Two quarks scatter off each other

PHYSICS · Multi-part · Fermi University Physics · Particle Physics & Quantum Fields · Interacting fields, Feynman diagrams and QED · Interacting fields, Feynman diagrams and QED

Particle Physics, Ch Exchange, range and coupling: diagrams as bookkeeping

Problem

Two quarks scatter off each other, once by exchanging a photon and once by exchanging a

W

boson, at the same momentum transfer

\Delta p = 50\,\mathrm{MeV}/c

. Take the

W

mass as

M_W = 80.37\,\mathrm{GeV}/c^2

, the weak coupling as

\alpha_{\rm W} \approx 1/30

and the electromagnetic coupling as

\alpha \approx 1/137

, so that

(\alpha_{\rm W}/\alpha)^2 \approx 21

. ((a)) Estimate the factor by which the amplitude for

W

exchange is suppressed relative to photon exchange, from the mass of the exchanged quantum alone. ((b)) Hence estimate the factor by which the

W

-exchange rate is suppressed relative to the photon-exchange rate, for two quarks with the same couplings. ((c)) Now include the actual coupling ratio

(\alpha_{\rm W}/\alpha)^2 \approx 21

and give an order-of-magnitude estimate for how much rarer virtual

W

exchange is than virtual photon exchange between two quarks at this momentum transfer.

Browse the problem library