The measured Dalitz plot of shows two features:

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

\Lambda_c^+\to pK^-\pi^+

shows two features: (i) a narrow band at

m_{pK^-} = 1519\,\mathrm{MeV}

, corresponding to the

\Lambda(1520)

resonance, running the full range of

m_{K^-\pi^+}^2

; (ii) an enhanced density near the upper kinematic edge of

m_{K^-\pi^+}^2

, where

m_{K^-\pi^+}

approaches its maximum allowed value. Take

M_{\Lambda_c^+}=2286.46\,\mathrm{MeV}

m_p=938.272\,\mathrm{MeV}

m_{K^-}=493.677\,\mathrm{MeV}

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

. ((a)) The uniform-phase-space result derived for constant

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

predicts a perfectly flat density all the way to the plot's edges, with no extra enhancement there. Given this, can feature (ii) be attributed to phase space alone? Justify your answer. ((b)) State, for each of the two features, whether it reflects a property of

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

or of phase space, and name what each is most likely evidence for.

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