Vertex Corrections Research Articles

Dependence of the Landau gauge ghost-gluon-vertex on the number of flavors

The gauge-boson, ghost and fermion propagators as well as the gauge-boson-ghost vertex function are studied for SU(N), Sp(2N), and SO(N) gauge groups. We solve a set of coupled Dyson-Schwinger equations in Landau gauge for a variable, fractional number Nf of massless fermions in the fundamental representation. For large Nf we find a phase transition from a chirally broken into a chirally symmetric phase that is consistent with the behavior expected inside the conformal window. Even in the presence of fermions the gauge-boson-ghost-vertex dressing remains small. In the conformal window this vertex shows the expected power law behavior. It does not assume its tree-level value in the far infrared, but the respective dressing function is a constant greater than 1. Published by the American Physical Society 2024

Fully Dynamic G3W2 Self-Energy for Finite Systems: Formulas and Benchmark.

Over the years, Hedin's GW self-energy has been proven to be a rather accurate and simple approximation to evaluate electronic quasiparticle energies in solids and in molecules. Attempts to improve over the simple GW approximation, the so-called vertex corrections, have been constantly proposed in the literature. Here, we derive, analyze, and benchmark the complete second-order term in the screened Coulomb interaction W for finite systems. This self-energy named G3W2 contains all the possible time orderings that combine 3 Green's functions G and 2 dynamic W. We present the analytic formula and its imaginary frequency counterpart, with the latter allowing us to treat larger molecules. The accuracy of the G3W2 self-energy is evaluated on well-established benchmarks (GW100, Acceptor 24, and Core 65) for valence and core quasiparticle energies. Its link with the simpler static approximation, named SOSEX for static screened second-order exchange, is analyzed, which leads us to propose a more consistent approximation named 2SOSEX. In the end, we find that neither the G3W2 self-energy nor any of the investigated approximations to it improve over one-shot G0W0 with a good starting point. Only quasi-particle self-consistent GW HOMO energies are slightly improved by addition of the G3W2 self-energy correction. We show that this is due to the self-consistent update of the screened Coulomb interaction, leading to an overall sign change of the vertex correction to the frontier quasiparticle energies.

Superfluid stiffness within Eliashberg theory: The role of vertex corrections

Superfluid stiffness within Eliashberg theory: The role of vertex corrections

The B0→J/ψf0(1370,1500,1710)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$B^0 \\rightarrow J/\\psi f_0(1370,1500,1710)$$\\end{document} decays: an opportunity for scalar glueball hunting

The scalars f0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f_0$$\\end{document} closest to 1.5 GeV contain the mesons f0(1370)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f_0(1370)$$\\end{document}, f0(1500)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f_0(1500)$$\\end{document} and f0(1710)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f_0(1710)$$\\end{document}, and the latter two ones are usually viewed as the potential candidates for the scalar glueballs. In this work, by including the important contributions from the vertex corrections, we study the decays B0→J/ψf0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$B^0 \\rightarrow J/\\psi f_0$$\\end{document} within the improved perturbative QCD approach and analyze the possible scalar glueball hunting. Together with the two mixing models, namely, f0(1500)(f0(1710))\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f_0(1500) (f_0(1710))$$\\end{document} being the primary scalar glueball in model I (II), and two classification scenarios, namely, f0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f_0$$\\end{document} being the qq¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$q\\bar{q}$$\\end{document} excited (ground) states in scenario 1 (2), the branching fractions associated with their ratios for B0→J/ψf0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$B^0 \\rightarrow J/\\psi f_0$$\\end{document} are evaluated comprehensively. The predictions with still large uncertainties in the considered two mixing models are roughly consistent with currently limited data, which indicates that both more rich data and more precise predictions are urgently demanded to figure out the scalar glueball clearly in the future. Moreover, several interesting ratios between the branching fractions of B0→J/ψf0(→π+π-/K+K-)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$B^0 \\rightarrow J/\\psi f_0(\\rightarrow \\pi ^+ \\pi ^-/K^+ K^-)$$\\end{document} and B0→J/ψρ0/ϕ(→π+π-/K+K-)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$B^0 \\rightarrow J/\\psi \\rho ^0/\\phi (\\rightarrow \\pi ^+ \\pi ^-/ K^+ K^-)$$\\end{document} that could help us to understand the nature of scalar f0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f_0$$\\end{document} are defined and predicted theoretically. These ratios should be examined in future experiments.

