Dalitz plot kinematics for a Lorentz-violating three-body decay

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 <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mrow> <a:msub> <a:mrow> <a:mi>c</a:mi> </a:mrow> <a:mrow> <a:mi>μ</a:mi> <a:mi>ν</a:mi> </a:mrow> </a:msub> </a:mrow> </a:math> -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:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:msub> <c:mi>c</c:mi> <c:mrow> <c:mi>μ</c:mi> <c:mi>ν</c:mi> </c:mrow> </c:msub> </c:math> 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 <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:mi>η</e:mi> <e:mo stretchy="false">→</e:mo> <e:mn>3</e:mn> <e:msup> <e:mi>π</e:mi> <e:mn>0</e:mn> </e:msup> </e:math> .