(a) The cross-section Ï(udÌ W + ) near the mass of the W + is given by...

(a) The cross-section σ(udÌ… †’ W⁺) near the mass of the W⁺is given by a Breit€“Wigner formula (3.34b). For σ(udÌ… †’ W⁺) this may be written as

where (M,Γ) are the mass and total width of the W⁺, ΓudÌ… is the partial width for W⁺ †’ udÌ… and E is the total centre-of-mass energy of the udÌ… pair. Find σ_max, the maximum value of σ, in practical units, given that the branching ratio for W⁺ †’ udÌ… is 1/3.

(b) Find an expression for the cross-section σ(ppÌ… †’ W⁺ + · · ·) via the mechanism of Figure 4.19 in terms of the quark distributions in the proton, assuming that the p¯p total centre-of-mass energy ˆšs is sufficiently small for the contributions of sea quarks to be neglected. Use the narrow width approximation (cf. Equation (B.47b) of Appendix B), which can be rewritten in the form

where δ is the Dirac delta function, to find an expression for the cross-section σ(ppÌ… †’ W⁺ + · · ·) in terms of σ_max, the ppÌ… total centre-of- mass energy squared s, and a single integral over the quark distribution functions of the proton.

Figure 4.19

Transcribed Image Text:

12тГ Гиd M?/4(Е — М)? + Г?] Oud пГ E? Oud(E) M - Omax8 (1 – M²