Properties of jet fragmentation using charged particles measured with the ATLAS detector in $pp$ collisions at $\sqrt{s}=13\mathrm{TeV}$

This paper presents a measurement of quantities related to the formation of jets from high-energy quarks and gluons (fragmentation). Jets with transverse momentum 100 GeV $<p_{\mathrm{T}}<2.5\mathrm{TeV}$ and pseudorapidity $|\eta |<2.1$ from an integrated luminosity of $33{\mathrm{fb}}^{-1}$ of $\sqrt{s}=13\mathrm{TeV}$ proton-proton collisions are reconstructed with the ATLAS detector at the Large Hadron Collider. Charged-particle tracks with $p_{\mathrm{T}}>500\mathrm{MeV}$ and $|\eta |<2.5$ are used to probe the detailed structure of the jet. The fragmentation properties of the more forward and the more central of the two leading jets from each event are studied. The data are unfolded to correct for detector resolution and acceptance effects. Comparisons with parton shower Monte Carlo generators indicate that existing models provide a reasonable description of the data across a wide range of phase space, but there are also significant differences. Furthermore, the data are interpreted in the context of quark- and gluon-initiated jets by exploiting the rapidity dependence of the jet flavor fraction. A first measurement of the charged-particle multiplicity using model-independent jet labels (topic modeling) provides a promising alternative to traditional quark and gluon extractions using input from simulation. The simulations provide a reasonable description of the quark-like data across the jet $p_{\mathrm{T}}$ range presented in -this measurement, but the gluon-like data have systematically fewer charged particles than the simulation.

Figure 1

Left: The transverse momentum, $p_{\mathrm{T}}$, spectrum for the selected jets; the simulation is normalized to the data. The normalization is dominated by the first bin, which accounts for the overall offset in the other bins for some of the predictions. Right: The pseudorapidity, $\eta$, distribution for the selected jets, split into the more forward and the more central of the two jets. Error bars only include the statistical uncertainty.

Figure 2

The detector-level distributions of (top left) the number of charged-particle tracks $n_{\text{track}}$, (top right) the transverse momentum fraction $\zeta$, (bottom left) the transverse momentum $p_{\mathrm{T}}^{\mathrm{rel}}$, and (bottom right) the radial profile in bins of the distance $r$ from the jet axis for jets with transverse momentum $1\mathrm{TeV}<p_{\mathrm{T}}^{\text{jet}}<1.2\mathrm{TeV}$. Error bars include the statistical uncertainty only.

Figure 3

Left: The gluon-jet fraction as a function of jet transverse momentum $p_{\mathrm{T}}$ and jet pseudorapidity $\eta$. Right: the fraction of the more forward and the more central jets that are gluon initiated. The error bars in the right plot represent the uncertainty computed from the 100 NNPDF2.3LO replicas [78]. See Sec. 8b for more details about quark/gluon definitions and uncertainties.

Figure 4

The probability distribution for the detector-level combined transverse momentum fraction $\zeta$ and jet transverse momentum $p_{\mathrm{T}}$ distribution normalized in bins of the particle-level variable using the pythia simulation. The $\zeta$ distribution is concatenated with the jet $p_{\mathrm{T}}$ so that every 21 bins is a different $\mathrm{jet}\text{−}{p}_{\mathrm{T}}$ bin. The first 315 bins represent the more central of the two jets and the second 315 bins correspond to the more forward jet. The $z$-axis is truncated at ${10}^{-3}$ for visualization only, to aid readability.

Figure 5

An overview of the statistical and systematic uncertainties for the average value of (top left) charged-particle multiplicity $n_{\mathrm{ch}}$, (top right) transverse momentum fraction $\zeta$, (bottom left) transverse momentum $p_{\mathrm{T}}^{\mathrm{rel}}$, and (bottom right) radial profile as a function of jet transverse momentum $p_{\mathrm{T}}$. The MC statistical uncertainties are negligible and are not shown. When the uncertainties go through zero (as for the unfolding uncertainty in the top left), the signed uncertainty has changed from positive to negative or vice versa. Most of the lines are the sum in quadrature of individual sources of uncertainty in each category, such as the various sources of tracking uncertainties as described in Sec. 7a.

