Dark matter stability and Dirac neutrinos using only standard model symmetries

Abstract

We provide a generic framework to obtain stable dark matter along with naturally small Dirac neutrino masses generated at the loop level. This is achieved through the spontaneous breaking of the global U (1)B−L symmetry already present in Standard Model. The U (1)B−L symmetry is broken down to a residual even Zn; n ≥ 4 subgroup. The residual Zn symmetry simultaneously guarantees dark matter stability and protects the Dirac nature of neutrinos. The U (1)B−L symmetry in our setup is anomaly free and can also be gauged in a straightforward way. Finally, we present an explicit example using our framework to show the idea in action.

Dirac neutrino mass generation from a Majorana messenger

“…In other words, bearing in mind that M Z /g ≈ 3v S /2 5 we have that the energy scale of the U(1) X symmetry breaking must be at least ∼ 24 TeV (note that the U(1) X having the lowest M Z /g ratio features a X charge l = −6/11 ≈ −1/2). Similar constraints would apply to all gauged and anomaly free U(1) X extensions of the SM with Dirac neutrino masses, where light right handed neutrinos are associated to the solution (−4, −4, +5) [17,24,25,[73][74][75]. On the other hand, it is remarkable the fact the next generation of CMB experiments [67][68][69] has the potential to entirely probe all the not-so minimal models [76,77].…”

“…However, tree-level Dirac type-I seesaw with proper choices for the U(1) B−L charges have been shown to be consistent without require any extra ad-hoc discrete symmetries [17]. In recent works, it has been shown that even for one-loop Dirac neutrino masses, it is possible to have U(1) B−L as the only extra symmetry beyond the SM [24][25][26] 1 .…”

Systematic classification of two-loop d = 4 Dirac neutrino mass models and the Diracness-dark matter stability connection

“…This can also happen naturally in many models involving an additional Z 2 symmetry [31], a flavour symmetry [32,34] or chiral U (1) L charges for ν R [27-29, 52, 58]. In fact, it has been recently shown that an appropriate residual subgroup of the lepton number (or equivalently B − L symmetry) alone is enough to guarantee the Dirac nature of neutrinos to all loops and ensure that the leading contribution to neutrino mass only arises at higher loops [52]. Since all the requirements to have Dirac neutrino masses with a leading contribution at two-loops can always be meet, henceforth we will take a different approach and not bother about the details of the symmetries required for an specific model.…”

“…It is important to clarify that if one imposes a symmetry that forbids the tree-level Dirac mass term, all the realizations of the operatorLφ c ν R (φ † φ) n with n ∈ N will automatically vanish. For this reason, one must break such a symmetry, either softly or spontaneously, in order to allow radiative or higher-dimensional Dirac neutrino mass models such that the tree-level term is still absent [27,31,52].…”

“…In this sense, the symmetry protecting the Dirac nature of neutrinos can play a double role and also be used to stabilize a dark matter candidate [31,32,34,52,58]. Moreover, it has recently been shown that all these features, namely Dirac neutrinos, absence of lower order mass terms (tree-level and one-loop) and a stable dark matter can be obtained with chiral, yet anomaly free B − L charges without the need of any other symmetry, either explicit or accidental [52].…”