Dynamic jet charge

We propose a modified definition of the jet charge, the “dynamic jet charge,” where the constant jet momentum fraction weighting parameter $\kappa$ in the standard jet charge definition is generalized to be a function of a dynamical property of the jet or the individual jet constituents. The dynamic jet charge can complement analyses based on the standard definition and give improved discrimination between quark and gluon initiated jets and between jets initiated by different quark flavors. We focus on the specific scenario where each hadron in the jet contributes to the dynamic jet charge with a $\kappa$-value dynamically determined by its jet momentum fraction. The corresponding dynamic jet charge distributions have qualitatively distinct features and are typically characterized by a multiple peak structure. For proton-proton collisions, compared to the standard jet charge, the dynamic jet charge gives significantly improved discrimination between quark and gluon initiated jets and comparable discrimination between $u$- and $d$-quark initiated jets. In pythia simulations of heavy ion collisions, the dynamic jet charge is found to have higher jet discrimination power compared to the standard jet charge, remaining robust against the increased contamination from underlying event. We also present phenomenological applications of the dynamic jet charge to probe nuclear flavor structure.

Figure 1

Normalized standard jet charge distributions for the more forward (top panel) and more central (bottom panel) of the leading jets in pythia8 simulations of $pp\to j_1{j}_{2}X$ at $\sqrt{s}=8\mathrm{TeV}$ with hadronization and multiparton interaction (MPI) effects turned on. Selection cuts of $200\mathrm{GeV}<p_{T_{j_1,j_2}}<300\mathrm{GeV}$, $|{\eta }_{j1,j2}|<2.1$, and $p_{T_{j_1}}/p_{T_{j_2}}<1.5$ on the leading ($j_1$) and subleading ($j_2$) anti-$k_T$ jets of jet radius $R=0.4$ are applied. The blue, red, and green curves correspond to $\kappa =0.3$, 0.5, and 0.7, respectively.

Figure 2

Comparison of the ATLAS data [19] for the standard jet charge with pythia8.240 simulations (default tune). The average standard jet charge is plotted as a function of the jet $p_T$ in $pp\to j_1{j}_{2}X$ at $\sqrt{s}=8\mathrm{TeV}$. The average jet charge of the more forward (top panel) and more central (bottom panel) of the two leading jets are shown for the values $\kappa =0.3$, 0.5, 0.7 corresponding to the blue, red, and green curves, respectively. Selection cuts of $200\mathrm{GeV}<p_{T_{j_1,j_2}}<300\mathrm{GeV}$, $|{\eta }_{j1,j2}|<2.1$, and $p_{T_{j_1}}/p_{T_{j_2}}<1.5$ on the leading ($j_1$) and subleading ($j_2$) anti-$k_T$ jets of jet radius $R=0.4$ are applied. The jet charge values correspond to an average over the jet $p_T$ bins: [50 GeV,100 GeV], [100 GeV, 200 GeV], [200 GeV, 300 GeV], [300 GeV, 400 GeV], [400 GeV, 500 GeV], [500 GeV, 600 GeV], [600 GeV, 800 GeV], [800 GeV, 1000 GeV], [1000 GeV, 1200 GeV], and [1200 GeV, 1500 GeV].

Figure 3

Normalized dynamic jet charge distributions for the more forward (top panel) and more central (bottom panel) jets from pythia8 simulations of $pp\to j_1{j}_{2}X$ at $\sqrt{s}=13\mathrm{TeV}$ with hadronization and MPI effects turned on. Selection cuts of $200\mathrm{GeV}<p_{T_{j_1,j_2}}<300\mathrm{GeV}$, $|{\eta }_{j1,j2}|<2.1$, and $p_{T_{j_1}}/p_{T_{j_2}}<1.5$ on the leading ($j_1$) and subleading ($j_2$) anti-$k_T$ jets of jet radius $R=0.4$ are applied. These distributions are for ${\xi }_{\text{cut}}=0.3$, $k_{<}=1.0$ and the blue, red, and green curves correspond to $k_{>}=0.3$, 0.5, and 0.7, respectively.

