Problems are listed in approximate order of difficulty. A single dot (•) indicates straightforward problems involving just one main concept and sometimes requiring no more than substitution of numbers in the appropriate formula. Two dots (••) identify problems that are slightly more challenging and usually involve more than one concept. Three dots (•••) indicate problems that are distinctly more challenging, either because they are intrinsically difficult or involve lengthy calculations. Needless to say, these distinctions are hard to draw and are only approximate.
••• The π° decays electromagnetically with τ(π°) = 8.7 × 10−17 s, but the π+ decays only weakly with τ(π+) = 2.6 × 10−8 s. You can explain the large difference between these lifetimes in terms of the different ranges of the electromagnetic and weak interactions: First, recall that any meson is composed of two quarks. Next, note that, according to the electroweak theory, the intrinsic strengths of the electromagnetic and weak interactions are the same; this means that the probabilities for either kind of interaction are about the same, provided that two quarks are within the relevant range. Now the two quarks in a meson are always within the (infinite) range of the electromagnetic force; on the other hand, they are very seldom within the range of the weak force. Given that the two quarks move more or less randomly inside the volume of the meson (radius of order 1 fm) and that the range of the weak force is of order 10−3 fm, estimate what fraction of the time the two quarks are within the range required for weak interaction. Use these considerations to estimate the ratio τ(π°)/τ(π+), and show that your answer is of the same order as the observed ratio.
We need at least 10 more requests to produce the solution.
0 / 10 have requested this problem solution
The more requests, the faster the answer.