Dalitz Plot Kinematics for a Lorentz-Violating Three-Body Decay

TL;DR

This work analyzes how Lorentz-violating kinematics from the minimal SME, encoded by a symmetric background tensor $c_{\mu\nu}$, modify three-body decay phase space and Dalitz-plot boundaries for identical spinless daughters. By focusing on a constant matrix element and employing two texture models for $c_{\mu\nu}$, the authors derive leading-order corrections to the decay rate $\Gamma$ in the ultrarelativistic limit, obtaining explicit expressions for the cases $c_{13}=0$ and nonzero $c_{13}$ that reveal logarithmic enhancements and angular dependencies. They then formulate the modified Dalitz-plot boundary, showing how Lorentz violation reshapes the kinematically allowed region in the $(m_{13}^{2},m_{23}^{2})$ plane and discuss how precision measurements of these boundaries could constrain SME coefficients, with η→3π^0 serving as a practical example. The study highlights the potential of Dalitz-plot analyses to bound Lorentz violation in heavy-meson sectors and suggests future extensions, including sidereal-time binning and more general $c_{\mu\nu}$ textures, as well as applications to muon decays. Overall, the paper provides a concrete framework to connect Lorentz-violating kinematics to observable shifts in three-body decay kinematics and Dalitz-plot boundaries.

Abstract

Rates for particle interaction processes and decays will be modified in a Lorentz-violating quantum field theory, because of changes to the particle kinematics$-$particularly through the modified dispersion relations affecting the outgoing particle phase space. We outline here these changes to the rates for three-particle decays. Considering a process with a constant scattering amplitude (not directly modified by the Lorentz violation), we calculate leading order corrections to the kinematics for a decay into three identical spinless particles whose propagation is affected by a $c_{μν}$-type symmetric tensor background. We examine the angular distribution of the daughter particles and describe the shape of the corresponding Dalitz plot outlining the kinematically allowed region, according to two toy models for the $c_{μν}$ textures. Precision measurements of the boundaries of this region could be used to constrain Lorentz violation coefficients for the particles involved in processes such as $η\rightarrow 3π^{0}$.

Figures (4)

• Figure 1: Configuration of the $x$- and $z$-axes and the outgoing three-momenta in the plane of the decay.
• Figure 2: Shape of the Dalitz plot for the $\sqrt{s}/m$ value corresponding to $\eta\rightarrow3\pi^{0}$. The standard outline is shown, along with outlines for two nonzero values of the Lorentz violation parameter $c$.
• Figure 3: Shape of the Dalitz plot for a $\sqrt{s}/m=6.5$ value.
• Figure 4: Shape of the Dalitz plot for an ultrarelativistic value of $\sqrt{s}/m=15.0$.