UMN-TH-4021/21 Light Sterile Neutrinos and a High-Quality Axion from a Holographic Peccei-Quinn Mechanism Peter Cox,1, ∗ Tony Gherghetta,2, y and Minh D. Nguyen2, z 1School of Physics, The University of Melbourne, Victoria 3010, Australia 2School of Physics and Astronomy, University of Minnesota, Minneapolis, Minnesota 55455 USA We present a 5D axion-neutrino model that explains the Standard Model fermion mass hierarchy and flavor structure, while simultaneously generating a high-quality axion. The axion and right- handed neutrinos transform under a 5D Peccei-Quinn gauge symmetry, and have highly suppressed profiles on the UV brane where the symmetry is explicitly broken. This setup allows neutrinos to be either Dirac, or Majorana with hierarchically small sterile neutrino masses. The axion decay constant originates from the IR scale, which in the holographically dual 4D description corresponds to the confinement scale of some new strong dynamics with a high-quality global Peccei-Quinn symmetry that produces a composite axion and light, composite sterile neutrinos. The sterile neutrinos could be observed in astrophysical or laboratory experiments, and the model predicts specific axion{neutrino couplings. INTRODUCTION work. Two unsettled issues in the Standard Model are neu- The PQ symmetry forbids an explicit or spontaneously trino masses and the strong CP problem. A natural so- generated bulk Majorana mass for the right-handed neu- lution to the origin of the neutrino masses is the Type-I trinos, leading to an accidental lepton number symmetry. seesaw mechanism [1{5] with Majorana masses at an in- However, explicit PQ (and L) violating terms are allowed 10 termediate scale & 10 GeV. On the other hand, the on the UV brane, and the fundamental Majorana mass most popular solution to the strong CP problem is the scale is tied to explicit Planck-scale PQ (and L) viola- Peccei-Quinn (PQ) mechanism [6], where the axion is a tion. Despite this connection, the sterile neutrino mass pseudo-Nambu-Goldstone boson [7, 8] that results from eigenstates can be naturally light. This is because the the spontaneous breaking of a global U(1)PQ symmetry. right-handed neutrino profiles can be localized towards These two solutions appear to be unrelated; however, the the IR brane, away from the explicit symmetry viola- similarity of the PQ-breaking and Majorana mass scales tion. In fact, the sterile neutrino masses can range from suggests there could be an underlying mechanism respon- the intermediate scale down to the eV scale (in the see- sible for both neutrino masses and the axion. saw mechanism limit), or even lower to the theoretical Any axion solution to the strong CP problem must Dirac limit. The model also predicts axion couplings to address the axion quality problem, which requires extra- both the active and sterile neutrinos; however, these are neous, explicit violations of the global PQ symmetry to well below the current experimental limits [15]. be sufficiently suppressed compared to that arising from non-perturbative QCD. Recently, a possible solution was A connection between neutrino masses and axions was given in Ref. [9], where the axion propagates in a slice of first discussed in the context of the grand unified group AdS5. The PQ symmetry is gauged in the bulk, and the 0 SO(10) × U(1) , where the U(1)PQ symmetry is realised axion profile is suppressed near the sources of explicit PQ 0 as a linear combination of U(1)B−L and U(1) [16]. Other symmetry violation on the UV brane. The warped geom- models based on the DFSZ axion with a connection to arXiv:2107.14018v1 [hep-ph] 29 Jul 2021 etry [10] can also naturally explain fermion mass hierar- neutrino masses include [17{19]. In contrast, our 5D chies [11], and a holographic DFSZ-type [12, 13] axion model automatically addresses the axion quality prob- model that incorporates Standard Model flavor was pre- lem while simultaneously explaining the hierarchies of sented in Ref. [14], giving predictions for flavor-violating the Standard Model fermion masses and flavor structure axion{fermion couplings. The 5D framework, therefore, in the quark and lepton sectors. Furthermore, by the provides a natural setting to seek a connection between AdS/CFT correspondence [20], the 5D model is dual to a neutrino masses and the axion. strongly-coupled 4D theory where the intermediate scale In this Letter, we extend the model of Refs. [9, 14] to