How Do Resonances Differ from Virtual States in Quantum Physics?

[snorkack]

What´s the difference between a resonance and a virtual state?
For comparison, a standard moderately lived state, hydrogen 2p state, has energy of 10,2 eV above ground, and width 4*10ˇ-7 eV.
An example of resonance is Delta - with mass 1232 MeV, it´s energy is about 290 MeV above ground (nucleon) and width around 110 MeV.
And then there are virtual states, like virtual paradeuteron. Paradeuteron is supposed to be a state unbound by around 60 keV, and is very important for proton-neutron scattering.

What is technical difference then comparing a resonance with a virtual state?

 

[mfb]

There is no fixed boundary, and different fields (particle physics, nuclear physics, ...) can use different names for the same things. In particle physics, the dividing line between "resonance" and "particle" is usually drawn somewhere at a width of something like 1/10 the particle mass. If the width is larger, you don't have a chance to get a reasonable mass peak.

 

[vanhees71]

Both, "virtual particles" and "resonances" can, strictly speaking, occur only as internal lines in Feynman diagrams and thus are (strictly speaking) not easily interpretable as particles.

A resonance occurs usually in an s-channel scattering diagram, and is defined by a pole in the complex energy plane of the corresponding S-matrix element. If such a pole is not too far from the real axis, you see a sharp peak. The full-width-half-maximum width then gives approximately the "lifetime" of the resonance (a better estimate is the energy derivative of the scattering phase shift of the scattering process in question). For narrow resonances one has an approximate "particle interpretation", because it lives long enough as an excitation of the quantum field. E.g., pions decay only through the electroweak interaction and are thus long lived on a typical time scale for reactions in the strong interaction.

Hadron resonances are usually not that stable, because they decay through the strong interaction. E.g., the $\Delta(1232)$ resonance in the elastic pion-nucleon scattering has a mass of about $1232 \,\text{MeV}$ and a width of about $120 \, \text{MeV}$.