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 Incoming links: Effective hadronic vertex

Past exam of the particle and nuclear physics course of the University of Cambridge / 2016 / Paper 1 / 3 / a 2026-10-20

The original Feynman diagrams below distinguish elementary weak and electromagnetic vertices from an effective hadronic vertex. fermion arrows track fermion number; time runs left to right.

Figure 1.
Four decay channels and their dominant interactions
. Original diagrams. Panel (iii) is an effective strong hadronic vertex; panel (iv) brackets the quark pair forming the pion. Details.

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Past exam of the particle and nuclear physics course of the University of Cambridge / 2016 / Paper 1 / 3 / a / iii / Solution 2026-10-20

The dominant interaction is strong. At hadron level, panel (iii) is an effective hadronic vertex for

Δ p π

. The initial

uuu

constituents rearrange into

uu d

and

u \overset{ˉ}{d}

after creation of a

d \overset{ˉ}{d}

uuu ⟶ (uu d) + (u \overset{ˉ}{d}) .

One original up quark enters the charged pion; the other two join the new down quark in the proton. Gluon-induced pair creation supplies the quark-flow diagram interpretation. This is nonperturbative hadronization: the effective hadronic vertex does not claim that one elementary perturbative quark graph calculates its width. Charge, baryon number and net quark flavor are conserved.

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