New CTEQ global analysis of quantum chromodynamics with high-precision data from the LHC

We present the new parton distribution functions (PDFs) from the CTEQ-TEA collaboration, obtained using a wide variety of high-precision Large Hadron Collider (LHC) data, in addition to the combined HERA $\mathrm{I}+\text{II}$ deep-inelastic scattering dataset, along with the datasets present in the CT14 global QCD analysis. New LHC measurements in single-inclusive jet production with the full rapidity coverage, as well as production of Drell-Yan pairs, top-quark pairs, and high-$p_T$ $Z$ bosons, are included to achieve the greatest sensitivity to the PDFs. The parton distributions are determined at next-to-leading order and next-to-next-to-leading order, with each of these PDFs accompanied by error sets determined using the Hessian method. Fast PDF survey techniques, based on the Hessian representation and the Lagrange multiplier method, are used to quantify the preference of each data set to quantities such as ${\alpha }_s(m_Z)$, and the gluon and strange quark distributions. We designate the main resulting PDF set as CT18. The ATLAS 7 TeV precision $W/Z$ data are not included in CT18, due to their tension with other datasets in the global fit. Alternate PDF sets are generated including the ATLAS precision 7 TeV $W/Z$ data (CT18A), a new scale choice for low-$x$ DIS data (CT18X), or all of the above with a slightly higher choice for the charm mass (CT18Z). Theoretical calculations of standard candle cross sections at the LHC (such as the $gg$ fusion Higgs boson cross section) are presented.

Figure 1

The CT18 dataset, represented in a space of partonic $(x,Q)$, based on Born-level kinematical matchings, $(x,Q)=(x_B,Q)$, in DIS, etc. The matching conventions used here are described in Ref. [20]. Also shown are the ATLAS 7 TeV $W/Z$ production data (Exp. $\mathrm{ID}=248$), labeled ATL7WZ’12, fitted in CT18Z.

Figure 2

Upper panels: The CT18 parton distribution functions at $Q=2\mathrm{GeV}$ and $Q=100\mathrm{GeV}$ for $u,\overline{u},d,\overline{d},s=\overline{s}$, and $g$. Lower panels: the analogous curves, but obtained for CT18Z. In all instances, the gluon PDF has been scaled down as $g(x,Q)/5$. The charm distribution, $c(x,Q)$, which is perturbatively generated by evolving from $Q_0=1.3$ and 1.4 GeV, respectively, in CT18 and CT18Z, is also shown.

Figure 3

Left: the ratios of the candidate CT18 NNLO PDFs obtained with the $x_B$-dependent and standard factorization scales in DIS datasets. Right: the ${\chi }^2/N_{pt}$ values for four HERA datasets in the CT18Z fit with the $x_B$-dependent DIS factorization scale and varied statistical weight of the HERA $\mathrm{I}+\mathrm{II}$ inclusive DIS dataset.

Figure 4

A histogram of the effective Gaussian variable ($S_E$) distributed over all CT18 datasets. Two squares and two stars indicate the $S_E$ values for the NuTeV dimuon and CCFR dimuon data, respectively.

Figure 5

Left: candidate data considered for inclusion in CT18 according to the magnitude of the Pearson correlation $C_f$ between the total Higgs cross section at 14 TeV, ${\sigma }_H(14\mathrm{TeV})$ and the residual of each point as determined within the pdfsense framework [20]. Right: a similar assessment of the CT18 candidate data, but computed on the basis of the sensitivity, $|S_f|(x_i,Q_i)$. In both panels, a highlighting cut has been imposed to draw attention to the $\sim 300$ highest-impact points according to each metric.

Figure 6

To understand the parametrization dependence in the CT18 fit, we performed $\mathcal{O}(250)$ candidate PDF analyses using a wide range of alternative functional forms for $f_a(x,Q_0)$. The green curves in the panels above illustrate the spread of central fits achieved with the various candidate fits, evaluated as ratios with respect to the central CT18 fit.

Figure 7

A comparison of 90% C.L. PDF uncertainties from CT18 (violet solid), $\mathrm{CT}{14}_{\mathrm{HERAII}}$ (gray short-dashed line), and CT18Z (magenta long-dashed line) NNLO ensembles at $Q=100\mathrm{GeV}$. The uncertainty bands are normalized to the central CT18 NNLO PDFs.

