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One of the main goals of the BaBar experiment is to study particles that we call B mesons. To make these particles, electrons and positrons (the electron's anti-matter partner, with the opposite electric charge) are accelerated to speeds close to the speed of light and collided into each other. The result is often the creation of a pair of B mesons (or more precisely, a B and a B-bar, its anti-particle). We produce about half a million such pairs per day.
These B mesons quickly decay into other particles. Therefore, we have to learn about them indirectly by studying these other particles. The B particles are created with a very small momentum. The initial energy available in the collision is 10.58 GeV. Energy is conserved, and after the collision each B has 5.29 GeV of energy. (Click here to learn more about a GeV and other units used by particle physicists.)
The picture below shows a computerized representation of the particles coming from the decay of a pair of B particles. The small circles and green bars represent the raw data from our detection systems, and the solid curves show the particle paths as deduced from the data. The measured energy and momentum of each of the detected particles is listed in the table below the figure. Click on the figure for a higher-resolution version.
| Track | p = (px, py, pz) | E |
|---|---|---|
| A | (-0.9, -0.2, -1.0) GeV/c | 1.4 GeV |
| B | (-1.1, -0.3, -0.6) GeV/c | 1.3 GeV |
| C | ( 1.2, 0.2, 0.8) GeV/c | 1.5 GeV |
| D | ( 0.9, 0.0, 0.5) GeV/c | 1.1 GeV |
| E | ( 0.9, 0.5, 0.0) GeV/c | 1.2 GeV |
| F | ( 0.1, -0.5, 0.0) GeV/c | 0.5 GeV |
| G | (-0.2, -0.3, -0.1) GeV/c | 0.4 GeV |
| H | ( 0.1, -1.1, 0.6) GeV/c | 1.3 GeV |
If we look closely, we see that when we add up the momentum vectors for tracks A and B on the left and C and D on the right, we get:
pnet = pA + pB + pC + pD
= (-0.9,-0.2,-1.0) + (-1.1,-0.3,-0.6) + (1.2,0.2,0.8) + (0.9,0.0,0.5)
= (0.1,-0.3,-0.3) GeV/c.
This net momentum is close to (0,0,0). The sum of the energies for these four tracks is
Etotal = 1.4 + 1.3 + 1.5 + 1.1 = 5.3 GeV.Because these tracks have almost no net momentum and exactly the right energy, it is very likely that they came from a decay of one of the B particles.
What about the other particles in the picture? Because B particles are always created in pairs, tracks E, F, G, and H must have come from the other B. Find the net momentum and total energy. Do you get the answer you expect? If not, why? [Solution]