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Results for “INFRARED DIVERGENCES”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
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DOE OSTI2017

Infrared divergences in QED revisited

Recently it has been demonstrated that the vacuum state in QED is infinitely degenerate. Moreover a transition among the degenerate vacua is induced in any nontrivial scattering process and determined from the associated soft factor. Conventional computations of scattering amplitudes in QED do not account for this vacuum degeneracy and therefore always give zero. This vanishing of all conventional QED amplitudes is usually attributed to infrared divergences. In this work, we show that if these vacuum transitions are properly accounted for, the resulting amplitudes are nonzero and infrared finite. Our construction of finite amplitudes is mathematically equivalent to, and amounts to a physical reinterpretation of, the 1970 construction of Faddeev and Kulish.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2017

Gauge-invariance and infrared divergences in the luminosity distance

Measurements of the luminosity distance have played a key role in discovering the late-time cosmic acceleration. However, when accounting for inhomogeneities in the Universe, its interpretation has been plagued with infrared divergences in its theoretical predictions, which are in some cases used to explain the cosmic acceleration without dark energy. The infrared divergences in most calculations are artificially removed by imposing an infrared cut-off scale. We show that a gauge-invariant calculation of the luminosity distance is devoid of such divergences and consistent with the equivalence principle, eliminating the need to impose a cut-off scale. We present proper numerical calculations of the luminosity distance using the gauge-invariant expression and demonstrate that the numerical results with an ad hoc cut-off scale in previous calculations have negligible systematic errors as long as the cut-off scale is larger than the horizon scale. We discuss the origin of infrared divergences and their cancellation in the luminosity distance.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Celestial IR divergences and the effective action of supertranslation modes

Infrared divergences in perturbative gravitational scattering amplitudes have been recently argued to be governed by the two-point function of the supertranslation Goldstone mode on the celestial sphere. We show that the form of this celestial two-point function simply derives from an effective action that also controls infrared divergences in the symplectic structure of General Relativity with asymptotically flat boundary conditions. This effective action finds its natural place in a path integral formulation of a celestial conformal field theory, as we illustrate by re-deriving the infrared soft factors in terms of celestial correlators. Our analysis relies on a well-posed action principle close to spatial infinity introduced by Compère and Dehouck.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

De Sitter diagrammar and the resummation of time

Light scalars in inflationary spacetimes suffer from logarithmic infrared divergences at every order in perturbation theory. This corresponds to the scalar field values in different Hubble patches undergoing a random walk of quantum fluctuations, leading to a simple toy “landscape” on superhorizon scales, in which we can explore questions relevant to eternal inflation. However, for a sufficiently long period of inflation, the infrared divergences appear to spoil computability. Some form of renormalization group approach is thus motivated to resum the log divergences of conformal time. Such a resummation may provide insight into De Sitter holography. We present here a novel diagrammatic analysis of these infrared divergences and their resummation. Basic graph theory observations and momen- tum power counting for the in-in propagators allow a simple and insightful determination of the leading-log contributions. One thus sees diagrammatically how the superhorizon sector consists of a semiclassical theory with quantum noise evolved by a first-order, interacting classical equation of motion. This rigorously leads to the “Stochastic Inflation” ansatz developed by Starobinsky to cure the scalar infrared pathology nonperturbatively. Our approach is a controlled approximation of the underlying quantum field theory and is systematically improvable.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2019

Prescriptive unitarity for non-planar six-particle amplitudes at two loops

We extend the applications of prescriptive unitarity beyond the planar limit to provide local, polylogarithmic, integrand-level representations of six-particle MHV scattering amplitudes in both maximally supersymmetric Yang-Mills theory and gravity. The integrand basis we construct is diagonalized on a spanning set of non-vanishing leading singularities that ensures the manifest matching of all soft-collinear singularities in both theories. As a consequence, this integrand basis naturally splits into infrared-finite and infrared-divergent parts, with hints toward an integrand-level exponentiation of infrared divergences. Importantly, we use the same basis of integrands for both theories, so that the presence or absence of residues at infinite loop momentum becomes a feature detectable by inspecting the cuts of the theory. Complete details of our results are provided as sup- plementary material.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Integrating the full four-loop negative geometries and all-loop ladder-type negative geometries in ABJM theory

