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Results for “renormalization-group theory”

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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27 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Cold neutron-deuteron capture and Wigner-SU(4) symmetry

We calculate the cold neutron-deuteron (nd) capture cross section,σ nd to next-to-next-to leading order (NNLO) using the model-independent approach of pionless effective-field theory [EFT(π)]. At leading order we find σ nd = 0.314 ± 0.217 mb, while the experimental result is 0.508(15) mb for a laboratory neutron velocity of 2200 m/s. At next-to-leading-order (NLO), we show that σnd is sensitive to the low-energy constant (LEC) $L$$^{(0)}_{1}$ of the two-nucleon isovector current appearing at NLO. A fit of $L$$^{(0)}_{1}$ at NLO to the triton magnetic moment yields a NLO prediction of σ nd = 0.393 ± 0.164 mb, where the error comes from propagating the error from the $L$$^{(0)}_{1}$ fit. At NNLO, we find that a new three-nucleon magnetic moment counterterm is required for renormalization-group invariance of both σnd and the triton magnetic moment. Fitting the NNLO correction to $L$$^{(0)}_{1}$ (denoted $L$$^{(1)}_{1}$) to cold neutron-proton capture (σnp) yields a NNLO prediction of σ nd = 0.447 ± 0.130 mb, where the error comes from propagating the error from the $L$$^{(1)}_{1}$ fit. We also study different fittings of $L$$^{(0)}_{1}$ and $L$$^{(1)}_{1}$ to σ np , σ nd , and/or the triton magnetic moment. For example, fitting $L$$^{(0)}_{1}$ simultaneously to σ np , σ nd , and the triton magnetic moment at NLO, and fitting $L$$^{(1)}_{1}$ simultaneously to σ np and σnd at NNLO, yields σ nd = 0.480 ± 0.114 mb and 0.511 ± 0.042 mb, respectively, where errors are naively estimated from EFT(π) power counting. Additionally, we discuss how Wigner SU(4) symmetry may alter the naive EFT(π) expansion of σ nd .

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

Continuous phase transition between bosonic integer quantum Hall liquid and a trivial insulator: Evidence for deconfined quantum criticality

The deconfined quantum critical point, a prototype Landau-forbidden transition, could exist, in principle, in the phase transitions involving a symmetry-protected topological phase; however, examples of such kinds of transitions in physical systems are rare beyond one-dimensional systems. Here, using a density-matrix renormalization-group calculation, we unveil a bosonic integer quantum Hall phase in a two-dimensional correlated honeycomb lattice, by full identification of its internal structure from the topological K matrix. Furthermore, we demonstrate that imbalanced periodic chemical potentials can destroy the bosonic integer quantum Hall state and drive it into a featureless trivial (Mott) insulator, where all physical observables evolve smoothly across the critical point. At the critical point, the entanglement entropy reveals a characteristic scaling behavior, which is consistent with the critical field theory as an emergent QED3 with two flavors of Dirac fermions.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Renormalization group effects in dark matter interactions

We present a renormalization-group (RG) analysis of dark matter interactions with the standard model, where dark matter is allowed to be a component of an electroweak multiplet, and has a mass at or below the electroweak scale. We consider, in addition to the gauge interactions, the complete set of effective operators for dark matter interactions with the standard model above the weak scale, up to and including mass dimension six. We calculate the RG evolution of these operators from the high scale Λ down to the weak scale, and perform the matching to the tower of effective theories below the weak scale. We also summarize the RG evolution below the weak scale and the matching to the nonrelativistic nuclear interactions. We present several numerical examples and show that in certain cases the dark matter — nucleus scattering rate can change by orders of magnitude when the electroweak running is included.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2026

Proton isovector helicity PDF at NNLO and the twist-3 moment $\tilde{d}$ 2 from lattice QCD at physical quark masses