Polynomial Superpotential for Grassmannian $${\text {Gr}}(k,n)$$ from a Limit of Vertex Function

Polynomial Superpotential for Grassmannian $${\text {Gr}}(k,n)$$ from a Limit of Vertex Function

Absolute energy levels of liquid water from many-body perturbation theory with effective vertex corrections

We demonstrate the importance of addressing the Γ vertex and thus going beyond the GW approximation for achieving the energy levels of liquid water in many-body perturbation theory. In particular, we consider an effective vertex function in both the polarizability and the self-energy, which does not produce any computational overhead compared with the GW approximation. We yield the band gap, the ionization potential, and the electron affinity in good agreement with experiment and with a hybrid functional description. The achieved electronic structure and dielectric screening further lead to a good description of the optical absorption spectrum, as obtained through the solution of the Bethe-Salpeter equation. In particular, the experimental peak position of the exciton is accurately reproduced.

Nonperturbative theory for the QED corrections to elastic electron-nucleus scattering

A potential for the vertex and self-energy correction is derived from the first-order Born theory. The inclusion of this potential in the Dirac equation, together with the Uehling potential for vacuum polarization, allows for a nonperturbative treatment of these quantum electrodynamical effects within the phase-shift analysis. Investigating the 12C and 208Pb targets, a considerable deviation of the respective cross section change from the Born results is found for the heavier target. It is shown that at low impact energies the dispersion effects play no role. Estimates for the correction to the beam-normal spin asymmetry and its accuracy at 5 MeV (for 208Pb and 197Au) are also provided.

On the vertex functions of type A quiver varieties

The goal of this paper is to better understand the quasimap vertex functions of type A Nakajima quiver varieties. To that end, we construct an explicit embedding of any type A quiver variety into a type A quiver variety with all framings at the rightmost vertex of the quiver. Then, we consider quasimap counts, showing that the map induced by this embedding on equivariant K-theory preserves vertex functions.

Cumulant Green's function methods for molecules.

The cumulant expansion of the Green's function is a computationally efficient beyond-GW approach renowned for its significant enhancement of satellite features in materials. In contrast to the ubiquitous GW approximation of many-body perturbation theory, ab initio cumulant expansions performed on top of GW (GW + C) have demonstrated the capability to handle multi-particle processes by incorporating higher-order correlation effects or vertex corrections, yielding better agreements between experiment and theory for satellite structures. While widely employed in condensed matter physics, very few applications of GW + C have been published on molecular systems. Here, we assess the performance of this scheme on a series of 10-electron molecular systems (Ne, HF, H2O, NH3, and CH4) where full configuration interaction estimates of the outer-valence quasiparticle and satellite energies are available.

Unfolded dynamics approach and quantum field theory

We study quantization of a self-interacting scalar field within the unfolded dynamics approach. To this end we find and analyze a classical unfolded system describing 4d off-shell scalar field with a general self-interaction potential. Then we systematically construct three different but related unfolded formulations of the corresponding quantum field theory, supporting them with illustrative calculations: an unfolded functional Schwinger-Dyson system, an unfolded system for correlation functions and an unfolded effective system for vertex functions. The most curious feature we reveal is that an unfolded quantum commutator gets naturally regularized: a standard delta-function is replaced with a heat kernel, parameterized by the unfolded proper time. We also identify an auxiliary 5d system, having this proper time as a physical time, which generates 4d scalar action as its on-shell action.

Three-loop b → sγ vertex with current-current operators

We compute three-loop vertex corrections to b → sγ induced by current-current operators. The results are presented as expansions in mc/mb with numerical coefficients which allow to cover all relevant values for the heavy quark masses in different renormalization schemes. Moreover we provide for the first time analytic results for the next-to-leading order contribution. Our results present an important building block to the next-to-next-to-leading order interference contributions of the current-current operators Q1 and Q2 with the electric dipole operator Q7.

