How Do You Calculate Invariant Mass in Particle Physics?

[v0id19]

Homework Statement

so I'm doing some proof-of-concept data analysis this summer and I've never taken a relativistic mechanics class and I'm a bit stuck. i need to figure out if there was a rho⁰ decay to pi⁺/pi^- in some hypothetical 900GeV collision data. If there is, there should be a spike on the histogram i make right around its invariant mass (all the technical stuff and programmy bits i know I've done right).
the information i have:
- momentum of particles
- charge of particles

Homework Equations

M_inv² = E² - p²

The Attempt at a Solution

i was told to calculate the energy sqrt(m² + p²) for all particles assuming they had the mass of a pion.
then i calculated the invariant mass: M²=(E_pi+ + E_pi-)² - (p_pi+ + p_pi-)²
i should get a spike in my histogram at the mass of the rho (about 770 MeV). But i get the spike roughly from 1500-3500MeV.
it seems when looking at my formulas there is some circular derivation going on, but I'm not sure.

if anyone could give me some advice that would be great

 

[vela]

One of the basic problems with particle physics is you can detect a particle, but you have no idea what particle it actually is. The momenta you have could be from a pion, or it could be some other charged particle.

So you start by assuming that there is a decay $\rho^0\to\pi^+\pi^-$. The momenta you have should therefore be the pions', so you can calculate their energies and ultimately the invariant mass of the $\rho^0$. The fact that you don't see a spike at the mass of the $\rho^0$ suggests your assumption is wrong, that you are not, in fact, seeing that decay.

You should check out Griffith's Introduction to Elementary Particles. There's an excellent chapter on special relativity, and it's a great book from which to learn the basics of particle physics.