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Accessible Lepton-Number-Violating Models and Negligible Neutrino Masses

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Accessible Lepton-Number-Violating Models and Negligible Neutrino Masses PHYSICAL REVIEW D 100, 075033 (2019) Accessible lepton-number-violating models and negligible neutrino masses † ‡ Andr´e de Gouvêa ,1,* Wei-Chih Huang,2, Johannes König,2, and Manibrata Sen 1,3,§ 1Northwestern University, Department of Physics and Astronomy, 2145 Sheridan Road, Evanston, Illinois 60208, USA 2CP3-Origins, University of Southern Denmark, Campusvej 55, DK-5230 Odense M, Denmark 3Department of Physics, University of California Berkeley, Berkeley, California 94720, USA (Received 18 July 2019; published 25 October 2019) Lepton-number violation (LNV), in general, implies nonzero Majorana masses for the Standard Model neutrinos. Since neutrino masses are very small, for generic candidate models of the physics responsible for LNV, the rates for almost all experimentally accessible LNV observables—except for neutrinoless double- beta decay—are expected to be exceedingly small. Guided by effective-operator considerations of LNV phenomena, we identify a complete family of models where lepton number is violated but the generated Majorana neutrino masses are tiny, even if the new-physics scale is below 1 TeV. We explore the phenomenology of these models, including charged-lepton flavor-violating phenomena and baryon- number-violating phenomena, identifying scenarios where the allowed rates for μ− → eþ-conversion in nuclei are potentially accessible to next-generation experiments. DOI: 10.1103/PhysRevD.100.075033 I. INTRODUCTION Experimentally, in spite of ambitious ongoing experi- Lepton number and baryon number are, at the classical mental efforts, there is no evidence for the violation of level, accidental global symmetries of the renormalizable lepton-number or baryon-number conservation [5]. There Standard Model (SM) Lagrangian.1 If one allows for are a few different potential explanations for these (neg- generic nonrenormalizable operators consistent with the ative) experimental results, assuming degrees-of-freedom SM gauge symmetries and particle content, lepton number beyond those of the SM exist. Perhaps the new particles are and baryon number will no longer be conserved. Indeed, either very heavy or very weakly coupled in such a way that lepton-number conservation is violated by effective oper- phenomena that violate lepton-number or baryon-number ators of dimension five or higher while baryon-number conservation are highly suppressed. Another possibility is conservation (sometimes together with lepton number) is that the new interactions are not generic and that lepton- violated by effective operators of dimension six or higher. number or baryon-number conservation are global sym- In other words, generically, the addition of new degrees-of- metries of the beyond-the-Standard-Model Lagrangian. freedom to the SM particle content violates baryon-number Finally, it is possible that even though baryon number or and lepton-number conservation. lepton number are not conserved and the new degrees-of- freedom are neither weakly coupled nor very heavy, only a subset of baryon-number-violating or lepton-number- violating phenomena are within reach of particle physics *[email protected] † experiments. This manuscript concentrates on this third [email protected] ‡ option, which we hope to elucidate below. [email protected] §[email protected] The discovery of nonzero yet tiny neutrino masses is 1At the quantum level these symmetries are anomalous, i.e., often interpreted as enticing—but certainly not definitive— they are violated by nonperturbative effects [1,2]. These are only indirect evidence for lepton-number-violating new physics. relevant in extraordinary circumstances (e.g., very high temper- In this case, neutrinos are massive Majorana fermions and atures) much beyond the reach of particle physics experiments one can naturally “explain” why the masses of neutrinos [3,4]. Nonperturbative effects still preserve baryon-number- minus-lepton number, the nonanomalous possible global sym- are much smaller than those of all other known massive metry of the renormalizable SM Lagrangian. particles (see, e.g., [6–8] for discussions of this point). Searches for the nature of the neutrino—Majorana fermion Published by the American Physical Society under the terms of versus Dirac fermion—are most often searches for lepton the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to number violation (LNV). The observation of LNV implies, the author(s) and the published article’s title, journal citation, generically, that neutrinos are Majorana fermions [9], and DOI. Funded by SCOAP3. while Majorana neutrino masses imply nonzero rates for 2470-0010=2019=100(7)=075033(21) 075033-1 Published by the American Physical Society DE GOUVÊA, HUANG, KÖNIG, and SEN PHYS. REV. D 100, 075033 (2019) Al −14 lepton-number-violating phenomena. The most powerful ∶ − þ ≳ 10 ð Þ COMET Phase-I Rμ e : 1:3 probes of LNV are searches for neutrinoless double-beta decay (0νββ, see [10] for a review); several of these are For a recent, more detailed discussion, see [20]. ongoing, e.g., [11–13]. The growing excitement behind There are several recent phenomenological attempts at searches for 0νββ is the fact that these are sensitive enough understanding whether there are models consistent with to detect LNV mediated by light Majorana neutrino current experimental constraints where the rate for exchange if the neutrino masses are above a fraction on μ− → eþ-conversion in nuclei is sizable [19,21,22]. The an electronvolt. In many models that lead to Majorana main challenges are two-fold. On the one hand, the light- neutrino masses, including, arguably, the simplest, most Majorana-neutrino exchange contribution to μ− → eþ- elegant, and best motivated ones, LNV phenomena are conversion in nuclei is tiny. On the other hand, while it predominantly mediated by light Majorana neutrino is possible to consider other LNV effects that are not exchange. Hence, we are approaching sensitivities to captured by light-Majorana-neutrino exchange, most of 0νββ capable of providing nontrivial, robust information these scenarios lead, once the new degrees of freedom are on the nature of the neutrino. integrated out, to Majorana neutrino masses that are way Other searches for LNV are, in general, not as sensitive too large and safely excluded by existing neutrino data. 0νββ as those for . Here, we will highlight searches for In [19], an effective operator approach, introduced and μ− → eþ-conversion in nuclei, for a couple of reasons. One – − þ exploited in, e.g,, [23 26], was employed to both diagnose is that, except for searches for 0νββ, searches for μ → e - the problem and identify potentially interesting directions conversion in nuclei are, arguably, the most sensitive to for model building. generic LNV new physics.2 Second, several different − − New-physics scenarios that violate lepton-number con- experiments aimed at searching for μ → e -conversion servation at the tree level in a way that LNV low-energy in nuclei are under construction, including the COMET phenomena are captured by the “all-singlets” dimension- [15] and DeeMe experiments [16] in J-PARC, and the nine operator: Mu2e experiment [17] in Fermilab. These efforts are expected to increase the sensitivity to μ− → e−-conversion 1 L ⊃ O ; where O ¼ ecμcucucdc dc; ð1:4Þ by, ultimately, four orders of magnitude and may also be Λ5 s s able to extend the sensitivity to μ− → eþ-conversion in nuclei by at least a few orders of magnitude. and Λ is the effective scale of the operator, were flagged as − þ The best bounds on the μ → e -conversion rate relative very “inefficient” when it comes to generating neutrino − to the capture rate of a μ on titanium were obtained by the Majorana masses. According to [19], the contribution SINDRUM II experiment [18] over twenty years ago: to Majorana neutrino masses from the physics that leads to Eq. (1.4) at the tree level saturates the upper bound on Γðμ− þ Ti → eþ þ CaÞ neutrino masses for Λ ∼ 1 GeV. This means that, for Ti ≡ Rμ−eþ − Λ ≫ 1 Γðμ þ Ti → νμ þ ScÞ GeV, the physics responsible for Eq. (1.4) will lead to neutrino masses that are too small to be significant 1.7 × 10−12 ðGS; 90% CLÞ < ; ð1:1Þ while the rates of other LNV phenomena, including 3.6 × 10−11 ðGDR; 90% CLÞ μ− → eþ-conversion in nuclei, may be within reach of next-generation experiments. According to [19], this where GS considers scattering off titanium to the ground happens for Λ ≲ 100 GeV. state of calcium, whereas GDR considers the transition to The effective operator approach from [23–26] is mostly a giant dipole resonance (GDR) state. Next-generation powerless when it comes to addressing lepton-number- experiments like Mu2e, DeeMe, and COMET have the conserving, low-energy effects of the same physics that potential to be much more sensitive to μ− → eþ-conversion. leads to Eq. (1.4). One way to understand this is to The authors of [19] naively estimated the future sensitivities appreciate that lepton-number-conserving phenomena are of these experiments to be captured by qualitatively different effective operators and, in general, it is not possible to relate different “types” of Al −16 operators in a model-independent way. Concrete results can Mu2e∶ R − þ ≳ 10 ; ð1:2Þ μ e only be obtained for ultraviolet (UV)-complete scenarios. In this manuscript, we systematically identify all possible UV-completemodels that are predominantly captured, when O 2 it comes to LNV phenomena, by s at the tree level. All It was recently pointed out that searches for nonstandard these models are expected to have one thing in common: neutrino interactions from long-baseline neutrino experiments are also sensitive to certain LNV new physics and involve all lepton potentially large contributions to LNV processes combined flavors [14]. In some cases, the resulting limits are stronger than with insignificant contributions to the light neutrino masses. those from μ− → eþ-conversion. Such models are expected to manifest themselves most 075033-2 ACCESSIBLE LEPTON-NUMBER-VIOLATING MODELS AND … PHYS.
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