Standard Model and Beyond · Problem 2.32

Lie Groups, Lie Algebras, and Symmetries

Physics — Particle Physics · proton-form-factors-breit-frame

Problem

Consider the proton matrix element uˉ(p⃗2)ΓQμ(q)u(p⃗1)\bar{u}(\vec{p}_2)\Gamma^\mu_Q(q)u(\vec{p}_1) of the electromagnetic current in (2.393), with ΓQμ\Gamma^\mu_Q given by (2.397). Calculate this explicitly in the Breit frame, in which q0=0q^0 = 0, i.e., q=(0,0,0,Q2),p1=(E,0,0,−Q2/2),p2=(E,0,0,+Q2/2).q = (0,0,0,\sqrt{Q^2}), \qquad p_1 = (E,0,0,-\sqrt{Q^2}/2), \qquad p_2 = (E,0,0,+\sqrt{Q^2}/2). Express the time and space components in terms of the electric and magnetic form factors defined in (2.398) and interpret the results.

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