=== Model: grok-4.6-direct | Task: bench:gpqa_diamond | Rep: 1 ===
=== Score: 5/5 | Wall: 20.345s | Cost: $0.011228 ===
=== Pass: True | Finish: stop | In-reasoning-only: False ===

--- JUDGE ---
gpqa_diamond

--- RESPONSE ---
The pion is at rest, so the decay \(\pi^+ \to \mu^+ + \nu\) is a two-body process that conserves both energy and momentum in the pion rest frame. The neutrino is taken to be massless. The total energies of the two daughters are therefore
\[
E_\mu=\frac{M^2+m^2}{2M},\qquad E_\nu=\frac{M^2-m^2}{2M},
\]
where \(M=139.6\,\mathrm{MeV}\) and \(m=105.7\,\mathrm{MeV}\). Substituting the numerical values yields
\[
E_\mu=109.82\,\mathrm{MeV},\qquad E_\nu=29.78\,\mathrm{MeV}.
\]
The corresponding kinetic energies are
\[
K_\mu=E_\mu-m=4.12\,\mathrm{MeV},\qquad K_\nu=E_\nu=29.8\,\mathrm{MeV}.
\]
These match option D.

The answer is (D)