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Dark hyperCharge Symmetry

Hemant Prajapati, Rahul Srivastava

Abstract

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.

Dark hyperCharge Symmetry

Abstract

We introduce a new class of symmetries where all Standard Model fermions are ``chiral," i.e., the left- and right-handed components have different charges under the symmetry. Gauge anomaly cancellation is achieved by introducing three Standard Model gauge singlet dark fermions (; ) 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 symmetry. The 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 gauge boson mediates interactions between the dark and visible sectors, and we call this symmetry as the ``dark hyperCharge" symmetry. Using a benchmark model, we explore phenomenological implications in the heavy case (), 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.

Paper Structure

This paper contains 14 sections, 21 equations, 12 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Anomaly Cancellation in SM: Uniqueness of Hypercharge
  3. One generation of SM fermions
  4. Three generations of SM fermions
  5. anomaly cancellation for $U(1)_{X}$ gauge symmetry
  6. Vector solutions for $U(1)_{X}$
  7. Chiral solutions for $U(1)_{X}$
  8. Dark Hypercharge Solutions
  9. Dark HyperCharge Gauge Boson
  10. $Z^{\prime}$ production and decay at colliders
  11. The Dark Sector
  12. conclusion
  13. Partial decay widths of the $Z'$ boson
  14. Feynman diagrams for DM relic density and direct detection

Figures (12)

  • Figure 1: The triangle diagram which can induce gauge anomalies. The chiral fermions $\psi_i$ run in the loop with gauge bosons $E^a_{\mu}$ emitted at each vertex.
  • Figure 2: Gauge mixing angle $\alpha$ vs $M_{Z'}$ for varying values of $\textsl{g}_{_{x}}$. Higgs $U(1)_{X}$ charge is fixed to $X_{\Phi}=2$.
  • Figure 3: $\rho$ parameter vs mass of $Z'$, $M_{Z'}$ for varying $\textsl{g}_{_{x}}$ values and fixed Higgs $U(1)_{X}$ charge $X_{\Phi} =2$.
  • Figure 4: $Z'$ production cross-section in $pp$ collisions at $\sqrt{s}=13$ TeV for various $\textsl{g}_{_{x}}$ values. The solid lines represent DHC symmetry, while dashed lines represents $B-L$ symmetry.
  • Figure 5: $Z'$ invisible branching fraction versus $M_{Z'}$. The solid (dashed) lines represent DHC ($B-L$) symmetries. DF masses are set at 0.5 TeV, 1 TeV, and 2 TeV. Compared to $B-L$ case, the DHC $Z'$ has much larger invisible branching fraction.
  • ...and 7 more figures