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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
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Renormalon cancellation and linear power correction to threshold-like asymptotics of space-like parton correlators

Abstract In this paper, we show that the common hard kernel of double-log-type or threshold-type factorization for certain space-like parton correlators that arise in the context of lattice parton distributions, theheavy-light Sudakov hard kernel, has linear infrared (IR) renormalon. We explicitly demonstrate how this IR renormalon correlates with ultraviolet (UV) renormalons of next-to-leading power operators in two explicit examples: threshold asymptotics of space-like quark-bilinear coefficient functions and transverse momentum dependent (TMD) factorization of quasi wave function amplitude. Theoretically, the pattern of renormalon cancellation complies with general expectations to marginal asymptotics in the UV limit. Practically, this linear renormalon explains the slow convergence of imaginary parts observed in lattice extraction of the Collins-Soper kernel and signals the relevance of next-to-leading power contributions. Fully factorized, fully controlled threshold asymptotic expansion for space-like quark-bilinear coefficient functions in coordinate and moment space has also been proposed.

Physics↗
DOE OSTI2019

Non-local Lagrangians from renormalons and analyzable functions

We embed in a generalized Borel procedure the notion of renormalization and renormalons. While there are several efforts in literature to have a semi-classical understanding of the renormalons, here we argue that this is not the fundamental issue and show how to deal with the problem. We find that the effective Lagrangians describing the effects of renormalons are non-local in space but local in time. The quark–antiquark potential in QCD with an infinite number of fermions is also analyzed. The connection between the analyzable functions, the Callan–Symanzyk equation and the renormalons, provides an insight of a non-perturbative renormalization from the standard perturbative renormalization approach.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Effects of renormalon scheme and perturbative scale choices on determinations of the strong coupling from e + e − event shapes

We study the role of renormalon cancellation schemes and perturbative scale choices in extractions of the strong coupling constant α s ( m Z ) and the leading nonperturbative shift parameter Ω 1 from resummed predictions of the e + e − event shape thrust. We calculate the thrust distribution to N L 3 L ′ resummed accuracy in soft-collinear effective theory (SCET) matched to the fixed-order O ( α s 2 ) prediction, and perform a new high-statistics computation of the O ( α s 3 ) matching in , although we do not include the latter in our final α s fits due to some observed systematics that require further investigation. We are primarily interested in testing the phenomenological impact sourced from varying amongst three renormalon cancellation schemes and two sets of perturbative scale profile choices. We then perform a global fit to available data spanning center-of-mass energies between 35–207 GeV in each scenario. Relevant subsets of our results are consistent with prior SCET-based extractions of α s ( m Z ) , but we are also led to a number of novel observations. Notably, we find that the combined effect of altering the renormalon cancellation scheme and profile parameters can lead to few-percent-level impacts on the extracted values in the α s − Ω 1 plane, indicating a potentially important systematic theory uncertainty that should be accounted for. We also observe that fits performed over windows dominated by dijet events are typically of a higher quality than those that extend into the far tails of the distributions, possibly motivating future fits focused more heavily in this region. Finally, we discuss how different estimates of the three-loop soft matching coefficient c S ˜ 3 can also lead to measurable changes in the fitted { α s , Ω 1 } values. Published by the American Physical Society 2024

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2018

The MSR mass and the $ \mathcal{O}\left({\Lambda}_{\mathrm{QCD}}\right) $ renormalon sum rule

Here, we provide a detailed description and analysis of a low-scale short-distance mass scheme, called the MSR mass, that is useful for high-precision top quark mass determinations, but can be applied for any heavy quark Q. In contrast to earlier low-scale short-distance mass schemes, the MSR scheme has a direct connection to the well known MS¯ mass commonly used for high-energy applications, and is determined by heavy quark on-shell self-energy Feynman diagrams. Indeed, the MSR mass scheme can be viewed as the simplest extension of the MS¯mass concept to renormalization scales << mQ. The MSR mass depends on a scale R that can be chosen freely, and its renormalization group evolution has a linear dependence on R, which is known as R-evolution. Using R-evolution for the MSR mass we provide details of the derivation of an analytic expression for the normalization of the $ \mathcal{O}\left({\Lambda}_{\mathrm{QCD}}\right) $ renormalon asymptotic behavior of the pole mass in perturbation theory. This is referred to as the $ \mathcal{O}\left({\Lambda}_{\mathrm{QCD}}\right) $ renormalon sum rule, and can be applied to any perturbative series. The relations of the MSR mass scheme to other low-scale short-distance masses are analyzed as well.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2019

