Freeze-In Dark Matter from a Minimal B-L Model and Possible Grand

PHYSICAL REVIEW D 101, 115022 (2020) Freeze-in dark matter from a minimal B − L model and possible grand unification Rabindra N. Mohapatra1 and Nobuchika Okada 2 1Maryland Center for Fundamental Physics and Department of Physics, University of Maryland, College Park, Maryland 20742, USA 2Department of Physics and Astronomy, University of Alabama, Tuscaloosa, Alabama 35487, USA (Received 5 May 2020; accepted 5 June 2020; published 17 June 2020) We show that a minimal local B − L symmetry extension of the standard model can provide a unified description of both neutrino mass and dark matter. In our model, B − L breaking is responsible for neutrino masses via the seesaw mechanism, whereas the real part of the B − L breaking Higgs field (called σ here) plays the role of a freeze-in dark matter candidate for a wide parameter range. Since the σ particle is unstable, for it to qualify as dark matter, its lifetime must be longer than 1025 seconds implying that the B − L gauge coupling must be very small. This in turn implies that the dark matter relic density must arise from the freeze-in mechanism. The dark matter lifetime bound combined with dark matter relic density gives a lower bound on the B − L gauge boson mass in terms of the dark matter mass. We point out parameter domains where the dark matter mass can be both in the keV to MeV range as well as in the PeV range. We discuss ways to test some parameter ranges of this scenario in collider experiments. Finally, we show that if instead of B − L, we consider the extra Uð1Þ generator to be −4I3R þ 3ðB − LÞ, the basic phenomenology remains unaltered and for certain gauge coupling ranges, the model can be embedded into a five-dimensional SOð10Þ grand unified theory. DOI: 10.1103/PhysRevD.101.115022 I. INTRODUCTION possibility with the following new results. First is that the minimal version of the B − L model itself, without any If small neutrino masses arise via the seesaw mechanism extra particles, can provide a dark matter (DM) candidate. [1–5], the addition of a local B − L symmetry [6,7] to the The DM turns out to be the real part (denoted here as σ)of standard model (SM) provides a minimal scenario for the complex B − L ¼ 2 Higgs field, that breaks B − L and beyond the standard model physics to achieve this goal. gives mass to the right-handed neutrinos in the seesaw There are two possible classes of B − L models: one where formula. Even though this particle is not stable, there are the B − L generator contributes to the electric charge [6–8] certain allowed parameter ranges of the model, where its and another where it does not [9–11]. In the first case, the lifetime can be so long that it can play the role of a decaying B − L gauge coupling g has a lower limit, whereas in the BL dark matter. We isolate this parameter range and show that second case it does not and therefore can be arbitrarily in this case, the freeze-in mechanism [17] can generate its small. There are constraints on the allowed ranges of g BL relic density. We find this possibility to be interesting since from different observations [12,13] in the second case it unifies both neutrino masses and dark matter in a single depending on whether there is or is not a dark matter minimal framework [18]. We show how a portion of the particle in the theory. There are also possible ways to look parameter range of the model suggested by the dark matter B − L for gravitational wave signals of breaking in the possibility can be probed by the recently approved FASER early Universe [14]. experiment at the LHC [19] and other Lifetime Frontier In Refs. [15,16], it was shown that if we added a B − L − experiments. charge carrying vectorlike fermion to the minimal B L We then show that if we replace the B − L symmetry by model and want it to play the role of dark matter, new ˜ I ≡ −4I3 þ 3ðB − LÞ (where I3 is the right-handed weak constraints emerge. In this note, we discuss an alternative R R isospin), the dark matter phenomenology remains largely unchanged and the model can be embedded into the SOð10Þ grand unified theory in five space-time dimensions. Published by the American Physical Society under the terms of Such a symmetry breaking of SOð10Þ to SUð5Þ × Uð1Þ˜ the Creative Commons Attribution 4.0 International license. I Further distribution of this work must maintain attribution to has already been shown to arise from a symmetry breaking the author(s) and the published article’s title, journal citation, by a particular alignment for a vacuum expectation value and DOI. Funded by SCOAP3. (VEV) of a 45-dimensional Higgs field [20]. 