Spatio–Spectral Limiting on Replacements of Tori by Cubes

A class of graphs is defined in which each vertex of a discrete torus is replaced by a Boolean hypercube in such a way that vertices in a fixed subset of each replacement cube are adjacent to corresponding vertices of a neighboring replacement cube. Bases of eigenvectors of the Laplacians of the resulting graphs are described in a manner suitable for quantifying the concentration of a low-spectrum vertex function on a single vertex replacement. Functions that optimize this concentration on these graphs can be regarded as analogues of Slepian prolate functions that optimize concentration of a bandlimited signal on an interval in the classical setting of the real line. Comparison to the case of a simple discrete cycle shows that replacement allows for higher concentration.

Boundaries & localisation with a topological twist

We study the partition functions of topologically twisted 3d N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 2 gauge theories on a hemisphere spacetime with boundary HS2 × S1. We show that the partition function may be localised to either the Higgs branch or the Coulomb branch where the contributions to the path integral are vortex or monopole configurations respectively. Turning to N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 4 supersymmetry, we consider partition functions for exceptional Dirichlet boundary conditions that yield a complete set of ‘IR holomorphic blocks’. We demonstrate that these correspond to vertex functions: equivariant Euler characteristics of quasimap moduli spaces. In this context, we explore the geometric interpretation of both the Higgs and Coulomb branch localisation schemes in terms of the enumerative geometry of quasimaps and discuss the action of mirror symmetry.

Larmor precession in strongly correlated itinerant electron systems

Many-electron systems undergo a collective Larmor precession in the presence of a magnetic field. In a paramagnetic metal, the resulting spin wave provides insight into the correlation effects generated by the electron-electron interaction. Here, we use dynamical mean-field theory to investigate the collective Larmor precession in the strongly correlated regime, where dynamical correlation effects such as quasiparticle lifetimes and non-quasiparticle states are essential. We study the spin excitation spectrum, which includes a dispersive Larmor mode as well as electron-hole excitations that lead to Stoner damping. We also extract the momentum-resolved damping of slow spin waves. The accurate theoretical description of these phenomena relies on the Ward identity, which guarantees a precise cancellation of self-energy and vertex corrections at long wavelengths. Our findings pave the way towards a better understanding of spin wave damping in correlated materials.

The top quark chromomagnetic dipole moment in the SM from the 4-body vertex function

A new proposal to compute the anomalous chromomagnetic dipole moment of the top quark, , in the Standard Model is presented. On the basis of the five-dimensional effective Lagrangian operator that characterizes the quantum-loop induced chromodipolar vertices and , the anomaly is derived via radiative correction at the 1-loop level from the non-Abelian 4-body vertex function . We evaluate as a function of the energy scale s = ±E 2, for E = [10, 1000] GeV, taking into account the running of the quark masses and alpha strong through the scheme. In particular, we find that at the typical energy scale E = m Z for high-energy physics, similarly to , and , the spacelike evaluation yields = −0.025 + 0.00384i and the timelike = −0.0318 − 0.0106i. This Re = −0.025 from is even closer to the experimental central value −0.024, than that coming from the known 3-body vertex function , −0.0224. Once again, the Im part is due to the contribution of virtual charged currents, just like in the case. We can infer that the spacelike prediction is the favored one.

Codebase release 1.0 for GRIFFIN

This paper describes a modular framework for the description of electroweak scattering and decay processes, including but not limited to Z-resonance physics. The framework consistently combines a complex-pole expansion near an s-channel resonance with a regular fixed-order perturbative description away from the resonance in a manifestly gauge-invariant scheme. Leading vertex correction contributions are encapsulated in form factors that can be predicted or treated as numerical fit parameters. This framework has been implemented in the publicly available object-oriented C++ library GRIFFIN. Version 1.0 of this library provides Standard Model predictions for the IR-subtracted matrix elements for the process f\bar{f} \to f'\bar{f}'ff‾→f′f‾′ with full NNLO and leading higher-order contributions on the Z-resonance, and with NLO corrections off-resonance. The library can straightforwardly be extended to include higher-order corrections, should they become available, or predictions for new physics models. It can be interfaced with Monte-Carlo programs to account for QED and QCD initial-state and final-state radiation.

