A meson ( ) decays semileptonically,

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

Symmetry and Flavour, Ch Heavy flavour: charm and beauty decays and the magnitudes of the CKM elements

Problem

B^+

meson (

m_{B^+} = 5.2793\,\mathrm{GeV}

) decays semileptonically,

B^+ \to X\ell^+\nu

. For

b \to c

the lightest hadronic system

X

is a

\bar D^0

(

m = 1.8648\,\mathrm{GeV}

); for

b \to u

it is a

\pi^0

(

m = 0.1350\,\mathrm{GeV}

). Treat the lepton as massless. ((a)) Find the largest lepton energy for each transition in the

B^+

rest frame. ((b)) The

B^+

mesons come from

\Upsilon(4S)

decays at

\sqrt s = 10.5794\,\mathrm{GeV}

, each

\Upsilon(4S)

giving a

B^+B^-

pair. Find the

B^+

momentum in the

e^+e^-

centre-of-mass frame, and the largest energy a lepton from

b \to c

can have in that frame. ((c)) Two leptons are measured in the centre-of-mass frame, with energies

2.40\,\mathrm{GeV}

and

2.55\,\mathrm{GeV}

. For each, say whether it must come from

b \to u

, and why.

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