The charmonium state has spin

PHYSICS · Subjective · Fermi University Physics · Particle Physics & Quantum Fields · Particles, interactions and experiment · Particles, interactions and experiment

Symmetry and Flavour, Ch Resonances: the relativistic Breit-Wigner, unitarity and the Z line shape

Problem

The

\psi(2S)

charmonium state has spin

J=1

, mass

M=3686.1\,\mathrm{MeV}

and hadronic branching ratio

\mathcal{B}_{\rm had}=97.85\%

. Its natural width is far narrower than the spread of collision energies at the collider where it was studied, so its partial width to

e^+e^-

must be extracted from the area under the observed hadronic cross-section peak, measured to be

\int\sigma_{\rm had}\,\mathrm{d}E = 3.87\,\mathrm{nb\,GeV}

. Using the narrow-width area formula for a

J=1

state formed in

e^+e^-

collisions,

\int\sigma_f\,\mathrm{d}E = \dfrac{6\pi^2\Gamma_{ee}\Gamma_f}{M^2\Gamma}

, together with

\Gamma_f/\Gamma = \mathcal{B}_{\rm had}

for

f=\text{hadrons}

, extract

\Gamma_{ee}

for the

\psi(2S)

, in keV.

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