The measured Dalitz plot of shows an intense

PHYSICS · Multi-part · Fermi University Physics · Particle Physics & Quantum Fields · Particles, interactions and experiment · Particles, interactions and experiment

Symmetry and Flavour, Ch From amplitude to rate: Lorentz-invariant phase space, widths and cross sections

Problem

The measured Dalitz plot of

D_s^+\to K^+K^-\pi^+

shows an intense, narrow band running the full length of the plot at

m_{K^+K^-} = 1019.4\,\mathrm{MeV}

, with roughly uniform density elsewhere except for this band. The kinematic range of

m_{K^+K^-}

runs from

m_{K^+}+m_{K^-} = 987.35\,\mathrm{MeV}

up to

M_{D_s^+}-m_{\pi^+}

, with

M_{D_s^+}=1968.35\,\mathrm{MeV}

and

m_{\pi^+}=139.570\,\mathrm{MeV}

. ((a)) Compute the allowed range of

m_{K^+K^-}

and confirm whether

1019.4\,\mathrm{MeV}

lies well inside it or at an edge. ((b)) Given that three-body phase space with constant

\overline{|\mathcal{M}|^2}

gives a uniform density in

m_{12}^2

and

m_{23}^2

, state what the band running at fixed

m_{K^+K^-}

across the full range of the other Dalitz variable implies about

\overline{|\mathcal{M}|^2}

, and name the physical origin of the band in one sentence.

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