Scale Invariant Instantons and the Complete Lifetime of the Standard Model

Abstract

In a classically scale-invariant quantum field theory, tunneling rates are infrared divergent due to the existence of instantons of any size. While one expects such divergences to be resolved by quantum effects, it has been unclear how higher-loop corrections can resolve a problem appearing already at one loop. With a careful power counting, we uncover a series of loop contributions that dominate over the one-loop result and sum all the necessary terms. We also clarify previously incomplete treatments of related issues pertaining to global symmetries, gauge fixing and finite mass effects. In addition, we produce exact closed-form solutions for the functional determinants over scalars, fermions and vector bosons around the scale-invariant bounce, demonstrating manifest gauge invariance in the vector case. With these problems solved, we produce the first complete calculation of the lifetime of our universe: 10^139 years. With 95% confidence, we expect our universe to last more than 10^58 years. The uncertainty is part experimental uncertainty on the top quark mass and on $\alpha s$ and part theory uncertainty from electroweak threshold corrections. Using our complete result, we provide phase diagrams in the $mt/mh$ and the $mt/\alpha s$ planes, with uncertainty bands. To rule out absolute stability to $3\sigma$ confidence, the uncertainty on the top quark pole mass would have to be pushed below 250 MeV or the uncertainty on $\alpha s(mZ)$ pushed below 0.00025.

arXiv commentTypos corrected, numbers updated

References in corpus (52)

• Higgs mass and vacuum stability in the Standard Model at NNLO
• Investigating the near-criticality of the Higgs boson
• Higgs boson mass and new physics
• On the metastability of the Standard Model vacuum
• Strong Coupling Constant with Flavour Thresholds at Four Loops in the MS-bar Scheme
• Improved Higgs Mass Stability Bound in the Standard Model and Implications for Supersymmetry
• Analytic Continuation Of Chern-Simons Theory
• Baryon Washout, Electroweak Phase Transition, and Perturbation Theory
• The Standard Model Effective Potential at Two Loops
• Stability of the Electroweak Vacuum: Gauge Independence and Advanced Precision
• Cosmological implications of the Higgs mass measurement
• The Probable Fate of the Standard Model
• Stability, Higgs Boson Mass and New Physics
• Three-loop β-functions for top-Yukawa and the Higgs self-interaction in the Standard Model
• IMPROVED METASTABILITY BOUNDS ON THE STANDARD MODEL HIGGS MASS
• The lifetime of the electroweak vacuum and sensitivity to Planck scale physics
• Functional determinants by contour integration methods
• Why should we care about the top quark Yukawa coupling?
• Four-loop renormalization of QCD: full set of renormalization constants and anomalous dimensions
• Consistent Use of the Standard Model Effective Potential
• Top Mass Measurements from Jets and the Tevatron Top-Quark Mass
• Functional determinants for general Sturm-Liouville problems
• Top mass determination, Higgs inflation, and vacuum stability
• Precision decay rate calculations in quantum field theory
• Consistent Use of Effective Potentials
• On the gauge dependence of vacuum transitions at finite temperature
• Beyond the thin-wall approximation : precise numerical computation of prefactors in false vacuum decay
• On the ultimate uncertainty of the top quark pole mass
• Multi-Instantons and Exact Results III: Unified Description of the Resonances of Even and Odd Anharmonic Oscillators
• Vacuum Decay in Theories with Symmetry Breaking by Radiative Corrections
• Top Quark Mass Calibration for Monte Carlo Event Generators
• Complexified path integrals, exact saddles and supersymmetry
• Gauge independence of the bubble nucleation rate in theories with radiative symmetry breaking
• Gravity Waves from a Cosmological Phase Transition: Gauge Artifacts and Daisy Resummations
• A direct approach to quantum tunneling
• Higher-order scalar interactions and SM vacuum stability
• Stability of the electroweak ground state in the Standard Model and its extensions
• Gauge Invariant Treatment of the Electroweak Phase Transition
• mr: a C++ library for the matching and running of the Standard Model parameters
• On the Gauge Invariance of the Decay Rate of False Vacuum
• The gauge invariant effective potential: equilibrium and non-equilibrium aspects
• Stationary configurations of the Standard Model Higgs potential: electroweak stability and rising inflection point
• Vacuum decay and internal symmetries
• False Vacuum Decay in Gauge Theory
• Explicit construction of constrained instantons
• Gauge fixing and renormalisation scale independence of tunneling rate in abelian Higgs model and in the Standard Model
• The Case of the Disappearing Instanton
• Displacement Operator Formalism for Renormalization and Gauge Dependence to All Orders
• Gauge Independent Effective Potential and the Higgs Mass Bound
• Reducing the Top Quark Mass Uncertainty with Jet Grooming
• Stability of the EW vacuum, Higgs boson, and new physics
• Instanton constraints and renormalization

Cited by in corpus (86)

