Renormalization Factor Research Articles

Flavor factorization at two-loops

Recently, a factorization theorem was proposed for partonic flavor evolution as defined by the net flavor of the Winner-Take-All axis of a jet. We validate the factorization theorem through explicit calculation at two-loop order, and in the process extract all anomalous dimensions and renormalization factors for any ultraviolet-to-infrared flavor transition at this order. These results can then be used to extract the renormalized hard function for flavored jet production at next-to-next-to-leading order for any process of interest.

Spontaneous CP violation in supersymmetric QCD

We investigate a composite model of spontaneous CP violation based on a new supersymmetric QCD as a solution to the strong CP problem. The scalar components of the meson chiral superfields obtain complex vacuum expectation values to break CP symmetry spontaneously. Then, wavefunction renormalization for the quark kinetic terms provides the Cabibbo-Kobayashi-Maskawa (CKM) phase, while the strong CP phase θ¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\overline{\ heta} $$\\end{document} is protected by nonrenormalization of the superpotential and hermiticity of the wavefunction renormalization factor. In our model, the right-handed down-type quark multiplets are given by composite states, enhancing their couplings to CP breaking fields, which is essential to realize the observed CKM phase. The non-perturbative dynamics generates the scale of spontaneous CP violation hierarchically lower than the Planck scale. We discuss potential corrections to θ¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\overline{\ heta} $$\\end{document} and find a viable parameter space of the model to solve the strong CP problem without fine-tuning.

Quantum and classical spin dynamics across temperature scales in the S=1/2 Heisenberg antiferromagnet

Using the framework of semiclassical Landau-Lifshitz dynamics (LLD), we conduct a systematic investigation of the temperature-dependent spin dynamics in the S=1/2 Heisenberg square-lattice antiferromagnet (SAFM). By performing inelastic neutron scattering measurements on Zn2VO(PO4)2 (ZVPO) and corresponding finite-temperature spin dynamics simulations based on LLD, we present a comprehensive analysis that bridges quantum and classical spin dynamics over a broad temperature range. First, remarkable agreement between experimental data and LLD simulations is found in the paramagnetic phase of ZVPO, demonstrating the capability of LLD in accurately determining the spin Hamiltonian of S=1/2 systems and capturing the quantum-to-classical crossover of their spin dynamics. Second, by analyzing the discrepancies between the experimental data and the LLD simulations at lower temperatures, we determine the experimental temperature dependence of the quantum effects in the excitation spectrum of the S=1/2 SAFM: the quantum renormalization factor for the magnon energies and the quantum continuum above the one-magnon bands. Notably, the emergence of each quantum effect is found to correlate with the formation of three-dimensional long-range order. This work demonstrates the utility of LLD in gaining experimental insights into the temperature-induced modifications of quantum spin dynamics and their convergence towards classical expectations at higher temperatures. This motivates further applications to more challenging quantum antiferromagnets dominated by stronger quantum fluctuations. Published by the American Physical Society 2024

Renormalization of nonlocal gluon operators on the lattice

Wen study the renormalization of a complete set of gauge-invariant gluon nonlocal operators in lattice perturbation theory. We determine the mixing pattern under renormalization of these operators using symmetry arguments, which extend beyond perturbation theory. Additionally, we derive the renormalization factors of the operators within the modified minimal subtraction (MS¯) scheme up to one loop. To enable a nonperturbative renormalization procedure, we investigate a suitable version of the modified regularization-invariant (RI′) scheme, and we calculate the conversion factors from that scheme to MS¯. The computations are performed by employing both dimensional and lattice regularizations, using the Wilson gluon action. This work is relevant to nonperturbative studies of the gluon parton distribution functions (PDFs) on the lattice. Published by the American Physical Society 2024

Non-perturbative renormalisation and improvement of non-singlet tensor currents in Nf = 3 QCD

Hadronic matrix elements involving tensor currents play an important rôle in decays that allow to probe the consistency of the Standard Model via precision lattice QCD calculations. The non-singlet tensor current is a scale-dependent (anomalous) quantity. We fully resolve its renormalisation group (RG) running in the continuum by carrying out a recursive finite-size scaling technique. In this way ambiguities due to a perturbative RG running and matching to lattice data at low energies are eliminated. We provide the total renormalisation factor at a hadronic scale of 233 MeV, which converts the bare current into its RG-invariant form.Our calculation features three flavours of O(a) improved Wilson fermions and tree-level Symanzik-improved gauge action. We employ the (massless) Schrödinger functional renormalisation scheme throughout and present the first non-perturbative determination of the Symanzik counterterm cT derived from an axial Ward identity. We elaborate on various details of our calculations, including two different renormalisation conditions.

