Narrow-width approximation accuracy

TL;DR

The work provides a rigorous treatment of the narrow-width approximation (NWA) for resonant processes with on-shell intermediate states, proving that polarization/spin decorrelation does not affect inclusive rates and that the relative error scales as $\mathcal{O}(\Gamma)$. Through a comprehensive model-independent scan of 48 resonant 3-body decays and targeted MSSM (SPS1a) analyses, the authors demonstrate that off-shell effects can be significant near kinematic bounds, sometimes exceeding naive expectations by large factors and depending on chiral couplings. To address these limitations, they introduce PSINWA, a process-independent improvement that shifts the effective resonance mass to $M_{\text{eff}}$, derived from maximizing $D(q^2)\text{PS}(q^2)$, thereby stabilizing predictions near thresholds while preserving NWA simplicity. The proposed method, along with MSSM-specific results, provides a more reliable framework for collider predictions involving heavy resonances and supports more accurate extraction of model parameters in BSM scenarios. The findings have practical impact for precision phenomenology at the LHC and future colliders where resonant dynamics and off-shell effects compete with higher-order corrections.

Abstract

A study of general properties of the narrow-width approximation (NWA) with polarization/spin decorrelation is presented. We prove for total rates of arbitrary resonant decay or scattering processes with an on-shell intermediate state decaying via a cubic or quartic vertex that decorrelation effects vanish and the NWA is of order Gamma. Its accuracy is then determined numerically for all resonant 3-body decays involving scalars, spin-1/2 fermions or vector bosons. We specialize the general results to MSSM benchmark scenarios. Significant off-shell corrections can occur - similar in size to QCD corrections. We qualify the configurations in which a combined consideration is advisable. For this purpose, we also investigate process-independent methods to improve the NWA.

Figures (7)

• Figure 1: Resonant decay or scattering process kinematics with total incoming momentum $P$.
• Figure 2: Resonant $3$-body decay kinematics.
• Figure 3: Resonant $1\to 3$ decay SSS-SSV (see main text): The graph displays the $q^2$-dependence of the Breit-Wigner that is integrated out in the NWA (dashed) and of the complete integrand of Eq. (\ref{['ofsdec_eq:ampfac']}) (solid) for $m_3=M-3\Gamma$. The contour plot shows $R':=|R|/(\Gamma/M)$, i.e. the magnitude of the relative NWA error in units of $\Gamma/M$, as function of $m_3$ and $M$ with $m_1=m_2=0$. The width-mass ratio $\Gamma/M$ is $0.01$.
• Figure 4: Dependence of the magnitude of the relative NWA error $R'$ (see Fig. \ref{['ofsdec_fig:sss-ssv']}) on the strength of the chiral components of the 1st-stage decay vertex $\gamma^\mu(\alpha P_L+\beta P_R)$ for process FFV-VFF at the parameter point $M/M_I=0.68$, $m_1/M_I=0.3$ and $m_2=m_3=0$ with $\Gamma/M=0.01$. Color code as in Fig. \ref{['ofsdec_fig:sss-ssv']}.
• Figure 5: Complete set of Feynman graphs for the MSSM $3$-body decay $\tilde{g} \rightarrow \widetilde{\chi}_1^0 d \bar{d}$.