PRL-TH/95-11 INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS QUASI GOLDSTONE FERMION AS A STERILE NEUTRINO Eung Jin Chun Anjan S. Joshipura and INTERNATIONAL ATOMIC ENERGY Alexei Yu. Smirnov AGENCY UNITED NATIONS EDUCATIONAL, SCIENTIFIC AND CULTURAL MIRAMARE-TRIESTE ORGANIZATION IC/95/164 PRL-TH/95-11 1 Introduction International Atomic Energy Agency and All the experimentally known fermions transform uon-trivially under the gauge group 677(3) x United Nations Educational Scientific and Cultural Organization SU(2) x f/(l) of the standard model (SM). However there are experimental hints in tiu> INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS neutrino sector which suggest the existence of SU(S) x SU[2) x (7(1) - singlet fermions mixing appreciably with the known neutrinos. These hints come from (a) the deficits m the solar [1] and atmospheric [2] neutrino fluxes (b) possible need of significant hot. component [3] in tin- QUASI GOLDSTONE FERMION AS A STERILE NEUTRINO dark matter of the universe and (c) some indication of v, - vl:. oscillations in the laboratory [4], These hints can be reconciled with each other if there exists a fourth very light (< (9(eV)) Eung Jin Chun neutrino mixed with some of the known neutrinos preferably with the electron out-. The fourth International Center for Theoretical Physics, Trieste, Italy, neutrino is required to be sterile in view of the strong bounds on number of neutrino flavours Anja.li S. .loshipura coming both from the LEP experiment as well as from the primordial nucleosynthesis [5]. Theoretical Physics Group, Physical Research Laboratory, The existence of very light sterile neutrino demands theoretical justification since unlike a. Ahmedabad, 380 009, India the active neutrinos, the mass of the sterile state is not. protected by the gauge symmetry of and the SM and hence could be very large. Usually the sterile neutrino is conskiercd on the saint- Alexei Yu. Smirnov footing as the active neutrinos and some ad hoc symmetry is introduced to keep this neutrino International Center for Theoretical Physics, Trieste, Italy light. Recently there arc several attempts to construct models for sterile neutrinos which have and Institute for Nuclear Research, Russian Academy of Sciences, the origin beyond the usual lepton structure [6, 7, 8], In particular in Ref. [6] we suggested 117312 Moscow, Russian Federation. a possibility that supersymmetry (SUSY) may be responsible for both the existence and tin- lightness of the sterile fermions. ABSTRACT One could consider three different ways in which supersymmetry can keep sterile states The existence of sterile neutrino is hinted by simultaneous explanation of diverse neutrino very light. anomalies. We suggest that the quasi Goldstone fermions (QGF) arising in supersymmetric (1) Combination of supersymmetry and the (continuous) R symmetry present in many Hiipcr- theory as a result, of spontaneous breaking of global symmetry like the Peccei-Quinn symmetry symmetric models may not allow a mass term for the light sterile state. or the lepton number symmetry can play a role of the sterile neutrino. The smallness of mass (2) Spontaneous breakdown of some other global symmetry in supersymmetric theory can lead : of QGF (ms ~ 10~* - 10 eV) can be related to the specific choice of superpotential or to massless fermions which form the superpartners of the Goldstone bosons. Kahler potential (e.g., no-scale kinetic terms for certain superfields). Mixing of QGF with (3) The spontaneous breakdown of the global supersymmetry itself would give rise to a massless neutrinos implies the R-parity violation. It can proceed via the coupling of QGF with the fermion, the goldstino. Higgs supermultiplets or directly with the lepton doublet. A model which accounts for the The mechanism (1) and its phcnomenological consequences were discussed in Ref. ((>]. solar and atmospheric anomalies and the dark matter is presented. Mechanism (3) though appealing is not favoured phenomenologieally in view of the difficulties in building realistic models based on the spontaneously broken global SUf'Y. We discuss in this paper implications of the mechanism (2) concentrating for definiteness on the simplest MIRAMARE • TRIESTE case of a global U (!)<-,•. July 1995 The spontaneously broken global symmetries are required for reasons unrelated to the •"Wp.lli!! existence of ljf;;ht sterile states. The most interestim;, example:- being spontaneously broken In liic supersynunetnc limit ihe fermiouic component of the Goldstone boson is masslcss. lepton number .symmetry [9] and the Peceei-Quinri (PQ) syimnetry imposed [10] to :-<i|v<* In i he case (2) this Goldstone fermion is contained in the strong CP problem. The PQ symmetry arise naturally in many supcrsymmetric models. Apart, from solving the strong CP problem, this symmetry can also explain the smallness of the /(.