Mapping quark-level kinematics to hadrons in a new hybrid model of semileptonic $B$ meson decays

Abstract

The need to map parton-level processes to color-neutral hadrons in a way that respects quark-hadron duality arises in several areas of physics, including in the semileptonic decays of $B$ mesons. Integrated over large regions of phase space, the quark-level and hadron-level quantities are expected to be equal. However, the breakdown of duality is manifest at low hadron-system invariant masses, where discrete resonances dominate. In practice, this means independent simulations of decays to low-lying resonances and to higher-mass hadronic systems must be merged into a coherent model. We present a novel method to combine these resonant and non-resonant components in simulations of inclusive $b \to u\ellν$ decays that uses an optimal transport algorithm. The method currently used in measurements of inclusive semileptonic $B$ decay branching fractions introduces unphysical features in kinematic spectra such as large discontinuities and negative yields. The optimal transport method solves both of these issues and can be easily implemented in experimental studies of $B \to X_u \ell ν$ decays.

Figures (8)

• Figure 1: From left to right: distributions of $M_X$, $E_{\ell}^B$, $q^2$ and $\cos\theta_\ell$ for $B^+ \to X_u^0 \ell^+ \nu$ (top) and $B^0 \to X_u^- \ell^+ \nu$ (bottom) decays after applying the hybrid weights defined in Eq. \ref{['equ:classic_hybrid_weights']}. The DFN model is used to simulate inclusive decays (light green). The binning used to compute the hybrid weights is given in Ref. 59ws-zxbt.
• Figure 2: $P_+$ versus $P_-$ distributions for inclusive DFN (left) and resonant (right) $B^+ \to X_u^0 \ell^+ \nu$ events. The black line indicates the edge of the physical range where $M_X = 0$.
• Figure 3: Optimal transport hybrid weights in the $P_- P_+$ plane for $B^+ \to X_u^0 \ell^+ \nu$ decays simulated with the DFN model. Bins with weights close to unity (dark purple) are largely unaffected by the hybridization, while the light-colored band at low $P_+$, which corresponds to the resonant region, is mostly depleted.
• Figure 4: As Fig. \ref{['fig:classic_hybrid']}, but using the optimal transport hybrid weights (Eq. \ref{['equ:emd_hybrid_weights']}) with bins of width 0.08 GeV in $P_+$ and $P_-$.
• Figure 5: Moment conservation comparison between the optimal transport hybrid (solid green) and bin-by-bin hybrid (dashed yellow) for the (a) charged and (b) neutral modes. Top and bottom rows show raw and central moments of $M_X^2$, $q^2$, and $E_\ell^B$, plotted as the ratio to the DFN inclusive prediction. Full numerical values are given in Tables \ref{['tab:charged-moments']} and \ref{['tab:neutral-moments']}.