We present a lattice quantum chromodynamics calculation of the 𝑥-dependent isovector quark helicity parton distribution function (PDF) of the proton in the large momentum effective theory (LaMET) framework. Through operator product expansion (OPE) we also extract the $\tilde{d}$ 2 moment of the twist-3 PDF 𝑔 𝑇 ⁡(𝑥) for the first time in the $\overline{MS}$ scheme, which is proportional to the average color Lorentz force experienced by the quark in the proton. This calculation is performed on a lattice of spacing 𝑎 =0.076 fm at physical quark masses. The quasi-PDF matrix elements are measured in proton states boosted to momenta 𝑃 𝑧 ={0,0.25,1.02,1.53} GeV. We first extract the lowest few helicity PDF moments from the renormalization-group (RG) invariant ratios of the matrix elements with OPE. Combined with the matrix elements relevant for 𝑔 𝑇 ⁡(𝑥), we obtain $\tilde{d}$$^{u-d}_2$⁡(2 GeV) =0.0024⁢(46) at next-to-leading order in $\overline{MS}$. Then, the helicity quasi-PDF matrix elements are renormalized in the hybrid scheme with linear renormalon resummation and Fourier transformed to the 𝑥-space after an asymptotic extrapolation. The quasi-PDF is perturbatively matched to the $\overline{MS}$ PDF with RG and threshold resummations at next-to-leading power and next-to-next-to-leading logarithmic accuracies. After resummations, we determine the PDF in the region 𝑥 ∈[0.25,0.75]. The end-point regions are then parametrized, combined with the LaMET prediction at moderate 𝑥, and fitted to the short-distance matrix elements in coordinate space.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Pion valence quark distribution at physical pion mass of N f = 2 + 1 + 1 lattice QCD

Abstract We present a state-of-the-art calculation of the unpolarized pion valence-quark distribution in the framework of large-momentum effective theory (LaMET) with improved handling of systematic errors as well as two-loop perturbative matching. We use lattice ensembles generated by the MILC collaboration at lattice spacinga≈ 0.09 fm, lattice volume 64 3 × 96,N f = 2 + 1 + 1 flavors of highly-improved staggered quarks and a physical pion mass. The LaMET matrix elements are calculated with pions boosted to momentumP z ≈ 1.72 GeV with high-statistics ofO(10 6 ) measurements. We study the pion PDF in both hybrid-ratio and hybrid-regularization-independent momentum subtraction (hybrid-RI/MOM) schemes and also compare the systematic errors with and without the addition of leading-renormalon resummation (LRR) and renormalization-group resummation (RGR) in both the renormalization and lightcone matching. The final lightcone PDF results are presented in the modified minimal-subtraction scheme at renormalization scaleμ= 2.0 GeV. We show that thex-dependent PDFs are compatible between the hybrid-ratio and hybrid-RI/MOM renormalization with the same improvements. We also show that systematics are greatly reduced by the simultaneous inclusion of RGR and LRR and that these methods are necessary if improved precision is to be reached with higher-order terms in renormalization and matching.

Physics↗
DOE OSTI2021

Factorization at subleading power and endpoint divergences in h → γγ decay. Part II. Renormalization and scale evolution

Building on the recent derivation of a bare factorization theorem for the b-quark induced contribution to the h → γγ decay amplitude based on soft-collinear effective theory, we derive the first renormalized factorization theorem for a process described at subleading power in scale ratios, where λ = m b /M h « 1 in our case. We prove two refactorization conditions for a matching coefficient and an operator matrix element in the endpoint region, where they exhibit singularities giving rise to divergent convolution integrals. The refactorization conditions ensure that the dependence of the decay amplitude on the rapidity regulator, which regularizes the endpoint singularities, cancels out to all orders of perturbation theory. We establish the renormalized form of the factorization formula, proving that extra contributions arising from the fact that “endpoint regularization” does not commute with renormalization can be absorbed, to all orders, by a redefinition of one of the matching coefficients. We derive the renormalization-group evolution equation satisfied by all quantities in the factorization formula and use them to predict the large logarithms of order $αα^2_sL^k$ in the three-loop decay amplitude, where $L=ln(-M^2_h/m^2_b)$ and k = 6, 5, 4, 3. We find perfect agreement with existing numerical results for the amplitude and analytical results for the three-loop contributions involving a massless quark loop. On the other hand, we disagree with the results of previous attempts to predict the series of subleading logarithms $~αα^n_sL^{2n+1}$

