Yes, there is a difference between a partial decay width and the amplitude of a Feynman diagram.
In particle physics, a Feynman diagram is a graphical representation of a particle interaction or decay process. It depicts the initial and final states of the particles involved and the exchange of virtual particles between them. The amplitude of a Feynman diagram represents the complex number associated with the probability of that specific process occurring. It encapsulates the quantum mechanical aspects of the interaction, including the coupling constants and the propagators of the particles involved.
On the other hand, the partial decay width, also known as the decay rate or decay width, is a measure of the probability that a particle will decay into a specific set of final states per unit time. It is a property of the decaying particle and is typically denoted by the symbol Γ (gamma). The partial decay width is related to the amplitude of the Feynman diagram through the following equation:
Partial Decay Width = |Amplitude|^2 / (2π)
Here, |Amplitude|^2 represents the squared magnitude of the amplitude, which gives the probability of the decay process occurring.
In summary, the amplitude of a Feynman diagram quantifies the probability of a particle interaction or decay process occurring, while the partial decay width quantifies the rate at which a particle decays into a specific set of final states.