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Dark Matter, Baryon Asymmetry, and Spontaneous B and L Breaking

Timothy R. Dulaney, Pavel Fileviez Perez, Mark B. Wise

TL;DR

The paper investigates two simple extensions of the Standard Model in which baryon number $B$ and lepton number $L$ are local gauge symmetries spontaneously broken near the weak scale, yielding stable dark matter candidates. In Model (2), the DM candidate $X$ with $B=-2/3$ can annihilate through a leptophobic $Z_B$ or via the Higgs portal; relic-density requirements demand near-resonant annihilation, with viable regions such as $M_{Z_B}=500$ GeV giving $235 ext{ GeV}\nobreak\, ext{(}M_X ext{)} obreak\, ext{to} obreak\,250 ext{ GeV}$ and $g_B\, ext{below}\,0.1$, or Higgs-portal with $M_H=120$ GeV yielding $51 ext{ GeV} obreak\, ext{to} obreak\,63 ext{ GeV}$ and $\\lambda_1\lesssim 10^{-1.5}$. Direct-detection bounds constrain these channels, pushing viable regions toward resonance: in the $ ext{Z}_B$ channel, $\sigma_{SI}^B \gtrsim 5\times10^{-46} ext{ cm}^2$ for certain masses, while in the Higgs channel, $\sigma_{SI}^H \gtrsim 10^{-48} ext{ cm}^2$ for $M_X$ in the 50–60 GeV range. In Model (1), leptogenesis plus a primordial $B$-number density can generate the observed baryon asymmetry even with $B$-breaking at the weak scale, aided by a mass-splitting mechanism to evade direct-detection bounds. Overall, the study highlights that reconciling the observed dark matter density and baryon asymmetry is challenging but feasible in these gauged-B/L frameworks, with viable parameter space emerging near annihilation resonances and requiring modest tuning between high- and low-scale sectors.

Abstract

We investigate the dark matter and the cosmological baryon asymmetry in a simple theory where baryon (B) and lepton (L) number are local gauge symmetries that are spontaneously broken. In this model, the cold dark matter candidate is the lightest new field with baryon number and its stability is an automatic consequence of the gauge symmetry. Dark matter annihilation is either through a leptophobic gauge boson whose mass must be below a TeV or through the Higgs boson. Since the mass of the leptophobic gauge boson has to be below the TeV scale one finds that in the first scenario there is a lower bound on the elastic cross section of about 5x10^{-46} cm^2. Even though baryon number is gauged and not spontaneously broken until the weak scale, a cosmologically acceptable baryon excess is possible. There is tension between achieving both the measured baryon excess and the dark matter density.

Dark Matter, Baryon Asymmetry, and Spontaneous B and L Breaking

TL;DR

The paper investigates two simple extensions of the Standard Model in which baryon number and lepton number are local gauge symmetries spontaneously broken near the weak scale, yielding stable dark matter candidates. In Model (2), the DM candidate with can annihilate through a leptophobic or via the Higgs portal; relic-density requirements demand near-resonant annihilation, with viable regions such as GeV giving and , or Higgs-portal with GeV yielding and . Direct-detection bounds constrain these channels, pushing viable regions toward resonance: in the channel, for certain masses, while in the Higgs channel, for in the 50–60 GeV range. In Model (1), leptogenesis plus a primordial -number density can generate the observed baryon asymmetry even with -breaking at the weak scale, aided by a mass-splitting mechanism to evade direct-detection bounds. Overall, the study highlights that reconciling the observed dark matter density and baryon asymmetry is challenging but feasible in these gauged-B/L frameworks, with viable parameter space emerging near annihilation resonances and requiring modest tuning between high- and low-scale sectors.

Abstract

We investigate the dark matter and the cosmological baryon asymmetry in a simple theory where baryon (B) and lepton (L) number are local gauge symmetries that are spontaneously broken. In this model, the cold dark matter candidate is the lightest new field with baryon number and its stability is an automatic consequence of the gauge symmetry. Dark matter annihilation is either through a leptophobic gauge boson whose mass must be below a TeV or through the Higgs boson. Since the mass of the leptophobic gauge boson has to be below the TeV scale one finds that in the first scenario there is a lower bound on the elastic cross section of about 5x10^{-46} cm^2. Even though baryon number is gauged and not spontaneously broken until the weak scale, a cosmologically acceptable baryon excess is possible. There is tension between achieving both the measured baryon excess and the dark matter density.

Paper Structure

This paper contains 11 sections, 43 equations, 4 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Spontaneous $B$ and $L$ Breaking
  3. Model (1)
  4. Model (2)
  5. $X$ as a candidate for the cold dark matter in Model (2)
  6. Constraints from the Relic Density
  7. Constraints from Direct Detection
  8. Cosmological Baryon Number
  9. Model (1)
  10. Model (2)
  11. Summary

Figures (4)

  • Figure 1: In these figures, we plot the values of the (logarithm of the) coupling $g_B$ and dark matter mass $M_X$ that lead to the value of the dark matter relic abundance measured by WMAP assuming annihilation through intermediate $Z_B$ is dominant. We use $M_{Z_B} = 500$ GeV for these plots. The plot on the right is an enlarged version of the left plot around the region near the resonance. For dark matter masses around $250$ GeV, CDMS II excludes dark matter-nucleon elastic scattering cross sections larger than $6 \times 10^{-44} \text{cm}^2$. The region below the dashed line is allowed by CDMS II Ahmed:2009zw.
  • Figure 2: In these figures, we plot the values of the (logarithm of the) coupling $\lambda_1$ and dark matter mass $M_X$ that lead to the value of the dark matter relic abundance measured by WMAP assuming annihilation through intermediate Higgs is dominant. We use $M_{H} = 120$ GeV for this plots.
  • Figure 3: In this figure, we plot the results of the numerical relic abundance calculation with the correct thermal averaging around the resonance. The contour plotted shows the values of the (logarithm of the) coupling $g_B$ and dark matter mass $M_X$ that lead to the value of the dark matter relic abundance measured by WMAP assuming annihilation through an intermediate $Z_B$ is dominant. We use $M_{Z_B} = 500$ GeV for this plot.
  • Figure 4: In this figure, we plot the results of the numerical relic abundance calculation with the correct thermal averaging around the resonance. The contour plotted shows the values of the (logarithm of the) coupling $\lambda_1$ and dark matter mass $M_X$ that lead to the value of the dark matter relic abundance measured by WMAP assuming annihilation through an intermediate Higgs is dominant and taking $M_{H} = 120$ GeV.