Revisiting large neutrino magnetic moments

Published for SISSA by Springer Received: June 16, 2017 Accepted: July 19, 2017 Published: July 28, 2017 Manfred Lindner, Branimir Radovčić and Johannes Welter Max-Planck-Institut für Kernphysik, Saupfercheckweg 1, 69117 Heidelberg, Germany E-mail: , , Abstract: Current experimental sensitivity on neutrino magnetic moments is many orders of magnitude above the Standard Model prediction. A potential measurement of nextgeneration experiments would therefore strongly request new physics beyond the Standard Model. However, large neutrino magnetic moments generically tend to induce large corrections to the neutrino masses and lead to fine-tuning. We show that in a model where neutrino masses are proportional to neutrino magnetic moments. We revisit, discuss and propose mechanisms that still provide theoretical consistent explanations for a potential measurement of large neutrino magnetic moments. We find only two viable mechanisms to realize large transition magnetic moments for Majorana neutrinos only. Keywords: Beyond Standard Model, Neutrino Physics ArXiv ePrint: 1706.02555 Open Access, c The Authors. Article funded by SCOAP3 . https://doi.org/10.1007/JHEP07(2017)139 JHEP07(2017)139 Revisiting large neutrino magnetic moments Contents 1 2 Naturalness bounds 2.1 New physics above the electroweak scale 2.2 New physics below the electroweak scale 2 2 3 3 Natural large NMM via millicharged particles 4 4 Radiative neutrino mass model 5 5 Naturally large NMM via symmetries 5.1 BFZ model 5.2 Voloshin-type symmetry 5.3 Horizontal symmetry 7 8 10 10 6 Discussion and conclusion 11 1 Introduction The neutrino magnetic moment (NMM) in the Standard Model (SM)1 is of the order e 10−19 µB [1–5], where µB = 2m is the Bohr magneton. At the same time reactor, accelere ator and solar neutrino experiments as well as astrophysical observations are lacking many orders of magnitude in sensitivity in order to test the small SM prediction (for a recent review see [6]). The best current laboratory limit is given by GEMMA, an experiment measuring the electron recoil of antineutrino-electron scattering near the reactor core. It constrains the effective magnetic moment to be less than 2.9 · 10−11 µB [7]. A recent study by Cañas et al. [8] showed that results of the solar neutrino experiment Borexino give similar limits. They obtain for the individual Majorana transition moments in the mass basis |Λ1 | ≤ 5.6 · 10−11 µB , |Λ2 | ≤ 4.0 · 10−11 µB , |Λ3 | ≤ 3.1 · 10−11 µB . On the other hand, the smallness of the SM prediction imply that a non-zero measurement of NMM would be a clear indication for new physics beyond the SM. In view of upcoming experiments, that are able to further increase the sensitivity on the NMM, it is worthy to ask what kind of new physics could explain large NMM. In other words, we want to address the question of how to generate large NMM in a theoretically consistent way. The paper is organized as follows. In section 2 we review model independent bounds on the NMM from corrections to the neutrino mass. In section 3 we consider a model with 1 In the pure SM neutrinos are massless and therefore the NMM is zero. Here we refer to the extensions of the SM allowing for neutrino masses. –1– JHEP07(2017)139 1 Introduction light millicharged particles. In section 4 we explicate the generic difficulty to obtain a large NMM without fine-tuning neutrino masses in a particularly insightful model. In section 5 we revisit and update constraints on existing models that successfully avoid fine-tuning. We discuss and conclude in section 6. 2 2.1 Naturalness bounds New physics above the electroweak scale µν ∼ 2 QeGvH , Λ3 v2 δmν ∼ G H Λ   (2.1) leading to δmν 1 ∼ 0.1 eV Q µν 10−19 µB Λ TeV 2 , (2.2) where vH is the vacuum expectation value of the Higgs and Q is the charge of the particles running inside the loop in units of the electron charge e. To avoid fine-tuning, the radiative neutrino mass correction should not be larger than the measured neutrino masses, δmν . mν . Using reasonable numbers, mν ∼ 0.1 eV, Λ ∼ TeV and Q ∼ 1 we obtain the naive limit µν . 10−19 µB . (2.3) For Dirac neutrinos the 1-loop effective NMM and neutrino mass operators are of dimension six and four respectively. With diagrams similar to figure 1 this leads to µν ∼ QeGvH , Λ2 δmν ∼ GvH . (2.4) By taking the ratio δmν /µν we get the same constraint as in eqs. (2.2) and (2.3). The current best laboratory experimental limit for the NMM is at µν ∼ 2.9·10−11 µB [7], while neutrino masses above 0.2 eV are in conflict with cosmological observations [9]. Therefore the above estimate shows that generating large NMM while simultaneously keeping the radiative mass correction δmν low, requires a significant amount of fine-tuning. To reach values µν & 10−12 µB , which will be probed in future experiments [10–13], fine-tuning of seven orders of magnitude is required. If the contribution to neutrino masses from the diagram in figure 1(b) is suppressed for some reason, there are still contributions from higher-loop diagrams induced by the –2– JHEP07(2017)139 Since neutrinos are neutral, the leading contribution to the NMM is given by quantum corrections. Consider a theory with new physics at the scale Λ and new couplings G that introduces the NMM at 1-loop. The Feynman diagram generating the NMM µν for Majorana neutrinos is depicted in figure 1(a). Removing the photon line will directly result in a radiative neutrino mass correction δmν from the diagram in figure 1(b). With the new physics above the electroweak scale, the effective NMM operator in the case of Majorana neutrino is of dimension seven and the effective mass operator is of dimension five. The generic estimate thus gives γ H ν Λ H H ν ν H Λ (a) ν (b) Figure 1. Feynman diagrams generating the NMM and the radiative neutrino mass for Majorana neutrinos induced by new physics above the electroweak scale. ν Figure 2. Higher-loop neutrino mass contribution induced by the presence of the NMM operator. NMM operator like the one in figure 2. In order to derive constraints on the NMM, Bell et al. [14, 15] and Davidson et al. [16] performed effective operator analyses for Dirac and Majorana neutrinos. Requiring the naturalness condition δmν . mν to avoid the fine-tuning they found the model independent bound for Dirac neutrinos of the order µν . 10−15 µB , when taking the new physics scale Λ = 1 TeV and δmν . 0.2 eV [14]. A similar analysis for Majorana neutrinos [15, 16] shows more room for large NMMs. The reason is that for Majorana neutrinos the NMM operator is flavour antisymmetric while the mass operator is flavour symmetric. For Λ = 1 TeV and mν . 0.3 eV, they obtain the model independent limits µντ νµ , µντ νe . 10−9 µB , µνµ νe . 3 · 10−7 µB [15], which are already worse than current experimental constraints. 2.2 New physics below the electroweak scale Now let us assume that the new physics is generate (...truncated)