Measurement of the transverse momentum and [Formula: see text] distributions of Drell-Yan lepton pairs in proton-proton collisions at [Formula: see text] TeV with the ATLAS detector

Abstract

Distributions of transverse momentum [Formula: see text] and the related angular variable [Formula: see text] of Drell–Yan lepton pairs are measured in 20.3 fb[Formula: see text] of proton–proton collisions at [Formula: see text] TeV with the ATLAS detector at the LHC. Measurements in electron-pair and muon-pair final states are corrected for detector effects and combined. Compared to previous measurements in proton–proton collisions at [Formula: see text] TeV, these new measurements benefit from a larger data sample and improved control of systematic uncertainties. Measurements are performed in bins of lepton-pair mass above, around and below the Z-boson mass peak. The data are compared to predictions from perturbative and resummed QCD calculations. For values of [Formula: see text] the predictions from the Monte Carlo generator ResBos are generally consistent with the data within the theoretical uncertainties. However, at larger values of [Formula: see text] this is not the case. Monte Carlo generators based on the parton-shower approach are unable to describe the data over the full range of [Formula: see text] while the fixed-order prediction of Dynnlo falls below the data at high values of [Formula: see text]. ResBos and the parton-shower Monte Carlo generators provide a much better description of the evolution of the [Formula: see text] and [Formula: see text] distributions as a function of lepton-pair mass and rapidity than the basic shape of the data.

Fig. 1

The distribution of events passing the selection requirements in the electron-pair channel as a function of dilepton invariant mass $m_{\ell \ell }$ (left) and electron pseudorapidity $\mathit{\eta }$ (right). Events are shown for the $m_{\ell \ell }$ range 46 to $150\mathrm{GeV}$. The MC signal sample (yellow) is simulated using Powheg+Pythia. The statistical uncertainties on the data points are smaller than the size of the markers and the systematic uncertainties are not plotted. The prediction is normalised to the integral of the data. The vertical dashed lines on the left-hand plot at $m_{\ell \ell }$ values of 66 and $116\mathrm{GeV}$ indicate the boundaries between the three principal $m_{\ell \ell }$ regions employed in the analysis. The small discontinuities in the $m_{\ell \ell }$ distribution at 66 and $116\mathrm{GeV}$ are due to the absence of the isolation requirement around the $Z$ -boson mass peak

Fig. 2

The distribution of events passing the selection requirements in the muon-pair channel as a function of dilepton invariant mass $m_{\ell \ell }$ (left) and muon pseudorapidity $\mathit{\eta }$ (right). Events are shown for the $m_{\ell \ell }$ range 46 to $150\mathrm{GeV}$. The MC signal sample (yellow) is simulated using Powheg+Pythia. The statistical uncertainties on the data points are smaller than the size of the markers and the systematic uncertainties are not plotted. The prediction is normalised to the integral of the data. The vertical dashed lines on the left hand plot at $m_{\ell \ell }$ values of 66 and $116\mathrm{GeV}$ indicate the boundaries between the three principal $m_{\ell \ell }$ regions employed in the analysis

Fig. 3

Left The distribution of the smallest of the isolation variables of the two electrons $I_e^{\text{min}}$. Right The distribution of the muon isolation variable $I_{\mathit{\mu }}$. The data for $66\mathrm{GeV}<m_{\ell \ell }<116\mathrm{GeV}$ are compared to the sum of the estimated multi-jet background and all other processes, which are estimated from MC simulation. The red dashed lines indicate the range over which the fit is performed

Fig. 4

Uncertainty from various sources on $(1/\mathit{\sigma })\mathrm{d}\mathit{\sigma }/\mathrm{d}{\mathit{\varphi }}_{\mathit{\eta }}^{\ast }$ (top) and $(1/\mathit{\sigma })\mathrm{d}\mathit{\sigma }/\mathrm{d}{p}_{\mathrm{T}}^{\ell \ell }$ (bottom) for events with $66\mathrm{GeV}<m_{\ell \ell }<116\mathrm{GeV}$ and $|y_{\ell \ell }|<2.4$. Left Electron-pair channel at dressed level. Right Muon-pair channel at bare level

Fig. 5

The Born-level distributions of $(1/\mathit{\sigma })\mathrm{d}\mathit{\sigma }/\mathrm{d}{\mathit{\varphi }}_{\mathit{\eta }}^{\ast }$ for the combination of the electron-pair and muon-pair channels, shown in three $m_{\ell \ell }$ regions from 46 to $150\mathrm{GeV}$ for $|y_{\ell \ell }|<2.4$. The central panel of each plot shows the ratios of the values from the individual channels to the combined values, where the error bars on the individual-channel measurements represent the total uncertainty uncorrelated between bins. The light-green band represents the data statistical uncertainty on the combined value and the dark-green band represents the total uncertainty (statistical and systematic). The ${\mathit{\chi }}^2$ per degree of freedom is given. The lower panel of each plot shows the pull, defined as the difference between the electron-pair and muon-pair values divided by the uncertainty on that difference

