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, also decays toe−νeνμ. Look up theτlifetime on pdglive and use it andprevious parts to estimate theτmass. Which ofmW, g, mμtheμ-lifetime, or the2π′sdoes your prediction depend on?f) Look up the branching ratioτ→e−νeνμ, listed on pdglive as Fraction(ΓiΓ). This is thefraction of timeτdecays this way. Can you use this to refine your answer for parte?g) How can you measuregandMWseparately using very precise measurements of theμandτdecay distributions? What precision would you need (in %)?2. Breit-Wigner distrubition. Let’s see what happens ifiǫin the propogator is not small.a) What would the cross section be fors-channel scattering if the intermediate propogatorwereip2−m2+imΓ, whereΓ>0?b) Sketch the cross section as a function ofx=sm2forΓmsmall and forΓmlarge.c) * Now assumeΓis small and Taylor expand the matrix element as a series in(iΓ)n.d) * What kinds of degenerate-looking Feynman diagrams would generate this series?3. Calculate the classical propogator for a massive spin 1 particle by inverting the equations ofmotion to the formVμ= ΠμνJν.4. Vector polarization sums. Calculate the