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Results for “Renormalization and Regularization”

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DOE OSTI2022

Interacting fractons in 2+1-dimensional quantum field theory

We analyze, in perturbation theory, a theory of weakly interacting fractons and non-relativistic fermions in a 2+1 dimensional Quantum Field Theory. In particular we compute the 1-loop corrections to the self energies and interaction vertex, and calculate the associated 1-loop Renormalization Group flows of the coupling constants. Surprisingly, we find that the fracton-fermion coupling does not flow due to an emergent coordinate-dependent symmetry of the effective Lagrangian, making this model a well-defined quantum field theory. We provide additional discussions on the regularization and renormalization of interacting fractonic theories, as well as both qualitative and quantitative remarks regarding the theory at finite temperature and finite chemical potential.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Factorization at subleading power and endpoint-divergent convolutions in h → γγ decay

t is by now well known that, at subleading power in scale ratios, factorization theorems for high-energy cross sections and decay amplitudes contain endpoint-divergent convolution integrals. The presence of endpoint divergences hints at a violation of simple scale separation. At the technical level, they indicate an unexpected failure of dimensional regularization and the $\overline{MS}$ subtraction scheme. In this work, we start a detailed discussion of factorization at subleading power within the framework of soft-collinear effective theory. As a concrete example, we factorize the decay amplitude for the radiative Higgs-boson decay h → γγ mediated by a b-quark loop, for which endpoint-divergent convolution integrals require both dimensional and rapidity regulators. We derive a factorization theorem for the decay amplitude in terms of bare Wilson coefficients and operator matrix elements. We show that endpoint divergences caused by rapidity divergences cancel to all orders of perturbation theory, while endpoint divergences that are regularized dimensionally can be removed by rearranging the terms in the factorization theorem. We use our result to resum the leading double-logarithmic corrections of order $α^n_sln^{2n+2}(-M^2_h/m^2_b)$ to the decay amplitude to all orders of perturbation theory.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

A technical analog of the cosmological constant problem and a solution thereof

The near vanishing of the cosmological constant is one of the most puzzling open problems in theoretical physics. We consider a system, the so-called framid, that features a technically similar problem. Its stress-energy tensor has a Lorentz-invariant expectation value on the ground state, yet there are no standard, symmetry-based selection rules enforcing this, since the ground state spontaneously breaks boosts. We verify the Lorentz invariance of the expectation value in question with explicit one-loop computations. These, however, yield the expected result only thanks to highly nontrivial cancellations, which are quite mysterious from the low-energy effective theory viewpoint.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

On ambiguities and divergences in perturbative renormalization group functions

There is an ambiguity in choosing field-strength renormalization factors in the $ \overline{\mathrm{MS}} $ scheme starting from the 3-loop order in perturbation theory. More concerning, trivially choosing Hermitian factors has been shown to produce divergent renormalization group functions, which are commonly understood to be finite quantities. We demonstrate that the divergences of the RG functions are such that they vanish in the RG equation due to the Ward identity associated with the flavor symmetry. It turns out that any such divergences can be removed using the renormalization ambiguity and that the use of the flavor-improved β-function is preferred. We show how our observations resolve the issue of divergences appearing in previous calculations of the 3-loop SM Yukawa β-functions and provide the first calculation of the flavor-improved 3-loop SM β-functions in the gaugeless limit.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Generic one-loop matching conditions for rare meson decays

Leptonic and semileptonic meson decays that proceed via flavour-changing neutral currents provide excellent probes of physics of the standard model and beyond. We present explicit results for the Wilson coefficients of the weak effective Lagrangian for these decays in any perturbative model in which these processes proceed via one-loop contributions. We explicitly show that our results are finite and gauge independent, and provide Mathematica code that implements our results in an easily usable form.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

One-loop matching for quark dipole operators in a gradient-flow scheme

The quark chromoelectric dipole (qCEDM) operator is a CP-violating operator describing, at hadronic energies, beyond-the-standard-model contributions to the electric dipole moment of particles with nonzero spin. In this paper we define renormalized dipole operators in a regularization-independent scheme using the gradient flow, and we perform the matching at one loop in perturbation theory to renormalized operators of the same and lower dimension in the more familiar MS scheme. We also determine the matching coefficients for the quark chromo-magnetic dipole operator (qCMDM), which contributes for example to matrix elements relevant to CP-violating and CP-conserving kaon decays. The calculation provides a basis for future lattice QCD computations of hadronic matrix elements of the qCEDM and qCMDM operators.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Evanescent operators in one-loop matching computations

Effective Field Theory calculations used in countless phenomenological analyses employ dimensional regularization, and at intermediate stages of computations, the operator bases extend beyond the four-dimensional ones. The extra pieces — the evanescent operators — can ultimately be removed with a suitable renormalization scheme, resulting in a finite shift of the physical operators. Modern Effective Field Theory matching techniques relying on the method of expansion by regions have to be extended to account for this. After illustrating the importance of these shifts in two specific examples, we compute the finite shifts required to remove all evanescent operators appearing in the one-loop matching of generic ultraviolet theories to the Standard Model Effective Field Theory and elucidate the formalism for generic Effective Field Theory calculations.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Renormalization-group equations of the LEFT at two loops: dimension-six baryon-number-violating operators

