The bottomonium ground state has mass and total width (PDG 2024)

PHYSICS · Multi-part · Fermi University Physics · Particle Physics & Quantum Fields · Particles, interactions and experiment · Symmetry, groups and the quark model

Symmetry and Flavour, Ch Hadron spectroscopy: quarkonium, orbital excitations and exotic states

Problem

The

\Upsilon(1S)

bottomonium ground state has mass

9460.4\,\mathrm{MeV}

and total width

54.0\,\mathrm{keV}

(PDG 2024). The

\Upsilon(4S)

has mass

10579.4\,\mathrm{MeV}

and total width

20.5\,\mathrm{MeV}

(PDG 2024). The lightest open-beauty meson, the

B

, has mass

5279.3\,\mathrm{MeV}

, so a bottom-antibottom state can decay into a

B\bar B

pair once its mass exceeds

2m_B=10558.6\,\mathrm{MeV}

. ((a)) Compute the ratio

\Gamma(\Upsilon(4S))/\Gamma(\Upsilon(1S))

. ((b)) Using the position of each state relative to the

B\bar B

threshold and the OZI rule, explain in one or two sentences why the widths differ so much.

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