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Secluded U(1) below the weak scale

Maxim Pospelov

TL;DR

Pospelov analyzes a secluded U(1)' that mixes with the photon through kinetic mixing κ and has a breaking scale below 1 GeV. By combining precision QED tests, especially (g-2) for e and μ, with radiative decays of kaons and hyperons, he constrains the (m_V, κ) parameter space and assesses whether a 214 MeV V boson could account for the HyperCP anomaly without conflicting with existing data. The study finds that a small κ^2 in the vicinity of 3×10^-5 to a few×10^-4 can be compatible with HyperCP hints and may modestly alleviate the muon g-2 tension, though many natural regions are constrained by kaon data. He identifies ultra-fine energy scans in e^+e^- collisions and detailed analyses of K^+ and Σ^+ decay spectra as key tests to decisively confirm or refute the scenario, and discusses possibilities for richer mediator sectors such as a doubly secluded Higgs'.

Abstract

A secluded U(1) sector with weak admixture to photons, O(10^{-2}-10^{-3}), and the scale of the breaking below 1 GeV represents a natural yet poorly constrained extension of the Standard Model. We analyze g-2 of muons and electrons together with other precision QED data, as well as radiative decays of strange particles to constrain mass--mixing angle (m_V-κ) parameter space. We point out that m_V = 214 MeV and κ^2 > 3\times 10^{-5} can be consistent with the hypothesis of HyperCP collaboration, that seeks to explain the anomalous energy distribution of muon pairs in the Σ^+ \to p μ^+μ^- process by a resonance, without direct contradiction to the existing data on radiative kaon decays. The same parameters lead to O({\rm few} \times 10^{-9}) upward correction to the anomalous magnetic moment of the muon, possibly relaxing some tension between experimental value and theoretical determinations of g-2. The ultra-fine energy resolution scan of e^+e^-\to μ^+μ^- cross section and dedicated analysis of lepton spectra from K^+\to π^+ e^+e^- decays should be able to provide a conclusive test of this hypothesis and improve the constraints on the model.

Secluded U(1) below the weak scale

TL;DR

Pospelov analyzes a secluded U(1)' that mixes with the photon through kinetic mixing κ and has a breaking scale below 1 GeV. By combining precision QED tests, especially (g-2) for e and μ, with radiative decays of kaons and hyperons, he constrains the (m_V, κ) parameter space and assesses whether a 214 MeV V boson could account for the HyperCP anomaly without conflicting with existing data. The study finds that a small κ^2 in the vicinity of 3×10^-5 to a few×10^-4 can be compatible with HyperCP hints and may modestly alleviate the muon g-2 tension, though many natural regions are constrained by kaon data. He identifies ultra-fine energy scans in e^+e^- collisions and detailed analyses of K^+ and Σ^+ decay spectra as key tests to decisively confirm or refute the scenario, and discusses possibilities for richer mediator sectors such as a doubly secluded Higgs'.

Abstract

A secluded U(1) sector with weak admixture to photons, O(10^{-2}-10^{-3}), and the scale of the breaking below 1 GeV represents a natural yet poorly constrained extension of the Standard Model. We analyze g-2 of muons and electrons together with other precision QED data, as well as radiative decays of strange particles to constrain mass--mixing angle (m_V-κ) parameter space. We point out that m_V = 214 MeV and κ^2 > 3\times 10^{-5} can be consistent with the hypothesis of HyperCP collaboration, that seeks to explain the anomalous energy distribution of muon pairs in the Σ^+ \to p μ^+μ^- process by a resonance, without direct contradiction to the existing data on radiative kaon decays. The same parameters lead to O({\rm few} \times 10^{-9}) upward correction to the anomalous magnetic moment of the muon, possibly relaxing some tension between experimental value and theoretical determinations of g-2. The ultra-fine energy resolution scan of e^+e^-\to μ^+μ^- cross section and dedicated analysis of lepton spectra from K^+\to π^+ e^+e^- decays should be able to provide a conclusive test of this hypothesis and improve the constraints on the model.

Paper Structure

This paper contains 6 sections, 22 equations, 2 figures.

Table of Contents

  1. Introduction
  2. QED tests of secluded U(1)
  3. Production of U(1)$'$ bosons in hyperon and $K$ decays
  4. Radiative Kaon decays
  5. Radiative hyperon decay, HyperCP anomaly, and the hypothesis of 214 MeV boson
  6. Discussion

Figures (2)

  • Figure 1: Combination of $g-2$ and $\alpha$ measurement constraints on $m_V-\kappa^2$ parameter space. The dark grey color indicate the excluded region. The light grey band is where the consistency of theoretical and experimental values of $(g-2)_\mu$ improves to $2\sigma$ or less. The grey line inside this band indicate $0\sigma$ relative to experimental value, ı.e. a positive shift of $3\times 10^{-9}$ to $a_\mu^{\rm th}$.
  • Figure 2: Same as Figure 1, but with some conditional constraints in the assumption of purely "visible" decays of $V$. The darkest grey region is from ${\rm Br}^V_{K^+\to \pi^+e^+e^-} < 3.\times 10^{-8}$; and the similarly shaped grey line is possible to achieve with re-analysis of $V_{K^+\to \pi^+e^+e^-}$ at $\Delta$Br$<6\times 10^{-9}$ level. The grey diagonal straight line indicates the level of sensitivity that can be achieved via the $e^+e^-$ search of extremely narrow resonances. The thick vertical bar indicates the region consistent with the HyperCP hypothesis (\ref{['whatyouneed']}) and other constraints.