Disentangling heavy flavor at colliders

We propose two new analysis strategies for studying charm and beauty quarks at colliders. The first strategy is aimed at testing the kinematics of heavy-flavor quarks within an identified jet. Here, we use the SoftDrop jet-declustering algorithm to identify two subjets within a large-radius jet, using subjet flavor tagging to test the heavy-quark splitting functions of QCD. For subjets containing a $J/\psi$ or $\mathrm{\Upsilon }$, this declustering technique can also help probe the mechanism for quarkonium production. The second strategy is aimed at isolating heavy-flavor production from gluon splitting. Here, we introduce a new FlavorCone algorithm, which smoothly interpolates from well-separated heavy-quark jets to the gluon-splitting regime where jets overlap. Because of its excellent ability to identify charm and beauty hadrons, the LHCb detector is ideally suited to pursue these strategies, though similar measurements should also be possible at ATLAS and CMS. Together, these SoftDrop and FlavorCone studies should clarify a number of aspects of heavy-flavor physics at colliders, and provide crucial information needed to improve heavy-flavor modeling in parton-shower generators.

Figure 1

Leading diagrams in QCD that contribute to heavy-flavor production at the LHC: (a) gluon splitting, where a $Q\overline{Q}$ pair arises from a timelike off-shell gluon; (b) flavor excitation, where $Q$ is excited from an incoming proton; and (c), (d) flavor creation, where the $Q\overline{Q}$ pair originates directly from the hard scattering. The precise ${\alpha }_s$ order at which these diagrams appear depends on whether one is working in a three-, four-, or five-flavor scheme for parton distribution functions (PDFs). Note that at higher orders, there is no gauge-invariant distinction between these categories.

Figure 2

Event displays for SoftDrop subjets with (a) no flavor-tagged hadrons, (b), (c), (d) $c$-tagged hadrons, and (e), (f), (g) $b$-tagged hadrons. The fat anti-$k_t$ jet axis defines $\mathrm{\Delta }y=\mathrm{\Delta }\varphi =0$. The filled black boxes represent particles clustered by anti-$k_t$, where the area of the box is proportional to the $p_{\mathrm{T}}$ of the particle. The flavor-tagged ghost particles are shown as open circles, with blue for charm and red for beauty. The (darker) leading and (lighter) subleading SoftDrop subjets are displayed as shaded gray regions. Because these are relatively low-$p_{\mathrm{T}}$ jets that are heavily contaminated by underlying event activity, the SoftDrop procedure often terminates at the first stage of declustering, such that no particles are removed from the anti-$k_t$ jet.

Figure 3

The SoftDrop $z_g$ distributions for the (a) $c$-tagged and (b) $b$-tagged categories. Shown here are the results for the (0,0), (0,1), and (1,1) categories obtained from Pythia.

Figure 4

Same as Fig. 3, but for Herwig++.

Figure 5

Same as Fig. 3 for Pythia for the (a) $c$-tagged and (b) $b$-tagged categories, but comparing quarkonium-tagged jets to flavor-tagged jets in the (0,1) and (0,2) categories. Note that the solid line for the (0,1) category matches Fig. 3.

Figure 6

Same as Fig. 5, but for Herwig++. Quarkonium production is not available in Herwig++.

Figure 7

Event displays using the FlavorCone algorithm, for (a) a gluon-splitting $c\overline{c}$ event, (b) a nonsplitting $c\overline{c}$ event, (c) a gluon-splitting $b\overline{b}$ event, and (d) a nonsplitting $b\overline{b}$ event. The flavor-tagged ghost particles are shown as small open circles, with blue for charm and red for beauty, and the FlavorCone jet boundaries are shown in the corresponding color. The shaded gray regions show the two hardest flavor-tagged anti-$k_t$ jets for comparison. Here we have selected gluon-splitting events where the two anti-$k_t$ jets remain resolved, although we emphasize that in many such events the anti-$k_t$ jets in fact merge.

Figure 8

The azimuthal separation between the two FlavorCone axes seeded by (a) $c$-tagged and (b) $b$-tagged hadrons. The normalized distributions are shown for Pythia, which allows a useful (but ambiguous) categorization into splitting and nonsplitting events. Low values of $\mathrm{\Delta }\varphi$ probe the phase-space region dominated by gluon splitting. The FlavorCone algorithm is ideally suited to study this region, with no anomalous features at the jet radius $R=0.5$.

Figure 9

Same observable and event selection as Fig. 8 for (a) $c$-tagged and (b) $b$-tagged hadrons, but now comparing four different predictions. The qualitative behavior is similar between the generators, but quantitatively they differ at a level that should be testable at the LHC. These are normalized distributions; see Table 2 for the differences in the absolute cross section.

Figure 10

Same event selection as Fig. 8 for (a) $c$-tagged and (b) $b$-tagged hadrons, but now comparing four different definitions for the $\mathrm{\Delta }\varphi$ observable. Here, the distributions are normalized to the FlavorCone approach in order to highlight the loss in efficiency for the anti-$k_t$ method below $\mathrm{\Delta }\varphi \simeq R$. For the $Q$-hadron method, we use an additional offset factor to partially account for the difference in $p_{\mathrm{T}}$ acceptance for hadrons versus jets. For FlavorConeJet, the feature at $\mathrm{\Delta }\varphi \simeq 0.3$ is due to the misalignment of the jet axis and jet momentum for abutting jets.

Figure 11

The distributions examining hadronization effects in (left) $c$-tagged and (right) $b$-tagged events. The top row (a), (b) shows the $\mathrm{\Delta }R$ between the flavor-tagged hadron and its parent parton before hadronization, and the bottom row (c), (d) shows $z_g$ without hadronization effects included (to be compared to Figs. 3 and 5).

Figure 12

The distribution for SoftDrop $R_g$ in (left) $c$-tagged and (right) $b$-tagged events. The top row (a), (b) shows the same flavor categories as Fig. 3, and the bottom row (c), (d) shows the same flavor categories as Fig. 5.

Figure 13

Separation observable from the FlavorCone algorithm for (left) $c$-tagged and (right) $b$-tagged hadrons. The event selection is the same as Fig. 8, but now showing in the top row (a), (b) $\mathrm{\Delta }y$, in the middle row (c), (d) $\mathrm{\Delta }R$, and in the bottom row (e), (f) $m_{jj}$.

Figure 14

The distribution at a GPD for SoftDrop $z_g$ in (left) $c$-tagged and (right) $b$-tagged events. The top row (a), (b) is analogous to the LHCb results in Fig. 3, and the bottom row (c), (d) corresponds to Fig. 5.

Figure 15

The distributions at a GPD examining hadronization effects in (left) $c$-tagged and (right) $b$-tagged events. The top row (a), (b) shows the $\mathrm{\Delta }R$ between the tagged hadron and parton before hadronization, and the bottom row (c), (d) shows $z_g$ without hadronization included (to be compared to Fig. 14).

Figure 16

The distribution at a GPD for the FlavorCone $\mathrm{\Delta }\varphi$ observable in (a) $c$-tagged and (b) $b$-tagged events. These plots are analogous to the LHCb results in Fig. 8.