On the simulated kinematic distributions of semileptonic $B$ decays

TL;DR

The paper identifies a systematic bias in EvtGen phase-space sampling for semileptonic B decays into resonances, where neglected phase-space factors yield unphysical kinematic features. It analyzes the sampling structure, demonstrates distortions that are especially pronounced for broad resonances, and quantifies the impact on observables such as hadronic-mass moments, $R(X)$, and $R(D^{**})$, arguing that these effects can exceed current experimental uncertainties. A practical short-term solution is developed: event-wise reweighting to align generated distributions with the correct phase-space behavior, with explicit forms described for semileptonic decays and for nonleptonic decays into two resonances, enabling corrections to existing samples. The work highlights potential biases in precision flavour analyses and advocates for implementing a new phase-space sampling algorithm in EvtGen and cross-checking with other generators like Sherpa or Herwig to ensure robust, reliable predictions.

Abstract

Modern measurements in flavour physics rely on accurate simulations of signal and background processes, provided by a wide range of general-purpose and specialised Monte-Carlo event generators. Due to the inclusion of a larger amount of specialised decays of heavy hadrons, EvtGen is often the tool of choice for many scenarios. We investigate the phase-space sampling algorithm of EvtGen and demonstrate that it generates unphysical features in kinematic distributions of semileptonic $B$ decays involving resonances, originating from neglected phase-space factors. We provide a short-term solution to correct the affected simulated samples through reweighting of the hadronic invariant mass distribution.

Figures (8)

• Figure 1: One-dimensional $D^\ast\pi$ invariant mass spectrum of $B^+ \rightarrow D_1'(2430)\mu^+\nu_\mu$ decays generated with EvtGen and by sampling from an implementation of Eq. \ref{['eq::simpledec2']} (Full PS) with the same building blocks as used in EvtGen. The zoom-in focuses on the region near the phase-space boundaries, where the unphysical step is clearly visible.
• Figure 2: One-dimensional $q^2$ and $E_\mu^B$ spectra of $B^+ \rightarrow D_1'(2430)\mu^+\nu_\mu$ decays generated with EvtGen and by sampling from an implementation of Eq. \ref{['eq::simpledec2']}.
• Figure 3: One-dimensional $D^\ast\pi$ invariant mass and $q^2$ spectra of $B^+ \rightarrow D_1'(2430)\tau^+\nu_\tau$ decays generated with EvtGen and by sampling from an implementation of Eq. \ref{['eq::simpledec2']}.
• Figure 4: $q^2$ spectra of $B^+ \rightarrow D_1(2420)\tau^+\nu_\tau$ and $B^+ \rightarrow D_2^\ast(2460)\tau^+\nu_\tau$ decays generated with EvtGen and by sampling from an implementation of Eq. \ref{['eq::simpledec2']}.
• Figure 5: $q^2$ spectra of $B^+ \rightarrow D_1(2420)/D_1'(2430)\tau^+\nu_\tau$ decays generated with EvtGen and by sampling from an implementation of Eq. \ref{['eq::simpledec2']}. The bin size is chosen to match Ref. LHCb:2025fri.