Figure 6

The unfolded measured averages for the (top left) charged-particle multiplicity $n_{\mathrm{ch}}$, (top right) transverse momentum fraction $\zeta$, (bottom left) transverse momentum $p_{\mathrm{T}}^{\mathrm{rel}}$, and (bottom right) radial profile as a function of the jet transverse momentum $p_{\mathrm{T}}$ for the more forward and more central of the two jets, separately. The uncertainty bands show the combined statistical and systematic uncertainty.

Figure 7

The unfolded measured averages (top left) charged-particle multiplicity $n_{\mathrm{ch}}$, (top right) transverse momentum fraction $\zeta$, (bottom left) transverse momentum $p_{\mathrm{T}}^{\mathrm{rel}}$, and (bottom right) radial profile as a function of the jet transverse momentum $p_{\mathrm{T}}$. The lower panel shows the ratio of various MC predictions to the data, with the total uncertainty band centered on the data at unity.

Figure 8

The unfolded fraction of charged particles carrying a fraction $\zeta \lesssim 10\%$ (top left), 1% (top right), and 0.1% (bottom) of the jet transverse momentum $p_{\mathrm{T}}$. The exact fractions are given in the figures and correspond to powers of 1.5 so that the values align precisely with bin edges and thus no binning correction is required. The lower panels show the ratio of various MC predictions to the data, with the total uncertainty band centered on the data at unity.

Figure 9

Top: The unfolded (left) $1/2$ and (right) second moments of the transverse momentum fraction, $\zeta$, distribution as a function of the jet transverse momentum $p_{\mathrm{T}}$. Bottom: The unfolded moment of (left) $\sum _{i\in \text{jet}}{\zeta }^{1/2}$ and (right) $\sum _{i\in \text{jet}}{\zeta }^2$ as a function of the jet $p_{\mathrm{T}}$. Section 2 presents the definitions of both classes of observables. The lower panels show the ratio of various MC predictions to the data, with the total uncertainty band centered on the data at unity. The values are computed from the moments of the unfolded distributions in each $\mathrm{jet}\text{−}{p}_{\mathrm{T}}$ bin, with a small correction added to account for binning effects.

Figure 10

The distribution of charged-particle multiplicity $n_{\mathrm{ch}}$ in four bins of jet transverse momentum: (top left) $100\mathrm{GeV}<p_{\mathrm{T}}^{\text{jet}}<200\mathrm{GeV}$, (top right) $400\mathrm{GeV}<p_{\mathrm{T}}^{\text{jet}}<500\mathrm{GeV}$, (bottom left) $900\mathrm{GeV}<p_{\mathrm{T}}^{\text{jet}}<1000\mathrm{GeV}$, and (bottom right) $2000\mathrm{GeV}<p_{\mathrm{T}}^{\text{jet}}<2500\mathrm{GeV}$. The lower panels show the ratio of various MC predictions to the data, with the total uncertainty band centered on the data at unity. Additional $p_{\mathrm{T}}^{\text{jet}}$ bins can be found in Ref. [99].

Figure 11

The transverse momentum fraction $\zeta$ distribution in four bins of jet transverse momentum: (top left) $100\mathrm{GeV}<p_{\mathrm{T}}^{\text{jet}}<200\mathrm{GeV}$, (top right) $400\mathrm{GeV}<p_{\mathrm{T}}^{\text{jet}}<500\mathrm{GeV}$, (bottom left) $900\mathrm{GeV}<p_{\mathrm{T}}^{\text{jet}}<1000\mathrm{GeV}$, and (bottom right) $2000\mathrm{GeV}<p_{\mathrm{T}}^{\text{jet}}<2500\mathrm{GeV}$. The lower panels show the ratio of various MC predictions to the data, with the total uncertainty band centered on the data at unity. Additional $p_{\mathrm{T}}^{\text{jet}}$ bins can be found in Ref. [99].

Figure 12

The transverse momentum $p_{\mathrm{T}}^{\mathrm{rel}}$ distribution in four bins of jet transverse momentum: (top left) $100\mathrm{GeV}<p_{\mathrm{T}}^{\text{jet}}<200\mathrm{GeV}$, (top right) $400\mathrm{GeV}<p_{\mathrm{T}}^{\text{jet}}<500\mathrm{GeV}$, (bottom left) $900\mathrm{GeV}<p_{\mathrm{T}}^{\text{jet}}<1000\mathrm{GeV}$, and (bottom right) $2000\mathrm{GeV}<p_{\mathrm{T}}^{\text{jet}}<2500\mathrm{GeV}$. The lower panels show the ratio of various MC predictions to the data, with the total uncertainty band centered on the data at unity. Additional $p_{\mathrm{T}}^{\text{jet}}$ bins can be found in Ref. [99].

