Page 1 EP 228 Particle Physics, Lecture Notes on Conservation Laws, Oct 2020

Solved Problems Conservation Laws [1]. Consider a neutrino originating from the decay 휋 → 휇 + 푣. What is the type of the neutrino if pion All particle reactions and decays obey certain conservation laws: is positively charged?  Conservation of total energy  Conservation of linear momentum  Conservation of angular momentum (spin) [2]. Determine the unknown particles denoted by X or Y in the following reactions: − − −  Conservation of invariant mass (for all inertial coordinates) 푋 + 푝 → 푝 + 푝 + 푝 + 푝̅ 푛 → 푝 + 푒 + 푋 휇 → 푒 + 푋 + 푌  Conservation of charge  Conservation of lepton number  Conservation of baryon number

 Conservation of Strangeness (there is an exception for weak interactions)

For any decay: 푋 → 푌 + 푍 mX > mY + mZ (mass is not conserved) For any collision: 1 + 2 → 3 + 4, may be m + m ≠ m + m (mass is not conserved) 1 2 3 4 푋 + 푝 → 휇+ + 푛 휋+ + 푝 → 퐾+ + 푋 Λ0→ π-+X

Quantum numbers

Some quantum numbers are assigned to fundamental particles

Conservation of lepton number Conservation of baryon number Conservation of Strangeness

B = +1 for all baryons Strangeness (S) is conserved Le = +1 for e- and 푣푒 B = -1 for all anti-baryons in strong and electromagnetic Le = -1 for e+ and 푣̅푒 [3]. Explain why the following reactions are forbidden? Le = 0 for all other particles B = 0 for all other particles interactions but it may not be    conserved in weak   e      p  e  n L = +1 for μ- and 푣 interactions. μ μ L = -1 for μ + and 푣̅̅̅ μ μ L = 0 for all other particles ΔS = 0 for strong interactions μ ΔS = 0 for em interactions ΔS = 0 or 1 for weak inter. Lτ = +1 for τ- and 푣τ L = -1 for τ+ and 푣̅ τ τ Lτ = 0 for all other particles

 [4]. Which of the following weak decays is not possible for the  ? Note that   0  0   0   There is no conservation law for mesons         K       There is no conservation law for photons

Page 2 EP 228 Particle Physics, Lecture Notes on Conservation Laws, Oct 2020

[5]. A neutral particle X0 decays as X 0  p   . The measured momentum components [6]. An unknown particle X decays as follows: X     . Space momentum components of the decay products in GeV/c are given in the table. Determine particle X. of the photons in GeV/c are measured as p1 = (-0.01, 0.04, 0.17) and p2 = (-0.31, 0.91,-0.13). Calculate invariant mass of two photons and estimate the particle X.

Hint: Consider the natural units (c = 1) and use the following invariant mass formula:

2 2 mX  (E1  E2 )  (p1  p2 )