The decomposition of the four-point ABJM amplituhedron into negative geometries produces compact integrands of logarithmic of amplitudes such that the infrared divergence only comes from the last loop integration, from which we can compute the cusp anomalous dimension of the ABJM theory. In this note, we integrate L – 1 loop momenta of the L-loop negative geometries for all four-loop negative geometries and a special class of all-loop ladder-type negative geometries by a method based on Mellin transformation, and from these finite quantities we extract the corresponding contribution to the cusp anomalous dimension. We find that the infrared divergence of a box-type negative geometry at L = 4 is weaker than other negative geometries, then only tree-type negative geometries contribute to the cusp anomalous dimension at L = 4. For the all-loop ladder-type negative geometries, we prove and conjecture some recursive structures as integral equations in Mellin space and find that they cannot contribute zeta values like ζ 3 , ζ 5 to the cusp anomalous dimension.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2026

Soft factorisation and exponentiation from Schwinger-space geometry

Infrared divergences in Quantum Field Theory govern the low-energy dynamics of many physical theories, and their understanding is a crucial ingredient in predicting the outcomes of collider experiments. We present a novel approach to deriving the structure of these divergences by employing the Schwinger parametrization of Feynman integrals. After using tropical geometry to identify divergent limits, we study the all-orders asymptotic properties of Feynman diagrams via matrix manipulations of graph Laplacians, which allows us to analyse their IR behaviour systematically. We explicitly demonstrate the soft-hard factorization of the integrand for a broad class of diagrams, and reveal that when written in terms of worldline distances, topologically distinct diagrams asymptote to the same integrand at leading order in the soft limit. In particular, for the case of Quantum Electrodynamics (with massive fermions), we use this fact to show how ladder-type diagrams combine in Schwinger-parameter space to yield the correct exponentiated soft anomalous dimension. This framework provides a foundation for extending these methods to more complex theories like Quantum Chromodynamics and offers a pathway towards a systematic understanding of infrared divergences in perturbative amplitudes.

Factorization↗
DOE OSTI2016

Semi-classical Electrodynamics: A Short Note

I have previously claimed the key to understanding the numerical value of the fine structure constant is near-field corrections which terminate integrals at low virtual photon energies, thus obverting an infrared divergence common to many QED calculations. I have since switched to a physics-based calculation of the near-field corrections, instead of the previously used educated guess. The relevant equations are presented here.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2017

Compactly supported linearised observables in single-field inflation

We investigate the gauge-invariant observables constructed by smearing the graviton and inflaton fields by compactly supported tensors at linear order in general single-field inflation. These observables correspond to gauge-invariant quantities that can be measured locally. In particular, we show that these observables are equivalent to (smeared) local gauge-invariant observables such as the linearised Weyl tensor, which have better infrared properties than the graviton and inflaton fields. Special cases include the equivalence between the compactly supported gauge-invariant graviton observable and the smeared linearised Weyl tensor in Minkowski and de Sitter spaces. Our results indicate that the infrared divergences in the tensor and scalar perturbations in single-field inflation have the same status as in de Sitter space and are both a gauge artefact, in a certain technical sense, at tree level.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2016

Unified treatment of the luminosity distance in cosmology

Comparing the luminosity distance measurements to its theoretical predictions is one of the cornerstones in establishing the modern cosmology. However, as shown in Biern and Yoo, its theoretical predictions in literature are often plagued with infrared divergences and gauge-dependences. This trend calls into question the sanity of the methods used to derive the luminosity distance. Here we critically investigate four different methods—the geometric approach, the Sachs approach, the Jacobi mapping approach, and the geodesic light cone (GLC) approach to modeling the luminosity distance, and we present a unified treatment of such methods, facilitating the comparison among the methods and checking their sanity. All of these four methods, if exercised properly, can be used to reproduce the correct description of the luminosity distance.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

Critical properties of scalar field theory with Lorentz violation: Exact treatment of Lorentz-violating mechanism

In this work, we compute analytically the infrared divergences of massless O(N) self-interacting scalar field theories with Lorentz violation, which are exact in the Lorentz-violating K{sub μν} coefficients, for evaluating the corresponding next-to-leading order critical exponents. For that, we apply three distinct and independent field-theoretic renormalization group methods. We find that the outcomes for the critical exponents are the same in the three methods and, furthermore, are identical to their Lorentz invariant counterparts. We generalize the results for all loop levels by employing a general theorem arising from the exact procedure and give the corresponding physical interpretation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Logarithmic Corrections to Kerr Thermodynamics