GRIFFIN: A C++ library for electroweak radiative corrections in fermion scattering and decay processes

This paper describes a modular framework for the description of electroweak scattering and decay processes, including but not limited to Z-resonance physics. The framework consistently combines a complex-pole expansion near an s-channel resonance with a regular fixed-order perturbative description away from the resonance in a manifestly gauge-invariant scheme. Leading vertex correction contributions are encapsulated in form factors that can be predicted or treated as numerical fit parameters. This framework has been implemented in the publicly available object-oriented C++ library GRIFFIN. Version 1.0 of this library provides Standard Model predictions for the IR-subtracted matrix elements for the process f\bar{f} \to f'\bar{f}'ff‾→f′f‾′ with full NNLO and leading higher-order contributions on the Z-resonance, and with NLO corrections off-resonance. The library can straightforwardly be extended to include higher-order corrections, should they become available, or predictions for new physics models. It can be interfaced with Monte-Carlo programs to account for QED and QCD initial-state and final-state radiation.

Perturbative aspects of mass dimension one fermions non-minimally coupled to electromagnetic field

This paper addresses perturbative aspects of the renormalization of a fermion with mass dimension one non-minimally coupled to the electromagnetic field. Specifically, we calculate the one-loop corrections to the propagators and vertex functions of the model and determine the one-loop beta function of the non-minimal electromagnetic coupling. Additionally, we perform calculations of the two-loop corrections to the gauge field propagator, demonstrating that it remains massless and transverse up to this order. We also find that the non-minimal electromagnetic coupling can exhibit asymptotic freedom if a certain condition is satisfied. As a potential dark matter candidate, these findings suggest that the field may decouple at high energies. This aspect holds significance for calculating the relic abundance and freeze-out temperature of the field, particularly in relation to processes involving the ordinary particles of the Standard Model.

Crucial role of thermal fluctuations and vertex corrections for the magnetic pseudogap

Crucial role of thermal fluctuations and vertex corrections for the magnetic pseudogap

Two-Component GW Calculations: Cubic Scaling Implementation and Comparison of Vertex-Corrected and Partially Self-Consistent GW Variants.

We report an all-electron, atomic orbital (AO)-based, two-component (2C) implementation of the GW approximation (GWA) for closed-shell molecules. Our algorithm is based on the space-time formulation of the GWA and uses analytical continuation (AC) of the self-energy, and pair-atomic density fitting (PADF) to switch between AO and auxiliary basis. By calculating the dynamical contribution to the GW self-energy at a quasi-one-component level, our 2C-GW algorithm is only about a factor of 2-3 slower than in the scalar relativistic case. Additionally, we present a 2C implementation of the simplest vertex correction to the self-energy, the statically screened G3W2 correction. Comparison of first ionization potentials (IPs) of a set of 67 molecules with heavy elements (a subset of the SOC81 set) calculated with our implementation against results from the WEST code reveals mean absolute deviations (MAD) of around 70 meV for G0W0@PBE and G0W0@PBE0. We check the accuracy of our AC treatment by comparison to full-frequency GW calculations, which shows that in the absence of multisolution cases, the errors due to AC are only minor. This implies that the main sources of the observed deviations between both implementations are the different single-particle bases and the pseudopotential approximation in the WEST code. Finally, we assess the performance of some (partially self-consistent) variants of the GWA for the calculation of first IPs by comparison to vertical experimental reference values. G0W0@PBE0 (25% exact exchange) and G0W0@BHLYP (50% exact exchange) perform best with mean absolute deviations (MAD) of about 200 meV. Explicit treatment of spin-orbit effects at the 2C level is crucial for systematic agreement with experiment. On the other hand, eigenvalue-only self-consistent GW (evGW) and quasi-particle self-consistent GW (qsGW) significantly overestimate the IPs. Perturbative G3W2 corrections increase the IPs and therefore improve the agreement with experiment in cases where G0W0 alone underestimates the IPs. With a MAD of only 140 meV, 2C-G0W0@PBE0 + G3W2 is in best agreement with the experimental reference values.