Dark hyperCharge Symmetry

We introduce a new class of $U(1)X$ symmetries where all Standard Model fermions are chiral," i.e., the left- and right-handed components have different charges under the $U(1)_X$ symmetry. Gauge anomaly cancellation is achieved by introducing three Standard Model gauge singlet dark fermions ($f^i$; $i=1,2,3$) charged under this symmetry. We systematically present chiral solutions for cases in which (a) one, (b) two, or (c) all three generations of Standard Model fermions are charged under the $U(1)_X$ symmetry. The $U(1)_X$ charges of these dark fermions are uniquely determined by anomaly cancellation conditions. These new fermions belong to the dark sector, with the lightest of them being a good dark matter candidate. Additionally, the $Z'$ gauge boson mediates interactions between the dark and visible sectors, and we call this $U(1)_X$ symmetry as the dark hyperCharge" symmetry. Using a benchmark model, we explore phenomenological implications in the heavy $Z’$ case ($M{Z’} > M_Z$), analyzing collider constraints and examining the lightest dark fermion’s viability as dark matter. Our analysis shows that it satisfies all current dark matter constraints over a wide range of dark matter mass.

💡 Research Summary

The paper introduces a novel class of Abelian gauge extensions of the Standard Model (SM) called “dark hypercharge” (DHC) symmetries, denoted U(1)_X, in which all SM fermions are chiral under the new gauge group – i.e., left‑ and right‑handed components carry different X‑charges. This is in stark contrast to the majority of U(1) extensions where SM fields are taken to be vector‑like under the new symmetry for simplicity.

The authors begin by reviewing anomaly cancellation in the SM. They show that the usual hypercharge Y is not uniquely fixed by the four perturbative anomaly equations alone; additional constraints from electric charge assignments and Yukawa couplings are required to obtain the familiar SM hypercharge pattern. This discussion sets the stage for the analogous problem in a U(1)_X extension.

When a new U(1)_X is added, six extra anomaly conditions appear (mixed SU(3)^2‑X, SU(2)^2‑X, Y^2‑X, Y‑X^2, X^3, and gravitational‑X). Because the SM fermion content alone cannot satisfy these equations while remaining chiral, the authors introduce three SM‑singlet fermions f^i (i=1,2,3) that are neutral under SU(3)_C, SU(2)_L and U(1)_Y but carry X‑charges. Solving the full set of anomaly equations uniquely determines the X‑charges of these dark fermions; the solution is called a “dark hypercharge” because it mirrors the role of hypercharge in the SM but lives entirely in the dark sector.

Three families of charge assignments are systematically explored:
(a) only one SM generation carries X‑charge,
(b) two generations carry X‑charge, and
(c) all three generations carry X‑charge.
In each case the anomaly equations lead to distinct rational X‑charge patterns for both SM fields and the dark fermions. The most general case (c) yields fractional X‑charges reminiscent of the SM hypercharge pattern, but with the freedom to choose different rational numbers because electric charge is not tied to X.

The U(1)X gauge boson, Z′, acquires mass through the vacuum expectation values of SM‑singlet scalars χ_i. The authors discuss the scalar sector, the resulting Z–Z′ mixing, and constraints from the electroweak ρ‑parameter. They then define a benchmark model where M{Z′}>M_Z, the gauge coupling g_X≈0.1, and the lightest dark fermion f^1 is the dark‑matter (DM) candidate.

Phenomenologically, Z′ mediates interactions between the visible and dark sectors. The paper evaluates LHC Run‑2 dilepton, dijet and t\bar{t} searches, showing that for M_{Z′}≳3 TeV the model comfortably evades current bounds. The relic abundance of f^1 is computed assuming thermal freeze‑out; the required annihilation cross‑section ⟨σv⟩≈3×10^{‑26} cm³ s^{‑1} is achieved via s‑channel Z′ exchange for a broad range of f^1 masses (∼100 GeV–1 TeV). Direct‑detection limits are satisfied because the spin‑independent scattering cross‑section is suppressed either by small Z–Z′ mixing or by the heavy Z′ propagator, yielding σ_{SI}≲10^{‑46} cm², well below XENONnT/LZ limits. Indirect detection constraints (γ‑rays, neutrinos) are also found to be non‑restrictive.

The authors conclude that chiral U(1)_X extensions provide a self‑consistent framework where anomaly cancellation forces the introduction of a minimal dark sector, naturally supplying a viable DM candidate and a portal (Z′) that can be probed at colliders. The DHC approach differs from traditional vector‑like U(1) models by allowing a richer set of charge assignments, decoupling X‑charges from electric charge, and offering new model‑building possibilities (e.g., generation‑dependent charges, connections to flavor physics). Future directions suggested include exploring additional dark scalars, embedding the construction in grand unified theories, and studying cosmological implications such as dark radiation or early‑Universe phase transitions.