Recent work has shown that loop corrections from massless particles generate $\frac{3}{2}$ ⁢log⁡𝑇 Hawking corrections to black hole entropy which dominate the thermodynamics of cold near-extreme charged black holes. Here we adapt this analysis to near-extreme Kerr black holes. Like AdS 2 ×𝑆 2 , the near-horizon extreme Kerr (NHEK) metric has a family of normalizable zero modes corresponding to reparametrizations of boundary time. The path integral over these zero modes leads to an infrared divergence in the one-loop approximation to the Euclidean NHEK partition function. We regulate this divergence by retaining the leading finite temperature correction in the NHEK scaling limit. This “not-NHEK” geometry lifts the eigenvalues of the zero modes, rendering the path integral infrared finite. The quantum-corrected near-extremal entropy exhibits $\frac{3}{2}$ ⁢log⁡𝑇 Hawking behavior characteristic of the Schwarzian model and predicts a lifting of the ground state degeneracy for the extremal Kerr black hole.

General relativity↗
DOE OSTI2019

Gluon fragmentation into quarkonium at next-to-leading order using FKS subtraction

We present the calculation at next-to-leading order (NLO) in a s of the fragmentation function of a gluon into heavy quarkonium in the color-octet spin-singlet S-wave channel. To calculate the real NLO corrections, we adapt a subtraction scheme introduced by Frixione, Kunszt, and Signer. Ultraviolet and infrared divergences in the real NLO corrections are calculated analytically by evaluating the phase-space integrals of the subtraction terms using dimensional regularization. The subtracted phase-space integrals are then evaluated in 4 space-time dimensions. The divergences in the virtual NLO corrections are also calculated analytically. After renormalization, all the divergences cancel. The NLO corrections significantly increase the fragmentation probability for a gluon into the spin-singlet quarkonium states η c and η b .

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Classical eikonal from Magnus expansion

In a classical scattering problem, the classical eikonal is defined as the generator of the canonical transformation that maps in-states to out-states. It can be regarded as the classical limit of the log of the quantum S-matrix. In a classical analog of the Born approximation in quantum mechanics, the classical eikonal admits an expansion in oriented tree graphs, where oriented edges denote retarded/advanced worldline propagators. The Magnus expansion, which takes the log of a time-ordered exponential integral, offers an efficient method to compute the coefficients of the tree graphs to all orders. We exploit a Hopf algebra structure behind the Magnus expansion to develop a fast algorithm which can compute the tree coefficients up to the 12th order (over half a million trees) in less than an hour. In a relativistic setting, our methods can be applied to the post-Minkowskian (PM) expansion for gravitational binaries in the worldline formalism. We demonstrate the methods by computing the 3PM eikonal and find agreement with previous results based on amplitude methods. Importantly, the Magnus expansion yields a finite eikonal, while the naïve eikonal based on the time-symmetric propagator is infrared-divergent from 3PM on.

Black Holes↗
DOE OSTI2024

Light scalars at the cosmological collider

We study the self-energies of weakly interacting scalar fields in de Sitter space with one field much lighter than the Hubble scale. We argue that self-energies drastically simplify in this light limit. We illustrate this in theories with two scalar fields, one heavy and one light, interacting with one another through either cubic or quartic interactions. To regulate infrared divergences, we compute these self-energies in Euclidean de Sitter space and then carefully analytically continue to Lorentzian signature. In particular, we do this for the most general renormalizable theory of two scalar fields with even interactions to leading order in the coupling and the mass of the light field. These self-energies are determined by de Sitter sunset diagrams, whose analytic structure and UV divergences we derive. Even at very weak couplings, the light field can substantially change how the heavy field propagates over long distances. The light field’s existence may then be inferred from how it modifies the heavy field’s oscillatory contribution to the primordial bispectrum in the squeezed limit, i.e. its cosmological collider signal.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Renormalization group improvement of the effective potential: an EFT approach

We apply effective field theory (EFT) methods to compute the renormalization group improved effective potential for theories with a large mass hierarchy. Our method allows one to compute the effective potential in a systematic expansion in powers of the mass ratio, as well as to sum large logarithms of mass ratios using renormalization group evolution. The effective potential is the sum of one-particle irreducible diagrams (1PI) but information about which diagrams are 1PI is lost after matching to the EFT, since heavy lines get shrunk to a point. We therefore introduce a tadpole condition in place of the 1PI condition, and use the renormalization group improved value of the tadpole in computing the effective potential. We explain why the effective potential computed using an EFT is not the same as the effective potential of the EFT. We illustrate our method using the O(N) model, a theory of two scalars in the unbroken and broken phases, and the Higgs-Yukawa model. Our leading-log result, obtained by integrating the one-loop β-functions, correctly reproduces the log-squared term in explicit two-loop calculations. Our method does not have a Goldstone boson infrared divergence problem.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