The meson has mass and total width (PDG 2024)

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

Particle Physics, Ch Resonances, widths and the Breit-Wigner line shape

Problem

The

\Upsilon(1S)

meson has mass

9460.3\,\mathrm{MeV}/c^2

and total width

\Gamma = 54.02\,\mathrm{keV}

(PDG 2024). Its mass is far above the rest energy needed for many light-hadron final states: three pions, for instance, have a combined rest energy of only about

420\,\mathrm{MeV}

, leaving nearly all of the

9460\,\mathrm{MeV}

available as kinetic energy for the products of such a decay. A resonance with this much room for a strong decay is normally expected to have a width of the same order as the

\Delta(1232)

, whose width is

\Gamma_\Delta = 117\,\mathrm{MeV}

, or the

\rho^0

, whose width is

149\,\mathrm{MeV}

. ((a)) Find the lifetime of the

\Upsilon(1S)

from its width. ((b)) By what factor is

\Gamma_\Delta

larger than the width of the

\Upsilon(1S)

? ((c)) Following the style of reasoning that turned the narrowness of the

J/\psi

from a puzzle into evidence, explain what the result of part (b) says about the

\Upsilon(1S)

's decay, and state what a phase-space argument of this kind can and cannot conclude about the mechanism responsible.

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