A Note on the Analytic Structure of Celestial Amplitudes

Abstract

Celestial amplitudes, obtained by applying Mellin transform and analytic continuation on "ordinary" amplitudes, have interesting properties which may provide useful insights on the underlying theory. Their analytic structures are thus of great interest and need to be better understood. In this paper, we critically examine the analytic structure of celestial amplitudes in a massless low-energy effective field theory. We find that, fixed-order loop contributions, which generate multipoles on the negative $\beta$-plane, in general do not provide an accurate description of the analytic structure of celestial amplitudes. By resumming over the leading logarithmic contributions using renormalization group equations (RGEs), we observe much richer analytic structures, which generally contain branch cuts. It is also possible to generate multipoles or shifted single poles if the RGEs satisfy certain relations. Including sub-leading logarithmic contributions is expected to introduce additional corrections to the picture. However, without a new approach, it is difficult to make a general statement since the analytic form of the Mellin transform is challenging to obtain.

arXiv comment21 pages, 1 figure

References in corpus (40)

• Dimension-Six Terms in the Standard Model Lagrangian
• Causality, Analyticity and an IR Obstruction to UV Completion
• Symmetries and Strings in Field Theory and Gravity
• Renormalization Group Evolution of the Standard Model Dimension Six Operators III: Gauge Coupling Dependence and Phenomenology
• Renormalization Group Evolution of the Standard Model Dimension Six Operators II: Yukawa Dependence
• Renormalization Group Evolution of the Standard Model Dimension Six Operators I: Formalism and lambda Dependence
• Flat Space Amplitudes and Conformal Symmetry of the Celestial Sphere
• A Conformal Basis for Flat Space Amplitudes
• A holographic reduction of Minkowski space-time
• The EFT-Hedron
• Lectures on Celestial Amplitudes
• Gluon Amplitudes as 2d Conformal Correlators
• Holographic Symmetry Algebras for Gauge Theory and Gravity
• Low's Subleading Soft Theorem as a Symmetry of QED
• 4D Scattering Amplitudes and Asymptotic Symmetries from 2D CFT
• Three-loop β-functions for top-Yukawa and the Higgs self-interaction in the Standard Model
• New positivity bounds from full crossing symmetry
• Positivity Bounds for Scalar Theories
• Extremal Effective Field Theories
• Conformally Soft Photons and Gravitons
• Conformally Soft Theorem in Gauge Theory
• Celestial amplitudes and conformal soft theorems
• Non-renormalization Theorems without Supersymmetry
• Celestial Amplitudes from UV to IR
• Celestial Amplitudes: Conformal Partial Waves and Soft Limits
• Effective Field Theory Amplitudes the On-Shell Way: Scalar and Vector Couplings to Gluons
• S-matrix Bootstrap for Effective Field Theories: Massless Pions
• Structure of two-loop SMEFT anomalous dimensions via on-shell methods
• Loops and trees in generic EFTs
• Standard Model Effective Field Theory from On-shell Amplitudes
• Milli-Charged Dark Matter in Quantum Gravity and String Theory
• The Rise of SMEFT On-shell Amplitudes
• Non-renormalization and operator mixing via on-shell methods
• Constructing massive on-shell contact terms
• Lectures on Celestial Holography
• Minicharges and Magnetic Monopoles
• Bulk locality from the celestial amplitude
• Study of the conformal hyperscaling relation through the Schwinger-Dyson equation
• Constructing on-shell operator basis for all masses and spins
• Calculating $\beta$-function coefficients of Renormalization Group Equations