Figure 4

Average dynamic jet charge from pythia 8.240 simulations. The average dynamic jet charge is plotted as a function of the jet $p_{T_J}$ in $pp\to j_1{j}_{2}X$ at $\sqrt{s}=13\mathrm{TeV}$. The average dynamic jet charge of the more forward (top) and more central (bottom) of the two leading jets are shown for ${\xi }_{\text{cut}}=0.3,k_{<}=1.0$ and $k_{>}=0.3$, 0.5, 0.7 corresponding to the blue, red, and green curves, respectively. Selection cuts of $200\mathrm{GeV}<p_{T_{j_1,j_2}}<300\mathrm{GeV}$, $|{\eta }_{j1,j2}|<2.1$, and $p_{T_{j_1}}/p_{T_{j_2}}<1.5$ on the leading ($j_1$) and subleading ($j_2$) anti-$k_T$ jets of jet radius $R=0.4$ are applied. The jet charge values correspond to an average over the jet $p_{T_J}$ bins: [50 GeV,100 GeV], [100 GeV, 200 GeV], [200 GeV, 300 GeV], [300 GeV, 400 GeV], [400 GeV, 500 GeV], [500 GeV, 600 GeV], [600 GeV, 800 GeV], [800 GeV, 1000 GeV], [1000 GeV, 1200 GeV], and [1200 GeV, 1500 GeV].

Figure 5

Standard (top) and dynamic (middle) jet charge distributions in $pp$ collisions at $\sqrt{s}=13\mathrm{TeV}$ for quark (red) and gluon (blue) initiated jets with selection cuts $p_{T_J}=[200,300]\mathrm{GeV}$, $|{\eta }_J|<2.1$. A comparison of the corresponding quark-gluon discrimination receiver operating characteristic (ROC) curves for the standard (purple) and dynamic (green) jet charge distributions is given in the bottom panel.

Figure 6

Standard (top) and dynamic (middle) jet charge distributions in heavy ion (Pb-Pb) collisions at $\sqrt{s}=2.760\mathrm{TeV}$, for quark (red) and gluon (blue) initiated jets with selection cuts $p_{T_J}=[80,150]\mathrm{GeV}$, $|{\eta }_J|<0.9$. A comparison of the corresponding quark-gluon discrimination ROC curves for the standard (purple) and dynamic (green) jet charge distributions is given in the bottom panel.

Figure 7

Local ROC curves for the standard (purple) and dynamic (green) jet charge distributions described in Fig. 5 for $pp$ collisions at $\sqrt{s}=13\mathrm{TeV}$ with selection cuts $p_{T_J}=[200,300]\mathrm{GeV}$, $|{\eta }_J|<2.1$. The top and bottom panels correspond to the local ROC curves for the jet charge bins $|Q_J|<0.5$ and $|Q_J|>0.5$, respectively.

Figure 8

Standard (top) and dynamic (middle) jet charge distributions in $pp$ collisions at 13 TeV for $u$-quark (red) and $d$-quark (blue) initiated jets with selection cuts $p_{T_J}=[200,300]\mathrm{GeV}$, $|{\eta }_J|<2.1$. The channels $dg\to W^{-}u$ and $ug\to W^{+}d$ partonic channels where used to select the $u$-quark and $d$-quark initiated jets, respectively. A comparison of the corresponding “$u$” vs “$d$” discrimination ROC curves for the standard (purple) and dynamic (green) jet charge distributions is given in the bottom panel.

Figure 9

Standard (top) and dynamic (middle) jet charge distributions in PbPb collisions at 2.760 TeV for $u$-quark (red) and $d$-quark (blue) initiated jets with selection cuts $p_{T_J}=[80,150]\mathrm{GeV}$, $|{\eta }_J|<0.9$. The channels $dg\to W^{-}u$ and $ug\to W^{+}d$ partonic channels where used to select the $u$-quark and $d$-quark initiated jets, respectively. A comparison of the corresponding “$u$” vs “$d$” discrimination ROC curves for the standard (purple) and dynamic (green) jet charge distributions is given in the bottom panel.