Correction of cloud optical thickness retrievals from nadir reflectances in the presence of 3D radiative effects. Part I: concept and tests on 3D RT simulations

3D effects cause substantial underestimation of cloud optical thickness (COT) in airborne and satellite retrievals based on 1D radiative transfer computations (such as in the case of widely used bispectral technique). For a single-layer isolated cloud we propose a simple linear correction of the retrieved COT with the renormalization factor dependent on the cloud’s aspect ratio (the ratio between vertical and horizontal dimensions of the cloud). This is an empirical assumption which we successfully test using synthetic 3D RT data. We introduce a heuristic “block model” of 3D radiative effects and show that the functional form of the renormalization factor is consistent with the process of radiation escape from cloud sides in an essentially 3D geometry. We also extend the block model to the case of single-layer broken cloud field with radiative interaction between the neighboring clouds. In this case the renormalization factor depends also on the distance between clouds.

Electron-photon exchange-correlation approximation for quantum-electrodynamical density-functional theory

Quantum-electrodynamical density-functional theory (QEDFT) provides a promising avenue for exploring complex light-matter interactions in optical cavities for real materials. Similar to conventional density-functional theory, the Kohn-Sham formulation of QEDFT needs approximations for the generally unknown exchange-correlation functional. In addition to the usual electron-electron exchange-correlation potential, an approximation for the electron-photon exchange-correlation potential is needed. A recent electron-photon exchange functional [C. Schäfer , ], derived from the equation of motion of the nonrelativistic Pauli-Fierz Hamiltonian, shows robust performance in one-dimensional systems across weak- and strong-coupling regimes. Yet, its performance in reproducing electron densities in higher dimensions remains unexplored. Here we consider this QEDFT functional approximation from one- to three-dimensional finite systems and across weak to strong light-matter couplings. The electron-photon exchange approximation provides excellent results in the ultrastrong-coupling regime. However, to ensure accuracy also in the weak-coupling regime across higher dimensions, we introduce a computationally efficient renormalization factor for the electron-photon exchange functional, which accounts for part of the electron-photon correlation contribution. These findings extend the applicability of photon-exchange-based functionals to realistic cavity-matter systems, fostering the field of cavity QED (quantum-electrodynamics) materials engineering. Published by the American Physical Society 2024

Multicentric characterisation of lateral beam profiles generated by 6FFF beam of three 0.35 T MR-linac systems

BackgroundThe physical characterisation of FFF-beam profiles in the presence of a magnetic field requires a new standardization procedure and formulation. PurposeThe aim of this multicentric experience is to propose new normalisation factors to allow for the calculation of standard parameters typical of flattened beams, such as dosimetric field size and penumbra, for a 6 MV FFF beam from an MR-linac. MethodsThe measurements were carried out on three ViewRay-MRIdiansystems. An equal set of measurements was acquired using the same equipment. Transverse beam profiles were acquired at seven different depthsand for six beam dimensions.The inflection point was estimated as the position of the maximum of a Gaussian fit obtained from the first derivative of the profiles. The position of the minimum and maximum points of the second derivative of the above Gaussian described the fall-off region, and the external peaks of the third derivative were considered as the in-field and out-field points. The profile normalisation was determined by imposing a 55% dose level at the inflection point and the renormalisation factors were calculated. ResultsThe position of the inflection point, and the second and third derivatives peaks were analysed,and the renormalisation factors as a function of field size and depth were determined. The values of the unflatness and the slope have been calculated for different depths and field sizes. ConclusionThis study represents the first multi-centric evaluation of the profiles on different low-field MR-Linac systems and theset of renormalisation parameters to analyse the FFF-beam on that system was effectively proposed.

Supersymmetric QCD on the lattice: Fine-tuning of the Yukawa couplings

We determine the fine-tuning of the Yukawa couplings of supersymmetric QCD, discretized on a lattice. We use perturbation theory at one-loop level. The modified minimal subtraction scheme (MS¯) is employed; by its definition, this scheme requires perturbative calculations, in the continuum and/or on the lattice. On the lattice, we utilize the Wilson formulation for gluon, quark, and gluino fields; for squark fields we use naive discretization. The sheer difficulties of this study lie in the fact that different components of squark fields mix among themselves at the quantum level and the action’s symmetries, such as parity and charge conjugation, allow an additional Yukawa coupling. Consequently, for an appropriate fine-tuning of the Yukawa terms, these mixings must be taken into account in the renormalization conditions. All Green’s functions and renormalization factors are analytic expressions depending on the number of colors, Nc, the number of flavors, Nf, and the gauge parameter, α, which are left unspecified. Knowledge of these renormalization factors is necessary in order to relate numerical results, coming from nonperturbative studies, to the renormalized, “physical” Green’s functions of the theory. Published by the American Physical Society 2024