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Rethinking 𝛼−RuCl 3 : Parameters, models, and phase diagram

RuCl 3 was likely the first ever deliberately synthesized ruthenium compound, following the discovery of the 44 Ru element in 1844. For a long time it was known as an oxidation catalyst, with its physical properties being discrepant and confusing, until a decade ago when its allotropic form 𝛼−RuCl 3 rose to exceptional prominence. This “rediscovery” of 𝛼−RuCl 3 has not only reshaped the hunt for a material manifestation of the Kitaev spin liquid, but it has opened the floodgates of theoretical and experimental research in the many unusual phases and excitations that the anisotropic-exchange magnets as a class of compounds have to offer. Given its importance for the field of Kitaev materials, it is astonishing that the low-energy spin model that describes this compound and its possible proximity to the much-desired spin-liquid state is still a subject of significant debate ten years later. In the present study, we argue that the existing key phenomenological observations put strong natural constraints on the effective microscopic spin model of 𝛼−RuCl 3 , and specifically on its spin-orbit-induced anisotropic-exchange parameters that are responsible for the nontrivial physical properties of this material. These constraints allow one to focus on the relevant region of the multidimensional phase diagram of the 𝛼−RuCl 3 model, suggest an intuitive description of it via a different parametrization of the exchange matrix, offer a unifying view on the earlier assessments of its parameters, and bring closer together several approaches to the derivation of anisotropic-exchange models. We explore extended phase diagrams relevant to the 𝛼−RuCl 3 parameter space using quasiclassical, Luttinger-Tisza, exact diagonalization, and density-matrix renormalization-group methods, demonstrating a remarkably close quantitative accord between them on the general structure and hierarchy of the phases, with the zigzag, ferromagnetic, and incommensurate phases that are proximate to each other. As a result, one of the highlights is the detailed agreement on the nature of the incommensurate phases that realize two distinct counterrotating helical states.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Renormalization-group approach to Kohn-Luttinger superconductivity: Amplification of the pairing gap from ℓ 4 to ℓ

Here, we revisit the renormalization group (RG) analysis of the Kohn-Luttinger (KL) mechanism for superconductivity. The KL mechanism leads to superconductivity in a system with a repulsive bare interaction. The key ingredient is the screening effect that renders the induced interaction attractive in channels with nonzero angular momentum ℓ ≠ 0, thereby triggering the Bardeen-Cooper-Schrieffer (BCS) instability. According to the original argument, the resulting gap is exponentially small, with its exponent scaling as −ℓ 4 . However, the KL mechanism was originally formulated within perturbation theory, where the series is known to converge poorly in certain cases—most notably, for the 𝑝-wave paring gap induced by a repulsive 𝑠-wave contact interaction. This poor convergence may be attributed to a divergent integrand in a specific class of diagrams containing both the BCS logarithm and the Kohn anomaly, suggesting that one must resum the Kohn anomaly contributions separately from the BCS logarithm. In this work, we incorporate the Kohn anomaly contribution into the 𝛽 function of the RG equation governing the BCS instability near the Fermi surface. Our solution shows that the KL gap exponent is then proportional to −ℓ, indicating a significant enhancement of the KL mechanism beyond the previously known result. To illustrate this, we study the spin-triplet 𝑝-wave pairing gap arising from a repulsive 𝑠-wave contact interaction and compare our RG-based results with those obtained from the Bethe-Salpeter equation in perturbation theory.

nuclear matter in neutron stars↗
DOE OSTI2025

Holographic codes and bulk RG flows

We consider the coarse-graining of holographic quantum error correcting codes under a generalized notion of bulk renormalization-group flow. In particular, we study the renormalization under this flow of the $A/4G$ term in the Faulkner-Lewkowycz-Maldacena formula and in its Rényi generalization. This provides a general quantum code perspective on the arguments of Susskind and Uglum. Specifically, given a 'UV' code with two-sided recovery and appropriately flat entanglement spectrum together with a set of 'seed' states in the UV code, we explicitly construct an 'IR' code with corresponding properties which contains the given seed states and is of minimal size in a sense we describe.

FOS: Physical sciences↗