Figure 10

Local ROC curves for the standard (purple) and dynamic (green) jet charge distributions described in Fig. 8 for $pp$ collisions at 13 TeV with selection cuts $p_{T_J}=[200,300]\mathrm{GeV}$, $|{\eta }_J|<2.1$. The top, middle, and bottom panels correspond to the local ROC curves for the jet charge bins $Q_J<-0.5$, $|Q_J|<0.5$, and $Q_J>0.5$, respectively.

Figure 11

Local ROC curves for the standard (purple) and dynamic (green) jet charge distributions described in Fig. 9 for PbPb collisions at 2.760 TeV with selection cuts $p_{T_J}=[80,150]\mathrm{GeV}$, $|{\eta }_J|<2.1$. The top, middle, and bottom panels correspond to the local ROC curves for the jet charge bins $Q_J<-0.5$, $|Q_J|<0.5$, and $Q_J>0.5$, respectively.

Figure 12

Comparison of the dynamic jet charge distributions for quark (red) and gluon (blue) jets in $pp\to j_1{j}_{2}X$ at 13 TeV. Selection cuts of $|{\eta }_{j1,j2}|<2.1$ and $p_{T_{j_1}}/p_{T_{j_2}}<1.5$ on the leading ($j_1$) and subleading ($j_2$) anti-$k_T$ jets of jet radius $R=0.4$ are applied. The top and bottom panels correspond to jets in the $p_{T_J}$ bins, [100 GeV, 200 GeV] and [1200 GeV, 1500 GeV], respectively.

Figure 13

Comparison of the dynamic jet charge distributions for different choices of the dynamic jet charge parameters ${\xi }_{\text{cut}},k_{<}$, and $k_{>}$ for quark (red) and gluon (blue) jets in $pp\to j_1{j}_{2}X$ at 13 TeV in the jet $p_T$ bin: [200,300] GeV. Selection cuts of $|{\eta }_{j1,j2}|<2.1$ and $p_{T_{j_1}}/p_{T_{j_2}}<1.5$ on the leading ($j_1$) and subleading ($j_2$) anti-$k_T$ jets of jet radius $R=0.4$ are applied.

Figure 14

Standard (top) and dynamic (bottom) jet charge distributions with MPI switch turned on (solid) and off (dashed) for quark (red) and gluon (blue) jets in $pp\to j_1{j}_{2}X$ at $\sqrt{s}=13\mathrm{TeV}$ and in the jet $p_{T_J}$ bin: [50, 100] GeV. Selection cuts of $|{\eta }_{j1,j2}|<2.1$ and $p_{T_{j_1}}/p_{T_{j_2}}<1.5$ on the leading ($j_1$) and subleading ($j_2$) anti-$k_T$ jets of jet radius $R=0.4$ are applied.

Figure 15

Standard (top) and dynamic (bottom) jet charge distributions for ungroomed (solid) and groomed (dashed) quark and gluon jets in $pp\to j_1{j}_{2}X$ at $\sqrt{s}=13\mathrm{TeV}$ and in the jet $p_{T_J}$ bin: [50, 100] GeV. Selection cuts of $|{\eta }_{j1,j2}|<2.1$ and $p_{T_{j_1}}/p_{T_{j_2}}<1.5$ on the leading ($j_1$) and subleading ($j_2$) anti-$k_T$ jets of jet radius $R=0.4$ are applied.

Figure 16

Standard (top) and dynamic (bottom) jet charge distributions for ungroomed (solid) and groomed (dashed) quark and gluon jets in $\mathrm{PbPb}\to j_1{j}_{2}X$ at $\sqrt{s}=2.760\mathrm{TeV}$ and in the jet $p_{T_J}$ bin: [80, 150] GeV. Selection cuts of $|{\eta }_{j1,j2}|<0.9$ and $p_{T_{j_1}}/p_{T_{j_2}}<1.5$ on the leading ($j_1$) and subleading ($j_2$) anti-$k_T$ jets of jet radius $R=0.4$ are applied.

