Heavy flavor production in high-energy $pp$ collisions: Color dipole description

We present a detailed study of open heavy flavor production in high-energy $pp$ collisions at the LHC in the color dipole framework. The transverse momentum distributions of produced $b$-jets, accounting for the jet energy loss, as well as produced open charm $D$ and bottom $B$ mesons in distinct rapidity intervals relevant for LHC measurements are computed. The dipole model results for the differential $b$-jet production cross section are compared to the recent ATLAS and CMS data while the results for $D$ and $B$ mesons production cross sections—to the corresponding LHCb data. Several models for the phenomenological dipole cross section have been employed to estimate theoretical uncertainties of the dipole model predictions. We demonstrate that the primordial transverse momentum distribution of the projectile gluon significantly affects the meson spectra at low transverse momenta and contributes to the largest uncertainty of the dipole model predictions.

Figure 1

Typical contributions to the heavy quark $Q\overline{Q}$ pair production in $G_a\to Q\overline{Q}$ splitting subprocess in the color field of the target nucleon.

Figure 2

The relative fraction of the jet transverse momentum $p_T$ radiated outside the measured jet cone as a function of jet radius $R$ for various $p_T$ values.

Figure 3

The unintegrated KMR (solid lines), GBW (dashed lines) and BGBK (dash-dotted lines) gluon distributions in the target proton as functions of the longitudinal momentum fraction $x$ at fixed $k_T^2=1$, $10{\mathrm{GeV}}^2$ values (left panel) and the transverse momentum squared $k_T^2$ at fixed $x={10}^{-2}$, ${10}^{-4}$ values (right panel).

Figure 4

The dipole model results for the differential $D^0$-meson (left panels) and $B^{\pm }$-meson (right panels) production cross sections in two distinct rapidity bins, $2.0<Y<2.5$ (upper panels) and $4.0<Y<4.5$ (lower panels) as a function of meson transverse momentum $P_T$ versus the LHCb data at $\sqrt{s}=7\mathrm{TeV}$ [80, 81]. Here, the results for the BGBK [57] (in saturated and in quadratic forms) and GBW [63] dipole parametrizations are compared to the result obtained with KMR UGDF [79]. The collinear projectile gluon PDF in the CT10 model [83] is adopted here.

Figure 5

The dipole model results for the differential $B^{\pm }$-meson production cross section in two distinct rapidity intervals, $2.0<Y<2.5$ (left panel) and $4.0<Y<4.5$ (right panel), as a function of meson transverse momentum $P_T$ versus the LHCb data at $\sqrt{s}=7\mathrm{TeV}$ [81]. Here, the quadratic form of the BGBK model has been used for the target gluon while the projectile gluon has been set to be collinear (solid line) or having a primordial transverse momentum treated via the Gaussian smearing UGDF (6.1) with different values of the averaged $⟨k_T^2⟩=1.0$, 2.0 and $5.0{\mathrm{GeV}}^2$ depicted by dashed, dash-dotted and dotted lines, respectively.

Figure 6

A comparison of dipole model predictions for differential $B$-meson production cross section using different models of the primordial UGDF with the corresponding LHCb data [81] in two distinct rapidity intervals. Here, the quadratic form of the BGBK model has been used for the target gluon. The projectile gluon UGDF has been chosen to be KMR (solid line), GBW (dashed line) and Gaussian smearing (dash-dotted line) with $⟨k_T^2⟩=2.0{\mathrm{GeV}}^2$.

Figure 7

The effect of QCD evolution in the fragmentation function on the differential $D^0$-meson (left panel) and $B^{\pm }$-meson (right panel) production cross sections. Here, the quadratic form of the BGBK model has been used for the target gluon. Data are taken from the LHCb collaboration [80, 81].

Figure 8

The dipole model predictions with KMR UGDF and the BGBK model ([57]) for transverse momentum distributions of $D^0$ (left panels) and $B^{\pm }$ (right panels) mesons in various rapidity intervals at $\sqrt{s}=7\mathrm{TeV}$ versus data taken from the LHCb collaboration [80, 81].

Figure 9

The dipole model predictions with KMR UGDF and the $r^2$-approximated BGBK model ([57]) for transverse momentum distributions of $b$-jets at $\sqrt{s}=7\mathrm{TeV}$ integrated over two distinct rapidity intervals. The data are taken from the ATLAS collaboration for $|y|<0.3$, $1.2<|y|<2.1$ [91] (left panel) and from the CMS collaboration for $|y|<0.5$, $2.0<|y|<2.2$ [92] (right panel).