RapidSim: an application for the fast simulation of heavy-quark hadron decays

1 Introduction

• The analysis problem is to understand signal and background kinematics, especially invariant-mass shapes of final-state particles or subsets.Source: §1 · p. 2
• Full detector simulation and reconstruction can study background invariant-mass shapes, but typically require substantial generation time and storage.The backgrounds include partial signal final states, unreconstructed additional particles, and misidentified particles, alone or in combination.Source: §1 · p. 2
• RapidSim quickly generates large samples of potential background decays with kinematics, resolutions, and efficiency shapes approximating full detector simulation.The framework uses ROOT's TGenPhaseSpace and FONLL calculations for heavy-hadron kinematics.Source: §1 · p. 2
• RapidSim supports configurable decay chains, LHCb acceptance, user-defined kinematic efficiencies, and final-state particle mis-identification.Source: §1 · p. 2
• The paper outlines compilation and execution, configuration and an example, then details production, efficiencies, momentum resolution, and mis-identification.Source: §1 · pp. 2–3

2 Usage

• Build the executable with the listed CMake commands after obtaining the source code from GitHub.Source: §2 · p. 3
• Set RAPIDSIM_ROOT to the RapidSim directory before invoking the executable at its build path.Source: §2 · p. 3
• Run RapidSim.exe with a decay mode and event count, optionally adding a flag to save the output tree.The example runs Bs2Jpsiphi for 10,000 events and enables tree saving.Source: §2 · p. 3
• The run requires a user-provided decay file and may use a user-defined configuration file for that decay.The example names both files Bs2Jpsiphi.decay and Bs2Jpsiphi.config.Source: §2 · p. 3

3 Configuration

• Decay configuration files provide global and particle-specific settings, with common files also defining particle species, production kinematics, and momentum-resolution options.The decay-specific file is automatically created with defaults the first time a decay is generated.Source: §3 · pp. 3, 6, Table 1 · p. 4, Table 2 · p. 5
• A shape setting selects a TH1 or TH2 histogram and parameter axes, while a cut setting applies min, max, range, or veto thresholds to a named parameter.Source: §3 · p. 3
• The production-kinematics and momentum-resolution options are defined; further details on configuring these two features are provided in Sections 5.1 and 7.1, respectively.Source: §3 · p. 6

4 Example: B0

• Decay files express particle decays with arrows, braces for subdecays, and particle names from the configured particle list.The example encodes Bs0 decays to J/ψ and φ, followed by their muon and kaon decays.Source: §4 · p. 6
• The example configuration requests mass, momentum, and transverse momentum for decaying particles, momentum and transverse momentum for stable particles, and LHCb geometry.Source: §4 · p. 6
• The example assigns LHCbGeneric smearing to the two muons and names the kaons with alternative pion-mass hypotheses.Source: §4 · pp. 6–7
• Particle names label output variables and histograms, while smear applies momentum-resolution parameterisations and altMass computes four-vectors under another mass hypothesis.RapidSim includes smearing options for pions, kaons, protons, muons, and electrons, and users can extend these parameterisations.Source: §4 · p. 7

5.1 FONLL

• RapidSim samples the decaying particle’s η and pT from histograms generated using fixed-order next-to-leading-logarithm calculations, rather than simulating the underlying event.The particle-gun-like approach defines the generated particle kinematics; included histograms cover b- and c-hadrons in pp collisions at several centre-of-mass energies.Source: §5.1 · p. 7

5.1.1 Custom production kinematics

• Additional production histograms can be added as ROOT files containing pT and η distributions, with supported naming schemes usable without recompiling.The mother option can override the histogram choice; extending the naming scheme requires modifying RapidConfig::loadParentKinematics.Source: §5.1.1 · pp. 7–8

5.2 Non-phase space distributions

• A Monte Carlo accept/reject algorithm can shape phase-space decays to a one- or two-dimensional distribution in defined parameters.Inefficient accept/reject functions, such as Dalitz plots with narrow resonances, increase generation time because the requested event count is generated within the specified distribution.Source: §5.2 · p. 8, Figure 2 · p. 8

6 Efficiency

• RapidSim distinguishes geometrical acceptance from kinematic selection as its two types of efficiency effects.The examples include acceptance-dependent Bs kinematics and configurable requirements on decay parameters.Source: §6 · p. 9, §6.1 · p. 9, §6.2 · p. 9

6.1 Geometrical acceptance

• Geometrical acceptance can be configured as no requirement, a requirement on the mother, requirements on all final-state particles, or downstream acceptance for all final-state particles.The available LHCb-specific options are defined at compile time and selected at runtime; Figure 3 illustrates their effects on Bs transverse momentum and pseudorapidity distributions.Source: §6.1 · p. 9

6.2 Kinematic requirements

• Kinematic selection requirements can impose a minimum, maximum, range, or veto on any defined parameter.Requirements are configured with the global cut option; the passage gives pion pT between 1 and 100 as an example.Source: §6.2 · p. 9

6.3 Missing particles

• The invisible option models unreconstructed particles by excluding their momentum from reconstructed quantities while retaining it in true quantities.It is enabled by default for neutrinos and can also be used for other particle types; Figure 5 illustrates the option.Source: §6.3 · p. 9, Figure 5 · p. 11

7 Momentum smearing

• Stable-particle momenta are smeared with defined resolution functions, using p-dependent or pT- and η-dependent Gaussian widths, or histograms across momentum ranges.Histogram-based smearing can model asymmetric effects such as Bremsstrahlung; the predefined LHCbElectron option uses this approach.Source: §7 · p. 12
• RapidSim reproduces the J/ψK+ mass resolution observed in LHCb and ATLAS data using the relevant momentum-smearing options.The comparison uses selected B+ → J/ψK+ data distributions and corresponding RapidSim signal-only distributions.Source: §7 · p. 12, Figure 7 · p. 13

7.1 Configuration

• Each smearing option uses an ASCII configuration file and a ROOT file, with configuration specifying Gaussian or histogram-based resolution data.The configuration distinguishes p-dependent Gaussian widths, pT- and η-dependent Gaussian widths, and histograms assigned to momentum bins.Source: §7.1 · pp. 12–13

8 Particle mis-identification

• RapidSim lets users define multiple alternative mass hypotheses for each particle through its altMass option.For example, a particle can be assigned both kaon and muon mass hypotheses.Source: §8 · p. 14
• RapidSim calculates parameters for all combinations of hypotheses when two or fewer particles are mis-identified.The supplied example considers pion-to-muon, pion-to-kaon, and kaon-to-pion mis-identifications.Source: §8 · p. 14
• The example D0 → K−π+ decay yields five alternative mass hypotheses under the specified mis-identifications.They are K−μ+, K+K−, π−π+, π−μ+, and π−K+.Source: §8 · p. 14

• RapidSim generates heavy-flavour decays with realistic production kinematics, efficiencies, and momentum resolutions, controlled through configuration files and external parameterisations.Source: §9 · p. 14
• Misidentified final-state particles are handled through a configuration file, and the framework can be extended to alternative detector geometries.Source: §9 · pp. 14–15
• RapidSim provides large decay samples for analysis without fully simulated decays and their associated computing and storage resources; it is already used in ongoing LHCb analyses.Source: §9 · p. 15