Figure 17

Standard (top) and dynamic (bottom) jet charge distributions for $u$-quark (red) and $d$-quark (blue) jets, with (dashed) and without (solid) grooming, in $pp$ collisions at $\sqrt{s}=13\mathrm{TeV}$ with $R=0.4$, $p_{T_J}=[50,100]\mathrm{GeV}$, and $|{\eta }_J|<2.1$. The partonic channels $dg\to W^{-}u$ and $ug\to W^{+}d$ generated the $u$-quark and $d$-quark jets, respectively.

Figure 18

Standard (top) and dynamic (bottom) jet charge distributions for $u$-quark (red) and $d$-quark (blue) jets, with (dashed) and without (solid) grooming, in PbPb collisions at $\sqrt{s}=2.760\mathrm{TeV}$ with $R=0.4$, $p_{T_J}=[80,150]\mathrm{GeV}$, and $|{\eta }_J|<0.9$. The partonic channels $dg\to W^{-}u$ and $ug\to W^{+}d$ generated the $u$-quark and $d$-quark jets.

Figure 19

Top panel: contribution to the dynamic jet charge from the soft (dashed) and hard (solid) particles in quark (red) and (gluon) jets for the choice of parameters: ${\xi }_{\text{cut}}=0.3,k_{<}=1.0,k_{>}=0.3$. Middle panel: contribution to the dynamic jet charge from the soft (dashed) and hard (solid) particles in quark (red) and (gluon) jets for the choice of parameters: ${\xi }_{\text{cut}}=0.3,k_{<}=0.3,k_{>}=1.0$. Bottom panel: total dynamic jet charge distribution for ${\xi }_{\text{cut}}=0.3,k_{<}=0.3,k_{>}=1.0$. All the distributions above were generated for the more central jet in dijet production of $pp$ collisions at $\sqrt{s}=13\mathrm{TeV}$ with selection cuts $p_{T_J}=[200,300]\mathrm{GeV}$, $|{\eta }_J|<2.1$, and $p_{T_{j_1}}/p_{T_{j_2}}<1.5$ on the leading ($j_1$) and subleading ($j_2$) anti-$k_T$ jets of jet radius $R=0.4$.

Figure 20

Relative size of contributions from the unpolarized $u$-quark (red), $d$-quark (blue), and sea quark (green) transverse momentum dependents (TMDs) to the $q_T$ distribution integrated over all jet charge bins, corresponding to no jet charge measurement being made.

Figure 21

Relative size of contributions from the unpolarized $u$-quark (red) and $d$-quark (blue) TMDs to the $q_T$ distribution in different jet charge bins for the dynamic (solid) and standard (dashed) jet charges. The top and bottom panels correspond to the jet charge bins $Q_J<0.0$ and $Q_J<-0.25$, respectively.

Figure 22

Global ROC curves for discrimination between $u$- or $\overline{u}$-jets and $d$- or $\overline{d}$-jets in $pp\to \gamma +\text{jet}+X$ (top panel) and $\mathrm{PbPb}\to \gamma +\text{jet}+X$ (bottom panel) based on pythia simulations. The collision c.m. energy and selection cuts used are $\sqrt{s}=200\mathrm{GeV}$, $p_T>10.0\mathrm{GeV}$, $p_T^{\gamma }>30.0\mathrm{GeV}$, and $\mathrm{\Delta }\varphi >7/8\pi$.

