, respectively.
png pdf	Figure 25-b: The SS and OS three-particle correlators, $\gamma _{112}$ (upper) and $\gamma _{123}$ (middle), and two-particle correlator, $\delta$ (lower), as a function of ${\overline {p}_\mathrm {T}}$ for centrality class 40-50% in PbPb collisions at ${\sqrt {{s_{_{\mathrm {NN}}}}}}=$ 5.02 TeV. The SS and OS two-particle correlators are denoted by different markers. Statistical and systematic uncertainties are indicated by the error bars and shaded regions, respectively.
png pdf	Figure 25-c: The SS and OS three-particle correlators, $\gamma _{112}$ (upper) and $\gamma _{123}$ (middle), and two-particle correlator, $\delta$ (lower), as a function of ${\overline {p}_\mathrm {T}}$ for centrality class 50-60% in PbPb collisions at ${\sqrt {{s_{_{\mathrm {NN}}}}}}=$ 5.02 TeV. The SS and OS two-particle correlators are denoted by different markers. Statistical and systematic uncertainties are indicated by the error bars and shaded regions, respectively.
png pdf	Figure 25-d: The SS and OS three-particle correlators, $\gamma _{112}$ (upper) and $\gamma _{123}$ (middle), and two-particle correlator, $\delta$ (lower), as a function of ${\overline {p}_\mathrm {T}}$ for centrality class 60-70% in PbPb collisions at ${\sqrt {{s_{_{\mathrm {NN}}}}}}=$ 5.02 TeV. The SS and OS two-particle correlators are denoted by different markers. Statistical and systematic uncertainties are indicated by the error bars and shaded regions, respectively.
png pdf	Figure 25-e: The SS and OS three-particle correlators, $\gamma _{112}$ (upper) and $\gamma _{123}$ (middle), and two-particle correlator, $\delta$ (lower), as a function of ${\overline {p}_\mathrm {T}}$ for centrality class 70-80% in PbPb collisions at ${\sqrt {{s_{_{\mathrm {NN}}}}}}=$ 5.02 TeV. The SS and OS two-particle correlators are denoted by different markers. Statistical and systematic uncertainties are indicated by the error bars and shaded regions, respectively.

Tables
png pdf	Table 1: Summary of systematic uncertainties on SS and OS three-particle correlator $\gamma _{112}$ and $\gamma _{123}$ , and two-particle correlator $\delta$ in pPb collisions at ${\sqrt {{s_{_{\mathrm {NN}}}}}}=$ 8.16 TeV and PbPb collisions at 5.02 TeV.
png pdf	Table 2: The summary of slope and intercept parameter $a_{\text {norm}}$ and $b_{\text {norm}}$ for different ${N_\text {trk}^\text {offline}}$ classes in pPb collisions, and the goodness of fit $\chi ^{2}$ per degree of freedom (ndf). The statistical and systematic uncertainties are shown after the central values, respectively.
png pdf	Table 3: The summary of slope and intercept parameter $a_{\text {norm}}$ and $b_{\text {norm}}$ for different centrality classes in PbPb collisions, and the goodness of fit $\chi ^{2}$ per degree of freedom (ndf). The statistical and systematic uncertainties are shown after the central values, respectively.

Summary

Charge-dependent azimuthal correlations of same- and opposite-sign (SS and OS) pairs with respect to the second- and third-order event planes have been studied in pPb collisions at

$\sqrt{s_{\mathrm{NN}}} =$ 8.16 TeV and PbPb collisions at 5.02 TeV by the CMS experiment at the LHC. The correlations are extracted via three-particle correlators as functions of pseudorapidity difference, transverse momentum difference, and

$p_{\mathrm{T}}$ average of SS and OS particle pairs, in various multiplicity or centrality ranges of the collisions. The differences in correlations between OS and SS particles with respect to both second- and third-order event planes as functions of

$\Delta \eta$ and multiplicity are found to agree for pPb and PbPb collisions, indicating a common underlying mechanism for the two systems. Dividing the OS and SS difference of the three-particle correlator by the product of

$v_n$ harmonic of the corresponding order and the difference of the two-particle correlator, the ratios are found to be similar for the second- and third-order event planes, and show weak dependence on event multiplicity. These observations support a scenario in which the charge-dependent three-particle correlator is predominantly a consequence of charge-dependent two-particle correlations coupled to an anisotropic flow signal.

