Resummation effects in the forward production of $Z_0+\mathrm{jet}$ at the LHC

We calculate several differential cross sections for $Z_0$ and high-$p_T$ jet production in the forward rapidity region at the LHC using the hybrid high energy factorization. We test various unintegrated gluon distributions involving subleading Balitski-Fadin-Kuraev-Lipatov effects (such as kinematic constraint, running strong coupling and Dokshitzer-Gribov-Lipatov-Altarelli-Parisi correction) and compare the results with experimental data obtained by the LHCb experiment. We find that the hard scale dependence of unintegrated gluon distributions, which effectively resums the Sudakov-type logarithms on the top of the resummation of the small $x$ logarithms, is essential to describe the normalized azimuthal decorrelations between the $Z_0$-boson and the jet.

Figure 1

Diagrammatic representation of the hybrid high energy factorization for forward $Z_0+\text{jet}$ production. The upper blob corresponds to a collinear PDF, whereas the lower one corresponds to the unintegrated gluon distribution. The gluon entering the hard scattering is off-shell with virtuality $k_T^2$.

Figure 2

Azimuthal decorrelations for $p_{Tj}>10\mathrm{GeV}$ normalized to the total cross section.

Figure 3

Azimuthal decorrelations for $p_{Tj}>20\mathrm{GeV}$ normalized to the total cross section.

Figure 4

Transverse momentum spectrum for $Z_0$-boson for $p_{Tj}>10\mathrm{GeV}$ normalized to the total cross section.

Figure 5

Transverse momentum spectrum for $Z_0$-boson for $p_{Tj}>20\mathrm{GeV}$ normalized to the total cross section.

Figure 6

Rapidity spectrum of $Z_0$-boson for $p_{Tj}>10\mathrm{GeV}$ normalized to the total cross section.

Figure 7

Rapidity spectrum of $Z_0$-boson for $p_{Tj}>20\mathrm{GeV}$ normalized to the total cross section.

Figure 8

Differential cross section as a function of rapidity separation between the $Z_0$-boson and the jet for $p_{Tj}>10\mathrm{GeV}$ normalized to the total cross section.

Figure 9

Differential cross section as a function of rapidity separation between the $Z_0$-boson and the jet for $p_{Tj}>20\mathrm{GeV}$ normalized to the total cross section.

Figure 10

Transverse momentum spectrum of the jet normalized to the total cross section.