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Oblique corrections in general dark $U(1)$ models

Cheng-Wei Chiang, Kazuki Enomoto

TL;DR

This paper extends the oblique parameter framework to dark U(1) gauge sectors, analyzing one-loop corrections from dark photons and dark Z bosons that mix with SM gauge bosons via kinetic or mass mixing. Using Schwinger-Dyson equations, it derives a renormalization-scheme independent representation of four-fermion amplitudes and defines running parameters to describe oblique effects, showing that S, T, and U adequately capture leading new-physics contributions when the new-physics scale is high. It provides explicit one-loop formulae for DP and DZ scenarios, including two renormalization schemes for DZ, and demonstrates with a dark doublet scalar that novel mixing effects can drastically alter EWPO constraints, underscoring the importance of loop-level mixing physics. The results offer a framework to confront dark U(1) models with current and future electroweak precision data, with potential sensitivity improvements at experiments like GIGA-Z.

Abstract

We investigate the impact of dark Abelian gauge bosons on the electroweak precision measurements at the one-loop level. The dark gauge boson couples to the standard model fermions generally via two kinds of mixing with the electroweak gauge bosons: the kinetic mixing and the mass mixing. We solve the Schwinger-Dyson equation for the gauge boson propagators and derive a renormalization scheme-independent representation of the scattering amplitudes for four-fermion processes, including the full oblique corrections. We define the running parameters at the one-loop level and show that the leading new physics effects, including the mixing, in the electroweak precision observables can be described by the oblique parameters $S$, $T$, and $U$ as in the standard electroweak gauge theory when the new physics scale is sufficiently high and the dark gauge boson mass lies away from the $Z$ pole. We consider the dark doublet scalar boson as an example and numerically show that a novel one-loop effect can drastically change the parameter region allowed by the electroweak precision tests.

Oblique corrections in general dark $U(1)$ models

TL;DR

This paper extends the oblique parameter framework to dark U(1) gauge sectors, analyzing one-loop corrections from dark photons and dark Z bosons that mix with SM gauge bosons via kinetic or mass mixing. Using Schwinger-Dyson equations, it derives a renormalization-scheme independent representation of four-fermion amplitudes and defines running parameters to describe oblique effects, showing that S, T, and U adequately capture leading new-physics contributions when the new-physics scale is high. It provides explicit one-loop formulae for DP and DZ scenarios, including two renormalization schemes for DZ, and demonstrates with a dark doublet scalar that novel mixing effects can drastically alter EWPO constraints, underscoring the importance of loop-level mixing physics. The results offer a framework to confront dark U(1) models with current and future electroweak precision data, with potential sensitivity improvements at experiments like GIGA-Z.

Abstract

We investigate the impact of dark Abelian gauge bosons on the electroweak precision measurements at the one-loop level. The dark gauge boson couples to the standard model fermions generally via two kinds of mixing with the electroweak gauge bosons: the kinetic mixing and the mass mixing. We solve the Schwinger-Dyson equation for the gauge boson propagators and derive a renormalization scheme-independent representation of the scattering amplitudes for four-fermion processes, including the full oblique corrections. We define the running parameters at the one-loop level and show that the leading new physics effects, including the mixing, in the electroweak precision observables can be described by the oblique parameters , , and as in the standard electroweak gauge theory when the new physics scale is sufficiently high and the dark gauge boson mass lies away from the pole. We consider the dark doublet scalar boson as an example and numerically show that a novel one-loop effect can drastically change the parameter region allowed by the electroweak precision tests.

Paper Structure

This paper contains 26 sections, 112 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Dark $U(1)$ models
  3. Dark photon models
  4. Dark $Z$ models
  5. Oblique corrections in four-fermion processes and running parameters
  6. Amplitudes for four-fermion processes with oblique corrections
  7. Running parameters
  8. One-loop renormalization of couplings and mixing
  9. Dark photon models
  10. Dark $Z$ models
  11. Renormalization Scheme A: $\overline{MS}$ scheme for the mass mixing
  12. Renormalization Scheme B: Using $\xi$ to determine the mass mixing
  13. The $S$, $T$, and $U$ parameters
  14. Tree level formulas
  15. One-loop formulas
  16. ...and 11 more sections

Figures (3)

  • Figure 1: The EWPO constraints in the $M_D$-$\varepsilon$ plane. The gray region is the allowed region at tree level. The red, blue, and green regions are those at one-loop level with $a = 1$, $0$, and $-1$, respectively. The model parameters are fixed as $m_H = 400~\mathrm{GeV}$, $m_A = m_{H^\pm}^{} = 200~\mathrm{GeV}$.
  • Figure 2: Constraints in the $\varepsilon$-$\varepsilon_Z^{}$ plane in the dark $Z$ models using RS-A, for different choices of $M_D$ and $\varepsilon_Z$. The color scheme is the same as in Fig. \ref{['fig: DP']}.
  • Figure 3: Constraints in the $\hat{\varepsilon}$-$\hat{\varepsilon}_Z$ planes in the dark $Z$ models using RS-B. The color scheme is same as in Fig. \ref{['fig: DP']}.