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View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by CERN Document Server hep-ph/9810257 IC/98/163 WIS-98/25/Oct-DPP Naturally Light Sterile Neutrinos in Gauge Mediated Sup ersymmetry Breaking a b Gia Dvali and Yosef Nir a ICTP, Trieste, 34100, Italy b Department of Particle Physics, Weizmann Institute of Science, Rehovot 76100, Israel Mo duli are generic in string (M) theory. In a large class of gauge-mediated Sup ersymmetry breaking mo dels, the fermionic comp onents of such elds havevery light masses, around the eV scale, and non-negligible mixing with 4 active neutrinos, of order 10 . Consequently, these fermions could play the role of sterile neutrinos to which active neutrinos oscillate, thus a ecting measurements of solar neutrinos or of atmospheric neutrinos. They could also provide warm dark matter, thus a ecting structure formation. 10/98 1. Intro duction Light sterile neutrinos are o ccasionally invoked by theorists to explain various hints of neutrino masses which cannot b e accommo dated in a framework of only three light active neutrinos (see e.g. refs. [1-26]). There are, however, three puzzles related to the hyp othesis that light sterile neutrinos may play a role in various observations: (i) The Ma jorana mass term of a sterile neutrino is not protected byany Standard Mo del (SM) gauge symmetry and can, therefore, be arbitrarily large. The mass that is relevant to the various exp eriments is at or b elow the eV scale. (ii) The Dirac mass term that mixes a sterile neutrino with an active one is protected by the electroweak breaking scale and is exp ected to b e in the range m m . To explain e Z any of the exp erimental results we need this term to be at or b elow the eV scale. (iii) The two scales describ ed ab ove are in general indep endent of each other. Yet, the mixing b etween the sterile and the active neutrino, which is given by the ratio of the 2 two scales, cannot be much smaller than O (10 ) and, for some purp oses, needs to be of O (1). Then some mechanism that relates the two scales seems to be required. Many mo dels were prop osed that give sterile neutrinos with the required features. Most existing mo dels employ a rather ad-ho c symmetry structure (or just give an ansatz) to induce the relevant parameters. The case for light sterile neutrinos would b ecome much stronger if some well-motivated extension of the SM predicted their existence. We argue that in mo dels of Gauge Mediated Sup ersymmetry Breaking (GMSB), the fermionic comp onents of any SM singlet sup er eld N that it massless in the Sup ersymmetry N limit and, in particular, the mo duli elds, are generically exp ected to have masses and mixing that could be relevant to various exp erimental and observational results. 2. Light Singlet Fermions in Sup ersymmetric Mo dels We assume that the dominant source of sup ersymmetry breaking is an F term of a chiral sup er eld S : F 6= 0. Mass terms involving arise then from the Kahler S N p otential and involve sup ersymmetry breaking. The leading contribution to the mass term 1 m is of the form NN N N y F (S ) (NN) S =) m : (2:1) NN m m Pl Pl The singlet N eld can mix with a lepton doublet eld L. The leading contribution to the mass term m is of the form LN L N y ( ) (LN ) u d =) m : (2:2) LN m m Pl Pl Here, are the two Higgs elds of the MSSM and we used the fact that the term d;u u d in the sup erp otential leads to F . The mass terms m and m determine the u NN LN d two physically relevant quantities, that is the mass of , m m , and its mixing N N NN 1 with active neutrinos, s m =m . LN LN NN Note that the contribution from F to m is crucial for to be relevant to neu- LN N d trino physics. The reason is that m breaks b oth sup ersymmetry and the electroweak LN symmetry. Without F -terms of SU (2) non-singlets, there would b e a separate suppression L factor for each of the two breakings, making m to o small for our purp oses. Explicitly, LN F S u and conse- if the only F term to play a role were F , then we would get m 2 S LN m Pl 16 u quently s 10 , indep endent of the mechanism that mediates sup ersymmetry LN m Pl breaking. Such mixing is to o small to a ect any neutrino exp eriment. In contrast, the contribution to m from F leads toavalue for s that is mo del dep endent and that LN LN d can be sizable. Assuming that is of the order of the electroweak breaking scale, we get 2 m 5 Z 10 eV : (2:3) m LN m Pl The scale of F (and, consequently, the values of m and s ) dep ends on the S N LN mechanism that communicates SUSY breaking to the observable sector. In sup ergravity mo dels, where F m m , we get S Z Pl m Z 2 16 m m 10 GeV ; s 10 : (2:4) N Z LN m Pl 1 We implicitly assume here that the mass and mixing of are describ ed e ectively by a N < 2 2 matrix, and that m m . LL NN 2 Then is practically decoupled from the observable sector and do es not have any ob- N 2 servable signatures. 2 2 = , In GMSB mo dels [27-29] wehave a more interesting situation. There, F Cm S Z > where C 1 dep ends on the details of the mo del (for a review, see [30]). We now get 2 2 4 Cm 10 Z m 0:1 eV C; s : (2:5) N LN 2 m C C Pl The mass scale for is not far from those relevant to galaxy formation ( 10 eV ), N 3 atmospheric neutrinos ( 0:1 eV ) and solar neutrinos ( 10 eV ). The mixing is small but non-negligible. We conclude then that in GMSB mo dels, the fermionic elds in the mo duli can, in principle, play the role of sterile neutrinos that are relevant to various 3 observations. We emphasize that eq. (2.5) gives only naive order of magnitude estimates. Each of its relations might b e somewhat mo di ed by unknown co ecients, exp ected to b e of O (1). Furthermore, there might be other ingredients in the mo del that a ect even the order of magnitude estimates. In the next section we show how simple variations within our basic framework might bring the mass and the mixing of closer to those required to explain N the various exp erimental results. 3. Solar and Atmospheric Neutrinos Simple variations on the naive estimates given ab ove could make the sterile neutrino parameters consistent with solutions to the solar neutrino problem [32] or to the atmo- spheric neutrino problem [33]. Let us consider rst the p ossibility that the relevant sup er elds N transform under some approximate symmetry. This could b e a horizontal symmetry invoked to explain the smallness and hierarchy in the avor parameters. Take, for example, a U (1) symmetry 2 A sup ergravity scenario where the fermionic elds in the mo duli play the role of sterile neutrions was prop osed in ref. [12]. This was done, however, with a sp ecial ansatz for the sup ersymmetry breaking mass terms. 3 Neutrino masses in the GMSB framework were recently discussed in ref. [31]. Their mo del, however, has no sterile neutrinos and involves R parity violation. 3 broken by a small parameter , to which we attribute charge 1. Take N and L to carry charges p and q , resp ectively, under the symmetry. Then, (2.5) is mo di ed: p+q 2 2p 2 m Cm 2p p+q 5 Z Z C 0:1 eV ; m 10 eV ; m LN NN 2 m m Pl Pl (3:1) 2 4 10 s : LN pq pq C C 5 < 10 eV , so that is unlikely (in this To get s = O (1), we would need m N LN NN simple scenario) to play a role in the atmospheric neutrino anomaly or in the large angle MSW solution to the solar neutrino problem. On the other hand, two relevant sets of parameters can be easily pro duced by the approximate symmetry: p (I) Take C 1, 0:1, and q =0: 3 6 3 m 10 eV ; m 10 eV ; s 10 : (3:2) NN LN LN This is not far from the small angle MSW solution to the solar neutrino problem. (The mix- ing angle is somewhat small but, as mentioned ab ove, could be mo di ed by the unknown co ecients of O (1).) p 2 (I I) Take C 1, 10 , and q = p: 5 5 m 10 eV ; m 10 eV ; s 1: (3:3) NN LN LN This set of parameters is appropriate for the vacuum oscillation solution to the solar neutrino problem. Another variation on the naive estimates arises if the relevant heavy scale (call it m NP for New Physics) in the nonrenormalizable terms is lower than m . Then b oth m and Pl NN m will b e enhnaced compared to (2.1) and (2.2).

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