Why Plot Spin vs Mass^2 in Particle Physics?

In summary, the conversation discusses the concept of regge trajectories in particle physics, specifically the correlation between spin and mass^2 within particle families. The speaker mentions that this is a natural thing to plot and suggests that it may have been discovered empirically rather than emerging from theory. The use of mass^2 in plotting is also discussed, with the conclusion that it is equivalent to using mass, but may be more natural for particle physicists.
  • #1
BiGyElLoWhAt
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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?
 
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  • #2
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
hmmm... ok.
 
  • #4
BiGyElLoWhAt said:
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?
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
You seem to make the argument to plot ##\ell \ \text{vs} \ m## as opposed to ##\ell\ \text{vs.} \ m^2##
 
  • #6
BiGyElLoWhAt said:
You seem to make the argument to plot ##\ell \ \text{vs} \ m## as opposed to ##\ell\ \text{vs.} \ m^2##
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.
 
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1. Why is the plot of Spin vs Mass^2 important in scientific research?

The plot of Spin vs Mass^2 is important because it helps us understand the fundamental properties of particles. The spin of a particle is a fundamental characteristic that determines how it interacts with other particles, while the mass^2 is related to the energy of the particle. By plotting these two variables against each other, we can gain insights into the underlying structure and behavior of particles.

2. How is the Spin vs Mass^2 plot used in particle physics?

The Spin vs Mass^2 plot is used in particle physics to classify and identify different types of particles. By comparing the location of a particle on the plot to known particles, researchers can determine its spin and mass^2 and thus determine its identity. This is especially useful in experiments where particles are produced and detected at high energies.

3. What can the Spin vs Mass^2 plot tell us about the Standard Model of particle physics?

The Spin vs Mass^2 plot is an important tool for testing the predictions of the Standard Model of particle physics. By comparing the location of particles on the plot to the predicted values from the Standard Model, scientists can determine if the model is accurate or if there are gaps or discrepancies that need to be addressed.

4. How does the Spin vs Mass^2 plot relate to the Higgs boson?

The Higgs boson is a fundamental particle predicted by the Standard Model that gives mass to other particles. The Spin vs Mass^2 plot is used to determine the spin and mass^2 of the Higgs boson, which is important in confirming its existence and properties. Additionally, the plot can also be used to study the interactions between the Higgs boson and other particles.

5. Are there any limitations to using the Spin vs Mass^2 plot in particle physics?

While the Spin vs Mass^2 plot is a useful tool in particle physics, it does have some limitations. For example, it may not accurately represent all particles, particularly those with more complex structures. Additionally, the plot is limited to only two variables and may not fully capture the complexities of particle interactions and behavior. Therefore, it is important for scientists to use multiple tools and approaches to fully understand and study particles.

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