A Composite Ansatz for Calculation of Dynamical Structure Factor

We propose an ansatz without adjustable parameters for the calculation of a dynamical structure factor. The ansatz combines the quasi-particle Green’s function, especially the contribution from the renormalization factor, and the exchange-correlation kernel from time-dependent density functional theory together, verified for typical metals and semiconductors from a plasmon excitation regime to the Compton scattering regime. It has the capability to reconcile both small-angle and large-angle inelastic x-ray scattering (IXS) signals with much-improved accuracy, which can be used as the theoretical base model, in inversely inferring electronic structures of condensed matter from IXS experimental signals directly. It may also be used to diagnose thermal parameters, such as temperature and density, of dense plasmas in x-ray Thomson scattering experiments.

Phase coexistence in a half-filled extended Hubbard model

We analyze the coexisting ordered phases that arise in the half-filled [Formula: see text]-t-U-V extended Hubbard Model on the square lattice when tackled within the Kotliar and Ruckenstein slave boson representation in the thermodynamical limit. Particular emphasis is put on the dependence of the quasi-particle dispersions, the gaps, the spin-resolved renormalization factors, and the distribution of double occupancy on the microscopical parameters of the model. Our calculations are performed in a parameter range that is most suitable for resistive switching. In particular, the main contributions to the gaps are shown to either arise from [Formula: see text] in the weak coupling regime, or from U and V when they are the largest scales. The gaps are thus from joint spin and charge origin, and so are the order parameters.

Global density-dependent α–nucleon interaction for α–nucleus elastic scattering

Abstract We provide a global density-dependent 4He–nucleon (DD-αN) interaction to construct the α–nucleus optical model potential (OMP) across a wide range of incident energies. The global parametrization for the DD-αN interaction is obtained based on the proton–4He OMP, which reproduces the elastic scattering cross-section data very well in the incident energies of 12.04–500 MeV per nucleon. Using the present DD-αN interaction, we derive the α–nucleus potential by a folding procedure with the point-nucleon density obtained by a microscopic mean-field model. The density dependence of the DD-αN interaction is fixed phenomenologically to reproduce the α–nucleus elastic scattering cross-section data obtained from 16O, 40Ca, 58Ni, 90Zr, and 208Pb targets at E/A = 10–342.5 MeV. We also show the total reaction cross sections, which are helpful in fixing one free parameter, the renormalization factor for the imaginary part of the α–nucleus potential. Lastly, we show some examples, which clearly demonstrate the validity and power of the present DD-αN approach.

Double folding analysis of the α+28Si elastic scattering system

Using the double folding model (DFM), we reanalyzed 20 sets of experimental angular distributions for the elastic scattering [Formula: see text]+[Formula: see text]Si system in a wide energy range of [Formula: see text]-particles from 12.7[Formula: see text]MeV to 240[Formula: see text]MeV. We used three effective nucleon–nucleon (NN) interactions that are CDM3Y6, São Paulo Potential (SPP2), and Brazilian Nuclear Potential (BNP) to generate the DF potentials. The data analysis was performed using semi-microscopic (SM) and fully microscopic (FM) methods. In the SM approach, the real part of the optical potential (OP) is created with the DFM, and the Woods–Saxon (WS) potential is considered for the imaginary part of the OP. In the FM approach, the DF potential renormalization factors [Formula: see text] and [Formula: see text] for the real and imaginary parts of the OP were extracted. We investigated the energy dependencies of the [Formula: see text] and [Formula: see text] factors, as well as of nuclear potential volume integrals and reaction cross-sections. We reasonably reproduced the data using [Formula: see text] and [Formula: see text] factors obtained from their energy-dependent functions.

Nonperturbative renormalization of the supercurrent in N=1 supersymmetric Yang-Mills theory

In this work, we study the nonperturbative renormalization of the supercurrent operator in $\mathcal{N}=1$ supersymmetric Yang-Mills theory, using a gauge-invariant renormalization scheme (GIRS). The proposed prescription addresses successfully the unwanted mixing of the supercurrent with other operators of equal or lower dimension, which respect the same global symmetries. This mixing is introduced by the unavoidable breaking of supersymmetry on the lattice. In GIRS all gauge-noninvariant operators, which mix with the supercurrent, are excluded from the renormalization procedure. The one remaining mixing operator is accessible by numerical simulations. We present results for the renormalization of the supercurrent using GIRS. We also compute at one-loop order the conversion matrix which relates the nonperturbative renormalization factors in GIRS to the reference scheme $\overline{\mathrm{MS}}$.

