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Register a new userOperator Bases in Effective Field Theories with Sterile Neutrinos: $d leq 9$
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We obtain the complete and independent bases of effective operators at mass dimension 5, 6, 7, 8, 9 in both standard model effective field theory with light sterile right-handed neutrinos ($ u$SMEFT) and low energy effective field theory with light sterile neutrinos ($ u$LEFT). These theories provide systematical parametrizations on all possible Lorentz-invariant physical effects involving in the Majorana/Dirac neutrinos, with/without the lepton number violations. In the $ u$SMEFT, we find that there are 2 (18), 29 (1614), 80 (4206), 323 (20400), 1358 (243944) independent operators with sterile neutrinos included at the dimension 5, 6, 7, 8, 9 for one (three) generation of fermions, while 24, 5223, 3966, 25425, 789426 independent operators in the $ u$LEFT.
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We obtain the complete operator bases at mass dimensions 5, 6, 7, 8, 9 for the low energy effective field theory (LEFT), which parametrize various physics effects between the QCD scale and the electroweak scale. The independence of the operator basis regarding the equation of motion, integration by parts and flavor relations, is guaranteed by our algorithm, whose validity for the LEFT with massive fermions involved is proved by a generalization of the amplitude-operator correspondence. At dimension 8 and 9, we list the 35058 (756) and 704584 (3686) operators for three (one) generations of fermions categorized by their baryon and lepton number violations $(Delta B, Delta L)$, as these operators are of most phenomenological relevance.
We investigate neutrinoless double beta decay ($0 ubetabeta$) in the presence of sterile neutrinos with Majorana mass terms. These gauge-singlet fields are allowed to interact with Standard-Model (SM) fields via renormalizable Yukawa couplings as well as higher-dimensional gauge-invariant operators up to dimension seven in the Standard Model Effective Field Theory extended with sterile neutrinos. At the GeV scale, we use Chiral effective field theory involving sterile neutrinos to connect the operators at the level of quarks and gluons to hadronic interactions involving pions and nucleons. This allows us to derive an expression for $0 ubetabeta$ rates for various isotopes in terms of phase-space factors, hadronic low-energy constants, nuclear matrix elements, the neutrino masses, and the Wilson coefficients of higher-dimensional operators. The needed hadronic low-energy constants and nuclear matrix elements depend on the neutrino masses, for which we obtain interpolation formulae grounded in QCD and chiral perturbation theory that improve existing formulae that are only valid in a small regime of neutrino masses. The resulting framework can be used directly to assess the impact of $0 ubetabeta$ experiments on scenarios with light sterile neutrinos and should prove useful in global analyses of sterile-neutrino searches. We perform several phenomenological studies of $0 ubetabeta$ in the presence of sterile neutrinos with and without higher-dimensional operators. We find that non-standard interactions involving sterile neutrinos have a dramatic impact on $0 ubetabeta$ phenomenology, and next-generation experiments can probe such interactions up to scales of $mathcal O(100)$ TeV.
We revisit the effective field theory of the standard model that is extended with sterile neutrinos, $N$. We examine the basis of complete and independent effective operators involving $N$ up to mass dimension seven (dim-7). By employing equations of motion, integration by parts, and Fierz and group identities, we construct relations among operators that were considered independent in the previous literature, and find seven redundant operators at dim-6, sixteen redundant operators and two new operators at dim-7. The correct numbers of operators involving $N$ are, without counting Hermitian conjugates, $16~(Lcap B)+1~(slashed{L}cap B)+2~(slashed{L}capslashed{B})$ at dim-6, and $47~(slashed{L}cap B)+5~(slashed{L}capslashed{B})$ at dim-7. Here $L/B~(slashed L/slashed B)$ stands for lepton/baryon number conservation (violation). We verify our counting by the Hilbert series approach for $n_f$ generations of the standard model fermions and sterile neutrinos. When operators involving different flavors of fermions are counted separately and their Hermitian conjugates are included, we find there are $29~(1614)$ and $80~(4206)$ operators involving sterile neutrinos at dim-6 and dim-7 respectively for $n_f=1~(3)$.
Neutrinos, being the only fermions in the Standard Model of Particle Physics that do not possess electromagnetic or color charges, have the unique opportunity to communicate with fermions outside the Standard Model through mass mixing. Such Standard Model-singlet fermions are generally referred to as sterile neutrinos. In this review article, we discuss the theoretical and experimental motivation for sterile neutrinos, as well as their phenomenological consequences. With the benefit of hindsight in 2020, we point out potentially viable and interesting ideas. We focus in particular on sterile neutrinos that are light enough to participate in neutrino oscillations, but we also comment on the benefits of introducing heavier sterile states. We discuss the phenomenology of eV-scale sterile neutrinos in terrestrial experiments and in cosmology, we survey the global data, and we highlight various intriguing anomalies. We also expose the severe tension that exists between different data sets and prevents a consistent interpretation of the global data in at least the simplest sterile neutrino models. We discuss non-minimal scenarios that may alleviate some of this tension. We briefly review the status of keV-scale sterile neutrinos as dark matter and the possibility of explaining the matter-antimatter asymmetry of the Universe through leptogenesis driven by yet heavier sterile neutrinos.
Sterile neutrinos are natural extensions to the standard model of particle physics in neutrino mass generation mechanisms. If they are relatively light, less than approximately 10 keV, they can alter cosmology significantly, from the early Universe to the matter and radiation energy density today. Here, we review the cosmological role such light sterile neutrinos can play from the early Universe, including production of keV-scale sterile neutrinos as dark matter candidates, and dynamics of light eV-scale sterile neutrinos during the weakly-coupled active neutrino era. We review proposed signatures of light sterile neutrinos in cosmic microwave background and large scale structure data. We also discuss keV-scale sterile neutrino dark matter decay signatures in X-ray observations, including recent candidate $sim$3.5 keV X-ray line detections consistent with the decay of a $sim$7 keV sterile neutrino dark matter particle.
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