Unambiguously Testing Positivity at Lepton Colliders

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.

9 pages, 2+4 figures, v2: extended discussion on positivity bounds, matches published version

References in corpus (15)

• Measurement of the Positive Muon Anomalous Magnetic Moment to 0.46 ppm
• Causality, Analyticity and an IR Obstruction to UV Completion
• Helicity Selection Rules and Non-Interference for BSM Amplitudes
• Electroweak Couplings of the Higgs Boson at a Multi-TeV Muon Collider
• Symmetries, Sum Rules and Constraints on Effective Field Theories
• Novel measurements of anomalous triple gauge couplings for the LHC
• Muon Colliders
• Elastic positivity vs extremal positivity bounds in SMEFT: a case study in transversal electroweak gauge-boson scatterings
• Flavor Universal Resonances and Warped Gravity
• Positivity in electron-positron scattering: testing the axiomatic quantum field theory principles and probing the existence of UV states
• Signs, Spin, SMEFT: Sum Rules at Dimension Six
• Towards an Advanced Linear International Collider
• The CLIC potential for new physics
• Implications of the 750 GeV gamma-gamma Resonance as a Case Study for the International Linear Collider
• Positivity vs. Lorentz-violation: an explicit example

Cited by in corpus (17)

• SMEFTs living on the edge: determining the UV theories from positivity and extremality
• Moments for positivity: using Drell-Yan data to test positivity bounds and reverse-engineer new physics
• Constraints on anomalous dimensions from the positivity of the S-matrix
• Computing Tools for Effective Field Theories
• Spinning Sum Rules for the Dimension-Six SMEFT
• UV physics from IR features: new prospects from top flavor violation
• Renormalisation of SMEFT bosonic interactions up to dimension eight by LNV operators
• Dimension-8 SMEFT Matching Conditions for the Low-Energy Effective Field Theory
• Origin of Neutrino Masses on the Convex Cone of Positivity Bounds
• Positivity Bounds on parity-violating scalar-tensor EFTs
• Positivity Bounds in Scalar Effective Field Theories at One-loop Level
• EW corrections and Heavy Boson Radiation at a high-energy muon collider
• Positivity bounds at one-loop level: the Higgs sector
• Causality constraints on nonlinear supersymmetry
• Search for Neutral Triple Gauge Couplings with $ZZ$ Production at Future Electron Positron Colliders
• Positivity bounds in scalar-QED EFT at one-loop level
• Positivity and partial wave unitarity bounds on ALP theories via amplitude methods