Physics quiz question: weak interaction coupling constant

Physics 205A Quiz 1, fall semester 2014
Cuesta College, San Luis Obispo, CA

Cf. Giambattista/Richardson/Richardson, Physics, 2/e, Problems 1.37, 1.39

The relation between the weak interaction coupling constant g_W and the Higgs boson mass m_W (measured in units of kg) is given [*] by the expression:

(1/sqrt(32))·(g_W/m_W)² = 1.86873×10^–15 s⁴/(kg²·m⁴).

The units for the weak interaction coupling constant g_W are:
(A) kg^–2·m·s.
(B) kg²·m^–2·s².
(C) m^–2·s².
(D) m²·s^–2.

[*] wki.pe/Fermi's_interaction.

Correct answer (highlight to unhide): (C)

Replacing the quantities in the equation with their kg, m and s units, except for the weak interaction coupling constant g_W, and also dropping all numerical values:

(g_W/kg)² = s⁴/(kg²·m⁴),

g_W/kg = s²/(kg·m²),

g_W = s²/m².

Sections 70854, 70855, 73320
Exam code: quiz01w34K
(A) : 9 students
(B) : 7 students
(C) : 54 students
(D) : 4 students

Success level: 73%
Discrimination index (Aubrecht & Aubrecht, 1983): 0.54