Figure 8

Like Fig. 7, but with each error band normalized to its respective central PDF for the purpose of directly comparing the PDF uncertainties in CT18 NNLO with CT18Z and $\mathrm{CT}{14}_{\mathrm{HERAII}}$ NNLO.

Figure 9

Top: 90% C.L. uncertainties on the ratio $d(x,Q)/u(x,Q)$ for CT18, $\mathrm{CT}{14}_{\mathrm{HERAII}}$, and CT18Z NNLO ensembles at $Q=1.4$ and 100 GeV. Bottom: same, comparing CT18 and $\mathrm{CT}{14}_{\mathrm{HERAII}}$ NNLO ratios (bottom-left) and respective NLO ratios (bottom-right) to the CJ15 NLO ensemble at $Q=10\mathrm{GeV}$.

Figure 10

Like the upper panels of Fig. 9 for $d/u$, but normalizing each fit to its respective central value to compare PDF uncertainties.

Figure 11

A comparison of 90% C.L. uncertainties on the ratios $\overline{d}(x,Q)/\overline{u}(x,Q)$ and $(s(x,Q)+\overline{s}(x,Q))/(\overline{u}(x,Q)+\overline{d}(x,Q))$, for CT18 (solid blue line), CT18Z (magenta long-dashed line), and $\mathrm{CT}{14}_{\mathrm{HERAII}}$ NNLO (gray short-dashed line) ensembles at $Q=1.4$ or 100 GeV.

Figure 12

A comparison of 90% C.L. uncertainties on the ratios $\overline{d}(x,Q)/\overline{u}(x,Q)$ and $(s(x,Q)+\overline{s}(x,Q))/(\overline{u}(x,Q)+\overline{d}(x,Q))$, for CT18 (solid blue line), CT18Z (magenta long-dashed line), and $\mathrm{CT}{14}_{\mathrm{HERAII}}$ NNLO (gray short-dashed line) ensembles at $Q=1.4$ or 100 GeV, relative to their own central fit.

Figure 13

The scan of the strong coupling constant at the scale of $M_Z$ for CT18 at NNLO. Left: changes of ${\chi }^2$ of all the datasets together (heavy black line) and of several individual experiments with especially strong pull on ${\alpha }_s(M_Z)$. Right: values for the change in ${\chi }^2$ for all experiments fitted in CT18, but separately collected into combined DIS, DY, and top/jets datasets. The growth in $\mathrm{\Delta }{\chi }^2$ for the “jets+top” curve in the right panel is mainly driven by the constraints from jet production. While $t\overline{t}$ production has important sensitivity to ${\alpha }_s$, the comparatively small number of top data points leads to a more intermediate impact in the full fit.

Figure 14

Like Fig. 13, but now showing the scan of ${\alpha }_s(M_Z)$ at NLO precision in ${\alpha }_s$.

Figure 15

A ${\chi }^2$ scan over values of the charm pole mass, $m_c$, at NNLO, using the CT18 dataset. The settings of the fit are described in the text. The CT18Z counterpart to this $m_c$ scan is presented in Fig. 71 in Appendix pp1.

Figure 16

Parton luminosities for processes at the LHC at $\sqrt{s}=14\mathrm{TeV}$, in the central rapidity region $|y|<5$: $L_{qq}$ (upper panels), $L_{gq}$ (center panels), and $L_{gg}$ (lower panels); evaluated using CT18 (solid violet line), CT18Z (short-dashed gray line), and $\mathrm{CT}{14}_{\mathrm{HERAII}}$ (long-dashed magenta line) NNLO PDFs. The left panels give the luminosity ratios normalized to CT18, whereas the right panels show the error bands for each luminosity, normalized for each PDF ensemble to its own central prediction.

Figure 17

Same as Fig. 16, comparing the CT18 NLO and CJ15 NLO parton luminosities.

Figure 18

Same as Fig. 16, comparing the CT18, MMHT14, and nnpdf3.1 NNLO parton luminosities with ${\alpha }_s(M_Z)=0.118$.

Figure 19

A graphical comparison of the PDF moments summarized in Table 6, with the exception of the results for the zeroth moment of $\overline{d}-\overline{u}$ combination, relevant for studies of the Gottfried sum rule; this latter quantity is given in Fig. 20. The CJ15 global fit does not determine ${\kappa }_s$ and $⟨x{⟩}_s$ as independent entities from the data, their respective predictions are not shown.