Figure 23

Local ROC curves for discrimination between $u$- or $\overline{u}$-jets and $d$- or $\overline{d}$-jets in $pp\to \gamma +\text{jet}+X$ based on pythia simulations. The collision c.m. energy and selection cuts used are $\sqrt{s}=200\mathrm{GeV}$, $p_T>10.0\mathrm{GeV}$, $p_T^{\gamma }>30.0\mathrm{GeV}$, and $\mathrm{\Delta }\varphi >7/8\pi$. The top, middle, and bottom panels correspond to the jet charge bins $Q_J<-0.5,|Q_J|<0.5$, and $Q_J>0.5$, respectively.

Figure 24

Local ROC curves for discrimination between $u$- or $\overline{u}$-jets and $d$- or $\overline{d}$-jets in $\mathrm{PbPb}\to \gamma +\text{jet}+X$ based on pythia simulations. The collision c.m. energy and selection cuts used are $\sqrt{s}=200\mathrm{GeV}$, $p_T>10.0\mathrm{GeV}$, $p_T^{\gamma }>30.0\mathrm{GeV}$, and $\mathrm{\Delta }\varphi >7/8\pi$. The top, middle, and bottom panels correspond to the jet charge bins $Q_J<-0.5,|Q_J|<0.5$, and $Q_J>0.5$, respectively.

Figure 25

Standard (top panel) and dynamic (bottom panel) jet charge likelihood distributions for quark (red) and gluon (blue) jet samples. The $-2\ln {\lambda }_{\text{cut}}$ values for the standard and dynamic likelihood distributions are 0.103 and 1.90, respectively. The distributions above were generated for the more central jet in dijet production of $pp$ collisions at $\sqrt{s}=13\mathrm{TeV}$ with selection cuts $p_{T_J}=[200,300]\mathrm{GeV}$, $|{\eta }_J|<2.1$, and $p_{T_{j_1}}/p_{T_{j_2}}<1.5$ on the leading ($j_1$) and subleading ($j_2$) anti-$k_T$ jets of jet radius $R=0.4$.

Figure 26

Standard (top panel) and dynamic (bottom panel) jet charge likelihood distributions for quark (red) and gluon (blue) jet samples. The $-2\ln {\lambda }_{\text{cut}}$ values for the standard and dynamic likelihood distributions are -0.0308 and 2.17, respectively. The distributions above were generated for the more central jet in dijet production of PbPb collisions at $\sqrt{s}=2.760\mathrm{TeV}$ with selection cuts $p_{T_J}=[80,150]\mathrm{GeV}$, $|{\eta }_J|<0.9$, and $p_{T_{j_1}}/p_{T_{j_2}}<1.5$ on the leading ($j_1$) and subleading ($j_2$) anti-$k_T$ jets of jet radius $R=0.4$.

Figure 27

Standard (top panel) and dynamic (bottom panel) jet charge likelihood distributions for $u$-quark (red) and $d$-quark (blue) jet samples. The $-2\ln {\lambda }_{\text{cut}}$ values for the standard and dynamic likelihood distributions are 1.34 and 0.340, respectively. The distributions above were generated for the more central jet in dijet production of $pp$ collisions at $\sqrt{s}=13\mathrm{TeV}$ with $R=0.4$, $p_{T_J}=[200,300]\mathrm{GeV}$, and $|{\eta }_J|<2.1$. The partonic channels $dg\to W^{-}u$ and $ug\to W^{+}d$ generated the $u$-quark and $d$-quark jets, respectively.

Figure 28

Standard (top panel) and dynamic (bottom panel) jet charge likelihood distributions for $u$-quark (red) and $d$-quark (blue) jet samples. The $-2\ln {\lambda }_{\text{cut}}$ values for the standard and dynamic likelihood distributions are -0.0129 and 0.887, respectively. The distributions above were generated for the more central jet in dijet production of PbPb collisions at $\sqrt{s}=2.760\mathrm{TeV}$ with $R=0.4$, $p_{T_J}=[80,150]\mathrm{GeV}$, and $|{\eta }_J|<0.9$. The partonic channels $dg\to W^{-}u$ and $ug\to W^{+}d$ generated the $u$-quark and $d$-quark jets, respectively.