Fig. 6

The Born-level distributions of $(1/\mathit{\sigma })\mathrm{d}\mathit{\sigma }/\mathrm{d}{p}_{\mathrm{T}}^{\ell \ell }$ for the combination of the electron-pair and muon-pair channels, shown in six $m_{\ell \ell }$ regions for $|y_{\ell \ell }|<2.4$. The central panel of each plot shows the ratios of the values from the individual channels to the combined values, where the error bars on the individual-channel measurements represent the total uncertainty uncorrelated between bins. The light-blue band represents the data statistical uncertainty on the combined value and the dark-blue band represents the total uncertainty (statistical and systematic). The ${\mathit{\chi }}^2$ per degree of freedom is given. The lower panel of each plot shows the pull, defined as the difference between the electron-pair and muon-pair values divided by the uncertainty on that difference

Fig. 7

Born-level fiducial cross sections in bins of $m_{\ell \ell }$ for the combination of the electron-pair and muon-pair channels. The middle plot shows the ratios of the values from the individual channels to the combined values, where the error bars on the individual-channel measurements represent the total uncertainty uncorrelated between bins. The light-blue band represents the data statistical uncertainty on the combined value. The dark-blue band represents the total uncertainty (statistical and systematic), except for the uncertainty of 2.8 % on the integrated luminosity, which is fully correlated between channels and among all $m_{\ell \ell }$ bins. The ${\mathit{\chi }}^2$ per degree of freedom is given. The lower plot shows the pull, defined as the difference between the electron-pair and muon-pair values divided by the uncertainty on that difference. The fiducial regions to which these cross sections correspond are specified in Table 1. Note that $p_{\mathrm{T}}^{\ell \ell }$ is required to be greater than $45\mathrm{GeV}$ for $m_{\ell \ell }<46\mathrm{GeV}$

Fig. 8

The ratio of the predictions of ResBos for the Z-boson mass peak and for $|y_{\ell \ell }|$ < 2.4 to the combined Born-level data for $(1/\mathit{\sigma })\mathrm{d}\mathit{\sigma }/\mathrm{d}{\mathit{\varphi }}_{\mathit{\eta }}^{\ast }$ (top) and $(1/\mathit{\sigma })\mathrm{d}\mathit{\sigma }/\mathrm{d}{p}_{\mathrm{T}}^{\ell \ell }$ (bottom). The light-green (light-blue) band represents the statistical uncertainty on the data for ${\mathit{\varphi }}_{\mathit{\eta }}^{\ast }$ ($p_{\mathrm{T}}^{\ell \ell }$) and the dark-green (dark-blue) band represents the total uncertainty (statistical and systematic) on the data. The yellow band represents the uncertainty in the ResBos calculation arising from varying (See footnote 2) the QCD scales, the non-perturbative parameter $a_Z$, and PDFs

Fig. 9

The ratio of $(1/\mathit{\sigma })\mathrm{d}\mathit{\sigma }/\mathrm{d}{\mathit{\varphi }}_{\mathit{\eta }}^{\ast }$ as predicted by ResBos to the combined Born-level data, for the six $|y_{\ell \ell }|$ regions at the $Z$ -boson mass peak. The light-green band represents the statistical uncertainty on the data and the dark-green band represents the total uncertainty (statistical and systematic) on the data. The yellow band represents the uncertainty in the ResBos calculation arising from varying (See footnote 2) the QCD scales, the non-perturbative parameter $a_Z$, and PDFs

Fig. 10

The ratio of $(1/\mathit{\sigma })\mathrm{d}\mathit{\sigma }/\mathrm{d}{\mathit{\varphi }}_{\mathit{\eta }}^{\ast }$ as predicted by ResBos to the combined Born-level data, for the three $|y_{\ell \ell }|$ regions in the two $m_{\ell \ell }$ regions adjacent to the Z-boson mass peak. The light-green band represents the statistical uncertainty on the data and the dark-green band represents the total uncertainty (statistical and systematic) on the data. The yellow band represents the uncertainty in the ResBos calculation arising from varying (See footnote 2) the QCD scales, the non-perturbative parameter $a_Z$, and PDFs

Fig. 11

The distribution of $(1/\mathit{\sigma })\mathrm{d}\mathit{\sigma }/\mathrm{d}{\mathit{\varphi }}_{\mathit{\eta }}^{\ast }$ at Born level in each region of $|y_{\ell \ell }|$, shown as a ratio to the central rapidity region ($|y_{\ell \ell }|<0.4$), for events at the $Z$ -boson mass peak. The data, shown as points, are compared to the predictions of ResBos. The light-green band represents the statistical uncertainty on the data and the dark-green band represents the total uncertainty on the data (treating systematic uncertainties as uncorrelated between regions of $|y_{\ell \ell }|$). The yellow band represents the uncertainty in the ResBos calculation arising from varying (See footnote 2) the QCD scales, the non-perturbative parameter $a_Z$, and PDFs

