Isospin asymmetry of quark distributions and implications for single top-quark production at the LHC

We present an improved determination of the up- and down-quark distributions in the proton using recent data on charged lepton asymmetries from $W^{\pm }$ gauge-boson production at the LHC and Tevatron. The analysis is performed in the framework of a global fit of parton distribution functions. The fit results are consistent with a nonzero isospin asymmetry of the sea, $x(\overline{d}-\overline{u})$, at small values of Bjorken $x\sim {10}^{-4}$ indicating a delayed onset of the Regge asymptotics of a vanishing $(\overline{d}-\overline{u})$-asymmetry at small $x$. We compare with up- and down-quark distributions available in the literature and provide accurate predictions for the production of single top-quarks at the LHC, a process which can serve as a standard candle for the light quark flavor content of the proton.

Figure 1

The pulls of the new DØ data on the charged lepton asymmetry for $p\overline{p}\to W^{\pm }+X\to l^{\pm }\nu$ for electrons [6] (circles) and muons [5] (squares) at the Tevatron with $\sqrt{s}=1.96\mathrm{TeV}$, defined as a difference between the experimental data and the predictions with fewz (version 3.1) at NNLO in QCD computed in the present analysis, as a function of the pseudolepton rapidity ${\eta }_l$. The inner and outer bars at the data points display uncorrelated and total uncertainties, respectively. For comparison, the results of the ABM12 fit with the corresponding $1\sigma$ band of the combined PDF+${\alpha }_s$ uncertainty and the central fits of CT10 CT14, MMHT, and NN3.0 are displayed.

Figure 2

Same as Fig. 1 for the LHCb data [1] on the production of $W^{+}$- (left) and $W^{-}$-bosons (right) in the $pp$ collision at $\sqrt{s}=7\mathrm{TeV}$ (squares) in comparison with those data before a trigger efficiency has been fixed [2] (circles).

Figure 3

Same as Fig. 1 for the LHCb [1] and CMS [3] data on the muon charge asymmetry in inclusive $pp\to W^{\pm }+X\to {\mu }^{\pm }\nu$ production at the LHC with $\sqrt{s}=7\mathrm{TeV}$.

Figure 4

Same as Fig. 1 for the LHCb data on the $Z$-boson production [1, 4, 26] at the c.m.s. energy of 7 TeV (left) and 8 TeV (right) in the muon channel (circles) and the electron channel (squares).

Figure 5

The experimental uncertainties in the DØ data on the electron asymmetry [6] (points) compared with the numerical integration accuracy achieved with fewz (version 3.1) [24, 25] in the generation of the NNLO grids employed in present analysis (shaded area). The impact of the NNLO corrections on the hard scattering coefficient functions is indicated by the dashed curve.

Figure 6

Left panel: Correction for the final-state-radiation (FSR) effects applied in the LHCb analysis [1] to the data on the pseudorapidity distribution of muons produced in forward $W^{\pm }$-decays (dashes: ${\mu }^{+}$, dots: ${\mu }^{-}$, solid: difference between these two). Right panel: The same for the earlier LHCb analysis of Ref. [22].

Figure 7

The results of present analysis (solid lines) in comparison with the DØ [6](left panel) and LHCb [1] (right panel) data, both normalized to the corresponding DY NNLO grid predictions with its span given by the shaded area.

Figure 8

Left: The isospin asymmetry of the sea $I(x)$ in the 4-flavor scheme at the factorization scale $\mu =3\mathrm{GeV}$ obtained in the present variant of the ABM12 analysis (solid lines: central value, dots: $1\sigma$ error band) in comparison to the $1\sigma$ band of $I(x)$ obtained in the ABM12 fit [10] (shaded area). Right: Same for the ratio $d/u$ at large $x$.

Figure 9

Same as Fig. 1 for the DØ data on the charged $W^{\pm }$-asymmetry [34] extracted from the DØ data on the electron charge asymmetry [6] as a function of the $W^{\pm }$-rapidity ${\eta }_W$. The shaded area displays the PDF uncertainties in the predictions.

Figure 10

The $1\sigma$ band for the isospin asymmetry of the sea $I(x)$ for the 4-flavor scheme at the scale $\mu =2\mathrm{GeV}$ as a function of the Bjorken $x$ obtained in the present fit (gray shaded area) in comparison with the corresponding ones obtained in the CT14 [12] (red right-tilted hatch), MMHT14 [13] (blue dashed lines), and NN3.0 [14] (green left-tilted hatch) analyses.

Figure 11

Same as in Fig. 10 for the ratio $d/u$.

Figure 12

Cross sections together with their $1\sigma$ PDF uncertainties for the $t$-channel production of single (anti)top-quarks in $pp$ collision at $\sqrt{s}=7\mathrm{TeV}$ in comparison to ATLAS data [17] for a $\overline{\mathrm{MS}}$ mass $m_t(m_t)=163\mathrm{GeV}$ at the scale ${\mu }_R={\mu }_F=m_t(m_t)$ with PDF sets are taken at NNLO. The inner (yellow) band denotes the statistical uncertainty and the outer (green) band the combined uncertainty due to statistics and systematics.

Figure 13

Same as Fig. 12 for $pp$ collision at $\sqrt{s}=8\mathrm{TeV}$ in comparison to CMS data [18].

Figure 14

Same as in Fig. 12 for the ratio of cross sections $R_t={\sigma }_t/{\sigma }_{\overline{t}}$ in comparison to ATLAS data [17] at $\sqrt{s}=7\mathrm{TeV}$ (left) and to CMS data [18] at $\sqrt{s}=8\mathrm{TeV}$ (right).