A kaon beam is produced as pure at with momentum

PHYSICS · Multi-part · Fermi University Physics · Quantum Mechanics · Particle Physics & Quantum Fields · Quantum dynamics and its formulations

Symmetry and Flavour, Ch Neutral kaons: mixing, strangeness oscillation and CP violation

Problem

A kaon beam is produced as pure

K^0

t=0

with momentum

p=3.50\,\mathrm{GeV}/c

. Take

m_K=497.6\,\mathrm{MeV}/c^2

\tau_S=0.8954\times10^{-10}\,\mathrm{s}

(

c\tau_S=2.68\,\mathrm{cm}

\tau_L=5.116\times10^{-8}\,\mathrm{s}

, and

\Delta m_K\tau_S=0.474

. ((a)) Find the first proper time

t^*\gt0

, in units of

\tau_S

, at which a kaon born as

K^0

is equally likely to be found as

K^0

or as

\bar K^0

, excluding the equality that holds once the

K_S

component has essentially all decayed away, which is not an oscillatory crossing. ((b)) Convert

t^*

to a laboratory distance for this beam and give the common value of

P(K^0\to K^0;t^*)=P(K^0\to\bar K^0;t^*)

. ((c)) A thin slab of matter is placed at this distance. State, with a one-sentence reason, whether the slab adds a coherent

K_S

amplitude to the

K_S

amplitude still present in the beam, and whether the effect responsible is a strong- or a weak-interaction one.