Solution

ID: past-exam-of-the-gauge-field-theory-course-of-the-university-of-cambridge/2016/paper-1/2/c/solution

The evidence tests several linked claims: a weak neutral current, massive charged and neutral mediators, their chiral couplings, and the non-Abelian interactions among those mediators. A theory must describe these with a common set of electroweak parameters.
The Gargamelle neutral-current experiment supplied a particularly direct early test. A neutrino beam crossed a heavy-liquid bubble chamber; charged reaction products made visible tracks, while incoming and outgoing neutrinos did not. Neutral-current candidates had a hadronic vertex without an accompanying charged lepton, or an isolated recoiling electron. The visible final state differs from a muon-neutrino charged-current event with an outgoing muon. Neutral hadrons entering from surrounding material could imitate a hadronic vertex, so background rejection was essential. The 1973 observations supported an interaction carried by a neutral weak mediator; they did not directly reconstruct an on-shell Z resonance.[ref]
The UA1 experiment and UA2 experiment collider discoveries supplied complementary evidence in 1983. A proton–antiproton collider provided enough energy to produce the mediators. Charged W candidates used a high-transverse-momentum charged lepton and missing transverse momentum from an escaping neutrino; because its longitudinal momentum was not measured, a transverse-mass distribution was useful. Neutral Z candidates instead formed a charged-lepton pair with an invariant-mass peak. Observing both kinds of events and their masses tested the predicted mediator structure.[ref]
The Weinberg angle connects independent measurements. At tree level, a Higgs doublet gives
so . Neutral-current scattering, the mediator masses and electromagnetic measurements must be consistent with one mixing angle after a common renormalization prescription and radiative corrections are included. Precise Z-resonance widths and asymmetries test the left- and right-chiral couplings; a mass peak alone would not establish those coupling assignments.
At higher collider energies, W-pair production tested the electroweak triple gauge couplings. Reconstructing hadronic jets or a charged lepton plus missing momentum identifies W decays; total rates and production/decay angles constrain the and vertices. Their non-Abelian relations are required for the characteristic interference with neutrino exchange. L3's 2004 analysis used these channels and found agreement with the Standard Model expectation.[ref]
Finally, the 2012 Higgs boson discovery and subsequent coupling tests address the symmetry-breaking sector, beyond the existence of gauge mediators. The initial observation was a new resonance in several decay channels; establishing all its properties requires further measurements. These are mutually supporting tests of the electroweak interaction, with distinct apparatus, observables and background controls, rather than a claim that any single event proves the entire theory.

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