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Unambiguously Testing Positivity at Lepton Colliders
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abstract
The diphoton channel at lepton colliders, $e^+e^- (\mu^+\mu^-) \to \gamma \gamma$, has a remarkable feature that the leading new physics contribution comes only from dimension-eight operators. This contribution is subject to a set of positivity bounds, derived from the fundamental principles of Quantum Field Theory, such as unitarity, locality, analyticity and Lorentz invariance. These positivity bounds are thus applicable to the most direct observable -- the diphoton cross section. This unique feature provides a clear, robust, and unambiguous test of these principles. We estimate the capability of various future lepton colliders in probing the dimension-eight operators and testing the positivity bounds in this channel. We show that positivity bounds can lift certain flat directions among the effective operators and significantly change the perspectives of a global analysis. We also discuss the positivity bounds of the $Z\gamma/ZZ$ processes which are related to the $\gamma\gamma$ ones, but are more complicated due to the massive $Z$ boson.
Forward citations
Cited by 6 Pith papers
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Positivity in the Renormalization of Effective Field Theory
A general theorem fixes the sign of one-loop renormalization of even-dimension EFT couplings induced by equal-even-dimension operator pairs, with applications to SMEFT dimension-eight running and new non-renormalizati...
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Geometry of effective field theory positivity cones
For three particle flavors, the positivity cone C_W has exactly three families of extremal rays, one of which yields genuinely new inelastic constraints not implied by elastic bounds.
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Matrix moment approach to positivity bounds and UV reconstruction from IR
Positivity bounds for multi-field EFTs are formulated as matrix moment problems, yielding optimal bounds and a method to reverse engineer the UV mass, spin, and coupling spectrum from low-energy coefficients.
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S-matrix bootstrap bounds on self-interacting dark matter
Weakly coupled scalar self-interacting dark matter cannot be heavier than ~0.3 GeV (generic) or ~MeV (derivative-coupled pNGB), much tighter than the 12 GeV unitarity bound.
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Positivity and partial wave unitarity bounds on ALP theories via amplitude methods
Complete partial-wave unitarity and positivity bounds are derived for ALP effective interactions up to dimension 8, with new SMEFT positivity constraints as a byproduct.
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Fingerprinting New Physics with Effective Field Theories
A thesis compiling published SMEFT global fits, automated UV-model constraints, and ML-based unbinned observables, with projections for HL-LHC, FCC-ee, and CEPC.
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