Theta Warden

Theta Warden has one job: keep the scales perfectly level. Nobody ever told them why.

Quantum chromodynamics, the theory of the strong force, allows an extra term in its Lagrangian, the first equation on this page. It multiplies the gluon field strength G by its dual G̃, and its size is set by an angle θ̄. If θ̄ were not zero, the strong force would treat a process and its mirror-image, time-reversed version differently: it would violate CP symmetry. The physical angle is θ̄ = θ − arg det M_q, a combination of the bare vacuum angle and the phase of the quark masses (the sign convention varies between textbooks). Nothing in the Standard Model forces either piece to be small, so a value anywhere between 0 and 2π would look natural.

The neutron is the test. A non-zero θ̄ would give it an electric dipole moment of order d_n ~ 10⁻¹⁶ θ̄ e·cm; calculations of the coefficient differ by a factor of a few, so this is an order of magnitude. The PSI experiment (Abel et al., 2020) measured d_n = (0.0 ± 1.1 stat ± 0.2 sys)×10⁻²⁶ e·cm and set |d_n| < 1.8×10⁻²⁶ e·cm at 90% confidence. Worked number: 1.8×10⁻²⁶ / 10⁻¹⁶ ≈ 2×10⁻¹⁰, so |θ̄| ≲ 10⁻¹⁰. A dial that could point anywhere sits within a ten-billionth of zero.

That is the strong CP problem, and it is unsolved. In 1977 Roberto Peccei and Helen Quinn proposed a new symmetry that turns θ̄ into a field which relaxes to zero on its own, like a ball rolling to the bottom of the potential V(θ̄) ∝ 1 − cos θ̄ drawn on the back. Steven Weinberg and Frank Wilczek pointed out in 1978 that this predicts a new particle, the axion. Axions are searched for in many experiments and are also a dark matter candidate, but none has been found. The scales stay level, and the reason is still unknown.

Theta Warden: "I could tip either way. The universe checks to ten decimal places, and I never do. Ask me why and I will only point at the dial."