In the CPLEAR experiment (Chapter 12)

PHYSICS · Multi-part · Fermi University Physics · Quantum Mechanics · Particle Physics & Quantum Fields · Flavour, neutrinos and CP violation

Symmetry and Flavour, Ch B mesons: mixing, time-dependent CP asymmetries and the unitarity triangle

Problem

In the CPLEAR experiment (Chapter 12), a neutral kaon is produced by proton-antiproton annihilation,

p\bar p \to K^+\pi^-\bar K^0

p\bar p \to K^-\pi^+K^0

; the charge of the accompanying charged kaon tells which neutral kaon (strangeness

+1

-1

) was produced, and this instant is

t=0

for that kaon. At the

\Upsilon(4S)

, the two neutral

B

mesons are produced together in the antisymmetric

L=1

state derived from angular-momentum and Bose-symmetry arguments. ((a)) State what physical process fixes the flavour of the CPLEAR kaon at

t=0

, and what physical process fixes the flavour of each

B

meson at the tagging instant

t_{\rm tag}

in the

\Upsilon(4S)

pair. ((b)) Explain why, unlike the CPLEAR kaon, neither

\Upsilon(4S)

B

meson can be assigned a definite flavour at the moment of production, and give the quantum-mechanical reason only one of the pair is

B^0

(and the other

\bar B^0

) at every instant before either decays. ((c)) At the

\Upsilon(4S)

the tagging instant is not seen directly; it is inferred from the separation of the two decay vertices along the beam. SuperKEKB collides

7.0\ \mathrm{GeV}

electrons head on with

4.0\ \mathrm{GeV}

positrons. Find the invariant mass

M

of the collision, the boost

\beta\gamma

of the

\Upsilon(4S)

and the mean vertex separation

\langle\Delta z\rangle

, taking

c\tau_{B^0}=455\ \mu\mathrm{m}

. Compare with the

193\ \mu\mathrm{m}

at KEKB and say what the smaller separation asks of the vertex detector.