Use the method of dimensions to show that

if W-exchange is approximated by a zero-range interaction and the masses of all final-state particles are neglected. If quark mass corrections are taken into account, this result is modified to

Where

f(x) = 1 ˆ’ 8x² ˆ’ 24x⁴ ln(x) + 8x⁶ ˆ’ x⁸.

Use this, together with the constituent quark masses of Table 3.1 and the experimental result

Γ(b †’ c + e^ˆ’ + ν̅_e) + Γ(b †’ u + e^ˆ’ + vÌ…_e) = (6.6 ± 0.3) × 10¹⁰ s ^ˆ’1,

deduced from the decay B^ˆ’ †’ e^ˆ’ + ν̅_e + hadrons, to obtain upper bounds on the magnitudes of V_ub and V_cb.

Transcribed Image Text:

Г(6 — 9 +е + De) Г(т — v, +е +De) тi (9 %3D и, с), = [Vgb[? тg Г(Ь — q+е + De) T(T - v, +e- +De) mi f(m,/m), тs = |Vqbl?