Figure 20

A visual comparison of the results for ${\int }_0^{1}dx[\overline{d}(x)-\overline{u}(x)]$. The horizontal nested black and red bands correspond to the values extracted from the original NMC analyses from 1991 [155] and 1994 [156], respectively. These were based on direct quark-parton model extractions of the flavor asymmetry PDF from the deuteron-to-proton structure function ratio measured at $Q^2=4{\mathrm{GeV}}^2$ for a range of $x\lesssim 0.7$. While all but the highest $x$ bin in this dataset is consistent with CTEQ kinematical cuts, the very low $Q$ is exactly at the boundary of the $Q$ cut, and likely subject to substantial higher-twist corrections, especially for the higher $x$ bins.

Figure 21

LM scans for the gluon PDF at $Q=125\mathrm{GeV}$ and $x=0.01$ and 0.3, based upon the CT18 NNLO fits.

Figure 22

LM scans for the up- and down-quark PDF at $Q=100\mathrm{GeV}$ and $x=0.002$ and 0.3, based upon the CT18 fits.

Figure 23

Like Fig. 22, here giving LM scans for the $\overline{u}$-, $\overline{d}$-, and $s$-quark PDFs in CT18.

Figure 24

The LM scan over $R_s$ at $Q=1.5\mathrm{GeV}$, with $x=0.023$ and $x=0.1$, respectively, for the CT18 NNLO fit.

Figure 25

Like Fig. 22, for LM scans over the ratios $d/u$ and $\overline{d}/\overline{u}$.

Figure 26

The $x$-dependent $L_2$ sensitivity of the CT18 datasets with strongest pull upon the gluon PDF, $g(x,Q=100\mathrm{GeV})$. A number of tensions among the leading datasets are revealed by examining those regions of $x$ where $S_{f,L2}(E)$ peaks for certain experiments in the “positive direction” while $S_{f,L2}(E)$ is sharply negative for others. For instance, at $x=0.4$, the sensitivity curves indicate a strong competition of the CMS 8 TeV jet data (Exp. $\mathrm{ID}=545$) and the BCDMS $F_2^d$ data (Exp. $\mathrm{ID}=102$), both preferring a larger $g(0.4,100\mathrm{GeV})$, against the combined downward pull on the gluon by the BCDMS $F_2^p$ (101), CDHSW $F_3$ (109), E866 $pp$ Drell-Yan (204), and high-$p_T$ $Z$ boson production (253) datasets. At $x\approx 0.1$, the CMS 8 TeV jet data (Exp. $\mathrm{ID}=545$) strongly pulls against the ATLAS (544) and CMS 7 TeV (542) jet production, as well as measurements by CDHSW (108), CCFR (110), and BCDMS (102) of the DIS structure function $F_2(x,Q)$ on various targets.

Figure 27

$L_1$ sensitivities of experimental datasets to PDF flavors in the CT18 NNLO analysis, computed according to the methodology in Ref. [20]. The color of the cells in the upper (lower) inset, chosen according to the palettes on the right, indicates the point-average (cumulative) sensitivity of the experimental set on the vertical axis to the PDF flavor on the horizontal axis.

Figure 28

A comparison of the CT18 theory with the D0 run II electron charge-asymmetry data (Exp. $\mathrm{ID}=281$). Since the asymmetry crosses zero in the shown range, the right panel shows the difference, Data-Theory, rather than the ratio, $\text{Data}/\text{Theory}$, as done elsewhere in this section.

Figure 29

A comparison of the CT18 theoretical predictions to the $W^{+}$ (top), $W^{-}$ (middle), and $Z^0$ (bottom) cross section measurements by LHCb at 8 TeV in the muon decay channel (Exp. $\mathrm{ID}=250$). The data are presented as cross sections for each bin, $\sigma =\frac{d\sigma }{d{\eta }_{\mu }}\mathrm{\Delta }{\eta }_{\mu },\frac{d\sigma }{d{y}_Z}\mathrm{\Delta }{y}_Z$, rather than as differential cross sections. The bump in the histogram bin $3.5<{\eta }_{\mu }<4.0$ of $W^{-}$ plot thus results from its larger bin width. A similar bump occurs in the plots for the LHCb 7 TeV $W/Z$ data (Exp. $\mathrm{ID}=245$).

Figure 30

Same as Fig. 29, for the LHCb 7 TeV (Exp. $\mathrm{ID}=245$).

