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I have seen many plots and data tables which display the cross-section vs. center of mass energy for a particular nuclear reaction at a given angle. Here is an example.

csx

You can see that there are a few 'humps', which are the resonances. Now I can [somewhat] see how one could obtain the excitation energy and partial width for a resonance, but how does one measure the spin-parity (J$^{\pi}$) of a resonance? I see in most of those plots and tables that the researchers have also obtained the respective spin-parities for their respective resonances, but I have no idea how one could arrive at that.

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  • $\begingroup$ You can't and don't get it from only the data plotted here. No time to write a full answer now. $\endgroup$
    – dmckee --- ex-moderator kitten
    Feb 2, 2015 at 17:56
  • $\begingroup$ Oh I see. That's good to hear. Please get back to this when you can (I'll be very happy). $\endgroup$
    – Arturo don Juan
    Feb 2, 2015 at 20:40

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Such information can be inferred from the differential cross section.

Different spins and parities lead to different angular distributions of decay products / scattering partners. You find these correlations by using one decay product to define an axis and measuring the distribution of the other decay products with respect to that.

This requires a lot more data than just finding the resonance, though. You need to have enough observations in a suitable channel, in order to have relevant statistics when you only include decays with a specific angular distribution. That's why it was very quickly clear that the LHC found a new resonance, but took a while to ensure it's a CP-even spin 0 state that has been observed.

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  • $\begingroup$ Ah I see. Do you know of any links where I can read more about methods of obtaining the $J^{\pi}$ of resonances? $\endgroup$
    – Arturo don Juan
    Mar 2, 2015 at 14:50
  • $\begingroup$ @ArturoDonJuan I don't know of any pedagogical literature about this topic in particular. I am sure there are a lot of lecture notes out there covering experimental particle physics methods - you might want to look for lecture notes (especially from summer schools, those usually are quite neat and concise) at inspirehep.net $\endgroup$
    – Neuneck
    Mar 4, 2015 at 8:30

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