Resonant Leptogenesis Mechanism

• Resonant leptogenesis is a mechanism that leverages nearly mass-degenerate right-handed Majorana neutrinos to produce enhanced CP asymmetries driving baryogenesis.
• The model extends the Standard Model with a TeV-scale gauged U(1)_{B-L} symmetry, resulting in accessible collider signatures such as like-sign dilepton events.
• Experimental predictions include measurable CP asymmetries and event rates at the LHC that correlate with the observed baryon asymmetry of the Universe.

Resonant leptogenesis is a mechanism that generates the matter–antimatter asymmetry of the Universe via the out-of-equilibrium, CP-violating decays of nearly mass-degenerate right-handed (RH) Majorana neutrinos. In scenarios where the Standard Model (SM) is extended by new gauge symmetries or additional fields, such as a TeV-scale gauged $U(1)_{B-L}$, resonant enhancement of the CP asymmetry allows successful leptogenesis with RH neutrino masses much lower than in traditional hierarchical models. Experimental probes, such as those at the LHC, become feasible due to the accessible new particle spectrum and large theoretically required CP asymmetries.

1. Theoretical Structure of Resonant Leptogenesis

Resonant leptogenesis exploits a near-degeneracy in the mass spectrum of at least two RH Majorana neutrinos ($N_i$), such that their mass difference $\Delta M \equiv M_{N_2} - M_{N_1}$ is on the order of their decay widths $\Gamma_{N_i}$. In this regime, self-energy (“mixing”) loop corrections to the RH neutrino decay amplitudes yield a CP asymmetry $\varepsilon_i$ that is resonantly enhanced:

$$\varepsilon_i = \frac{ \sum_\alpha \left[ \Gamma(N_i \to \ell_\alpha^+ W^-) - \Gamma(N_i \to \ell_\alpha^- W^+) \right] }{ \sum_\alpha \left[ \Gamma(N_i \to \ell_\alpha^+ W^-) + \Gamma(N_i \to \ell_\alpha^- W^+) \right] }$$

where the sum is over SM lepton flavors $\alpha = e, \mu, \tau$. The CP asymmetry arises from the interference of tree-level decay diagrams with one-loop self-energy diagrams, which are resonantly enhanced when $|M_{N_2}^2 - M_{N_1}^2| \sim M_{N_i} \Gamma_{N_i}$. The baryon-to-photon ratio is approximately

$$\eta_B \;\simeq\; 10^{-2}\,\varepsilon\,\kappa^{\rm fin}$$

with $\kappa^{\rm fin}$ the efficiency factor, typically $\sim 10^{-7}$–$10^{-8}$ in TeV-scale models (0904.2174). This inefficiency requires $\varepsilon$ to be $\mathcal{O}(1)$ in these frameworks, resulting in strong collider phenomenology.

2. SM Extension by Gauged $U(1)_{B-L}$ and TeV-Scale Seesaw

The scenario discussed in (0904.2174) extends the SM with an extra gauged $U(1)_{B-L}$ symmetry, spontaneously broken at the TeV scale by a scalar (e.g., $\Delta$) with charge +2. This structure enforces several properties:

• SM quarks and leptons acquire $B-L$ charges ($1/3$ and $-1$, respectively), and three RH neutrinos are required for anomaly cancellation.
• The operator $(LH)^2$ responsible for Majorana neutrino mass in the SM is forbidden at dimension-5, necessitating the RHs.
• Breaking $U(1)_{B-L}$ generates a heavy neutral gauge boson $Z'$, as well as TeV-scale Majorana masses for the RH neutrinos via their coupling to $\Delta$.

This construction realizes an effective Type I seesaw mechanism with TeV-scale $M_{N}$ and tiny Yukawas $h$, yielding light neutrino masses $m_\nu \sim \frac{(hv)^2}{M_N}$, where $v$ is the Higgs vev.