Figure 31

A comparison of the CT18 theoretical predictions to the $Z$ rapidity distribution in $Z\to e^{+}{e}^{-}$ production by LHCb at 8 TeV (Exp. $\mathrm{ID}=246$).

Figure 32

Distributions of the residuals for the LHCb $W/Z$ production cross sections at 7 and 8 TeV: Exp. $\mathrm{ID}=245$ (left), 246 (center), and 250 (right).

Figure 33

Left: distribution of nuisance parameters for the LHCb 8 TeV $W/Z$ cross sections (Exp. $\mathrm{ID}=250$). Right: the pulls of these data on the CT18 NNLO PDFs at $Q=100\mathrm{GeV}$, computed in terms of the $L_2$ sensitivity of Eq. (21) [167].

Figure 34

A comparison of the CT18 theoretical predictions to the CMS 8 TeV charge asymmetry data (Exp. $\mathrm{ID}=249$).

Figure 35

Theoretical predictions for lepton pair transverse momentum distribution, $p_{T,\ell \overline{\ell }}$ based on the $\mathrm{CT}{14}_{\mathrm{HERAII}}$, CT18, and CT18Z NNLO PDFs, using QCD scales ${\mu }_R=M_{T,\ell \overline{\ell }}/2$, ${\mu }_F=M_{T,\ell \overline{\ell }}$ and compared with the ATLAS 8 TeV measurements. The yellow band represents the PDF uncertainty calculated with the symmetric Hessian method at the 68% C.L. The dashed band represents the scale uncertainty.

Figure 36

Left: Distribution of the ${\chi }^2$ residuals for the ATLAS 8 TeV $Z$ $p_T$ data (Exp. $\mathrm{ID}=253$) obtained using the nominal QCD scales in Eq. (27). Right: distributions of the respective nuisance parameters obtained for ${\mu }_R=M_{T,\ell \overline{\ell }}$ (default) and $M_{T,\ell \overline{\ell }}/2$, with ${\mu }_F=M_{T,\ell \overline{\ell }}$ in both cases.

Figure 37

$\text{Data}/\text{Theory}$ values for CT18 NNLO and CDF run-2 jet data (Exp. $\mathrm{ID}=504$).

Figure 38

$\text{Data}/\text{Theory}$ values for CT18 NNLO and D0 run-2 inclusive jet production (Exp. $\mathrm{ID}=514$).

Figure 39

$\text{Data}/\text{Theory}$ values for CT18 NNLO and CMS 7 TeV inclusive jet production (Exp. $\mathrm{ID}=542$).

Figure 40

$\text{Data}/\text{Theory}$ values for CT18 NNLO and ATLAS 7 TeV inclusive jet production (Exp. $\mathrm{ID}=544$).

Figure 41

$\text{Data}/\text{Theory}$ values for CT18 NNLO and CMS 8 TeV inclusive jet production (Exp. $\mathrm{ID}=545$).

Figure 42

$(\text{Data})/(\text{Theory})$ comparison for the CMS 8 TeV $t\overline{t}$ production data (Exp. $\mathrm{ID}=573$) as a function of the transverse momentum of the top (anti)quark.

Figure 43

$(\text{Data})/(\text{Theory})$ comparison for the ATLAS 8 TeV $t\overline{t}$ production data (Exp. $\mathrm{ID}=580$) as a function of the $t\overline{t}$ transverse momentum (left) and invariant mass (right).

Figure 44

Strange-quark distribution $s(x,Q)$ and ratio $R_s(x,Q)$ in CT18 (left) and CT18Z (right) NNLO fits, compared with alternative fits using QCD NNLO cross sections for CCFR and NuTeV measurements.

Figure 45

Comparison of $s$ PDF at $Q=100\mathrm{GeV}$ for various fits. See the main text for its detail.

Figure 46

The photon-induced contributions (photon PDF are taken from luxqed17_plus_pdf4lhc15) and NLO EW corrections to ATLAS 8 TeV high-mass Drell-Yan production.

Figure 47

The 90% C.L. error ellipses for the $ggH$, $t\overline{t}$, and $Z^0$ inclusive cross sections computed with the CT18 NNLO family of PDFs at the LHC 7, 8, 13, and 14 TeV.

Figure 48

Same as Fig. 47, but for the $W^{+}$, $W^{-}$, and $Z^0$ inclusive cross sections.