Break-up effect on 7Li + 28Si elastic scattering angular distributions

The 7Li + 28Si angular distributions for elastic scattering in the laboratory energy range of 8.5–36 MeV are reanalyzed using different approaches based on both phenomenological and microscopic potentials. Special attention is paid to the α + t cluster structure for 7Li, which appears at a threshold energy of 2.468 MeV. The performed analysis using the different implemented potentials showed that the breakup of 7Li in the field of 28Si plays a strong effect in forming the cross sections. Such an effect results in a significant reduction in the renormalization factors of the utilized potentials. A satisfactory description of the data is achieved using the different implemented approaches.

Five-loop anomalous dimensions of ϕQ operators in a scalar theory with O(N) symmetry

We compute the complete Q-dependence of anomalous dimensions of traceless symmetric tensor operator ϕQ in O(N) scalar theory to five-loop. The renormalization factors are extracted from ϕQ→ Qϕ form factors, and the integrand of form factors are constructed with the help of unitarity cut method. The anomalous dimensions match the known results in [1, 2], where the leading and subleading terms in the large Q limit were obtained using a semiclassical method.

Optical model and coupled reaction channels analyses of the 9Be+12C elastic scattering

This work analyzes the elastic scattering angular distribution data of the 9Be+12C system in the energy range of 13–50 MeV using the optical model (OM). The real and imaginary parts of the optical potential (OP) are generated using the double-folding (DF) model. In the DF model, three different effective nucleon-nucleon (NN) interactions are used. These effective NN interactions are the density-dependent CDM3Y6, the latest São Paulo Potential version 2 (SPP2), and the Brazilian Nuclear Potential (BNP). In the DF calculations, the renormalization factors NR and NI of real and imaginary parts of the OP were allowed to freely vary. We considered the elastic transfer of the 3He-cluster in our calculations using the coupled reaction channels (CRC) method. We extracted the optimum values of the spectroscopic amplitudes (SA) for the dissociation 12C→9Be+3He during the CRC analysis. The energy dependencies of real and imaginary potential depths, potential volume integrals, and reaction cross sections have been studied.

Perturbative renormalization of the supercurrent operator in lattice N=1 supersymmetric Yang-Mills theory

In this work we perform a perturbative study of the Noether supercurrent operator in the context of supersymmetric $\mathcal{N}=1$ Yang-Mills theory on the lattice. The supercurrent mixes with several other operators, some of which are not gauge invariant, having the same quantum numbers. We determine, to one-loop order, the renormalization and all corresponding mixing coefficients by computing the relevant Green's functions of each one of the mixing operators with external elementary fields. Our calculations are performed both in dimensional and lattice regularization. From the first regularization we obtain the $\overline{\mathrm{MS}}$-renormalized Green's functions; comparison of the latter with the corresponding Green's functions in the lattice regularization leads to the extraction of the lattice renormalization factors and mixing coefficients in the $\overline{\mathrm{MS}}$ scheme. The lattice calculations are performed to lowest order in the lattice spacing, using Wilson gluons and clover improved gluinos. The lattice results can be used in nonperturbative studies of supersymmetric Ward identities.

Eliashberg theory of the Jahn-Teller-Hubbard model

We study a multiorbital Hubbard model coupled to local Jahn-Teller phonons to investigate the superconducting state realized in fullerides. A weak-coupling approach is employed in combination with a local self-energy approximation. In addition to the normal and anomalous self-energies of the electrons, we consider the phonon self-energy, which allows a self-consistent treatment of the energetics. The frequency dependence of the self-energies and their characteristic coefficients, such as renormalization factors and dampings, are investigated in detail using numerical calculations. It is clarified that the anisotropic phonons play an important role in the stabilization of the superconducting state. By comparing the full results to those without phonon self-energies, we show that the superconductivity is stabilized by the softening of the phonon frequency. The effects of electronic fluctuations are also considered, which leads to the coupling to orbitons, an analog of plasmons in the electron gas. This additional contribution further stabilizes the superconducting state.

Gutzwiller approximation approach to the SU(4) t−J model

We develop the Gutzwiller approximation method to obtain the renormalized Hamiltonian of the SU(4) $t\text{\ensuremath{-}}J$ model with the corresponding renormalization factors. Subsequently, a mean-field theory is employed on the renormalized Hamiltonian of the model on the honeycomb lattice under the scenario of a cooperative condensation of carriers moving in the resonating valence bond state of flavors. In particular, we find that the extended $s$-wave superconducting state is more favorable than the $d\ifmmode\pm\else\textpm\fi{}id$-wave superconducting state in the doping range close to quarter filling. The pairing states of the SU(4) case reveal the property that the spin-singlet pairing and the spin-triplet pairing can coexist simultaneously. Our results might provide new insights into the twisted bilayer graphene system.