Bion non-perturbative contributions versus infrared renormalons in two-dimensional $\mathbb{C}$P N - 1 models

We derive the semiclassical contributions from the real and complex bions in the two-dimensional $\mathbb{C}$ P N 1 sigma model on $\mathbb{R}$× S 1 with a twisted boundary condition. The bion configurations are saddle points of the complexified Euclidean action, which can be viewed as bound states of a pair of fractional instantons with opposite topological charges. We first derive the bion solutions by solving the equation of motion in the model with a potential which simulates an interaction induced by fermions in the $\mathbb{C}$ P N - 1 quantum mechanics. The bion solutions have quasi-moduli parameters corresponding to the relative distance and phase between the constituent fractional instantons. By summing over the Kaluza-Klein modes of the quantum fluctuations around the bion backgrounds, we find that the effective action for the quasi-moduli parameters is renormalized and becomes a function of the dynamical scale (or the renormalized coupling constant). Based on the renormalized effective action, we obtain the semiclassical bion contribution in a weak coupling limit by making use of the Lefschetz thimble method. We find in the supersymmetric case that the bion contribution vanishes as expected from supersymmetry. In non-supersymmetric cases, the non-perturbative contribution has an imaginary ambiguity which is consistent with the expected infrared renormalon ambiguity. Our results explicitly demonstrate that the complex bion can explain the infrared renormalon.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

Renormalons in the energy-energy correlator

The energy-energy correlator (EEC) is an observable of wide interest for collider physics and Standard Model measurements, due to both its simple theoretical description in terms of the energy-momentum tensor and its novel features for experimental studies. Significant progress has been made in both applications and higher-order perturbative predictions for the EEC. Here, we analyze the nature of the asymptotic perturbative series for the EEC by determining its analytic form in Borel space under the bubble-sum approximation. This result provides information on the leading and subleading nonperturbative power corrections through renormalon poles. We improve the perturbative convergence of the $\overline{MS}$ series for the EEC by removing its leading renormalon using an MSR scheme, which is independent of the bubble-sum approximation. Using the leading MSR scheme power correction determined by fits to thrust, we find good agreement with EEC OPAL data already at O(α$^{2}_{s}$).

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2018

Renormalons in a general Quantum Field Theory

We generalize the concept of Borel resummability and renormalons to a quantum field theory with an arbitrary number of fields and couplings, starting from the known notion based on the running coupling constants. An approach to identify the renormalons is provided by exploiting an analytic solution of the generic one-loop renormalization group equations in multi-field theories. Methods to evaluate the regions in coupling space where the theory is resummable are described. The generalization is then illustrated in a toy model with two coupled scalar fields, representing the simplest extension of the one-field analysis presented in the seminal works of the subject. Furthermore, possible links to realistic theories are briefly discussed.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

More on minimal renormalon subtraction

The minimal renormalon subtraction (MRS) [arXiv:1802.04248; arXiv:1712.04983; arXiv:1701.00347; arXiv:2310.15137] technique is summarized. A new result is a study of the scale dependence of the pole-mass--$\overline{\rm MS}$-mass ratio in MRS perturbation theory. As expected, the scale dependence is much milder than in standard perturbation theory, but it is a bit larger than other truncation effects such as omitting the N3LO term or varying the normalization of the renormalon subtraction.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2026

Renormalon subtracted nonrelativistic QCD for heavy hadron systems

We present a renormalon-subtracted formulation of potential nonrelativistic QCD (pNRQCD) for precision spectroscopy of heavy hadron systems, combining variational and Green's function Monte Carlo (VMC/GFMC) methods with NNLO static two- and three-body potentials. Minimal renormalon subtraction (MRS) systematically sums leading factorially growing terms, thereby stabilizing perturbative convergence and reducing renormalization-scale dependence. We tune charm and bottom quark masses to spin-averaged $1S$ quarkonium states and predict $Ω_{ccc}$, $Ω_{ccb}$, $Ω_{cbb}$, and $Ω_{bbb}$ baryon masses, as well as QCD-stable baryons containing top quarks. NNLO MRS results undershoot lattice QCD by 125--175~MeV, with fractional differences decreasing as $\sim 1/m_Q$, consistent with neglected $\mathcal{O}(1/m_Q)$ corrections. Applying these methods to unequal-mass fully-heavy tetraquarks, we determine the critical heavy-to-light mass ratio for binding and compute binding energies across the mass-ratio landscape.

