Gauging U(1) symmetries and the number of right-handed neutrinos

Abstract

In this letter we consider that assuming: a) that the only left-handed neutral fermions are the active neutrinos, b) that B − L is a gauge symmetry, and c) that the L assignment is restricted to the integer numbers, the anomaly cancellation imply that at least three right-handed neutrinos must be added to the minimal representation content of the electroweak standard model. However, two types of models arise: i) the usual one where each of the three identical right-handed neutrinos has total lepton number L = 1; ii) and the other one in which two of them carry L = 4 while the third one carries L = −5.It is well known that it is possible to enlarge the representation content of the minimal electroweak standard model (ESM) by adding an arbitrary number of right-handed neutrinos. Since they are sterile under the interactions of that model they do not contribute to the anomaly cancellation of the gauge symmetries, then nothing determine their number. Until now, it has been a question of taste to consider a particular number of these fields in extensions of the model. It is also well known that within the ESM (no right-handed neutrinos) both, baryon (B) and total lepton (L) numbers, are conserved automatically up to anomaly effects: both global U(1) B and U(1) L are anomalous [1] (but their consequences are well suppressed at least at zero temperature) and only the combination U(1) B−L is a global anomaly free symmetry if right-handed neutrinos are added for cancelling the mixed gauge-gravitational anomaly [2].

Complex scalar dark matter in aB-Lmodel

“…[20,21]. It is an extension of the SM based on the gauge symmetry SUð2Þ L ⊗ Uð1Þ Y 0 ⊗ Uð1Þ B−L , where B and L are the usual baryonic and leptonic numbers, respectively, and Y 0 is a new charge different from the hypercharge Y of the SM.…”

“…The values of Y 0 are chosen to obtain the hypercharge Y through the relation Y ¼ ½Y 0 þ ðB − LÞ , after the first spontaneous symmetry breaking. Assuming a generationindependent charge assignment and the nonexistence of mirror fermions, and by restricting ourselves to integer quantum numbers for the Y 0 charge, the anomaly cancellation constrains the number of right-handed neutrinos, n R ≥ 3 [20]. Considering n R ¼ 3, there is an exotic charge assignment for the Y 0 charge where Y 0 n R1 ;n R2 ¼ −4 and Y 0 n R3 ¼ 5 besides the usual one where Y 0 n Ri ¼ 1 with i ¼ 1; 2; 3.…”

“…In this paper, we focus on the possibility of having a viable scalar DM candidate in a U(1) gauge extension of the SM. In particular, this model, sometimes referred as the flipped B − L model [20,21] has a very rich scalar content, which allows us to obtain a complex scalar DM candidate.…”

Anomaly-Free Constraints in Neutrino Seesaw Models

“…Assuming three generations, two active and one sterile right-handed neutrinos, the anomaly-free system of equations implies the charge assignments given in the last column of Table I. For ¼ 6, the hypercharge is reproduced, while ¼ 3 does not lead to B À L since x ';e ¼ À1, x u;d;q ¼ 1=3, x ¼ À4, and x S ¼ 5 [10].…”

ZB−L′phenomenology at the LHC

“…Some models which have an extra U (1) gauge group [13,14] also deserve a detailed study in order to predict new physics behavior. The cumulative study of different models, candidates to describe the electroweak interaction, can guide the LHC data analysis if in fact a Z ′ is discovered.…”