Figure 49

Theoretical predictions of the total production cross sections of $W$ and $Z$ bosons at $\sqrt{s}=7\mathrm{TeV}$ as relevant for the ATLAS 7 TeV $W/Z$ data (Exp. $\mathrm{ID}=248$). Here, we also include several calculations which include an intrinsic charm (IC) PDF based upon either the BHPS valencelike model (with three different normalizations) or a sealike model (with two different normalizations) in addition to CT14, as described in Ref. [150].

Figure 50

Comparison of the LHCb 7 TeV $W$ and $Z$ data to CT18 predictions, with either NNLO (labeled as CT18), resbos (labeled by CT18 resbos) or resbos2 (labeled by CT18 resbos2) calculations. The prediction of CT18Z NNLO is also shown.

Figure 51

Comparison of the CT18(Z) and $\mathrm{CT}{14}_{\mathrm{HERAII}}$ NNLO predictions for ATLAS 7 TeV $W^{+}+\overline{c}$ jet (left) and $W^{-}+c$ jet (right) production, respectively, for the combined electron and muon decay channels. The CT18 PDF uncertainty is evaluated at 68% C.L. The scale choice is ${\mu }_R={\mu }_F=M_W$.

Figure 52

Comparison of CT18(Z) and $\mathrm{CT}{14}_{\mathrm{HERAII}}$ predictions with CMS 7 TeV $W+c$ data, with lepton transverse momentum cut $p_T^l>25\mathrm{GeV}$ (left), for the muon channel, and $p_T^l>35\mathrm{GeV}$ (right), for the combined electron and muon channels, respectively. The scale choice is ${\mu }_R={\mu }_F=M_W$.

Figure 53

Left: top-quark transverse momentum $p_{T,t}$ distribution. Right: unshifted data vs theory plot including CT18Z, CT18X, CT18A NNLO. In the right figure, data and theory predictions are normalized to CT18NNLO theory. The error bars indicate statistical and total systematic errors summed in quadrature.

Figure 54

Left: Top-quark rapidity $y_t$ distribution. Right: Unshifted data vs theory plot including CT18, CT18Z, CT18X, CT18A NNLO. Data and theory predictions are normalized to CT18NNLO theory. The error bars indicate statistical and total systematic errors summed in quadrature.

Figure 55

Left: invariant mass distribution of the top-quark pair. Right: unshifted data vs theory plot including CT18, CT18Z, CT18X, CT18A NNLO. Data and theory predictions are normalized to CT18NNLO theory. The error bars are statistical and total systematic errors summed in quadrature.

Figure 56

Impact of NLO EW corrections. Unshifted data vs theory plot for top-quark $p_T$ distribution and the invariant mass distribution of the $t\overline{t}$ pair. The error bars are statistical and total systematic errors summed in quadrature. The red data points with dashed error bars represent data divided by the CT18NNLO theory with NLO EW corrections. The black data points with solid error bars represent data normalized to the CT18NNLO theory. The CT18ZNNLO theory prediction (black dashed error band) is also normalized to CT18NNLO. The data vs ($\mathrm{theory}+\mathrm{EW}$) points are slightly shifted to the right in the same bin to improve visualization.

Figure 57

Impact of the $y_{t\overline{t}}$ differential cross section measurements of the CMS 13 TeV $t\overline{t}$ data on the CT18 (left) and CT18Z (right) gluon PDFs.

Figure 58

Theoretical predictions based on CT18 (black outer band) and CT18Z (green inner band) for the fixed-target Drell-Yan cross section, ${\sigma }_{pd}/2{\sigma }_{pp}$, in the region of larger $x_2\gtrsim 0.1$ to be probed by the SeaQuest experiment [182] at Fermilab. For comparison, we also plot the higher-$x_2$ portion of the older E866 data [68] (blue diamonds).

Figure 59

Analogous to Fig. 4, the effective Gaussian variable ($S_E$) distribution of all CT18Z datasets. Two squares and two stars indicate the $S_E$ values for the NuTeV dimuon and CCFR dimuon experiments, respectively.

Figure 60

The $L_2$ sensitivity of the ATL7ZW data to the PDFs of several individual parton flavors. The pull on the strangeness distribution, $s(x,Q)$, is particularly large, peaking at $S_{s,L2}\sim -20$ for $x\sim 0.02–0.05$; although opposing pulls on the $d$-, $\overline{u}$-, and $\overline{d}$-quark PDFs are also significant in a similar region of $x$.

