Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 1910.01248

High-precision calculation of the 4-loop QED contribution to the slope of the Dirac form factor

Stefano Laporta
View original source ↗Read source document ↗Export metadata ↓

Abstract

We have evaluated with 1100 digits of precision the contribution of all the 891 mass-independent four-loop Feynman diagrams contributing to the slope of the Dirac form factor in QED. The total 4-loop contribution is $ m^2 F_1^{(4)'}(0) = 0.886545673946443145836821730610315359390424032660064745... \left(\fracαπ\right)^4$. We have fit a semi-analytical expression to the numerical value. The expression contains harmonic polylogarithms of argument $e^{\frac{iπ}{3}}$, $e^{\frac{2iπ}{3}}$, $e^{\frac{iπ}{2}}$, one-dimensional integrals of products of complete elliptic integrals and six finite parts of master integrals, evaluated up to 4800 digits. I show the correction on the shift of the energy levels of the hydrogen atom due to the slope.

Explore related subjects

hep-ph

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Stefano Laporta. 2019-12-08. High-precision calculation of the 4-loop QED contribution to the slope of the Dirac form factor. https://doi.org/10.1016/j.physletb.2019.135137

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Exploring the Singlino-dominated Thermal Neutralino Dark Matter in the $Z_3$ invariant NMSSM

We examine the parameter space of the Next to Minimal Supersymmetric Standard Model (NMSSM) with Singlino-dominated neutralino $\widetildeχ_1^0$ as the lightest supersymmetric particle (LSP). Our study focuses on identifying the regions within this parameter space that produce a thermal relic abundance of $\widetildeχ_1^0$ smaller than the observed cold dark matter relic density while remaining consistent with constraints from LEP measurements, low-energy experiments, Higgs measurements, LHC data, and dark matter direct detection experiments. We identify the dominant annihilation modes of the LSP neutralino across varying LSP mass ranges $\sim \mathcal{O}(1)-\mathcal{O}(10^{3})~$GeV. Furthermore, we conduct a benchmark study to assess the production rates of triple-boson final states emerging from direct electroweakino pair production at the LHC. Drawing insights from these findings, we perform a detailed collider analysis to explore the future potential of probing the triple-boson final states involving a light Higgs boson at the high-luminosity LHC (HL-LHC).

hep-ph↗
arXiv2026

Unveiling the Collins-Soper kernel in inclusive DIS at threshold

We revisit the factorization of inclusive deep inelastic scattering (DIS) near the kinematic threshold in terms of collinear, off-light-cone operators. At threshold, particle production develops around two opposite near-light-cone directions in close analogy with transverse-momentum-dependent semi-inclusive DIS. The Collins-Soper kernel then emerges as the universal function governing the rapidity evolution of the relevant parton correlators in both cases. Our new framework also clarifies outstanding issues related to soft radiation and rapidity divergences at threshold.

hep-ph↗
arXiv2026

Novel Light Dark Matter Detection with Quantum Parity Detector Using Qubit Arrays

We present the design and the sensitivity reach of the Qubit-based Light Dark Matter detection experiment. We propose the novel two-chip design to reduce signal dissipation, with quantum parity measurement to enhance single-phonon detection sensitivity. We demonstrate the performance of the detector with full phonon and quasiparticle simulations. The experiment is projected to detect $\gtrsim 30$ meV energy deposition with nearly $100\%$ efficiency and high energy resolution. The sensitivity to $m_χ\gtrsim 0.01$ MeV dark matter scattering cross section is expected to be advanced by orders of magnitude for both light and heavy mediators, and similar improvements will be achieved for axion and dark photon absorption in the $0.04$-$0.2$ eV mass range.

hep-ph↗