• Cosmological phase transitions: from perturbative particle physics to gravitational waves
• Theoretical uncertainties for cosmological first-order phase transitions
• FindBounce: package for multi-field bounce actions
• The Higgs Portal to Cosmology
• Constraining power of asymptotic safety for scalar fields
• BubbleProfiler: finding the field profile and action for cosmological phase transitions
• Decay Rate of Electroweak Vacuum in the Standard Model and Beyond
• Self-Organised Localisation
• BubbleDet: A Python package to compute functional determinants for bubble nucleation
• Functional methods for false vacuum decay in real time
• Standard Model Meets Gravity: Electroweak Symmetry Breaking and Inflation
• A Fresh Look at the Calculation of Tunneling Actions in Multi-Field Potentials
• Initial Conditions for Critical Higgs Inflation
• Black hole induced false vacuum decay from first principles
• Higher-Order Corrections to the Bubble-Nucleation Rate at Finite Temperature
• Formulating the Kramers problem in field theory
• False vacuum decay: an introductory review
• Shape Is Destiny II: Configurational Information Approach to Instantons and False Vacuum Decay in D-dimensional Spacetime
• Gauge hierarchy from electroweak vacuum metastability
• Bubble Nucleation to All Orders
• Two-loop effective potential for generalized gauge fixing
• The Self-Organized Critical Multiverse
• Bounce Configuration from Gradient Flow
• Tunneling Without Bounce
• Assessing Perturbativity and Vacuum Stability in High-Scale Leptogenesis
• Higgs-Inflaton Mixing and Vacuum Stability
• Higgs Criticality beyond the Standard Model
• Radiative effects on false vacuum decay in Higgs-Yukawa theory
• Accessibility Measure for Eternal Inflation: Dynamical Criticality and Higgs Metastability
• Search Optimization, Funnel Topography, and Dynamical Criticality on the String Landscape
• Impact of New Physics on the EW vacuum stability in a curved spacetime background
• Protecting the Stability of the EW Vacuum from Planck-Scale Gravitational Effects
• Implications of the detection of primordial gravitational waves for the Standard Model
• Primordial Black Holes as Dark Matter through Higgs Criticality
• Signatures of microscopic black holes and extra dimensions at future neutrino telescopes
• Gradient effects on false vacuum decay in gauge theory
• QCD Axion Window and False Vacuum Higgs Inflation
• Negative modes of Coleman-de Luccia and black hole bubbles
• Dilaton-assisted generation of the Fermi scale from the Planck scale
• Exact one-loop false vacuum decay rate
• Prospect of measuring the top quark mass through energy correlators
• Direct Higgs-gravity interaction and stability of our Universe
• Gravitational corrections to electroweak vacuum decay: metric vs. Palatini
• Analytic thin wall false vacuum decay rate
• Vacuum Decay in the Standard Model: Analytical Results with Running and Gravity
• Fluctuations about the Fubini-Lipatov instanton for false vacuum decay in classically scale invariant models
• Early-Time Measure in Eternal Inflation
• Gravity-improved metastability bounds for the Type-I Seesaw Mechanism
• False vacuum decay rates, more precisely
• Hidden Dark Matter from Starobinsky Inflation
• Scheme dependence of asymptotically free solutions
• Pseudo-Bounces vs. New Instantons
• Schwinger effect and false vacuum decay as quantum-mechanical tunneling of a relativistic particle
• Correspondence between Thermal and Quantum Vacuum Transitions around Horizons
• Domain walls in the extensions of the Standard Model
• Massless Preheating and Electroweak Vacuum Metastability
• Reconstruction of Unstable Heavy Particles Using Deep Symmetry-Preserving Attention Networks
• Parameter Inference from Event Ensembles and the Top-Quark Mass
• Two-loop corrections to false vacuum decay in scalar field theory
• Instability of the Electroweak Vacuum in Starobinsky Inflation
• Finite-Temperature Instantons from First Principles
• Toward quantum tunneling from excited states: Recovering imaginary-time instantons from a real-time analysis
• High Scale Validity of the DFSZ Axion Model with Precision
• Precise Calculation of the Decay Rate of False Vacuum with Multi-Field Bounce
• Higgs chameleon
• False vacuum decay of excited states in finite-time instanton calculus
• False vacuum decay beyond the quadratic approximation: summation of non-local self-energies
• Three-loop jet function for boosted heavy quarks
• Millicharged Scalar Fields, Massive Photons and the Breaking of $SU(3{)}_C\times U(1{)}_{\mathrm{EM}}$
• Flow-based Nonperturbative Simulation of First-order Phase Transitions
• Vacuum decay and quadratic gravity: the massive case
• Gauge hierarchy and metastability from Higgs-driven crunching
• Higgs domain walls in the thermal background
• NNLO corrections to false vacuum decay rate in thin-wall approximation
• Vacuum decay in quadratic gravity
• Unitarily Inequivalent Vacua and Long-Range Forces: Phenomenology with Scalar Boson Mass-Shift
• Stability of the Higgs Potential in the Standard Model and Beyond
• Theoretical and Experimental Constraints on ${\mathbb{Z}}_{2n}$ Multi-Component Dark Matter Models
• The Higgs boson, naturalness, and the Universe
• On equivalent methods for functional determinants
• The tunneling decay rate in QFT beyond the thin wall approximation
• Upper bound on the smuon mass from vacuum stability in the light of muon $g-2$ anomaly
• Symmetries, Dark Matter and Minicharged Particles
• On the Effects of Elementary and Bound State Fields on Vacuum Stability in $t\bar{t}$ Production at the LHC
• Top-mass observables: all-orders behaviour, renormalons and NLO + Parton Shower effects
• Scalar field with a time-independent classical source, not trivial after all: from vacuum decay to scattering