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Supersymmetry and Neutrino Mass Proc Indian Natn Sci Acad, 70, A No.1, January 2004, pp.239–249 c Printed in India. SUPERSYMMETRY AND NEUTRINO MASS BISWARUP MUKHOPADHYAYA Harish-Chandra Research Institute, Chhatnag Road, Jhusi, Allahabad - 211 019 (India) (Received 31 January 2003; Accepted 30 June 2003) The existence of neutrino mass and mixing is a strong pointer towards physics beyond the Standard Model. An overview of the possibility of having neutrino masses in supersymmetric theories is attempted here. Some of the recent works reviewed suggest Dirac masses, whereas others include Majorana masses as well. Side by side, it is shown how R-parity violating supersymmetry opens new avenues in the neutrino sector. Reference is also made to light sterile neutrinos, nearly degenerate neutrinos and neutrinos acquiring masses from hard supersymmetry breaking terms which are suppressed by the Planck scale. In several of the cases, it is pointed out how the models that give neutrino masses and mixing have independent motivations of their own, and can be tested in accelerator experiments. Key Words: R-Parity Violation; Light Sterile Neutrinos; Quasidegenerate Neutrinos; Neutrino Masses Sup- pressed by Planck Scale 1 Introduction entails lepton number violation clearly entails new physics, albeit at high scale, the first one can be prima As has been amply established in the other articles facie dismissed as a ‘trivial’ extension in the form of in this volume, there is a strong evidence nowadays a right-handed neutrino component for each family. in favour of neutrino masses. In addition, the solar1 However, the fact that such a right-handed neutrino and atmospheric2 neutrino data have their most obvi- has none of the strong, weak and electromagnetic in- ous explanation in neutrino oscillation, requiring mix- teractions is curious, if not suggestive of some new ing among neutrinos, or, more generally speaking, interaction in which it takes part. The extreme sup- in the leptonic sector, in analogy with quark mix- pression of neutrino Yukawa couplings necessitated ing which is controlled by the Cabibbo-Kobayashi- by sub-eV Dirac masses is also puzzling. Side by Maskawa (CKM) matrix3. However, in contrast to side, if the LSND claim suggesting the disappearance quark mixing, the most favoured explanations of the of νµ ’s is to taken seriously4 , we most likely need a solar and atmospheric neutrino deficits require very fourth light neutrino, sterile in nature. Since the mass large—even close to maximal—mixing between the of a sterile vectorlike neutrino is not protected by any first two families and the last two. Side by side, the symmetry, and since we can hardly think of any new data indicate a hierarchy of mass splitting, the mass- physics scale below a TeV or so, a light sterile neu- 3 2 2 ¡ squared difference being in the range 10 ¡ -10 eV trino, if it is there at all, warrants a drastically novel between the second and the third families, and, most mechanism for its justification. 5 4 2 ¡ favourably, 10 ¡ -10 eV between the first and the The new physics scale to which appeal has mostly second. Though such splittings are most often trans- been made to understand neutrino masses is that per- lated into a corresponding hierarchy in the masses taining to Grand Unified Theories (GUT), restricted themselves, the existence of near-degenerate neutri- to be at least5 about 1016 GeV. However, there are nos, too, cannot be ruled out. other motivations for physics beyond the Standard According to many, all this is an indication of Model within the TeV scale itself. One such is the physics beyond the Standard Model. To see why, let so-called naturalness problem which reflects our lack us recall that, thanks to the electrically neutral charac- of understanding why the Higgs mass (and conse- ter of neutrinos, they can have both Dirac and Ma- quently the electroweak scale MEW ) should be stable jorana masses. While the second possibility which against quadratically divergent radiative corrections. 240 BISWARUP MUKHOPADHYAYA The most popular solution to this problem has been portant goal of accelerator experiments, it should be offered in terms of supersymmetry (SUSY), a sym- really interesting to look for the particular signatures metry between bosons and fermions, which can pro- of such theoretical schemes as are able explain the ob- vide the necessary cancellations to control the large servations in the neutrino sector. In other words, the radiative corrections6 . Most importantly, it is possi- issue of neutrino masses could provide not only useful ble to keep the Higgs mass within acceptable limits guidelines for theorisation, but might also end up pre- even if SUSY is broken in mass, so long as the break- dicting specific experimental signals in high-energy ing scale (characterising the