Fig. 12

The distribution of $(1/\mathit{\sigma })\mathrm{d}\mathit{\sigma }/\mathrm{d}{\mathit{\varphi }}_{\mathit{\eta }}^{\ast }$ at Born level in each region of $|y_{\ell \ell }|$, shown as a ratio to the central rapidity region ($|y_{\ell \ell }|<0.8$), for events with $m_{\ell \ell }$ between 46 to $66\mathrm{GeV}$ (upper plots) and 116 to $150\mathrm{GeV}$ (lower plots). The data, shown as points, are compared to the predictions of ResBos. The light-green band represents the statistical uncertainty on the data and the dark-green band represents the total uncertainty on the data (treating systematic uncertainties as uncorrelated between regions of $|y_{\ell \ell }|$). The yellow band represents the uncertainty in the ResBos calculation arising from varying (See footnote 2) the QCD scales, the non-perturbative parameter $a_Z$, and PDFs

Fig. 13

The ratio of $(1/\mathit{\sigma })\mathrm{d}\mathit{\sigma }/\mathrm{d}{\mathit{\varphi }}_{\mathit{\eta }}^{\ast }$ in the $m_{\ell \ell }$ region from 116 to $150\mathrm{GeV}$ to that in the $m_{\ell \ell }$ region from 46 to $66\mathrm{GeV}$, for three regions of $|y_{\ell \ell }|$. The data, shown as points, are compared to the predictions of ResBos. The light-green band represents the statistical uncertainty on the data and the dark-green band represents the total uncertainty on the data (treating systematic uncertainties as uncorrelated between the mass regions). The yellow band represents the uncertainty in the ResBos calculation arising from varying (See footnote 2) the QCD scales, the non-perturbative parameter $a_Z$, and PDFs

Fig. 14

The ratio of $(1/\mathit{\sigma })\mathrm{d}\mathit{\sigma }/\mathrm{d}{p}_{\mathrm{T}}^{\ell \ell }$ as predicted by various MC generators to the combined Born-level data, in six different regions of $m_{\ell \ell }$ for $|y_{\ell \ell }|<2.4$. The light-blue band represents the statistical uncertainty on the data and the dark-blue band represents the total uncertainty (statistical and systematic) on the data

Fig. 15

The ratio of $(1/\mathit{\sigma })\mathrm{d}\mathit{\sigma }/\mathrm{d}{p}_{\mathrm{T}}^{\ell \ell }$ as predicted by various MC generators to the combined Born-level data, in different $|y_{\ell \ell }|$ ranges for events at the $Z$ -boson mass peak. The light-blue band represents the statistical uncertainty on the data and the dark-blue band represents the total uncertainty (statistical and systematic) on the data

Fig. 16

The distribution of $(1/\mathit{\sigma })\mathrm{d}\mathit{\sigma }/\mathrm{d}{p}_{\mathrm{T}}^{\ell \ell }$ at Born level in each region of $|y_{\ell \ell }|$, shown as a ratio to the central rapidity region ($|y_{\ell \ell }|<0.4$), for events at the $Z$ -boson mass peak. The data, shown as points, are compared to the predictions of various MC generators. The light-blue band represents the statistical uncertainty on the data and the dark-blue band represents the total uncertainty on the data (treating systematic uncertainties as uncorrelated between regions of $|y_{\ell \ell }|$)

Fig. 17

The ratio of $(1/\mathit{\sigma })\mathrm{d}\mathit{\sigma }/\mathrm{d}{\mathit{\varphi }}_{\mathit{\eta }}^{\ast }$ as predicted by various MC generators to the combined Born-level data, in three different regions of $m_{\ell \ell }$ for $|y_{\ell \ell }|<2.4$. The light-green band represents the statistical uncertainty on the data and the dark-green band represents the total uncertainty (statistical and systematic) on the data

Fig. 18

The ratio of $\mathrm{d}\mathit{\sigma }/\mathrm{d}{p}_{\mathrm{T}}^{\ell \ell }$ as predicted by the Dynnlo MC generator to the combined Born-level data, for six regions of $m_{\ell \ell }$from 12 to $150\mathrm{GeV}$. Two sets of Dynnlo predictions are shown, one of which includes NLO EW corrections while the other does not. The error bars on the Dynnlo predictions represent the uncertainty arising from varying the QCD scales and PDFs. Additional uncertainties introduced by the inclusion of the EW corrections are at the level of 2–4 % and are always significantly smaller than the QCD scale and PDF uncertainties. Therefore for clarity these points are shown without uncertainty bars. The light-blue band represents the statistical uncertainty on the data and the dark-blue band represents the total uncertainty (statistical and systematic) on the data