Impact of vSMEFT operators on low-scale leptogenesis

Impact of vSMEFT operators on low-scale leptogenesis

ABSTRACT: We investigate the impact of higher-dimensional operators on low-scale leptogenesis via oscillations of right-handed neutrinos within the neutrino-extended Standard Model Effective Field Theory and discuss the connection to neutrinoless double beta decay. Focusing on a dimension-six, lepton number conserving operator, we explore how new interactions can significantly alter the production and equilibration dynamics of right-handed neutrinos. We derive the relevant quantum kinetic equations incorporating both renormalizable and non-renormalizable interactions and perform a comprehensive numerical analysis for benchmark scenarios in both the oscillatory and overdamped regimes. Our results reveal that even in the absence of explicit lepton number violation by the operator, it can enhance or suppress the baryon asymmetry of the universe by several orders of magnitude, depending on the EFT scale. We further connect these effects to predictions for neutrinoless double beta decay, demonstrating that the same operator can lead to enhanced decay rates, potentially within reach of the next generation of experiments. Our findings indicate that the observation of neutrinoless double beta decay could rule out a large part of the parameter space for successful low-scale leptogenesis within the vSMEFT, implying low right-handed neutrino masses and low reheating temperatures.

One Introduction

The Standard Model successfully describes the known fundamental interactions, but clear evidence points to physics beyond it. Neutrino oscillations, for example, imply non-zero neutrino masses, which the Standard Model cannot accommodate. A minimal and well-motivated extension introduces right-handed neutrinos, allowing neutrinos to acquire Dirac masses. Being gauge singlets, right-handed neutrinos naturally admit Majorana mass terms.

The interplay between Dirac and Majorana masses leads to a set of Majorana mass eigenstates, with right-handed neutrino-dominated states potentially much heavier than the active neutrinos. This setup realizes the type-One seesaw mechanism.

Another indication of physics beyond the Standard Model is the baryon asymmetry of the Universe. Observations of the cosmic microwave background and predictions from Big Bang nucleosynthesis point to a baryon-to-photon ratio of nB equals six point two times ten to the negative ten, which the Standard Model fails to explain. A well-established mechanism for generating the baryon asymmetry is leptogenesis, which can be naturally realized through the dynamics of right-handed neutrinos. In standard leptogenesis scenarios, a lepton asymmetry is generated via Standard Model lepton number violating interactions involving right-handed neutrinos and subsequently converted into a baryon asymmetry via Standard Model (B plus L)-violating sphaleron processes.

Depending on the right-handed neutrino mass scale, different leptogenesis scenarios emerge: thermal leptogenesis and resonant leptogenesis operate via freeze-out dynamics, while leptogenesis via right-handed neutrino oscillations - also known as the Akhmedov-Rubakov-Smirnov mechanism - proceeds through freeze-in. Although these regimes differ in their dynamics and applicable temperature ranges, they are all continuously connected within the same underlying seesaw framework.

Probing right-handed neutrinos is difficult due to their gauge singlet nature and the seesaw relation, which implies either very heavy masses or suppressed Yukawa couplings. However, their characteristic lepton number violating interactions offer a promising avenue: observables that are highly suppressed or absent in the Standard Model may be significantly enhanced in the presence of right-handed neutrinos. A prime example is neutrinoless double beta decay, a rare nuclear process that would signify both lepton number violation and the Majorana nature of neutrinos. While essentially unobservable in the Standard Model, neutrinoless double beta decay is predicted in a wide range of beyond Standard Model scenarios involving right-handed neutrinos. Experimental searches have been conducted using different isotopes e.g. xenon one hundred thirty-six in the KamLAND-Zen experiment and germanium seventy-six in LEGEND. The most stringent bound currently comes from KamLAND-Zen, improving the half-life limit to greater than three point eight times ten to the twenty-six years, a factor of one point seven stronger than its previous result. Future experiments are expected to significantly extend this reach. KamLAND2-Zen aims to probe lifetimes of order ten to the twenty-seven years, while LEGEND is projected to reach sensitivities of ten to the twenty-eight years. These milestones will allow exploration of key regions in parameter space, including the standard inverted neutrino mass hierarchy.

