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Dirac Neutrino Mass Generation from a Majorana Messenger

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Dirac Neutrino Mass Generation from a Majorana Messenger PHYSICAL REVIEW D 101, 035004 (2020) Dirac neutrino mass generation from a Majorana messenger † ‡ Julian Calle ,1,* Diego Restrepo ,1,2, and Óscar Zapata 1,3, 1Instituto de Física, Universidad de Antioquia, Calle 70 No. 52-21, Apartado A´ereo 1226, Medellín, Colombia 2International Institute of Physics, Universidade Federal do Rio Grande do Norte, Campus Universitario, Lagoa Nova, Natal-RN 59078-970, Brazil 3Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, 34151, Trieste, Italy (Received 29 October 2019; accepted 19 December 2019; published 6 February 2020) The radiative type-I seesaw has been already implemented to explain the lightness of Majorana neutrinos with both Majorana and Dirac heavy fermions, and the lightness of Dirac neutrinos with Dirac heavy fermions. In this work, we present a minimal implementation of the radiative type-I seesaw with light Dirac neutrinos and heavy Majorana fermions. An inert doublet and a complex singlet scalar complete the dark sector, which is protected by an Abelian fermiophobic gauge symmetry that also forbids tree level mass contributions for the full set of light neutrinos. A fermion vectorlike extension of the model is also proposed where the light right-handed neutrinos can thermalize in the primordial plasma and the extra gauge boson can be directly produced at colliders. In particular, the current upper bound on ΔNeff reported by PLANCK 0 0 points to large ratios of MZ0 =g ≳ 40 TeV, which can be competitive with collider constraint for g sufficiently large in the ballpark of the Standard Model values, while future cosmic microwave background experiments may probe all the no minimal models presented here. DOI: 10.1103/PhysRevD.101.035004 I. INTRODUCTION Dirac neutrinos with heavy Dirac mediators [14–17]. The radiative type-I seesaw includes both [18] possibilities [19], The interpretation of neutrino experimental data in terms but now it is also possible to have light Majorana neutrinos of neutrino oscillations is compatible with both Majorana with heavy Dirac mediators [20]. In this work, we want to and Dirac neutrino masses [1]. The former possibility has explore the possibility to build a simple Dirac radiative received the most attention but given the lack of signals in type-I seesaw model with heavy Majorana mediators. It is neutrinoless double beta decay experiments [2–7], the latter worth noticing that this idea have been already illustrated cannot be dismissed. If neutrinos are Dirac particles, the in an extension of the minimal supersymmetric standard Standard Model (SM) particle content must be extended model [21] but without show any explicit solution. with right-handed neutrinos, which can increase the effec- In general, solutions for light Dirac neutrino masses tive number of light neutrinos, N , until six. Therefore, to eff require a continuous symmetry to guarantee their Diracness. be compatible with the current cosmological restrictions on This symmetry is usually identified as the local Uð1Þ . N , the interactions of the extra right-handed neutrinos B−L eff Additionally, ad hoc discrete symmetries are invoked to with the primordial plasma must be highly suppressed. forbid tree level Dirac or Majorana mass terms for the light On the other hand, to give small masses to at least two right-handed neutrinos [14,22,23]. However, tree-level Majorana or Dirac neutrinos, as required to explain the Dirac type-I seesaw with proper choices for the U 1 neutrino oscillation experiments [8,9], the seesaw mecha- ð ÞB−L charges have been shown to be consistent without requiring nism with heavy fermions is usually invoked. For the tree- ad hoc level type-I seesaw, we can have either light Majorana any extra discrete symmetries [17]. In recent works, it – has been shown that even for one-loop Dirac neutrino neutrinos with heavy Majorana mediators [10 13] or light 1 masses, it is possible to have Uð ÞB−L as the only extra symmetry beyond the SM [24–26].1 *[email protected] † As a bonus in this case, the new scalars and fermions [email protected] ‡ [email protected] circulating the loop can be dark matter candidates with the stability of the lightest of them guaranteed by the very same Published by the American Physical Society under the terms of continuous symmetry. We focus here on solutions for the the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, 1For extensions with only extra scalars, minimal solutions have and DOI. Funded by SCOAP3. been found with two and three loops [26]. 