The J/ψ particle was discovered at both the Stanford Linear Accelerator Center (SLAC) and Brookhaven National Laboratory in 1974. The SLAC data from the head-on collision of e^+ and e^- are shown in Figure 14.9. The width of the state was later determined to be Γ = 0.093 MeV. Discuss the evidence

Question

The [latex]J / \psi[/latex] particle was discovered at both the Stanford Linear Accelerator Center (SLAC) and Brookhaven National Laboratory in 1974. The SLAC data from the head-on collision of [latex]e^{+} ext {and } e^{-}[/latex] are shown in Figure 14.9. The width of the state was later determined to be [latex]\Gamma=0.093[/latex] MeV. Discuss the evidence that this resonance represents an elementary particle and determine the particle’s lifetime.

Accepted Answer

The data shown in Figure 14.9 represent a clear experimental example of a resonance. The peak near 3.1 GeV was also observed in other outgoing reaction channels, indicating that the resonant peak occurs in the “compound” system and not in the outgoing reaction channel.

The width of the resonance observed in Figure 14.9 is on the order of 5 MeV and is limited by experimental resolution, namely, the beam momentum. With better experimental energy resolution, the resonance would become much sharper. As stated, the actual energy width of the resonant state has been established to be 0.093 MeV and was determined by other means. We use Equation (14.6) to determine the lifetime of the [latex]J / \psi[/latex] particle.

[latex]\Delta t= au \approx \frac{\hbar}{2 \Delta E}=\frac{\hbar}{\Gamma} \quad ext { or } \quad au \approx \frac{\hbar}{\Gamma}[/latex] (14.6)

[latex] au=\frac{\hbar}{\Gamma}=\frac{1.055 imes 10^{-34} J \cdot s }{0.093 MeV }\left(\frac{1 MeV }{1.6 imes 10^{-13} J } ight)=7.1 imes 10^{-21} s[/latex]

The lifetime of [latex]10^{-20}[/latex] s is very long compared to the characteristic time taken by the [latex]e^{+} ext {and } e^{-}[/latex], traveling practically at the speed of light, to interact over the distance of a few fermi.

Question 14.3: The J/ψ particle was discovered at both the Stanford Linear ...

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