boson-fermion splitting) colliders. The present article is aimed at discussing is approximately within the TeV scale. Side by side, some of these possibilities. the observation that the threshold effects arising from In very general terms, some of the ways in which Tev scale SUSY breaking ensures better convergence SUSY can be of special significance to neutrino of the three coupling constants at the GUT scale pro- masses are as follows: vides an added impetus to SUSY7. § In the minimal SUSY Standard Model (MSSM)8, The phenomenon of SUSY can provide new the particle spectrum of the Standard Model (SM) gets scales (in addition to that brought by GUT doubled, there being a superpartner for each known in which most SUSY theories are embedded). particle, apart from the necessity of two Higgs dou- These scales open up additional possibilities in blets which lead to three neutral and a pair of mutually the neutrino sector and can be helpful in ex- conjugate singly charged scalars. There is no experi- plaining mass hierarchies. Also, some features mental evidence yet for any of these superparticles; of the SUSY theory might help us in under- collider experiments have set lower bounds of about standing ultra-small Yukawa couplings. 100 GeV upwards on most of them. Further conse- § The extended particle spectrum in SUSY can quences of SUSY also depend on the details of the lead to mechanisms for mass generation, for ex- spectrum which in turn is crucially dependent on the ample, through additional radiative effects. SUSY breaking mechanism. We know that SUSY has to be broken at any rate if it is there, since we do not § The possibility of low-energy lepton number vi- observe degenerate superpartners for the SM particles. olation inbuilt in certain types of SUSY theo- No completely acceptable SUSY breaking scheme has ries might lead to the generation of Majorana been found so far, although most studies depend upon masses. 9 ¢ a scenario based on N 1 supergravity (SUGRA) § SUSY could explain a naturally light sterile where gravitational interactions with a ‘hidden sec- neutrino, in case we need it to explain the ob- tor’ characterised by a high scale (O £¥¤ M M ) lead P EW ¦ served data. to soft SUSY breaking terms in the observable sector. In addition, schemes of SUSY breaking, for example, In section 2 we discuss Dirac masses in presence 10 via gauge interactions of a messenger sector or via of SUSY. Section 3 is devoted to Majorana neutri- 11 anomaly terms have also been investigated. nos in SUSY scenarios, where lepton number viola- The question is: since the search for physics be- tion takes place at high-scale. Section 4 contains a yond the Standard Model has found a strong candidate summary of neutrino mass generation mechanisms in in SUSY, could SUSY also be responsible for neu- R-parity violating SUSY where the low-energy La- trino masses (and mixing), the clue that nature seems grangian has lepton number violation. In section 5 we to dangle so tantalisingly in front of us? If that be discuss respectively the issues of degenerate neutri- so, then the mass patterns answering to the solar and nos in SUSY and neutrino masses from unusual SUSY atmospheric neutrino data should not only depend on breaking terms. We conclude in section 6. certain specific aspects of the SUSY model, but also impose constraints on it. It may also be more convinc- 2 When Lepton Number is Conserved–Dirac ing if models are built not just to answer questions on Masses in SUSY neutrinos but have independent motivations of their own from the viewpoint of SUSY as well. Side by If one takes the hierarchy in neutrino mass splitting to side, since the the search for SUSY is already an im- be an indication of the hierarchy in the masses them- SUPERSYMMETRY AND NEUTRINO MASS 241 3 selves, then, assuming that the solar and atmospheric is the gravitino mass), giving mν 10 eV . This νµ ντ ν νµ ¨ neutrino deficits are due to ¨ and e oscilla- is an unacceptably large value unless one has near- tions respectively, the two heaviest neutrinos are about degenerate neutrinos. The solution, therefore, lies 10 to 11 orders of magnitude smaller in mass than in having Az Fz, i.e. in the SUSY conserv- the τ and the µ. The simplest extension of the Stan- ing vev being much smaller than the SUSY break- dard Model spectrum that explains the above masses ing one. This can be realised, for example, in an is one right-handed neutrino per generation. However, O’Raifeartaigh-type model, where a hierarchy be- the onus then falls on us to explain the wide disparity tween the scalar and pseudoscalar components can be of Yukawa couplings that is responsible for the huge envisioned upon generating an effective low-energy mass splitting within the same families, as indicated scalar potential for Z through the condensation of above.
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