Intrinsic charm parton distribution functions from CTEQ-TEA global analysis

We study the possibility of intrinsic (nonperturbative) charm in parton distribution functions (PDF) of the proton, within the context of the CT10 next-to-next-to-leading order global analysis. Three models for the intrinsic charm (IC) quark content are compared: (i) $\widehat{c}(x)=0$ (zero-IC model); (ii) $\widehat{c}(x)$ is parametrized by a valence-like parton distribution (BHPS model); (iii) $\widehat{c}(x)$ is parametrized by a sea-like parton distribution (SEA model). In these models, the intrinsic charm content, $\widehat{c}(x)$, is included in the charm PDF at the matching scale $Q_c=m_c=1.3\mathrm{GeV}$. The best fits to data are constructed and compared. Correlations between the value of $m_c$ and the amount of IC are also considered.

Figure 1

The global chi-square function ${\chi }_F^2$ versus the charm momentum fraction $⟨x{⟩}_{\mathrm{IC}}$. The two approximately parabolic curves are determined from fits with many values of $⟨x{⟩}_{\mathrm{IC}}$. Two exemplary fits for each IC model are shown as dots. Blue denotes the BHPS model; the dots have $⟨x{⟩}_{\mathrm{IC}}=0.57\%$ and 2%, which are denoted BHPS1 and BHPS2 below. Red denotes the SEA model; the dots have $⟨x{⟩}_{\mathrm{IC}}=0.57\%$ and 1.5%, which are denoted SEA1 and SEA2 below.

Figure 2

Similar to Fig. 1, but the ${\chi }_F^2+T_2$ versus charm momentum fraction, $⟨x{⟩}_{\mathrm{IC}}$, is also shown as the dotted curve for both the SEA and BPHS models.

Figure 3

Charm quark distribution $xc(x,Q)$ from the BHPS1 and BHPS2 PDFs (which have 0.57% and 2% $⟨x{⟩}_{\mathrm{IC}}$); from SEA1 and SEA2 PDFs (which have 0.57% and 1.5% $⟨x{⟩}_{\mathrm{IC}}$); and from CT10. The four graphs correspond to $Q=2.0$, 3.16, 8.0, and 85 GeV.

Figure 4

Ratios of $c(x,Q{)}_{\mathrm{IC}}/c(x,Q{)}_{\mathrm{CT}10}$ for $Q=85\mathrm{GeV}$.

Figure 5

Ratios of $g(x{)}_{\mathrm{IC}}/g(x{)}_{\mathrm{CT}10}$ for $Q=85\mathrm{GeV}$.

Figure 6

Ratios of $(\overline{u}(x)+\overline{d}(x){)}_{\mathrm{IC}}/(\overline{u}(x)+\overline{d}(x){)}_{\mathrm{CT}10}$ for $Q=85\mathrm{GeV}$.

Figure 7

Ratios of $u_v(x{)}_{\mathrm{IC}}/u_v(x{)}_{\mathrm{CT}10}$ for $Q=85\mathrm{GeV}$.

Figure 8

Ratios of $d_v(x{)}_{\mathrm{IC}}/d_v(x{)}_{\mathrm{CT}10}$ for $Q=85\mathrm{GeV}$.

Figure 9

Comparison of theory and data for the H1 and ZEUS combined data on charm production in $ep$ collisions at HERA. Theory: The blue curves are the result for BHPS2; the red curves are the result for SEA2. The data is plotted as points; the error bars are the total errors. The CT10 prediction cannot be distinguished from that given by BHPS2.

Figure 10

Comparing $S_n$ as a function of charm momentum fraction, $⟨x{⟩}_{\mathrm{IC}}$, for two models of intrinsic charm. Upper: BHPS model; lower: SEA model.

Figure 11

Comparing $S_n$ as a function of charm momentum fraction, $⟨x{⟩}_{\mathrm{IC}}$, showing the data sets for which $S_n$ changes the most significantly. Upper: BHPS model; lower: SEA model.

Figure 12

Correlation plot for the predictions of $W^{-}$ and $W^{+}$ boson production cross sections at the LHC with $\sqrt{S}=8\mathrm{TeV}$ and 14 TeV. The tolerance ellipses are for 90% C.L. for the PDF uncertainties (unc.).

Figure 13

Correlation plot for the predictions of $Z$ and $W^{\pm }$ boson production cross sections at the LHC with $\sqrt{S}=8\mathrm{TeV}$ and 14 TeV. The tolerance ellipses are for 90% C.L.

Figure 14

Correlation plot for the predictions of Higgs and $Z$ boson production cross sections at the LHC with $\sqrt{S}=8\mathrm{TeV}$ and 14 TeV. The tolerance ellipses are for 90% C.L.

Figure 15

Correlation plot for the predictions of top quark pair and $Z$ boson production cross sections at the LHC with $\sqrt{S}=8\mathrm{TeV}$ and 14 TeV. The tolerance ellipses are for 90% C.L.

Figure 16

Rapidity distribution of the $W^{+}$ boson at the LHC with $\sqrt{S}=8\mathrm{TeV}$ and 14 TeV. The PDF uncertainties are for 90% C.L.

Figure 17

Rapidity distribution of the $W^{-}$ boson at the LHC with $\sqrt{S}=8\mathrm{TeV}$ and 14 TeV. The PDF uncertainties are for 90% C.L.

Figure 18

Rapidity distribution of the $Z$ boson at the LHC with $\sqrt{S}=8\mathrm{TeV}$ and 14 TeV. The PDF uncertainties are for 90% C.L.

Figure 19

The ratio $\frac{d{\sigma }_{W^{+}+W^{-}}}{d{\sigma }_Z}$ at the LHC with $\sqrt{S}=8\mathrm{TeV}$ and 14 TeV for four IC models at NNLO. Upper panel: differential distributions; lower panel: ratios normalized to the CT10 central prediction. The PDF uncertainties are for 90% C.L.

Figure 20

Transverse momentum distribution of the $Z$ boson in the production of $pp\to Zc$ at the LHC with $\sqrt{S}=8\mathrm{TeV}$ and 14 TeV. Upper panel: differential cross sections; lower panel: ratios normalized to the CT10 central prediction. The PDF uncertainties are for 90% C.L.

Figure 21

The global chi-square function ${\chi }_F^2$ versus the charm momentum fraction $⟨x{⟩}_{\mathrm{IC}}$ for the SEA model with $m_c=1.3\mathrm{GeV}$ and $m_c=1.67\mathrm{GeV}$.

Figure 22

Comparisons of $S_n$ as a function of $⟨x{⟩}_{\mathrm{IC}}$, showing the data sets for which $S_n$ changes the most significantly for the SEA model with $m_c=1.67\mathrm{GeV}$.