We present the second part of a systematic calculation of the two-loop anomalous dimensions for the low-energy effective field theory below the electroweak scale (LEFT): the baryon-number-violating sector at dimension six in the power counting. We obtain the results in two different schemes: in the algebraically consistent ’t Hooft-Veltman scheme for γ 5 , corrected for evanescent as well as chiral-symmetry-breaking effects through finite renormalizations; and in naive dimensional regularization, which in the considered sector of the theory does not lead to any ill-defined γ 5 -odd traces. Our results are of interest for a reanalysis of the constraints on physics beyond the Standard Model from proton-decay searches within an EFT framework at next-to-leading-logarithmic accuracy.

Baryon/Lepton Number Violation↗
DOE OSTI2022

Transient phenomena in the axion assisted Schwinger effect

Particle production induced by a time-dependent background is well understood as the projection of the time-evolved initial state onto a set of final states. While the asymptotic initial and final states are well defined in the usual way, the definition of particles and antiparticles at intermediate times in the presence of external fields is ambiguous. These external fields moreover induce divergences which require regularization. In this paper we clarify some subtleties in the computation of transient effects in physical quantities for fermions in a homogeneous axion background, including Schwinger production in background electromagnetic fields. The presence of the axion requires particular care as well as knowledge of the UV theory when regulating the theory and computing the vacuum contribution to the fermion energy.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2026

Unveiling horizons in quantum critical collapse

Critical gravitational collapse offers a unique window into regimes of arbitrarily high curvature, culminating in a naked singularity arising from smooth initial data — thus providing a dynamical counterexample to weak cosmic censorship. Near the critical regime, quantum effects from the collapsing matter are expected to intervene before full quantum gravity resolves the singularity. Despite its fundamental significance, a self-consistent treatment has so far remained elusive. In this work, we perform a one-loop semiclassical analysis using the robust anomaly-based method in the canonical setup of Einstein gravity minimally coupled to a free, massless scalar field. Focusing on explicitly solvable near-critical solutions in both 2 + 1 and 3 + 1 dimensions, we analytically solve the semiclassical Einstein equations and obtain controlled, quantitative results for several long-standing questions within the dominant s-wave sector. We find that regularity uniquely selects a Boulware-like quantum state, encoding genuine vacuum polarization effects from the collapsing matter. Remarkably, the resulting quantum corrections manifest as a growing mode. Horizon-tracing analyses, incorporating both classical and quantum modes, reveal the emergence of a finite mass gap, signaling a phase transition from classical Type II to quantum-modified Type I behavior, thereby providing a quantum enforcement of the weak cosmic censorship. The most non-trivial aspect of our analysis involves dealing with non-conformal matter fields in explicitly time-dependent critical spacetimes. Along the way, we uncover intriguing and previously underexplored features of quantum field theory in curved spacetime.

2D Gravity↗
DOE OSTI2023

Peculiarities of beta functions in sigma models

In this paper we consider perturbation theory in generic two-dimensional sigma models in the so-called first-order formalism, using the coordinate regularization approach. Our goal is to analyze the first-order formalism in application to β functions and compare its results with the standard geometric calculations. Already in the second loop, we observe deviations from the geometric results that cannot be explained by the regularization/renormalization scheme choices. Moreover, in certain cases the first-order calculations produce results that are not symmetric under the classical diffeomorphisms of the target space. Although we could not present the full solution to this remarkable phenomenon, we found some indirect arguments indicating that an anomaly similar to that established in supersymmetric Yang-Mills theory might manifest itself starting from the second loop. We discuss why the difference between two answers might be an infrared effect, similar to that in β functions in supersymmetric Yang-Mills theories.

Sigma Models↗
DOE OSTI2025

The approximate second order coupled-cluster method based on a size-consistent Brillouin–Wigner partitioning

We present a variant of the approximate second order coupled-cluster method (CC2) with a two-parameter size-consistent Brillouin–Wigner (BW-s) partitioning instead of a Møller–Plesset (MP) partitioning for the unperturbed Hamiltonian, which we refer to as BWs-CC2. The computational complexity of this model scales identically to CC2 with molecular size. Conventional CC2 and its regularized BWs-CC2 variants, as well as conventional MP2 and two of its regularized BW-s2 variants, were assessed on a 535 element database spanning thermochemistry, non-covalent interactions, barrier heights, and isomerization energies. To ensure a well-defined model chemistry, the assessment was performed using internally stable spin-polarized Hartree–Fock (HF) orbitals in the finite aug-cc-pVQZ basis without counterpoise corrections. As a result of using stable orbitals, contrary to conventional wisdom, we find that CC2 substantially outperforms MP2 on molecules with significantly spin contaminated reference orbitals without a significant increase in error on systems with a spin-pure reference, showing the value of its single substitutions. While no single choice of regularization parameters can be optimal for all datasets, we find that BWs-CC2 generally outperforms both CC2 and BW-s2 with a single judicious parameter choice. Additional tests on dipole moments and bond lengths of diatomics provide further support for the utility of this choice. Furthermore, the main outliers and poorest performing cases are associated with large amounts of spin-contamination in the HF reference, which is indicative of systems with either strong correlation or extensive artificial symmetry breaking. Overall, these findings argue that the perception of the quality of the CC2 ground state should be reevaluated and that it can be further improved upon by the soundly based BWs-CC2 variant with the recommended parameter choice.

