(By Giles Strong)

Alright pal? As promised, here I’ll be going into a bit more detail of heavy-flavour modelling in Monte Carlo (MC) generators. Specifically, b-quark pair production, which was the subject of my research at The University of Glasgow.

The investigation compared the angular distributions of B hadrons produced in MC to the distributions of non-prompt J/ψs from ATLAS data. The MC distributions were smeared to account for the missing B→J/ψ decay, rather than require B→J/ψ in MC, which would have caused a severe reduction in acceptance.

MC production channels

As I mentioned in my previous post, particle-processes occur in two simulation schemes: the matrix element (ME) and the parton shower (PS). b-quark pairs may then be produced directly in the ME (e.g. ggbb), with an analytic calculation in perturbative QCD and full accounting of the b-quark mass or in the subsequent PS of a light ME (e.g. gg→gg and g→bb in PS), where the process is approximated and the mass-effect not fully accounted for.

Pythia 8, Sherpa, and Herwig++ were used for MC generation, since each uses a different approach PS evolution. To account for quark mass effects, Pythia uses ME information to correct massless splittings, whereas Sherpa and Herwig both use quasi-collinear splitting functions. Pythia and Sherpa both use a ptordered shower, whereas Herwig uses an angular-ordered shower.

Figure 1: ME production of b-quark pairs

The investigation began by looking at the angular distributions of ME and PS production. Figure 1 shows the ΔΦ distribution of b-hadron pairs for ME production of b-quark pairs. Production here is seen to be concentrated around back-to-back production (peak at π), and the generators show similar distribution shapes. This is expected, since back-to-back production is required to conserve momentum in 2→2 interactions (deviation due to initial-state radiation and PS), and the same ME is being calculated by both generators.

Figure 2: PS production of b-quark pairs

Figure 2 (PS production), conversely, shows the generators demonstrating very different production characteristics. Sherpa shows highly peaked production in the low-angle region, whereas Pythia’s and Herwig’s production is slightly peaked at low ΔΦ and almost flat at high angle.

Inclusive MC production

Figure 3 shows the distributions for inclusive b-quark pair-production in MC. Pythia and Herwig show very similar production characteristics: flat low and mid angle production, and peaked production at high angle. Sherpa, instead, shows peaked production at both low and high angle, and a lack of mid-angle production.

Figure 3: Inclusive production of b-quark pairs

Unfortunately, not being an ATLAS author, I can’t show the comparison data here, but it’s certainly interesting to see that the choice of evolution ordering or approach to quark-mass modelling really can have large effects on a generator’s prediction. On the other hand, it’s also interesting to see how similar Pythia’s and Herwig’s distributions are, despite taking different approaches (spoiler: they demonstrated better data agreement).