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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 OSTI2011

Inflationary correlation functions without infrared divergences

Inflationary correlation functions are potentially affected by infrared divergences. For example, the two-point correlator of curvature perturbation at momentum k receives corrections ∼ ln (kL), where L is the size of the region in which the measurement is performed. We define infrared-safe correlation functions which have no sensitivity to the size L of the box used for the observation. The conventional correlators with their familiar log-enhanced corrections (both from scalar and tensor long-wavelength modes) are easily recovered from our IR-safe correlation functions. Among other examples, we illustrate this by calculating the corrections to the non-Gaussianity parameter f{sub NL} coming from long-wavelength tensor modes. In our approach, the IR corrections automatically emerge in a resummed, all-orders form. For the scalar corrections, the resulting all-orders expression can be evaluated explicitly.

79 ASTRONOMY AND ASTROPHYSICS↗
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 OSTI2010

de Sitter breaking through infrared divergences

Just because the propagator of some field obeys a de Sitter invariant equation does not mean it possesses a de Sitter invariant solution. The classic example is the propagator of a massless, minimally coupled scalar. We show that the same thing happens for massive scalars with M{sub S}{sup 2}<0 and for massive transverse vectors with M{sub V}{sup 2}<=-2(D-1)H{sup 2}, where D is the dimension of space-time and H is the Hubble parameter. Although all masses in these ranges give infrared divergent mode sums, using dimensional regularization (or any other analytic continuation technique) to define the mode sums leads to the incorrect conclusion that de Sitter invariant solutions exist except at discrete values of the masses.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2010

Infrared divergence does not affect the gauge-invariant curvature perturbation

We address the infrared (IR) divergence problem during inflation that appears in the loop corrections to the primordial perturbations. In our previous paper, we claimed that, at least in single field models, the IR divergence is originating from the gauge artifact. Namely, diverging IR corrections should not appear in genuine gauge-invariant observables. We propose here one simple but explicit example of such gauge-invariant quantities. Then, we explicitly calculate such a quantity to find that the IR divergence is absent at the leading order in the slow-roll approximation for the usual scale-invariant vacuum state. At the same time we notice that there is a subtle issue on the gauge invariance in how to specify the initial vacuum state.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2010

Inflationary infrared divergences: geometry of the reheating surface vs. δN formalism

We describe a simple way of incorporating fluctuations of the Hubble scale during the horizon exit of scalar perturbations into the δN formalism. The dominant effect comes from the dependence of the Hubble scale on low-frequency modes of the inflaton. This modifies the coefficient of the log-enhanced term appearing in the curvature spectrum at second order in field fluctuations. With this modification, the relevant coefficient turns out to be proportional to the second derivative of the tree-level spectrum with respect to the inflaton φ at horizon exit. A logarithm with precisely the same coefficient appears in a calculation of the log-enhancement of the curvature spectrum based purely on the geometry of the reheating surface. We take this agreement as strong support for the proposed implementation of the δN formalism. Moreover, our analysis makes it apparent that the log-enhancement of the inflationary power-spectrum is indeed physical if this quantity is defined using a global coordinate system on the reheating surface (or any other post-inflationary surface of constant energy density). However, it can be avoided by defining the spectrum using invariant distances on this surface.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2013

Slavnov-Taylor identities, non-commutative gauge theories and infrared divergences

In this work we clarify some properties of the one-loop IR divergences in nonAbelian gauge field theories on non-commutative 4-dimensional Moyal space. Additionally, we derive the tree-level Slavnov-Taylor identities relating the two, three and four point functions, and verify their consistency with the divergent one-loop level results. We also discuss the special case of two dimensions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
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 OSTI2012

Electroweak Radiative Corrections to the Parity-violating Asymmetry for SLAC Experiment E158

Electroweak radiative corrections to observable quantities of Moeller scattering of polarized particles are calculated. We emphasize the contribution induced by infrared divergent parts of cross section. The covariant method is used to remove infrared divergences, so that our results do not involve any unphysical parameters. When applied to the kinematics of SLAC E158 experiment, these corrections reduce the parity violating asymmetry by about -6.5% at E = 48 GeV and y = 0.5, and kinematically weighted 'hard' bremsstrahlung effect for SLAC E158 is {approx} 1%.

