5. A particle decays into K Tn with the following values measured for the moment

Question

5. A particle decays into K Tn with the following values measured for the momentum of the pion and the kaon (in the lab frame): px(n) = 2710 MeV/c, py(n) =-360 MeV/c, pz(T) = 0 MeV/c px(K) = 80 MeVic, py(K) = 360 MeV/c, pz(K) = 0 MeV/c (For convenience, we have oriented the coordinate axes so that the decay momenta lie in the x-y plane, and the total momentum lies along the x-axis) Find (a) the invariant mass of the parent particle (b) the momentum, energy, beta, and gamma of the parent particle in the lab frame (c) the energy and momentum of the kaon in the parent particle rest frame (d) the decay angle of the kaon in the parent particle rest frame (with respect to the direction of the parent momentum) Hint: components transverse to the boost direction are invariant. Try to calculate all these quantities without doing any explicit Lorentz transformations.

Explanation / Answer

(a) From the conservation of mass, total invariant mass of the parent particle = p/c=(2710+360+360+80)MeV/c2

(b)The momentum of parent particle =(2710+80)MeV/c

    The energy of the parent particle=p.c=(2710+80+360+360)MeV

    The beta particle can be estimated from the initial and final charge of parent nucleus and the gamma can be estimated from the difference of energy of the parent partcle before and after the emission.

(c) Same as lab frame

(d)At 180o

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