To establish the relation between the three-particle correlator and anisotropic flow harmonic in detail, an event shape engineering technique is applied. A linear relation for the ratio of three- to two-particle correlator difference as a function of

$v_2$ is observed, which extrapolates to an intercept that is consistent with zero within uncertainties. This observation in the pPb system is consistent with the expectation of a negligible CME contribution to the charge-dependent three particle correlator. An upper limit on the

$v_2$ -independent fraction of the three-particle correlator, or the possible CME signal contribution (assumed independent of

$v_2$ within the same narrow multiplicity or centrality range), is estimated to be 6.6% for pPb data and 3.8% for PbPb data at a 95% confidence level. The data presented in this paper provide new stringent constraints on the nature of the background contribution to the charge-dependent azimuthal correlations, and establish a new baseline for the search for the chiral magnetic effect in heavy ion collisions.

References
1	T. D. Lee	A theory of spontaneous $T$ violation	PRD 8 (1973) 1226
2	T. D. Lee and G. C. Wick	Vacuum stability and vacuum excitation in a spin-0 field theory	PRD 9 (1974) 2291
3	P. D. Morley and I. A. Schmidt	Strong P, CP, T violations in heavy-ion collisions	Z. Phys. C 26 (1985) 627
4	D. Kharzeev, R. D. Pisarski, and M. H. G. Tytgat	Possibility of spontaneous parity violation in hot QCD	PRL 81 (1998) 512	hep-ph/9804221
5	D. Kharzeev	Parity violation in hot QCD: Why it can happen, and how to look for it	PLB 633 (2006) 260	hep-ph/0406125
6	D. E. Kharzeev, L. D. McLerran, and H. J. Warringa	The effects of topological charge change in heavy ion collisions: 'Event by event P and CP violation'	NP A 803 (2008) 227	0711.0950
7	K. Fukushima, D. E. Kharzeev, and H. J. Warringa	The chiral magnetic effect	PRD 78 (2008) 074033	0808.3382
8	B. Q. Lv et al.	Experimental discovery of Weyl semimetal TaAs	PRX 5 (2015) 031013	1502.04684
9	X. Huang et al.	Observation of the chiral-anomaly-induced negative magnetoresistance in 3D Weyl semimetal TaAs	PRX 5 (2015) 031023	1503.01304
10	Q. Li et al.	Observation of the chiral magnetic effect in ZrTe5	NP 12 (2016) 550	1412.6543
11	STAR Collaboration	Azimuthal charged-particle correlations and possible local strong parity violation	PRL 103 (2009) 251601	0909.1739
12	STAR Collaboration	Observation of charge-dependent azimuthal correlations and possible local strong parity violation in heavy ion collisions	PRC 81 (2010) 054908	0909.1717
13	STAR Collaboration	Measurement of charge multiplicity asymmetry correlations in high-energy nucleus-nucleus collisions at $\sqrt{s_{\mathrm{NN}}}\ =$ 200 GeV	PRC 89 (2014) 044908	1303.0901
14	STAR Collaboration	Beam-energy dependence of charge separation along the magnetic field in Au+Au collisions at RHIC	PRL 113 (2014) 052302	1404.1433
15	STAR Collaboration	Fluctuations of charge separation perpendicular to the event plane and local parity violation in $\sqrt{s_{\mathrm{NN}}}\ =$ 200 GeV Au+Au collisions at the BNL Relativistic Heavy Ion Collider	PRC 88 (2013) 064911	1302.3802
16	ALICE Collaboration	Charge separation relative to the reaction plane in Pb-Pb collisions at $\sqrt{s_{\mathrm{NN}}}\ =$ 2.76 TeV	PRL 110 (2013) 012301	1207.0900
17	D. E. Kharzeev, J. Liao, S. A. Voloshin, and G. Wang	Chiral magnetic and vortical effects in high-energy nuclear collisions --- a status report	Prog. Part. NP 88 (2016) 1	1511.04050
18	F. Wang	Effects of cluster particle correlations on local parity violation observables	PRC 81 (2010) 064902	0911.1482
19	A. Bzdak, V. Koch, and J. Liao	Azimuthal correlations from transverse momentum conservation and possible local parity violation	PRC 83 (2011) 014905	1008.4919
