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Unbroken B-L Symmetry

Julian Heeck

TL;DR

This work argues that an unbroken gauged $U(1)_{B-L}$ is a viable extension of the Standard Model when three right-handed neutrinos are added, yielding Dirac neutrinos and a new $Z'$ mediator with a Stückelberg mass $M_{Z'}$. It compiles comprehensive bounds on the coupling $g'$ across the full testable range $M_{Z'}=0$--$10^{13}$ eV, highlighting resonant Big Bang Nucleosynthesis effects in the $10$ eV--$10^2$ GeV window as a key constraint, and showing that astrophysical and collider data typically set the strongest limits, translating into bounds on $M_{Z'}/g'$ from TeV to $10^{10}$ GeV. The analysis discusses extensions to broken $B-L$ and kinetic-mixing scenarios, noting how the invisible width and mixing with hypercharge modify the limits. Overall, the results demonstrate that the $Z'$ mediator can be tightly constrained across a wide mass range, with implications for early-universe phenomenology and collider searches.

Abstract

The difference between baryon number B and lepton number L is the only anomaly-free global symmetry of the Standard Model, easily promoted to a local symmetry by introducing three right-handed neutrinos, which automatically make neutrinos massive. The non-observation of any (B-L)-violating processes leads us to scrutinize the case of unbroken gauged B-L; besides Dirac neutrinos, the model contains only three parameters, the gauge coupling strength g', the Stueckelberg mass $M_{Z'}$, and the kinetic mixing angle $χ$. The new force could manifest itself at any scale, and we collect and derive bounds on g' over the entire testable range $M_{Z'}$ = 0 - $10^{13}$ eV, also of interest for the more popular case of spontaneously broken B-L or other new light forces. We show in particular that successful Big Bang nucleosynthesis provides strong bounds for masses 10 eV < $M_{Z'}$ < 10 GeV due to resonant enhancement of the rate $\bar{f} f \leftrightarrow \barν_R ν_R$. The strongest limits typically arise from astrophysics and colliders, probing scales $M_{Z'}/g'$ from TeV up to $10^{10}$ GeV.

Unbroken B-L Symmetry

TL;DR

This work argues that an unbroken gauged is a viable extension of the Standard Model when three right-handed neutrinos are added, yielding Dirac neutrinos and a new mediator with a Stückelberg mass . It compiles comprehensive bounds on the coupling across the full testable range -- eV, highlighting resonant Big Bang Nucleosynthesis effects in the eV-- GeV window as a key constraint, and showing that astrophysical and collider data typically set the strongest limits, translating into bounds on from TeV to GeV. The analysis discusses extensions to broken and kinetic-mixing scenarios, noting how the invisible width and mixing with hypercharge modify the limits. Overall, the results demonstrate that the mediator can be tightly constrained across a wide mass range, with implications for early-universe phenomenology and collider searches.

Abstract

The difference between baryon number B and lepton number L is the only anomaly-free global symmetry of the Standard Model, easily promoted to a local symmetry by introducing three right-handed neutrinos, which automatically make neutrinos massive. The non-observation of any (B-L)-violating processes leads us to scrutinize the case of unbroken gauged B-L; besides Dirac neutrinos, the model contains only three parameters, the gauge coupling strength g', the Stueckelberg mass , and the kinetic mixing angle . The new force could manifest itself at any scale, and we collect and derive bounds on g' over the entire testable range = 0 - eV, also of interest for the more popular case of spontaneously broken B-L or other new light forces. We show in particular that successful Big Bang nucleosynthesis provides strong bounds for masses 10 eV < < 10 GeV due to resonant enhancement of the rate . The strongest limits typically arise from astrophysics and colliders, probing scales from TeV up to GeV.

Paper Structure

This paper contains 14 sections, 15 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Model
  3. Limits
  4. Modified gravity and fifth force searches
  5. Stellar evolution
  6. Neutrino scattering
  7. Beam dump
  8. BaBar
  9. Thermalization in the early Universe
  10. Collider
  11. Comments
  12. Broken $B-L$
  13. Kinetic mixing
  14. Conclusion

Figures (3)

  • Figure 1: $Z'$ branching ratios to $e^+ e^-$ (blue), $\mu^+\mu^-$ (blue, dotdashed), neutrinos (green), and hadrons (red).
  • Figure 2: Qualitative behavior of the rate $\langle \Gamma (\overline{f} f\leftrightarrow \overline{\nu}_R\nu_R) \rangle$ (black) as a function of temperature. Also shown is the Hubble rate (red, dashed); in this example, the (massless) $\nu_R$ would enter equilibrium around $T \sim M_{Z'}$ and decouple around $T\sim M_{Z'}/10$.
  • Figure 3: Bounds on the $U(1)_{B-L}$ coupling constant $g'$ (fine-structure constant $\alpha = {g'}^2/4\pi$) and $Z'$ Stückelberg mass $M_{Z'}$ (corresponding to a range $\lambda = 1/M_{Z'}$) for vanishing kinetic-mixing angle $\chi=0$. The area on the upper left is excluded by limits from tests of the equivalence principle (EP, dark blue) Wagner:2012uiAdelberger:2009zz, gravitational inverse-square law (ISR, green) Adelberger:2009zz, Casimir effect (black) Bordag:2001qiDecca:2005qzSushkov:2011zz, neutron scattering (light green) Pokotilovski:2006upNesvizhevsky:2007by, energy loss via $\nu$ in red giants (RG/$\nu$, red) Davidson:2000hf, energy loss via $Z'$ in the Sun (Sun, yellow), horizontal branch stars (HB, orange), and red giants (RG, red) Redondo:2013lna, SN1987A ($Z'$) (grey, dashed) Dent:2012mx, SN1987A ($\nu_R$) (grey) Dreiner:2013mua, BBN (blue, Sec. \ref{['sec:bbn']}), beam dump searches (BD, green) Andreas:2012mt, neutrino--electron scattering ($e$--$\nu$, purple) Harnik:2012ni, BaBar (dark red) Lees:2014xha, neutrino--quark scattering ($q$--$\nu$, brown) Escrihuela:2011cf, ATLAS (LHC, black) Aad:2014cka, and LEP (orange) Carena:2004xsSchael:2013ita. Most (non-astrophysical) limits are at $95\%$ C.L., see text for details. Also shown are diagonals at scales $M_{Z'}/g' = \unit[100]{GeV}$ and $\unit[10^9]{GeV}$ for comparison (grey, dotdashed).