Selection Rules for Elementary Particle Reactions

For each of the following hypothetical reactions, state weather the process can respect or not the conservation of the following: energy and spatial momentum, angular momentum, electric charge, baryon and lepton number, strangeness, isospin and isospin projection. Then explain whether the transition is a process which can happen through strong interactions, with degenerate $u$ and $d$ quark masses. If not, explain whether the reaction is possible through weak or electromagnetic interactions (specify which) or if the transition is impossible in the standard model.
1. Strong interactions are interactions in which meson π (0,+,-) appears, weak interactions are interactions in which neutrino appear ν (e,,μ), electromagnetic interactions are interactions in which photon γ appears.

2. For strong interactions there are possible only the disintegrations in which ΔS=0 or ΔS=±1 (very improbable). If |ΔS|>1 the disintegrations are forbidden.

3. For weak interactions there are possible just the disintegrations in which the lepton and barion number is the same before and after.
4. $u$ and $d$ quarks are found only in π (0,+,-) mesons.
5. In all types of disintegrations (strong, weak or em) energy before >= energy after for disintegration to be allowed.

The attached images to this document should be helpful in determining the energy, momentum (=total spin), charge, barion number (no. of barions-no. of antibarions), lepton number (no. of leptons – no. of antileptons) and strangeness.

$Ω^-→Ξ^0+π^-$

Strong.

Ei=1672 MeV, Ef=1192+139.6= 1331.6 MeV

Charge Qi= -1, Qf= -1

Momentum  s(i)=3/2 , sf=1/2 +(-)0 =1/2

Barion number Bi=0, Bf=0

Lepton Number  Li=0, Lf=0

Strangeness S(i)=-3, S(f)=-1   NOT POSSIBLE

$Λ^0→n ̅+γ$
Electromagnetic

Ei=1115.6 MeV, Ef=939.6+0   Possible
Charge Qi=0   , Qf =0
Momentum s(i)=1/2  ; s(f)=1/2+(-)1=3/2 or -1/2

Barion number Bi=0; Bf=1

Lepton number Li=0; Lf=0

Strangeness S(i)=-1   and S(f)=0

$Σ^0→π^++π^-$
Strong

Ei=1192 MeV; Ef=2*139.6 MeV

Charge Qi=0;  Qf=+1-1=0

Momentum  s(i)=1/2; s(f) =0+0=0

Barion Number Bi=0; Bf=0

Lepton Number; Li=0; Lf=0

Strangeness S(i)=-1   S(f)=0   POSSIBLE

$ρ^0→π^-+π^+$
Strong

Ei=775.5 Mev   Ef=2*139.6 MeV
Charge Qi=0  Qf=0

Momentum s(i)=1  s(f)=0

Barion number Bi=Bf=0

Lepton Number Li=Lf=0

Strangeness Si=0  Sf=0

$K^++p→K^++Σ^++K^0$

Special rule for Kaons K: they decay only through weak interactions.

References