Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2604.20138

Graph-theoretic determination of massless modes in latticized theory-space models

Ketan M. Patel
View original source ↗Read source document ↗Export metadata ↓

Abstract

A graph-theoretic method is introduced for analyzing fermion mass spectra in latticized theory-space models, including chain models arising from dimensional deconstruction. Fermion mass terms are mapped to bipartite graphs, with fields as vertices and nonvanishing mass terms as edges. The number of massless modes is shown to be fixed by the cardinality of a maximum matching of the associated graph. Moreover, the wave-function support of these modes is restricted to fields reachable from exposed or unmatched vertices by even-length maximum-matching-alternating paths, as characterized by the Dulmage-Mendelsohn decomposition. These results depend only on the topology of latticized theory space and are independent of model parameters. The method enables a systematic construction of latticized models with prescribed numbers and localization properties of massless modes.

Explore related subjects

hep-phhep-thmath-phmath.MP

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Ketan M. Patel. 2026-04-22. Graph-theoretic determination of massless modes in latticized theory-space models. https://arxiv.org/abs/2604.20138

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↗