A beam of high-energy π− (negative pions) is shot at a flask of liquid hydrogen, and sometimes a pion interacts through the
strong interaction with a proton in the hydrogen, in the reaction π− + p+ → π− + X+, where X+ is a positively charged
particle of unknown mass.
The incoming pion momentum is 3 GeV/c (1GeV = 1000 MeV = 1 × 109 electron-volts). The pion is scattered through 40°,
and its momentum is measured to be 1510 MeV/c (this is done by observing the radius of curvature of its circular trajectory
in a magnetic field). A pion has a rest energy of 140 MeV, and a proton has a rest energy of 938 MeV.
What is the rest mass of the unknown X+ particle, in MeV/c2? Explain your work carefully.
It is advantageous to write the equations not in terms of v but rather in terms of E and p; remember that E2 − (pc)2 =
(mc2)
2.