Clock shift in a strongly interacting two-dimensional Fermi gas

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We derive universal relations for the radio-frequency (rf) spectroscopy of a two-dimensional Fermi gas consisting of two spin states with a resonant S-wave interaction. The rf transition rate has a high-frequency tail that is proportional to the contact and displays logarithmic scaling violations, decreasing asymptotically like 1/(ω² ² ω). Its coefficient is proportional to ²(a₂D'/a₂D), where a₂D and a₂D' are the 2-dimensional scattering lengths associated with initial-state and final-state interactions. The clock shift is proportional to the contact and to (a₂D'/a₂D). If |(a₂D'/a₂D)| ≫ 1, the clock shift arises as a cancellation between much larger contributions proportional to ²(a₂D'/a₂D) from bound-bound and bound-free rf transitions.