2470-0010=2020=101(3)=035004(10) 035004-1 Published by the American Physical Society CALLE, RESTREPO, and ZAPATA PHYS. REV. D 101, 035004 (2020) radiative Dirac type-I seesaw with Majorana mediators, TABLE I. The new scalars and fermions with their respective which have only an extra local symmetry responsible for charges. All the SM fields are neutral under the dark Uð1ÞD gauge the Diracness of the light neutrinos, the absence of any tree- symmetry. level mass, and the existence of a dark sector constituted by Fields SUð2Þ Uð1Þ Uð1Þ the particles circulating the loop. L Y D In fact, another evidence that the SM is not a complete η 2 11 1 theory is the missing matter content of the Universe, which S 02 σ 1 is known as dark matter (DM). The main proposals that 03 ν 1 0 −4 explain DM as a particle are given in Ref. [27]. However, Ri ν 3 1 05 there has been only gravitational evidence for the existence R ψ α 1 01 of dark matter so far. Without evidence of DM as a particle, R there is not a clear path to pin out the DM properties nor the possible heavier companions of some extended dark sector. are defined by the anomaly cancellation conditions and the Linking the dark sector to other specific phenomenology gauge invariance in Yukawa and scalar interactions. allows us to reduce the arbitrariness in the model building. 1 The most general Lagrangian for some gauge Uð ÞX In our construction, the dark sector is related to the heavy symmetry, which includes the trivial case X ¼ D, must sector responsible of the lightness of the neutrinos, and the contains the following gauge, Yukawa, and scalar inter- same symmetry that guarantees the lightness of the Dirac actions in order to realize O6 at one-loop: neutrinos is the responsible of the stability of the lightest D dark particle (LDP). Therefore, the number of specific X X L ⊃− 0 0 ¯ γμ ∂ 0 0 ϕ 2 models is quite restricted. g Zμ qFF F þ jð μ þ ig qϕZμÞ j ϕ The rest of the paper is organized as follows. In the next F − ηψ˜ ν σÃψ c κ ψ c ψ à section, we present the model and study the scalar mass ½hiαLi Rα þ yjα Rj Rα þ αβ Rα RβS þ H:c: spectrum after spontaneous symmetry breaking. In Sec. III, − VðH; S; η; σÞ: ð2Þ we present the radiative mechanism that generates Dirac neutrino masses and establish the lepton flavor violation 0 constraints. The different resulting DM scenarios are In the first row, g is the gauge coupling associated to the 1 0 discussed in Sec. IV, and in Sec. V, we show the Uð ÞX group and Zμ is its corresponding gauge boson, F (ϕ) denote the new fermions (scalars), and q ϕ their X cosmological restrictions (Neff) in a nonminimum model F; for different extra Abelian symmetries. charges. In the second row, Li (i ¼ 1, 2, 3) and H are the à SM lepton and Higgs doublets, respectively, η˜ ¼ iσ2η , and κ II. THE MODEL h, y, and are matrices in the flavor space. The scalar potential can be cast as We extend the SM with a spontaneously broken Abelian gauge symmetry which guarantees the Dirac-ness of the VðH;S;η;σÞ¼VðHÞþVðSÞþVðηÞþVðσÞ massive neutrinos. Only the new particles, including the † à † à right-handed partners of the SM neutrinos, are charged þ λ1ðH HÞðS SÞþλ2ðH HÞðσ σÞ under this new Uð1ÞD dark gauge symmetry [28–30] to † † à à þ λ3ðH HÞðη ηÞþλ4ðS SÞðσ σÞ obtain an anomaly free theory. We choose the new particle à † † à set such that the following dimension six operator is þ λ5ðS SÞðη ηÞþλ6ðη ηÞðσ σÞ realized at one-loop level, † † † à þ λ7ðη HÞðH ηÞþλ8ðη HS σ þ H:c:Þ; ð3Þ 1 ¯ ˜ 2 2 † † 2 O6 LHν S ; ω μ ω ω λ ω ω D ¼ Λ2 R ð1Þ with Vð Þ¼ ω þ ωð Þ . It is worth to emphasize that Uð1ÞD automatically allows for all the terms in Eqs. (2) where S is the singlet scalar field which spontaneously and (3), but other realizations will be checked later on. Note 1 breaks the Uð1ÞD symmetry needed to forbid the Dirac and that after the spontaneous symmetry breaking of Uð ÞX, the Majorana neutrino mass terms at tree level. λ8 term gives rise to the mixing between the neutral parts of With the aim to illustrate the one-loop Dirac neutrino η and σ, which is mandatory to generate nonzero radiative mass generation, we consider the particle content shown in masses. We assume λ8 and hSi reals to preserve the CP 2 2 Table I as a possible realization of the effective operator symmetry in the scalar sector, and μη, μσ > 0 to avoid tree- O6D. Specifically, we introduce three scalar fields η, σ, and level mixing terms among the fermions. Moreover, we also S, where only S develops a nonzero vacuum expectation assume λ1 ≪ 1 such that the scalar S and H do not mix value (VEV), a set of three singlet fermions, νRj (j ¼ 1,2) allowing us to identify the CP even scalar particle in H as and νR3, and another set of three heavy Majorana fermions, the SM Higgs boson.
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