Figure 13

Distribution of track radial profile in bins of the radial distance $r$ from the jet axis in four bins of jet transverse momentum: (top left) $100\mathrm{GeV}<p_{\mathrm{T}}^{\text{jet}}<200\mathrm{GeV}$, (top right) $400\mathrm{GeV}<p_{\mathrm{T}}^{\text{jet}}<500\mathrm{GeV}$, (bottom left) $900\mathrm{GeV}<p_{\mathrm{T}}^{\text{jet}}<1000\mathrm{GeV}$, and (bottom right) $2000\mathrm{GeV}<p_{\mathrm{T}}^{\text{jet}}<2500\mathrm{GeV}$. The lower panels show the ratio of various MC predictions to the data, with the total uncertainty band centered on the data at unity. Additional $p_{\mathrm{T}}^{\text{jet}}$ bins can be found in Ref. [99].

Figure 14

The extracted quark- and gluon-like distributions of (top left) charged-particle multiplicity $n_{\mathrm{ch}}$, (top right) transverse momentum fraction $\zeta$, (bottom right) transverse momentum $p_{\mathrm{T}}^{\mathrm{rel}}$, and (bottom right) the radial profile in bins of the radial distance $r$ from the jet axis for jets with transverse momentum $1000\mathrm{GeV}<p_{\mathrm{T}}^{\text{jet}}<1200\mathrm{GeV}$. The quark- and gluon-jet distributions from pythia are also shown for comparison. The uncertainty bands on the data include both statistical and systematic uncertainties while the error bars are due to statistical uncertainties only.

Figure 15

The jet topics extracted using charged-particle multiplicity $n_{\mathrm{ch}}$ for jets in two transverse momentum, $p_{\mathrm{T}}$, bins together with the topics and quark and gluon distributions from pythia. The uncertainty bands on the data include both statistical and systematic uncertainties while the error bars are due to statistical uncertainties only.

Figure 16

The dependence on transverse momentum $p_{\mathrm{T}}$ of the average extracted gluon-like transverse-momentum-fraction weighted sum $\sum _{i\in \text{jet}}{\zeta }_i^{\kappa }$ for (top left) $\kappa =0.5$, (top right) $\kappa =1.0$, and $\kappa =2.0$ (bottom). For comparison, the results from pythia and a simple leading-logarithm (LL) calculation are also presented. The prediction is normalized to the data in the sixth jet $p_{\mathrm{T}}$ bin, called the anchor bin and indicated by an arrow. The uncertainty band on the calculation is from varying $\mathrm{\Lambda }$ in Eq. (6) up and down by a factor of 2 from its nominal value of 400 MeV (in most regions, this band is not much wider than the linewidth and thus not visible). The uncertainty bands on the data include both statistical and systematic uncertainties while the error bars are due to statistical uncertainties only.

Figure 17

Left (right): The dependence on jet transverse momentum $p_{\mathrm{T}}$ of the mean charged-particle multiplicity $⟨n_{\mathrm{ch}}⟩$ for quark and gluon jets (topic 1 and topic 2) in data and in pythia as well as from a calculation using perturbative QCD. The calculation cannot predict the overall normalization and therefore the prediction is normalized to the data in the sixth $p_{\mathrm{T}}$ bin, called the anchor bin and indicated by an arrow. The binning correction is not applied to the average topics, as this correction is very sensitive to fluctuations due to the limited number of simulated events. The uncertainty bands on the data include both statistical and systematic uncertainties while the error bars are due to statistical uncertainties only.

Figure 18

The dependence on jet transverse momentum $p_{\mathrm{T}}$ of the average extracted quark and gluon (top left) transverse momentum fraction $\zeta$, (top right) transverse momentum $p_{\mathrm{T}}^{\mathrm{rel}}$, and (bottom) radial profile (per particle and not per jet). The uncertainty bands on the data include both statistical and systematic uncertainties while the error bars are due to statistical uncertainties only.