3. CP Asymmetry and Like-Sign Dilepton Signatures

The dominant decay channel for RH neutrinos is $N \to \ell^\pm W^\mp$. The CP asymmetry in these decays, $\varepsilon_i$, directly drives leptogenesis. Importantly, in collider experiments, the leptonic decays manifest as like-sign dilepton events due to the Majorana nature of $N$: $$pp \to Z' \to NN \to (\ell^\pm W^\mp)(\ell^\pm W^\mp)$$. The predicted asymmetry in dilepton event numbers is

$$\frac{N(\ell^+\ell^+) - N(\ell^-\ell^-)}{N(\ell^+\ell^+) + N(\ell^-\ell^-)} = \frac{2\sum_i \varepsilon_i}{\sum_i 1}$$

The baryon asymmetry of the Universe determines the sign of $\varepsilon$ required: an excess of antileptons (i.e., more $\ell^+\ell^+$ events) is expected. Given the low efficiency of leptogenesis, the magnitude $|\varepsilon|$ must be close to unity.

4. Collider Phenomenology and Experimental Tests

A central result of (0904.2174) is the direct testability of resonant leptogenesis at the LHC:

• The $Z'$ can be produced in $pp$ collisions if $M_{Z'} \gtrsim 2.5-5$ TeV, decaying to $NN$ for $M_{Z'} \geq 2M_N$.
• Each $N$ decays leptonically, leading to a distinct like-sign dilepton signature with a typical cross-section $\mathcal{O}(1\,\mathrm{fb})$. With $300\,\mathrm{fb}^{-1}$ of data, $\sim$300 events are anticipated for optimal masses.
• Measurement of an excess of antileptons over leptons is predicted, based on the sign of the BAU.
• The absence of such an asymmetry allows for stringent exclusion: for $300\,\mathrm{fb}^{-1}$, $\varepsilon \lesssim 0.22$ at $2\sigma$; for $1000\,\mathrm{fb}^{-1}$, $\varepsilon \lesssim 0.13$.

This experimental accessibility is contingent on the TeV-scale masses and sizable CP asymmetries required for resonant leptogenesis in these models.

5. Theoretical and Numerical Requirements

Achieving successful resonant leptogenesis in this framework requires:

• The mass splitting between participating RH neutrinos must be of order their decay widths; e.g., $|M_{N_2} - M_{N_1}| \sim \Gamma_N$.
• Small neutrino Yukawas ensure light neutrino masses, while the out-of-equilibrium condition for $N$ decays is naturally satisfied (since $\Gamma_N \ll H$ at the time of decay).
• The baryon-to-photon ratio is $\eta_B \sim 10^{-2}\varepsilon\kappa^{\rm fin}$, matching the observed value for TeV-scale seesaw if $\varepsilon \sim 1$.
• Numerical solutions require integrating Boltzmann equations for $N$ and $\ell$ number densities, accounting for all relevant $Z'$-mediated and Yukawa processes, and for dilution/washout from inverse decays and scatterings.

6. Summary of Key Expressions

Quantity	Definition/Value	Significance
CP asymmetry $\varepsilon$	See Eq. (1) above	Resonantly enhanced, $\sim 1$ for successful BAU
Final efficiency $\kappa^{\rm fin}$	$\sim10^{-7}$–$10^{-8}$	Small at TeV scale; demands large $\varepsilon$
Baryon asymmetry $\eta_B$	$10^{-2}\varepsilon\kappa^{\rm fin}$	Matches observed $\eta_B \sim 6\times10^{-10}$ for $\varepsilon\sim1$
Dilepton asymmetry	$$[N(\ell^+\ell^+)-N(\ell^-\ell^-)]/[N(\ell^+\ell^+)+N(\ell^-\ell^-)]$$	Experimental observable at the LHC

7. Implications and Outlook

Resonant leptogenesis in TeV-scale $U(1)_{B-L}$ extensions provides a consistent explanation for the baryon asymmetry, directly linkable to collider observables. The requirement of order-one CP asymmetry is testable via the sign and size of like-sign dilepton excesses. Furthermore, the scenario imposes a TeV-scale seesaw and predicts a spectrum (including $Z'$, RH neutrinos) accessible to collider searches. The framework connects flavor physics, baryogenesis, neutrino mass generation, and beyond-SM gauge symmetry in a phenomenologically predictive and experimentally accessible setup (0904.2174).