2470-0010=2020=101(11)=115022(9) 115022-1 Published by the American Physical Society RABINDRA N. MOHAPATRA and NOBUCHIKA OKADA PHYS. REV. D 101, 115022 (2020) We note that there are examples of other models in the symmetry breaking. However, it turns out that if 0 literature connecting neutrino mass generation mechanisms we set λ ¼ 0 at the tree level, it can be induced at the to dark matter; see, for example, Refs. [21,22]. one-loop level by fermion contributions and at the This paper is organized as follows: in Sec. II, after briefly two-loop level from the top loop as shown in introducing the model, we discuss the lifetime of the σ dark Ref. [11]. These induced couplings can be so small matter and its implications. In Sec. III, we discuss the small that they still lead to very long lifetimes for σ in the parameter range of interest to us. gauge coupling gBL range where the dark matter lifetime is long enough for it to play the role of dark matter. In Sec. IV, we show how freeze-in mechanism determines the relic III. DARK MATTER LIFETIME density of dark matter and its implications for the allowed σ parameter range of the model. We also discuss how to test As noted earlier in Sec. II, the field has couplings this model at the FASER and other Lifetime Frontier which could make it unstable and thereby disqualify it from experiments. In Sec. V, we show that this model can also being a dark matter. However, we will show that there is a accommodate a PeV dark matter. In Sec. VI, we discuss the viable parameter range of the model where this decay 25 SOð10Þ embedding of the closely allied model and in lifetime is longer than 10 seconds [24] so that it can be a Sec. VII, we conclude with some comments and other dark matter candidate. We discuss the following two implications of the model. modes now: (i) Decay mode σ → NN → lff¯lff¯: The decay width for this process is estimated as II. BRIEF OVERVIEW OF THE MODEL ð 2 2 Þ2 13 ð1Þ fhνhSM mσ Our model is based on the U B−L extension of the SM Γ ≃ ; ð1Þ ð1Þ NN ð4πÞ8 M4 m8 with gauge quantum numbers under U B−L determined N h by the baryon or lepton number of the particles. The gauge where hν is a neutrino Dirac Yukawa coupling, hSM group of the model is SUð3Þ ×SUð2Þ ×Uð1Þ ×Uð1Þ − , c L Y B L is a Yukawa coupling of an SM fermion f, and mh ¼ where Y is the SM hypercharge. We need three right- 125 GeV is the SM Higgs boson mass. For a GeV − ¼ −1 handed neutrinos (RHNs) with B L to cancel the mass σ and TeV mass RHN, the lifetime of σ B − L anomaly. The RHNs being SM singlets do not τ ½ ∼ 1037 ð 2 4 Þ turns out to be σ sec = f hSM , which is contribute to SM anomalies. The electric charge formula in quite consistent with the requirement for it to be a ¼ þ Y this case is same as in the SM, i.e., Q I3L 2. dark matter. Here, we have used the seesaw formula − 2 2 We break B L symmetry by giving a VEV to a hνv =M ≃ mν with v ¼ 246 GeV and a − ¼ 2 Δ hΔi¼ EW N EW B Lpffiffiffi SM neutral complex Higgs field , i.e., typical neutrino mass scale mν ≃ 0.1 eV. 2 ¯ ¯ vBL= . This gives Majorana masses to the right-handed (ii) Decay mode σ → ZBLZBL → ffff: The decay neutrinos (N) via the coupling fNNΔ. The real part of Δ width for this process is σ (denoted by ) is a physical field. Our goal in this paper is 4 2 4 7 6 7 σ ð2g Þ v g mσ g mσ to show that has the right properties to play the role of a Γ ≃ BL BL BL ¼ BL : ð2Þ ZBLZBL ð4πÞ5M8 256π5 M6 dark matter of the universe. There are three challenges to ZBL ZBL achieving this goal which are as follows: (i) The σ field has couplings to the RHNs which in turn This mode is sensitive to the values of gBL as well as M . The estimate of τσ due to this decay mode is couple to SM particles providing a way for σ to ZBL σ B − L given by decay. Also, the field has couplings to two gauge bosons (Z ) which in turn couple to SM 6 7 BL −20 1 1 GeV σ τσ ≃ 5.2 × 10 fields providing another channel for to decay. In g m the next section, we show that there are parameter BL σ M 6 regions of the model where these decay modes give a × ZBL seconds: ð3Þ long enough lifetimes for σ, so that it can be a viable 1 GeV unstable dark matter in the universe.

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