The W boson couples only to left-handed fermions and right-handed antifermions. This means W bosons produced in quark-antiquark annihilation at a hadron collider are longitudinally polarized at threshold but become increasingly longitudinally polarized at high energy. Why is the longitudinal polarization component particularly interesting?
ABecause longitudinal W bosons are easier to detect
BBecause the longitudinal polarization state comes from the Goldstone boson eaten by the W during electroweak symmetry breaking — it is directly connected to the Higgs mechanism, and its scattering amplitudes grow with energy, making it sensitive to the details of symmetry breaking
CBecause longitudinal W bosons have a larger cross section
DBecause transverse polarizations are forbidden at high energy
By the Goldstone boson equivalence theorem, at high energy the amplitude for longitudinal W scattering equals the amplitude for the corresponding Goldstone boson scattering. Without the Higgs boson, the WW scattering amplitude would grow as E^2 and violate unitarity at approximately 1.2 TeV. The Higgs boson cancels this growth, restoring unitarity. Measuring longitudinal WW scattering at the LHC (vector boson scattering) directly tests this cancellation mechanism.
Question 2 Short Answer
The Z boson decays to all kinematically accessible fermion-antifermion pairs. Its branching ratios are: hadrons ~70%, neutrinos ~20%, charged leptons ~10%. Why is the hadronic branching ratio so much larger than the leptonic one?
Think about your answer, then reveal below.
Model answer: The Z couples to all fermion pairs with strength proportional to their weak isospin and hypercharge quantum numbers. For each fermion, the partial width is proportional to (v_f^2 + a_f^2) * N_c, where v_f and a_f are the vector and axial-vector couplings and N_c is the color factor (3 for quarks, 1 for leptons). The Z can decay to 5 quark flavors (u, d, s, c, b -- not top, which is too heavy), each with N_c = 3, giving 15 'effective' quark channels versus 3 charged lepton channels and 3 neutrino channels. The large hadronic fraction is primarily a counting effect: more quark channels times the color factor of 3.
The precise branching ratios also depend on the electroweak couplings of each fermion. Up-type quarks have different v_f and a_f from down-type quarks, so the partial widths are not all equal. Measuring these ratios tests the electroweak coupling assignments of the Standard Model.
Question 3 Multiple Choice
At hadron colliders, W bosons are primarily produced by quark-antiquark annihilation: u dbar -> W+ and dbar u -> W+. The W+ and W- production cross sections are different at the LHC but equal at the Tevatron. Why?
ABecause the LHC uses different beam energies for each direction
BBecause the LHC is a pp collider (both beams are protons) while the Tevatron was ppbar — in pp collisions, the proton has more u quarks than d quarks (two u vs one d), so u dbar -> W+ is enhanced relative to d ubar -> W-, creating a charge asymmetry; at ppbar, the asymmetry from the proton is exactly compensated by the antiproton
CBecause the W+ is lighter than the W- at the LHC
DBecause QCD corrections are different for W+ and W-
The proton contains two valence u quarks and one valence d quark. At the LHC (pp), W+ production (mainly ud-bar) samples the u valence distribution while W- production (mainly du-bar) samples the d valence distribution. Since u(x) > d(x) at large x, sigma(W+) > sigma(W-) by about 30% at 13 TeV. This charge asymmetry, measured as a function of rapidity, directly constrains the ratio of u and d quark PDFs. At the Tevatron (ppbar), the antiproton provides the conjugate sea, and the charge asymmetry cancels in the total cross section.