20	S. Schlichting and S. Pratt	Charge conservation at energies available at the BNL Relativistic Heavy Ion Collider and contributions to local parity violation observables	PRC 83 (2011) 014913	1009.4283
21	CMS Collaboration	Observation of charge-dependent azimuthal correlations in pPb collisions and its implication for the search for the chiral magnetic effect	PRL 118 (2017) 122301	CMS-HIN-16-009 1610.00263
22	R. Belmont and J. L. Nagle	To CME or not to CME? Implications of p+Pb measurements of the chiral magnetic effect in heavy ion collisions		1610.07964
23	S. A. Voloshin	Parity violation in hot QCD: How to detect it	PRC 70 (2004) 057901	hep-ph/0406311
24	A. Bzdak, V. Koch, and J. Liao	Charge-dependent correlations in relativistic heavy ion collisions and the chiral magnetic effect	Lect. Notes Phys. 871 (2013) 503	1207.7327
25	B. Alver and G. Roland	Collision geometry fluctuations and triangular flow in heavy-ion collisions	PRC 81 (2010) 054905	1003.0194
26	ATLAS Collaboration	Measurement of event-plane correlations in $\sqrt{s_{\mathrm{NN}}}\ =$ 2.76 TeV lead-lead collisions with the ATLAS detector	PRC 90 (2014) 024905	1403.0489
27	CMS Collaboration	Measurement of higher-order harmonic azimuthal anisotropy in PbPb collisions at $\sqrt{s_{\mathrm{NN}}}\ =$ 2.76 TeV	PRC 89 (2014) 044906	CMS-HIN-11-005 1310.8651
28	CMS Collaboration	Multiplicity and transverse momentum dependence of two- and four-particle correlations in $\mathrm{ p Pb }\$ and $\mathrm{ Pp Pb }\$ collisions	PLB 724 (2013) 213	CMS-HIN-13-002 1305.0609
29	J. Schukraft, A. Timmins, and S. A. Voloshin	Ultra-relativistic nuclear collisions: event shape engineering	PLB 719 (2013) 394	1208.4563
30	CMS Collaboration	Description and performance of track and primary-vertex reconstruction with the CMS tracker	JINST 9 (2014) P10009	CMS-TRK-11-001 1405.6569
31	CMS Collaboration	The CMS experiment at the CERN LHC	JINST 3 (2008) S08004	CMS-00-001
32	CMS Collaboration	Observation of long-range near-side angular correlations in proton-proton collisions at the LHC	JHEP 09 (2010) 091	CMS-QCD-10-002 1009.4122
33	CMS Collaboration	Observation of long-range, near-side angular correlations in pPb collisions at the LHC	PLB 718 (2013) 795	CMS-HIN-12-015 1210.5482
34	CMS Collaboration	Evidence for collectivity in pp collisions at the LHC	PLB 765 (2017) 193	CMS-HIN-16-010 1606.06198
35	I. Selyuzhenkov and S. Voloshin	Effects of non-uniform acceptance in anisotropic flow measurement	PRC 77 (2008) 034904	0707.4672
36	A. Bilandzic et al.	Generic framework for anisotropic flow analyses with multiparticle azimuthal correlations	PRC 89 (2014) 064904	1312.3572
37	ALICE Collaboration	Event shape engineering for inclusive spectra and elliptic flow in Pb-Pb collisions at $\sqrt{s_{\mathrm{NN}}}\ =$ 2.76 TeV	PRC 93 (2016) 034916	1507.06194
38	T. Pierog et al.	EPOS LHC: Test of collective hadronization with data measured at the CERN Large Hadron Collider	PRC 92 (2015) 034906	1306.0121
39	GEANT4 Collaboration	GEANT4 --- a simulation toolkit	NIMA 506 (2003) 250
40	J. Allison et al.	Geant4 developments and applications	IEEE Trans. Nucl. Sci. 53 (2006) 270
41	CMS Collaboration	Centrality dependence of dihadron correlations and azimuthal anisotropy harmonics in PbPb collisions at $\sqrt{s_{\mathrm{NN}}}\ =$ 2.76 TeV	EPJC 72 (2012) 10052	CMS-HIN-11-006 1201.3158
42	Z.-W. Lin et al.	A multi-phase transport model for relativistic heavy ion collisions	PRC 72 (2005) 064901	nucl-th/0411110
43	G.-L. Ma and B. Zhang	Effects of final state interactions on charge separation in relativistic heavy ion collisions	PLB 700 (2011) 39	1101.1701
44	G. J. Feldman and R. D. Cousins	A unified approach to the classical statistical analysis of small signals	PRD 57 (1998) 3873	physics/9711021