Focused Angular $N$-Body Event Generator (FANG)

TL;DR

FANG addresses the inefficiency of conventional Monte Carlo sampling when observables are defined in restricted angular regions by integrating laboratory-frame angular constraints directly into the $n$-body Lorentz-invariant phase-space construction, while preserving correct weighting via the $dV_n$ measure. It extends the traditional $M$-generation (GENBOD) framework to allow constrained directions, derives the necessary Jacobians, and computes event weights with exact kinematics, enabling efficient evaluation of differential cross sections and decay rates. The authors validate FANG against RAMBO and GENBOD for full and partial phase spaces and demonstrate accurate differential observables for elementary lepton scattering and lepton–nucleus processes, including comparisons to GENIE in a controlled setup. The result is a versatile tool capable of dramatically reducing computational cost for detector-geometry–driven simulations and angular observables in high-energy and nuclear physics.

Abstract

We introduce FANG (Focused Angular $N$-body event Generator), a new Monte Carlo tool for efficient event generation in restricted Lorentz-Invariant Phase Space (LIPS). Unlike conventional approaches that sample the full $4π$ solid angle, FANG directly generates events in which selected final-state particles are constrained to fixed directions or finite angular regions in the laboratory frame. Because of the way the generator is constructed, angular constraints can be imposed directly in the laboratory frame while maintaining the correct LIPS structure, enabling differential and total cross sections or decay rates to be computed with high efficiency. The method is validated against analytic results and existing event generators, showing excellent agreement. By reducing the computational cost of full phase-space event generation by several orders of magnitude, FANG provides a robust and versatile framework applicable to particle, nuclear, and detector physics.

Figures (10)

• Figure 1: Generalized decay tree for $n$ final particles, described by $n-2$ virtual momenta $q_i$ with virtual masses $M_i$, and the final real on-shell momenta $p_i$ with corresponding real masses $m_i$.
• Figure 2: Comparison of the $\cos\theta$ distributions for all five particles between the full simulation with cuts and the FANG algorithm, which generates only events within the designated solid angles.
• Figure 3: Comparison of the $\varphi$ distributions for all five particles between the full simulation with cuts and the FANG algorithm, which generates only events within the designated solid angles.
• Figure 4: Comparison of the energy distributions (same units as mass) for all five particles between the full simulation with cuts and the FANG algorithm, which generates only events within the designated solid angles.
• Figure 5: Feynman diagram for $e^{-}\mu^{-} \rightarrow e^{-}\mu^{-}$ scattering.