$Z$ boson production in proton-lead collisions at the LHC accounting for transverse momenta of initial partons

We perform a calculation of inclusive $Z$ boson production in proton-lead collisions at the LHC taking into account the transverse momenta of the initial partons. We use the framework of $k_T$-factorization combining transverse momentum dependent parton distributions (TMDs) with off-shell matrix elements. In order to do it we need to construct appropriate TMDs for lead nuclei which is done using the parton branching method. Our computations are compared with data from CMS taken at $\sqrt{s}=5.02\mathrm{TeV}$. The results are in good agreement with the measurements especially the transverse momentum distribution of the $Z$ boson.

Figure 1

Up quark transverse momentum dependent parton density integrated over $k_t$ for different values of the scale $\mu$. The upper plots show the comparison with the corresponding collinear distribution. The lower plots compare two nuclear TMD distributions based on the nCTEQ15 (PB-nCTEQ15FullNuc_208_82) and EPPS16 (PB-EPPS16nlo_CT14nl_Pb208) nuclear PDFs with the PB-NLO_ptoPb208 TMD.

Figure 2

Transverse momentum dependent parton densities for different quark species at $x=0.01$ at the scale of $\mu =100\mathrm{GeV}$. The ratio is always taken with respect to the PB-NLO_ptoPb208 set2 distributions.

Figure 3

Comparison of different nuclear transverse momentum dependent parton densities for $u$ and $\overline{u}$ quarks at $x=0.01$ at the scale $\mu =100\mathrm{GeV}$. Depicted are the Set2 distributions that are used in the calculations in Sec. 3. The ratio is taken with respect to the proton PB-NLO_ptoPb208 set2 TMD.

Figure 4

Comparison of set2 nuclear PB-nCTEQ15FullNuc_208_82 and proton PB-NLO_ptoPb208 TMDs for up quark at several $k_t$ and $\mu$ scales as a function of $x$. The ratio plots take as a reference the proton TMDs (showing the nuclear modification factors).

Figure 5

Transverse momentum dependent parton densities for $u$ and $\overline{u}$ quarks at $x=0.01$ at the scale of $\mu =10\mathrm{GeV}$ (upper plots) and $\mu =100\mathrm{GeV}$ (lower plots). The ratio shows relative uncertainty of PB-nCTEQ15FullNuc_208_82 set2 TMDs.

Figure 6

Comparison of predictions for: (a) $Z$ boson (center of mass) rapidity $y^{*}$, and (b) $Z$ boson transverse momentum, $p_T$, distributions obtained within $k_T$-factorization using different PB nTMDs/TMDs with the CMS data [20].

Figure 7

Comparison of predictions for: (a) $Z$ boson (center of mass) rapidity $y^{*}$, and (b) $Z$ boson transverse momentum, $p_T$, distributions obtained within $k_T$-factorization using PB-nCTEQ15FullNuc_208_82 Set1 and Set2 nTMDs and within collinear factorization using nCTEQ15 nPDFs (nCTEQ15FullNuc_208_82) with the CMS data [20].

Figure 8

Comparison of predictions for: (a) $Z$ boson (center of mass) rapidity $y^{*}$, and (b) $Z$ boson transverse momentum, $p_T$, distributions obtained using nCTEQ15 TMDs/PDFs with $k_T$-factorization (TMD), hybrid approach with two choices for the off-shell initial partons ($p^{*}\mathrm{Pb}$, $p{\mathrm{Pb}}^{*}$) and collinear approach. The results are compared with the CMS data [20].

Figure 9

Comparison of $Z$ boson rapidity and transverse momentum distributions computed with scale $\mu =m_Z$ and $\mu =\sqrt{m_Z^2+p_{tZ}^2}$ using PB-nCTEQ15FullNuc_208_82 Set2 TMDs.

Figure 10

Scale variation for the predictions for $Z$ boson rapidity and transverse momentum distributions compute with PB-nCTEQ15FullNuc_208_82 Set2 TMDs.

Figure 11

TMD uncertainties for the predictions for $Z$ boson rapidity and transverse momentum distributions compute with PB-nCTEQ15FullNuc_208_82 Set2 TMDs.

Figure 12

Predictions for $Z$ boson rapidity and transverse momentum distributions in $p\mathrm{Pb}$ collisions at $\sqrt{s}=8.16\mathrm{TeV}$ in the invariant lepton pair mass range (a) $60<m_{ll}<120\mathrm{GeV}$, and (b) $15<m_{ll}<60\mathrm{GeV}$ computed with PB-nCTEQ15FullNuc_208_82 and PB-EPPS16nlo_CT14nl_Pb208 Set2 TMDs.