# Particle resonance and the resonance in a driven, damped classical

1. Dec 28, 2008

### Bobhawke

I am trying to understand the analogy between a particle resonance and the resonance in a driven, damped classical oscillator.

I guess I should first ask for a clear definition of a particle resonance - is this just an excited state which decays quickly?

I understand that the KG equation which all quantum fields obey is just the equation for the harmonic oscillator. I don't understand how exactly particle resonances are analagous to resonance in the classical harmonic oscillator - could someone explain please?

Thanks

2. Dec 28, 2008

Staff Emeritus
Re: Resonances

Many folks think this, but it's not quite it. You also have a phase shift in the scattering at the resomance mass. If you look at the relevant PDG section, it's covered in 38.5.3. In particular, the Argand plot in Figure 38.6 will indicate that there is a resonance.

3. Dec 29, 2008

### hamster143

Re: Resonances

This question can be answered from different angles.

When you scatter strong-interacting particles off one another, you experience resonant scattering near certain energies. Resonant means that the interaction probability goes up when the scattering goes through an intermediate state whose invariant mass is near a certain value. We call this a "particle resonance" if it appears that the resonance occurs because of an unstable intermediate strongly-bound state.

Classical damped harmonic oscillator exhibits a resonance (high amplitude) near a certain driving frequency. The amplitude of the oscillator as a function of the frequency follows a bell curve - the peak tells you the resonant frequency and the width tells you how much damping there is.

Particle scattering exhibits a resonance (high probability to interact) near a certain invariant mass. Interaction cross-section as a function of invariant mass follows a bell curve - the peak tells you the mass of the particle resonance and the width tells you how unstable it is. The more unstable the particle, the wider the peak.