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Light and Heavy $Z'$ from Flavored Chiral $U(1)_X$ Gauge Symmetries: Purely Axial and Mixed Vector-Axial Couplings

Hemant Kumar Prajapati, Rahul Srivastava

Abstract

Model independent phenomenological studies, ranging from neutrino to B-physics, often consider effective interactions involving either purely vector (V), purely axial vector (A), or mixed vector and axial vector (V, A) couplings. While pure vector $Z'$ interactions can naturally emerge in gauged $U(1)_X$ extensions of the Standard Model, such as the $B-L$ model, generating other coupling structures from a UV complete theory is highly nontrivial. To realize such couplings, we propose a new class of flavor specific chiral $U(1)_X$ gauge symmetries. Gauge anomaly cancellation is achieved by introducing three right-handed neutrinos charged under the $U(1)_X$ symmetry. We systematically classify anomaly free charge assignments and analyze viable ultraviolet completions with minimal scalar content, requiring no additional fermions beyond the three necessary for anomaly cancellation. We present several benchmark models illustrating the range of possible charge assignments, under which the quark and lepton flavor structures can differ substantially, leading to distinct phenomenological signatures. In particular, such non universal charge configurations naturally give rise to $Z'$ mediated flavor changing neutral currents in both the quark and lepton sectors. We also demonstrate that, within this framework, the $Z'$ boson can naturally acquire purely axial vector or mixed vector-axial couplings to the SM fermions, both in the heavy and light $Z'$ regimes.

Light and Heavy $Z'$ from Flavored Chiral $U(1)_X$ Gauge Symmetries: Purely Axial and Mixed Vector-Axial Couplings

Abstract

Model independent phenomenological studies, ranging from neutrino to B-physics, often consider effective interactions involving either purely vector (V), purely axial vector (A), or mixed vector and axial vector (V, A) couplings. While pure vector interactions can naturally emerge in gauged extensions of the Standard Model, such as the model, generating other coupling structures from a UV complete theory is highly nontrivial. To realize such couplings, we propose a new class of flavor specific chiral gauge symmetries. Gauge anomaly cancellation is achieved by introducing three right-handed neutrinos charged under the symmetry. We systematically classify anomaly free charge assignments and analyze viable ultraviolet completions with minimal scalar content, requiring no additional fermions beyond the three necessary for anomaly cancellation. We present several benchmark models illustrating the range of possible charge assignments, under which the quark and lepton flavor structures can differ substantially, leading to distinct phenomenological signatures. In particular, such non universal charge configurations naturally give rise to mediated flavor changing neutral currents in both the quark and lepton sectors. We also demonstrate that, within this framework, the boson can naturally acquire purely axial vector or mixed vector-axial couplings to the SM fermions, both in the heavy and light regimes.

Paper Structure

This paper contains 25 sections, 57 equations, 4 figures, 11 tables.

Table of Contents

  1. Introduction
  2. Mass Spectrum of Gauge Mediators
  3. Light $Z'$ scenario: $\mathbf{M_{Z'} < M_{Z}}$
  4. Heavy $Z'$ scenario: $\mathbf{M_{Z'} > M_{Z}}$
  5. Interactions between fermions and gauge bosons
  6. Light $Z'$ scenario: $\mathbf{M_{Z'} < M_{Z}}$
  7. Heavy $Z'$ scenario: $\mathbf{M_{Z'} > M_{Z}}$
  8. Anomaly Cancellation
  9. Scenario (I) : Single Higgs generates masses of all SM fermions
  10. Scenario (II) : Two Higgses generate masses of SM fermions
  11. Quark mixing pattern
  12. Models with single Higgs doublet
  13. Models with two Higgs doublets
  14. Extensions of Scenario (I)
  15. Extensions of Scenario (II)
  16. ...and 10 more sections

Figures (4)

  • Figure 1: Left (Right) panel shows mixing angle ($\rho$ parameter) as a function of $M_{Z'}$ for fixed values of gauge coupling $g_x$ and Higgs charge $X_{\Phi}$. The green band shows experimentally measured value of $\rho$ parameter at $3\sigma$, $\rho = 1.00038 \pm 0.00060$ParticleDataGroup:2020ssz.
  • Figure 2: Left (Right) panel shows mixing angle ($\rho$ parameter) as a function of $M_{Z'}$ for fixed values of gauge coupling $g_x$ and Higgs charge $X_{\Phi}$. The green band shows experimentally measured value of $\rho$ parameter at $3\sigma$, $\rho = 1.00038 \pm 0.00060$ParticleDataGroup:2020ssz.
  • Figure 3: Type-1 seesaw to generate Majorana neutrino masses.
  • Figure 4: Mass of the $Z'$ versus its gauge coupling $g_x$. The green band shows the region consistent with the current global two-dimensional fit to all $b \to s$ observables. The parameter space excluded by $B_s - \overline{B_s}$ and $B_d - \overline{B_d}$ mixing is shown in red.