Assi, Benoît [Cincinnati U.; Fermilab]↗
DOE OSTI2022

The QCD Adler Function and the Muon g − 2 Anomaly from Renormalons

We describe the Adler function in Quantum Chromodynamics using a transseries representation within a resurgent framework. The approach is based on a Borel-Ecalle resummation of the infrared renormalons combined with an effective running for the strong coupling. The new approach is flexible enough to give values in agreement with the current Adler function determinations. We then apply our finding to the muon’s anomalous magnetic moment studying the possibility of saturating, solely in terms of the vacuum polarization function, the current discrepancy between the best Standard Model value for the muon’s anomalous magnetic moment and the experimental value obtained by the most recent muon g−2 collaboration. The latter shows that the Adler function’s new representation can also be consistent with recent lattice determinations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Towards the QED beta function and renormalons at $1/N_f^2$ and $1/N_f^3$

We determine the 1 / N f 2 and 1 / N f 3 contributions to the QED beta function stemming from the closed set of nested diagrams. At the order of 1 / N f 2 , we discover a new logarithmic branch cut closer to the origin when compared to the 1 / N f results. The same singularity location appears at 1 / N f 3 , and these correspond to a UV renormalon singularity in the finite part of the photon two-point function.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Renormalons and power corrections in pseudo- and quasi-GPDs

High-order behavior of the perturbative expansion for short-distance observables in QCD is intimately related to the contributions of small momenta in the corresponding Feynman diagrams and this correspondence provides one with a useful tool to investigate power-suppressed nonperturbative corrections. We use this technique to study the structure of power corrections to parton quasi- and pseudo-GPDs which are used in lattice calculations of generalized parton distributions. As the main result, we predict the functional dependence of the leading power corrections to quasi(pseudo)-GPDs on x variable for nonzero skewedness parameter ξ . The kinematic point x = ± ξ turns out to be special. We find that the nonperturbative corrections to quasi-GPDs at this point are suppressed by the first power of the hard scale only. These contributions come from soft momenta and have nothing to do with the known UV renormalon in the Wilson line. We also show that power corrections can be strongly suppressed by the normalization procedure. Published by the American Physical Society 2024

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

Resurgence of the renormalization group equation

We show how the renormalons emerge from the renormalization group equation with a priori no reference to any Feynman diagrams. The proof is rather given by recasting the renormalization group equation as a resurgent equation studied in the mathematical literature, which describes a function with an infinite number of singularities in the positive axis of the Borel plane. Consistency requires a one-to-one correspondence between the existence of such kind of equation and the actual (generalized) Borel resummation of the renormalons through a one-parameter transseries. Our finding suggests how non-perturbative contributions can affect the running couplings. We also discuss these concepts within the context of gauge theories, making use of the large number of flavor expansion.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Factorial growth at low orders in perturbative QCD: control over truncation uncertainties

A method, known as “minimal renormalon subtraction”, relates the factorial growth of a perturbative series (in QCD) to the power p of a power correction Λ p /Q p . (Λ is the QCD scale, Q some hard scale.) Here, the derivation is simplified and generalized to any p , more than one such correction, and cases with anomalous dimensions. Strikingly, the well-known factorial growth is seen to emerge already at low or medium orders, as a consequence of constraints on the Q dependence from the renormalization group. The effectiveness of the method is studied with the gluonic energy between a static quark and static antiquark (the “static energy”). Truncation uncertainties are found to be under control after next-to-leading order, despite the small exponent of the power correction ( p = 1) and associated rapid growth seen in the first four coefficients of the perturbative series.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