43 PARTICLE ACCELERATORS↗
DOE OSTI2010

J{sub AW,WA} functions in Passarino-Veltman reduction

We continue to study a special class of Passarino-Veltman functions J arising at the reduction of infrared divergent box diagrams. We describe a procedure of separation of two types of singularities, infrared and mass singularities, which are absorbed in simple C{sub 0} functions. The infrared divergences of C{sub 0}'s can be regularized then by any method: photon mass, dimensionally or by the width of an unstable particle. Functions D{sub 0} are represented as certain linear combinations of the standard C{sub 0} Passarino-Veltman functions and infrared finite functions J. Then mass singularities are extracted from J to other combinations of C{sub 0}. The rests are free of both types of singularities and are expressed as explicit and compact linear combination of logarithms and dilogarithm functions. The extensive comparison of numerical results with those obtained with the aid of the Loop Tools package is presented.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2011

Regulating the infrared by mode matching: A massless scalar in expanding spaces with constant deceleration

In this paper we consider a massless scalar field, with a possible coupling {xi} to the Ricci scalar in a D dimensional Friedmann-Lemaitre-Robertson-Walker space-time with a constant deceleration parameter q={epsilon}-1, {epsilon}=-H/H{sup 2}. Correlation functions for the Bunch-Davies vacuum of such a theory have long been known to be infrared divergent for a wide range of values of {epsilon}. We resolve these divergences by explicitly matching the space-time under consideration to a space-time without infrared divergencies. Such a procedure ensures that all correlation functions with respect to the vacuum in the space-time of interest are infrared finite. In this newly defined vacuum we construct the coincidence limit of the propagator and as an example calculate the expectation value of the stress-energy tensor. We find that this approach gives both in the ultraviolet and in the infrared satisfactory results. Moreover, we find that, unless the effective mass due to the coupling to the Ricci scalar {xi}R is negative, quantum contributions to the energy density always dilute away faster, or just as fast, as the background energy density. Therefore, quantum backreaction is insignificant at the one-loop order, unless {xi}R is negative. Finally we compare this approach with known results where the infrared is regulated by placing the Universe in a finite box. In an accelerating universe, the results are qualitatively the same, provided one identifies the size of the Universe with the physical Hubble radius at the time of the matching. In a decelerating universe, however, the two schemes give different late time behavior for the quantum stress-energy tensor. This happens because in this case the length scale at which one regulates the infrared becomes sub-Hubble at late times.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2014

The Weyl tensor correlator in cosmological spacetimes

We give a general expression for the Weyl tensor two-point function in a general Friedmann-Lemaître-Robertson-Walker spacetime. We work in reduced phase space for the perturbations, i.e., quantize only the dynamical degrees of freedom without adding any gauge-fixing term. The general formula is illustrated by a calculation in slow-roll single-field inflation to first order in the slow-roll parameters ϵ and δ, and the result is shown to have the correct de Sitter limit as ϵ,δ→0. Furthermore, it is seen that the Weyl tensor correlation function in slow-roll does not suffer from infrared divergences, unlike the two-point functions of the metric and scalar field perturbations. Lastly, we show how to recover the usual tensor power spectrum from the Weyl tensor correlation function.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
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 OSTI2016

J functions for the process ud→WA

In this paper we present a description of the universal approach for analytic calculations for a certain class of J functions for six topologies of the boxes for the process ud → WA. These functions J arise at the reduction of the infrared divergent box diagrams. The standard Passarino–Veltman reduction of the four-point box diagram with an internal photon line connecting two external lines on the mass shell leads to infrared-divergent and mass-singular D{sub 0} functions. In the system SANC a systematic procedure is adopted to separate both types of singularities into the simplest objects, namely C{sub 0} functions. The functions J, in turn, are represented as certain linear combinations of the standard D{sub 0} and C{sub 0} functions. The subtracted J functions are free of both types of singularities and are expressed as explicit and compact linear combinations of dilogarithm functions. We present extensive comparisons of numerical results of SANC with those obtained with the aid of the LoopTools package.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2011

On infrared and ultraviolet divergences of cosmological perturbations

We study a consistent infrared and ultraviolet regularization scheme for the cosmological perturbations. The infrared divergences are cured by assuming that the Universe undergoes a transition between a nonsingular preinflationary, radiation-dominated phase and a slow-roll inflationary evolution. The ultraviolet divergences are eliminated via adiabatic subtraction. A consistent regularization of the field fluctuations through this transition is obtained by performing a mode matching for both the gauge invariant Mukhanov variable and its adiabatic expansion. We show that these quantities do not generate ultraviolet divergences other than the standard ones, when evolving through the matching time. We also show how the DeWitt-Schwinger expansion, which can be used to construct the counter-terms regularizing the ultraviolet divergences, ceases to be valid well before horizon exit of the scales of interest. Thus, such counter-terms should not be used beyond the time of the horizon exit and it is unlikely that the observed power spectrum is modified by adiabatic subtraction, as claimed in some literature. On the contrary, the infrared regularization might have an impact on the observed spectrum, and we briefly discuss this possibility.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