Figure 61

The $L_2$ sensitivity of the data fitted in CT18Z to the $x$-dependent strange PDF at $Q=2\mathrm{GeV}$. Given that the fitted behavior for $R_s(x,Q)$ is substantially driven by $s(x,Q)$, the information shown here is complementary to the LM scans in Fig. 68.

Figure 62

A comparison of the fitted strangeness PDF, $s(x,Q)$, at $Q=100\mathrm{GeV}$ as obtained with CT18 (solid violet line) as well as with CT18A (short-dashed gray line) and nnpdf3.1 (long-dashed magenta line).

Figure 63

(a) A comparison of theoretical predictions for the ATL7ZW data based on CT18 and CT18A/Z NNLO. The shifted data (magenta crosses) are computed based on CT18A NNLO. The upper panels give rapidity distributions of the differential cross sections in $|{\eta }_l|$ (for the charge-current processes) or $|y_{\ell \overline{\ell }}|$ (for neutral current), while the lower insets show the ratios of the data and theory, normalized to CT18A theory.

Figure 64

Bin-by-bin shifted Theory-Data residuals computed based on CT18(A/Z) for each of the three ATL7ZW processes shown in Fig. 63.

Figure 65

Histogram of (a) the shifted residuals and (b) nuisance parameters for the ATL7ZW data obtained for CT18A NNLO.

Figure 66

A plot, analogous to the $L_2$ sensitivity plots given above, showing the pulls of the correlated systematic uncertainties of the ATLAS $W/Z$ data on $R_s(x,Q=100\mathrm{GeV})$ in CT18A NNLO, as represented by shifts in the associated squared nuisance parameters, $\mathrm{\Delta }{\lambda }_{\alpha }^2$.

Figure 67

Left panel: the change in total ${\chi }^2$, $\mathrm{\Delta }{\chi }^2$, of the leading datasets included in the CT18Z NNLO fit when varying the weight of the ATL7ZW data away from weight $w=1$ as in the default fit. Right panel: the analogous plot for the NuTeV $\nu$, $\overline{\nu }$ SIDIS dimuon data (Exp. $\mathrm{IDs}=124$, 125).

Figure 68

The Lagrange multiplier scan of $R_s$ at $Q=1.5\mathrm{GeV}$, $x=0.023$, and $x=0.1$ for the (a),(b) CT18Z fit, analogous to Fig. 24 for CT18.

Figure 69

68% C.L. uncertainty ranges on $R_s(0.023,1.5\mathrm{GeV})$ obtained based on ${\chi }^2$ variations and Hessian estimates. For the dynamic tolerance and tolerance ranges for individual experiments, the green solid (red dashed) bands are described in the main text.

Figure 70

Scans over the strong coupling at the scale of $M_Z$ for CT18Z, analogous to Fig. 13 for CT18. As before, we show in the left panel the $\mathrm{\Delta }{\chi }^2$ variations for a number of experiments with leading sensitivity to ${\alpha }_s(M_Z)$, while the right panel again shows the change in ${\chi }^2$ for all experiments fitted in CT18Z, separately collected into combined DIS, DY, and top/jets datasets. Also as before, the “jets+top” curve in the right panel is primarily influenced by the jet production datasets. Due to the intermediate impact of the $t\overline{t}$ data noted in Fig. 13, variations in the CT18 fit leading to CT18Z are such that the ATLAS 8 TeV $t\overline{t}$ data (Exp. $\mathrm{ID}=580$) are now selected with the ensemble of sensitive experiments in the left panel.

Figure 71

Analogously to Fig. 15, the scan over values of the charm pole mass, $m_c$, computed here using CT18Z NNLO following the procedure described in Sec. 4b.

Figure 72

A flowchart of the CT18 global analysis consists of the outer layer (LY0), middle layer (LY1), and core process (LY2).

Figure 73

Gluon and strangeness PDFs at $Q=100\mathrm{GeV}$ for the CT18 (at 90% C.L.) and CT18A global fits, compared with the respective central PDFs obtained by epump dynamical-tolerance updating and the xfitter profiling of the CT18 PDFs by the ATLAS 7 TeV $W/Z$-production data. The xfitter-profiled PDFs are obtained with $T=1.645$ and include the diagonal second-order terms.

Figure 74

The comparison of $K$ factors for the ATLAS 7 TeV $W/Z$ data calculated with dynnlo, fewz, and mcfm. The error bars indicate the theoretical Monte Carlo uncertainties. The dynnlo curves are extracted from xfitter and include NLO EW corrections.