While right-handed neutrinos provide an elegant explanation for both neutrino masses and the baryon asymmetry of the Universe, considering them in isolation is likely an idealization. In realistic ultraviolet completions, additional fields or interactions are often required, not only to generate right-handed neutrino masses or explain flavor structures, but potentially also to address other open problems of the Standard Model. These extended models can alter the predictions for both leptogenesis and low-energy observables such as neutrinoless double beta decay. To study such effects in a systematic and model-independent way, it is useful to employ an effective field theory approach. While for the Standard Model, the Standard Model Effective Field Theory provides a powerful framework, right-handed neutrinos which are lighter than the cutoff scale, must be kept as explicit degrees of freedom - leading to the so-called neutrino-extended Standard Model Effective Field Theory. Examples of ultraviolet completions giving rise to additional operators in the Standard Model Effective Field Theory are leptoquark models, left-right-symmetric models, gauged baryon and lepton number models, and Grand Unified Theories.

The effect of Standard Model Effective Field Theory operators on leptogenesis has been studied, including implications on neutrino masses and neutrinoless double beta decay. While neutrinoless double beta decay in the Standard Model Effective Field Theory has been studied extensively, a corresponding study of leptogenesis within the Standard Model Effective Field Theory framework remains absent. Interestingly, it was found that a specific lepton number conserving dimension-six operator in the Standard Model Effective Field Theory can significantly enhance the neutrinoless double beta decay rate when right-handed neutrinos have masses in the megaelectronvolt to gigaelectronvolt range. Motivated by this result, we focus on this mass range, for which the dominant leptogenesis production occurs via freeze-in.

The standard freeze-in leptogenesis scenario has been established and refined and various extensions have been explored, including specific ultraviolet completions and effective field theory approaches with higher-dimensional operators. However, the scenario we consider here differs in several important ways from these other extensions. First, previous studies have focused primarily on lepton number violating interactions, while we focus exclusively on a lepton number conserving dimension-six operator. Second, generally focused on additional light particles, while we are interested in heavy particles in this work (such that they can be captured in the effective field theory approach). Third, examined only the impact of higher-dimensional operators on initial conditions of right-handed neutrinos, while we study their influence on the full dynamical evolution of right-handed neutrinos throughout the leptogenesis process.

In this work, we focus on a single LNC vSMEFT operator. As discussed, the operator can give a dominant contribution to zero v thirty-three process. A key result of our work is that also for freeze-in LG the final BAU can be altered by several orders of magnitude depending on the EFT operator scale. The BAU can be suppressed, as might be expected for a freeze-in process with additional interactions, but somewhat surprisingly the BAU can also be enhanced, even though the additional operator is LNC. The suppression happens usually for small EFT scales where they can lead to observable signatures in Ov beta beta decay. We show how an observation of Ov beta beta decay in this case can essentially exclude large parts of the freeze-in parameter space. Simultaneously observing Ov beta beta decay and requiring successful freeze-in LG could point us towards small RHN masses and low reheating temperatures. Moreover, we show how the enhancement of the BAU can be used to alleviate some of the mass degeneracy for the RHNs, which is typical for freeze-in LG.

This paper is structured as follows. In Section two we introduce the vSMEFT and the dimension-six LNC operator we consider in this work. Section three is devoted to the study of Ov beta beta decay. In Section four we set up the quantum kinetic equations, necessary in the freeze-in LG framework, including higher-dimensional operators. We estimate how the solution qualitative behaves and solve the QKEs for the final BAU numerically for a few representative benchmark points. In Section five we show how our results depend on the reheating temperature and connect to zero v beta beta decay experiments. We also show how to reduce the mass degeneracy between the RHNs before concluding in Section six.