Entanglement features in scattering mediated by heavy particles

TL;DR

This work investigates how an intermediate heavy particle in general $m→n$ inelastic scatterings propagates information between decay products and other final-state particles, quantifying it with entanglement entropy $S_{EE}$. By modeling the heavy propagator with a Breit-Wigner (Cauchy) distribution and developing a phase-space recursion, the authors show that the on-shell heavy-particle contribution is universally suppressed by the small decay rate $Γ$, leading to a characteristic dip in $S_{EE}$ as the total energy $E_t$ crosses $M$, while the low-energy EFT description yields entanglement that is unsuppressed by $Γ$. The paper provides concrete demonstrations in $2→3$ and $2→4$ scatterings, comparing full theory results with EFT and on-shell approximations, and highlights a beyond-area-law entanglement structure that arises from decay dynamics and phase-space multiplicities. The results suggest practical avenues to probe entanglement via marginalization over final-state phase-space distributions and point to EFT diagnostics based on entanglement features, with implications for understanding EFT breakdown and S-matrix pole structures.

Abstract

The amount of information propagated by an intermediate heavy particle exhibits characteristic features in inelastic scatterings with $n\geq 3$ final particles. As the total energy increases, the entanglement entropy, between its decay products and other final particles, exhibits a universal sharp dip, suppressed by its small decay rate. This indicates an entanglement suppression from a low-energy effective theory to a channel dominated by an on-shell heavy particle. As demonstrations of these entanglement features, we study concrete models of $2\to 3$ and $2\to 4$ scatterings, which shed light on the entanglement structure beyond the area law derived for $2\to 2$ scattering. In practice, these features may be probed by suitably marginalizing the phase-space distribution of final particles.

Figures (12)

• Figure 1: The information propagated by an intermediate heavy particle is quantified by the entanglement entropy between its decay products and other particles unrelated to the decay, highlighted in red and blue, respectively. For a realistic setup of $m\to n$ scattering, $j\geq 2$ and $n\geq j+1\geq 3$.
• Figure 2: Left: A general inelastic $m\to n-1$ scattering, represented by the part $i\mathcal{M}(m \to n-1)$, in which a heavy particle with momentum $p_{12}$ is produced. Solid and dashed lines represent light and heavy particles respectively, in the sense that it is heavy enough to decay into two light particles. Right: The heavy particle further decays into two light particles with momenta $p_1$ and $p_2$ respectively, leading to a $m \to n$ scattering, represented by $i\mathcal{M}(m \to n)$. The decay products generally entangle with the rest of the particles with momenta $p_3,\, \dots\, , \, p_n$.
• Figure 3: Applying the decomposition of phase-space integral (\ref{['eq:phase_space_decompose']}) to the diagram of (\ref{['eq:M_decompose']}), where the left and right blobs corresponding to $i\mathcal{M}(m\to n-j+1)$ and $i\mathcal{M}(1\to j)$ respectively.
• Figure 4: The case with $j=n-1$. Left: A general inelastic $m \to 2$ scattering, represents by the part $i\mathcal{M}(m\to2)$, where a heavy particle with momentum $p_{1-(n-1)}$ is produced. Right: The heavy particle further decays into $n-1$ light particles, forming a subsystem described by $\rho^{(m \to n)}_{1-(n-1)}$, and the whole scattering process is represented by $i\mathcal{M}(m \to n)$.
• Figure 5: Left: A simple $2\to 3$ scattering. The solid and dashed internal lines represent particles with masses $m_\chi$ and $M$ respectively, whereas the solid external lines are light particles. Right: An effective field theory obtained by the large $M$ expansion, and the three outgoing particles are connected by the effective vertex $-\frac{g_2g}{M^2}$.