is dynamically generated by dimensional transmutation. include neutrino masses. Right-handed neutrinos are in- The axion is identified as a composite pseudo-Nambu- troduced into the bulk and are charged under the U(1)PQ Goldstone boson, and the right-handed neutrinos are also symmetry. The model can explain neutrinos as either composite states. While right-handed neutrinos propa- Dirac or Majorana states, with hierarchies in the effective gating in a slice of AdS5 were previously considered in 4D neutrino Yukawa couplings and/or right-handed neu- Refs [21{28], our setup is the first model to amalgamate trino masses naturally generated within the 5D frame- neutrinos with axion physics. 2 AXION{NEUTRINO MODEL Li Ei Ni Hu Hd Φ 2 2 2 2 U(1)PQ 2 sin β 4 sin β 2 −2 cos β −2 sin β 1 Consider a 5D U(1) gauge theory with a complex 1 1 1 PQ U(1)Y − −1 0 − 0 scalar field Φ propagating in a slice of AdS bounded by 2 2 2 5 U(1)L 1 1 1 0 0 0 UV and IR branes located at zUV and zIR. The metric U(1)Φ 0 0 0 0 0 1 in 5D coordinates xM = (xµ; z) is given by 1 TABLE I: U(1) charges of the bulk fields. ds2 = dx2 + dz2 ≡ g dxM dxN ; (1) (kz)2 MN where the AdS curvature scale k M , with M = (5) (5) . P P ye,ν are 3 × 3 complex matrices and yN , bN are complex 2:435 × 1018 GeV the reduced Planck mass. The Yang- symmetric matrices. Mills{scalar action is given in [9], where it is also shown The model contains four U(1) symmetries in the bulk: that the usual global PQ symmetry that acts on the 4D the hypercharge and PQ gauge symmetries, and acciden- axion corresponds to a particular bulk U(1)PQ gauge tal global lepton number and U(1)Φ symmetries. The transformation. charges of the fields are given in table I. The PQ charges The complex, PQ-charged scalar field Φ obtains a VEV of the Higgs fields have been chosen so that there is no mixing between the axion and the longitudinal compo- η(z) = k3=2 λ(kz)4−∆ + σ(kz)∆ ; (2) nent of the Z boson, where tan β = vu=vd is the ratio of where ∆ is related to the bulk scalar mass-squared, the Higgs VEVs. 2 2 mΦ = ∆(∆ − 4)k . In the dual 4D interpretation [29] The U(1)PQ and U(1)Φ symmetries are spontaneously of our setup, σ is proportional to the PQ-breaking con- broken by the VEV of Φ and explicitly broken by the densate in the CFT, which has dimension ∆. The coeffi- scalar potential on the UV boundary. This results in a cient λ is associated with explicit breaking of the U(1)PQ single pseudo-Nambu-Goldstone boson, identified as the symmetry on the UV brane. Note that the boundary con- axion (see Refs. [9, 14] for details). Furthermore, the lep- ditions are such that the 5D gauge symmetry reduces to ton number and PQ symmetries are explicitly broken by (5) a global symmetry on the UV brane (guaranteeing there yN and bN . Note that the U(1)PQ gauge symmetry for- is no massless 4D U(1)PQ gauge boson), and therefore bids corresponding terms in the bulk. This has important the symmetry can be explicitly broken there (see Ref. [9] phenomenological consequences, since such terms would for details). lead to sterile neutrino zero-mode masses of order the In Ref. [14] this model was extended to include bulk PQ-breaking scale, as might be expected for a high-scale fermion and Higgs fields, creating a 5D version of the seesaw. The UV boundary terms, on the other hand, DFSZ axion model [12, 13] that could simultaneously ad- can naturally give rise to hierarchically smaller sterile dress both the axion quality and fermion mass hierarchy neutrino masses, as will be shown. These may then be problems. Here, we further extend the model to incorpo- accessible to experiments. rate the neutrino sector. Neutrino masses are obtained by including bulk right-handed neutrinos Ni (i = 1; 2; 3) with 5D Yukawa couplings and UV boundary localized Zero-mode profiles Majorana masses and Φ coupling terms. The relevant 1 part of the action is given by The equations of motion for the 5D fields can be solved Z zIR via the usual expansion in Kaluza-Klein (KK) modes. 5 p SN = −2 d x −g The massless 4D zero-modes are then identified with the zUV SM fermions and the axion. 1 (5) (5) The scalar fields are parameterized as × p y LiNjHu + y LiEjHd + h:c: k ν;ij e;ij (5) vu i a (xµ;z) 1 y vu u 1 c N;ij c Hu = p e ; + bN;ijN Nj + ΦN Nj + h:c: δ(z − zUV ) ; 2 0 2 i k3=2 i v i µ 0 (3) d v ad(x ;z) Hd = p e d ; 2 1 νi where Li = ei are the SU(2) lepton doublets and Ei ia(xµ;z) are the SU(2) singlet leptons.