Question

Which one of the following decays CAN occur? Explain why decay is possible or not. Draw the Feynman diagram for possible decays. a) π+ → μ+ + vμ b) p + n → p + p + c) K+ → π0 d) μ- → e- + ve + vμ e) K+ → 2π0 f) π0 → 2γ g) π+ + p → K+ + Σ+ h) π- + p → n + γ i) Σ- → π- + p

Answer 1

a)

(i) Charge conservation(ΔQ): Charge Conserved

(ii) Lepton Number(ΔL): ΔL conserved

(iii) Baryon Number(ΔB): ΔB Conserved

(iv) Strangeness (ΔS) :ΔS conserved

(v) Isospin(ΔI)

(vi) 3rd Comp. of Isospin(I₃):

It is a allowed decay. From relation (v) and (vi), we see that it is a semi-leptonic decay.

b)

(i)ΔQ: is not conserved

Hence the reaction is forbidden.

c)

(i)ΔQ: ΔQ is not conserved

Hence this decay is forbidden

(d)

(i)ΔQ:ΔQ is conserved

(ii)ΔL:ΔL is not conserved

Hence this decay is forbidden

(e)

(i)ΔQ: ΔQ is not conserved

Hence this decay is forbidden

(f)

(i) ΔQ: ΔQ is conserved

(ii)ΔL:ΔL is conserved

(iii)ΔB:ΔB is conserved

(iv)ΔS:ΔS is conserved

(v)ΔI:

(vi)ΔI₃:

This is a allowed decay.From (v) and (vi), we see that it is an EM Decay.

(g)

(i)ΔQ: ΔQ is conserved

(ii) ΔL: ΔL is conserved

(iii)ΔB: ΔB is conserved

(iv)ΔS: ΔS is conserved

(v)ΔI:

ΔI is conserved

(vi)ΔI₃: ΔI₃ is conserved

Hence this deacy is allowed.

(h)

(i)ΔQ: ΔQ is conserved

(ii)ΔL:ΔL conserved

(iii)ΔB: ΔB is conserved

(iv)ΔS: ΔS is conserved

(v)ΔI:

(vi)ΔI₃ :

This is a allowed decay. It's an EMI decay

(i)

(i) ΔQ: is not conserved

Hence this deacy is forbidden.

(a)

(b)