Generalized positivity bounds on chiral perturbation theory

Abstract

Recently, a new set of positivity bounds with $t$ derivatives have been discovered. We explore the generic features of these generalized positivity bounds with loop amplitudes and apply these bounds to constrain the parameters in chiral perturbation theory up to the next-to-next-to-leading order. We show that the generalized positivity bounds give rise to stronger constraints on the ${\bar{l}}_i$ constants, compared to the existing axiomatic bounds. The parameter space of the $b_i$ constants is constrained by the generalized positivity bounds to be a convex region that is enclosed for many sections of the total space. We also show that the improved version of these positivity bounds can further enhance the constraints on the parameters. The often used Padé unitarization method however does not improve the analyticity of the amplitudes in the chiral perturbation theory at low energies.

arXiv comment31 pages, 15 figures; JHEP version

References in corpus (65)

• Causality, Analyticity and an IR Obstruction to UV Completion
• Chiral dynamics in the presence of bound states: kaon-nucleon interactions revisited
• ππscattering
• Chiral Symmetry Amplitudes in the S-Wave Isoscalar and Isovector Channels and the σ, f_0(980), a_0(980) Scalar Mesons
• Chiral symmetry amplitudes in the s-wave isoscalar and isovector channels and the $\sigma ,f_0(980),a_0(980)$ scalar mesons
• N/D Description of Two Meson Amplitudes and Chiral Symmetry
• Chiral Perturbation Theory
• Non-perturbative Approach to effective chiral Lagrangians and Meson Interactions
• Chiral Unitary approach to meson-meson and meson-baryon interactions and nuclear applications
• The inverse amplitude method in Chiral Perturbation Theory
• The Mesonic Chiral Lagrangian of Order $p^6$
• Complete Electroweak Chiral Lagrangian with a Light Higgs at NLO
• The Effective Chiral Lagrangian for a Light Dynamical "Higgs Particle"
• Low-Energy Effective Field Theory below the Electroweak Scale: Anomalous Dimensions
• Meson-meson scattering within one loop Chiral Perturbation Theory and its unitarization
• Elastic $\pi \pi$ scattering to two loops
• Energy's and amplitudes' positivity
• Nature of the f_0(600) from its N_c dependence at two loops in unitarized Chiral Perturbation Theory
• Bethe-Salpeter Approach for Unitarized Chiral Perturbation Theory
• Renormalization of chiral perturbation theory to order p^6
• Positivity Bounds for Scalar Theories
• Beyond Amplitudes' Positivity and the Fate of Massive Gravity
• Softness and Amplitudes' Positivity for Spinning Particles
• Amplitudes' Positivity, Weak Gravity Conjecture, and Modified Gravity
• UV complete me: Positivity Bounds for Particles with Spin
• Signs of Analyticity in Single-Field Inflation
• Chiral perturbation theory
• Consistency of the Standard Model Effective Field Theory
• Quantum Gravity Constraints from Unitarity and Analyticity
• Effective Theory of a Dynamically Broken Electroweak Standard Model at NLO
• Massive Galileon Positivity Bounds
• Positivity Bounds for Massive Spin-1 and Spin-2 Fields
• Consistency of the Chiral Pion-Pion Scattering Amplitudes with Axiomatic Constraints
• The Electroweak Chiral Lagrangian for the Standard Model with a Heavy Higgs
• Positivity bounds on vector boson scattering at the LHC
• Positivity constraints on aQGC: carving out the physical parameter space
• Improved Positivity Bounds and Massive Gravity
• Positivity of Curvature-Squared Corrections in Gravity
• Positive Signs in Massive Gravity
• The Chiral Lagrangian parameters, ${\overline{\ell }}_1$, ${\overline{\ell }}_2$, are determined by the $\rho$--resonance
• $K_{\ell 4}$ Form-Factors and $\pi$-$\pi$ Scattering
• Falsifying Models of New Physics Via WW Scattering
• The Speed of Gravity
• Complete One-Loop Renormalization of the Higgs-Electroweak Chiral Lagrangian
• Positivity in the sky
• Positivity Constraints for Pseudo-linear Massive Spin-2 and Vector Galileons
• Dispersion Relation Bounds for pi pi Scattering
• Renormalization group evolution of Higgs effective field theory
• ZZ and Zgamma still haven't found what they are looking for
• Bounds on Amplitudes in Effective Theories with Massive Spinning Particles
• Massive Spin-2 Scattering and Asymptotic Superluminality
• Massive and Massless Spin-2 Scattering and Asymptotic Superluminality
• The Other Fermion Compositeness
• One-loop renormalization of the electroweak chiral Lagrangian with a light Higgs
• Constraints on Chiral Perturbation Theory Parameters from QCD Inequalities
• Positivity Constraints on Interacting Pseudo-Linear Spin-2 Fields
• Comment on the Prediction of Two-loop Standard Chiral Perturbation Theory for Low-Energy ππScattering
• Aspects of the low-energy constants in the chiral Lagrangian for charmed mesons
• Positivity Constraints on Chiral Perturbation Theory Pion-Pion Scattering Amplitudes
• The [1,2] Padé Amplitudes for $\pi \pi$ Scatterings in Chiral Perturbation Theory
• Positivity in the effective field theory of cosmological perturbations
• Pion Scalar Form Factor and the Sigma Meson
• Universal Bounds for SU(3) Low Energy Constants
• A Critical Examination to the Unitarized $\pi \pi$ Scattering Chiral Amplitudes
• Positivity constraints on the low-energy constants of the chiral pion-nucleon Lagrangian

Cited by in corpus (32)

• New positivity bounds from full crossing symmetry
• Causality constraints on corrections to Einstein gravity
• Convex Geometry Perspective to the (Standard Model) Effective Field Theory Space
• S-matrix Bootstrap for Effective Field Theories: Massless Pions
• Causality in Curved Spacetimes: The Speed of Light & Gravity
• Reverse Bootstrapping: IR lessons for UV physics
• Positivity in Multi-Field EFTs
• Bootstrapping Pions at Large $N$
• Bounding Violations of the Weak Gravity Conjecture
• Causal Effective Field Theories
• Elastic positivity vs extremal positivity bounds in SMEFT: a case study in transversal electroweak gauge-boson scatterings
• Gravitational Regge bounds
• Relative entropy in scattering and the S-matrix bootstrap
• Causality, Unitarity and Symmetry in Effective Field Theory
• Positivity in electron-positron scattering: testing the axiomatic quantum field theory principles and probing the existence of UV states
• Triple crossing positivity bounds for multi-field theories
• Positivity and Geometric Function Theory Constraints on Pion Scattering
• Positivity Bounds without Boosts
• SMEFTs living on the edge: determining the UV theories from positivity and extremality
• Signs, Spin, SMEFT: Sum Rules at Dimension Six
• Moments for positivity: using Drell-Yan data to test positivity bounds and reverse-engineer new physics
• UV graviton scattering and positivity bounds from IR dispersion relations
• Sum Rules in the Standard Model Effective Field Theory from Helicity Amplitudes
• Spinning Sum Rules for the Dimension-Six SMEFT
• NNLO Positivity Bounds on Chiral Perturbation Theory for a General Number of Flavours
• Positivity Bounds on Massive Vectors
• Locality and Analyticity of the Crossing Symmetric Dispersion Relation
• Positivity Bounds in Scalar Effective Field Theories at One-loop Level
• Positivity bounds at one-loop level: the Higgs sector
• A Celestial Route to AdS Bulk Locality
• Causality constraints on nonlinear supersymmetry
• Positivity bounds in scalar-QED EFT at one-loop level