# I Why plot l vs m^2?

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1. Feb 8, 2017

### BiGyElLoWhAt

Maybe this is more quantum, but I'm not sure.

I was watching Susskinds first String lecture on youtube, and he was talking about how, within each particle family, you get a straight line called a regge trajectory if you plot spin vs. mass^2.

He also mentioned that there was some slight insight as to how it came about, but also hinted that it might have been dumb luck at the time.

I'm not even sure what to google, I've looked up regge trajectories, pion-pion scattering, even plot spin vs mass squared, and am not turning anything up.

Does anyone have any insight as to why this would be a reasonable thing to plot?

2. Feb 8, 2017

### ChrisVer

It's not a reasonable thing to draw... it was something that was probably found empirically and before QCD... afterall, it's not emerging from theory (or at least we don't know how it does).

3. Feb 8, 2017

### BiGyElLoWhAt

hmmm... ok.

4. Feb 17, 2017

### nrqed

I find that it is a natural thing to plot. If you think of an elementary particle, it is described by two parameters: the spin and the mass. If some set of observables are described by two parameters, an obvious thing to do is to check if these are independent or are correlated. A priori, the theory did not suggest that they should have any connection but it is an obvious thing to check to see if theory is incomplete. That seems natural to me, but maybe I am in the minority.

5. Feb 18, 2017

### BiGyElLoWhAt

You seem to make the argument to plot $\ell \ \text{vs} \ m$ as opposed to $\ell\ \text{vs.} \ m^2$

6. Feb 18, 2017

### nrqed

It is totally equivalent. If you plot l vs m and you get a very nice fit to a quadratic, then you get the same information as plotting l vs m^2 and getting a nice fit to a straight line. If one finds straight lines nicer, then after discovering that l vs m gives a quadratic, one would go to l vs m^2 to get a straight line (a straight line is of course easier to visually understand, it is hard to tell without a computer if a curve is quadratic or something else, it is easier to spot a straight line, which is why people like to use variables that will lead to straight lines but from the point of view of fitting using a computer, it makes no difference to use one over the other).

However, for a particle physicist, it is also more natural to use m^2 because it is equal to P^2, so a theorist would probably plot l vs m^2 first, just out of habit.

Last edited: Feb 18, 2017