Beams of and mesons of the same intensity are fired

PHYSICS · Multi-part · Fermi University Physics · Particle Physics & Quantum Fields · Symmetry, groups and the quark model · Symmetry, groups and the quark model

Particle Physics, Ch Isospin: a symmetry used as bookkeeping

Problem

Beams of π+\pi^+ and π−\pi^- mesons of the same intensity are fired, in turn, at a liquid-deuterium target, and the elastically scattered pions are counted: π+d→π+d,π−d→π−d.\pi^+d \to \pi^+d, \qquad \pi^-d \to \pi^-d. The deuteron dd has isospin I=0I=0; the pion has I=1I=1. ((a)) Find the total isospin of the pion-deuteron system for each pion charge. Using the fact that the strong interaction depends only on total isospin II, never on I3I_3, predict the ratio of the two elastic rates, π+d→π+d:π−d→π−d\pi^+d\to\pi^+d : \pi^-d\to\pi^-d. ((b)) In the exposure, 505505 elastic π+d\pi^+d events and 480480 elastic π−d\pi^-d events are recorded under identical conditions. Compute the measured ratio and compare it with the prediction.

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