-parameter (11, 12]. Phenomenologically consistent breaking of these symmetries generally However, SUSY breakdown results in generation of mass of the Goldstone fermion. In general, needs [13] Higgs fields which aro singlets of 5(7(3) x SU(2) x (7(1). In the supersymmetric this mass can be as big as SUSY breaking scale, rn.svsv- Broken supersyimuetry itself cannot 1 il(t context, this automatically generates massless sterile fermion. While the existence of these automatically protect the masses of QGF in Eq. (3) much below msnsr- I' f , the mass quasi Goldstone fermions (QGF) is logically independent of neutrino physics, there are good of QGF depends on the manner in which SUSY is broken and on the way how this breaking reasons to expect that, these fermions will couple to neutrinos. Indeed, in the case of lepton is communicated to the singlet 5. It also depends on the structure of supcrpotential and Ihe number symmetry the superfiekl which is mainly responsible for the breakdown of f/(l)t scale /<;. In the below we identify theories which can allow for very light QGF (my < 1 carries nontrivial (7(1)^-charge and therefore it can directly couple to leptons if the charge cV). As the case of special interest we will consider the mass of QGF and its mixing with the is appropriate. In the case of the PQ symmetry, U(\)PQ, this superfield could couple to the electron neutrino: Higgs supormultiplet. If theory contains small violation of R parity then this mixing with vis ^ (2 - 3) • l(r:leV Higgs gets communicated to the neutrino sector. Thus the occurrence of the QGF can have i sinf?e., ~ UmBe!i^ (2-<j)-Vr' . (4) implications for neutrino physics. We wish to discuss in this paper prospects for building These values of parameters allow one to solve the solar neutrino problem through the resonance realistic: models based on this mechanism. conversion v,. —> S [14], In the following section we elaborate upon the expected properties of the QGF, especially their masses when SUSY is broken. Section 3 discusses various mechanisms of mixing of these One could consider different mechanisms for the QGF mass generation. formions with the active neutrinos. Explicit model based on the scenario presented in section Let us note that in models with spontaneously broken global SUSY tin; QGF generically mp Y 2 and 3 is given in section 4 and the last section presents our conclusions. acquire a mass of O( j'f ) [15]. But it can remain rna-ssless in spite of SUSY breaking (a) if SUSY is broken by a D-term of the gauge field or (b) if the F-terms that break SUSY do not 2 Quasi Goldstone fermions and their masses carry any G-charges. The latter is Exemplified by a. simple generalization of Eq. (2): In this section and subsequently, we will consider the following general superpotent.ial SUSY is broken in this example if f'f / f.j. For a minimum with the F-terms: /<„ = Fn, = 0, W = + Wm U) the Goldstone fermion in Eq. (3) remains massless at the tree level in spite of the SUSY where W is assumed to be invariant, under some global symmetry U{\)c;. As we outlined breakdown. As we noticed before this version has phenomenological problems and further on in the introduction, this symmetry may be identified with the PQ symmetry, lepton number we will concentrate on possibilities related to supergravity. symmetry or combination thereof. The first term in Bq. (1) refers to the superpot.ential of the The mass of the QGF in supergravity theory is typically of the order of gravitino mass minimal superaymmetric standard model (MSSM). The second term contains .5(7(3) x SU(2) x m :t/v (= WSVSY} [IS, 17, 18]. For instance, the superpot.ential in Eq. (2) leads to ms ~ mA/i C/(l) singlet superfields which arc responsible for the breakdown of U[l)c- The minimal choice when generic soft terms of SUSY breakdown are allowed [16]. Howerver, the mass m,s can be for Wg is much smaller lor specific choices of 1) the superpotential and/or 2) soft. SUSY breaking terms. Ws = \(U<J' - fl)y . (2) Let us consider these possibilities in order. where <r, u' carry non trivial G-charges and fr, sets the scale of f/(l)(; breaking. The last term 1). The superpotential 2 of Bq. (1) describes mixing of the singlet fields with the superfields of the MSSM. \(<T<J' - X )y + X'(X - f(:f 3 is shown [)7] to generate the tree level mass where we have omitted the generation indices. The first, term in E(j. (8) produces the Dirac masses of neutrinos, whereas the second one gives the Majorana masses of R.H neutrino com- 10 KI ponents. The scale fG ~ 1O - lO^GeV generates M ~ 10 - 10" GeV required by the as in the global < aso if the minimal kinetic terms of the fields are assumed. For commonly HDM and atmospheric neutrinos.