Correlation energy↗
DOE OSTI2024

Corrected calculation for the non-local solution to the g − 2 anomaly and novel results in non-local QED

We provide the corrected calculation of the (g − 2) μ in non-local QED previously done in the literature. In specific, we show the proper technique for calculating loops in non-local QED and use it to find the form factors F 1 (q 2 ) and F 2 (q 2 ) in non-local QED. We also utilize this technique to calculate some novel results in non-local QED, including calculating the correction to the photon self-energy, the modification to the classical Coulomb potential, the modification to the energy levels of the hydrogen atom, and the contribution to the Lamb shift. We also discuss charge dequantization through non-locality, and show that the experimental bounds on the electric charge on Dirac neutrinos, translate into strong flavor-dependent bounds on the scale on non-locality that range between 10 5 −10 10 TeV. We also discuss the inconsistencies of unrenormalized non-local Quantum Field Theories (QFTs) and the need for renormalizing them, even when they are free from UV divergences.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Loop corrections in Minkowski spacetime away from equilibrium. Part II. Finite-time results

Loop corrections to finite-time correlation functions in quantum field theories away from equilibrium can be calculated using the in-in path integral approach. In this paper, we calculate the unequal-time two-point correlator for different massless self-interacting scalar quantum field theories on a Minkowski background, starting the field evolution at an arbitrary initial time. We find the counterterms that need to be added to UV-renormalize the result, including usual in-out counterterms in the dynamics and additional initial state counterterms that are required to cancel all UV divergences. We find that the late-time limit of the renormalized correlation function exhibits a linear or logarithmic growth in time, depending on whether the interaction strength is dimension-one or dimensionless, respectively. The late-time correlations match those obtained in our companion paper and, as shown there, the divergences do not indicate a real IR issue, consistent with what one would expect in Minkowski.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

Quantum calculations of the cavity shift in electron magnetic moment measurements

The measurement of the anomalous electron magnetic moment g – 2 through quantum transitions of a single trapped electron is the most stringent test of quantum field theory. These experiments are now so precise that they must account for the effects of the cavity containing the electron. Classical calculations of this “cavity shift” must subtract the electron’s divergent self-field, and thus require knowledge of the exact Green’s function for the cavity’s electromagnetic field. We perform the first fully quantum calculation of the cavity shift in a closed cavity, which instead involves subtracting linearly divergent cavity mode sums and integrals. Using contour integration methods, we find perfect agreement with existing classical results for both spherical and cylindrical cavities, justifying their current use. Moreover, our mode-based results can be naturally generalized to account for systematic effects, necessary to push future measurements to the next order of magnitude in precision.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Detectors in weakly-coupled field theories

We initiate a study of asymptotic detector operators in weakly-coupled field theories. These operators describe measurements that can be performed at future null infinity in a collider experiment. In a conformal theory they can be identified with light-ray operators, and thus have a direct relation to the spectrum of the theory. After a general discussion of the underlying physical picture, we show how infrared divergences of general detector operators can be renormalized in perturbation theory, and how they give rise to detector anomalous dimensions. We discuss in detail how this renormalization can be performed at the intersections of the Regge trajectories where non-trivial mixing occurs, which is related to the poles in anomalous dimensions at special values of spin. Finally, we discuss novel horizontal trajectories in scalar theories and show how they contribute to correlation functions. Our calculations are done in the example of Φ 4 theory in d = 4 - ϵ dimensions, but the methods are applicable more broadly. At the Wilson-Fisher fixed point our results include an explicit expression for the Pomeron light-ray operator at two loops, as well as a prediction for the value of the Regge intercept at five loops.

47 OTHER INSTRUMENTATION↗
DOE OSTI2023

Polyakov’s confinement mechanism for generalized Maxwell theory

We study fractional-derivative Maxwell theory, as appears in effective descriptions of, for example, large N f QED 3 , graphene, and some types of surface defects. We argue that when the theory is realized on a lattice, monopole condensation leads to a confining phase via the Polyakov confinement mechanism.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Dirac traces and the Tutte polynomial

Perturbative calculations involving fermion loops in quantum field theories require tracing over Dirac matrices. A simple way to regulate the divergences that generically appear in these calculations is dimensional regularisation, which has the consequence of replacing 4-dimensional Dirac matrices with d-dimensional counterparts for arbitrary complex values of d. In this work, a connection between traces of d-dimensional Dirac matrices and computations of the Tutte polynomial of associated graphs is proven. The time complexity of computing Dirac traces is analysed by this connection, and improvements to algorithms for computing Dirac traces are proposed.

Renormalization and Regularization↗