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Decaying Sterile Neutrinos and the Short Baseline Oscillation Anomalies

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Decaying Sterile Neutrinos and the Short Baseline Oscillation Anomalies PHYSICAL REVIEW D 101, 115013 (2020) Decaying sterile neutrinos and the short baseline oscillation anomalies † ‡ Mona Dentler ,1,* Ivan Esteban ,2, Joachim Kopp ,3,4, and Pedro Machado 5,§ 1Institut für Astrophysik, Georg August-Universität Göttingen, 37077 Göttingen, Germany 2Departament de Fisíca Qu`antica i Astrofísica and Institut de Ciencies del Cosmos, Universitat de Barcelona, 08028 Barcelona, Spain 3Theoretical Physics Department, European Organization for Nuclear Research, 1211 Geneva, Switzerland 4PRISMA Cluster of Excellence and Mainz Institute for Theoretical Physics, Johannes Gutenberg-Universität Mainz, 55128 Mainz, Germany 5Fermi National Accelerator Laboratory, Batavia, 60510 Illinois, USA (Received 18 November 2019; accepted 6 May 2020; published 11 June 2020) The MiniBooNE experiment has observed a significant excess of electron neutrinos in a muon neutrino beam, in conflict with standard neutrino oscillations. We discuss the possibility that this excess is explained by a sterile neutrino with a mass ∼1 keV that decays quickly back into active neutrinos plus a new light boson. This scenario satisfies terrestrial and cosmological constraints because it has neutrino self- interactions built-in. Accommodating also the LSND, reactor, and gallium anomalies is possible, but requires an extension of the model to avoid cosmological limits. DOI: 10.1103/PhysRevD.101.115013 I. INTRODUCTION earlier LSND experiment [4], and with several reported hints for anomalous disappearance of electron neutrinos in reactor Many major discoveries in neutrino physics have started experiments [5,6] and in experiments using intense radio- out as oddball anomalies that gradually evolved into incon- active sources [7,8].2 However, the sterile neutrino parameter trovertible evidence. In this work, we entertain the possibility space consistent with MiniBooNE and these other anomalies that history is repeating itself in the context of the MiniBooNE is in severe tension with the nonobservation of anomalous νμ anomaly. From 2002 to 2019, the MiniBooNE experiment disappearance [9–19], unless several additional new physics has been searching for electron neutrinos (νe) appearing in a 1 effects are invoked concomitantly [20,21]. muon neutrino (νμ)beam[1–3], and has found a corre- 4 8σ In this work, we propose a different explanation for the sponding signal at . statistical significance. For some MiniBooNE anomaly, and possibly also for the LSND, time, the simplest explanation for this signal appeared to be reactor, and gallium anomalies. In particular, we consider a the existence of a fourth neutrino species νs, called “sterile ” sterile neutrino that rapidly decays back into Standard neutrino because it would not couple to any of the Standard Model (“active”) neutrinos ν [22–24]. The MiniBooNE Model interactions, but would communicate with the a ν excess is then interpreted as coming from these decay Standard Model only via neutrino mixing. If s has small products. We will see that this scenario requires only very but nonzero mixing with both ν and νμ and if the corre- e small mixing between ν and νμ, thus avoiding the strong νμ ν s sponding mostly sterile neutrino mass eigenstate 4 is some- disappearance constraints. It also requires somewhat larger what heavier (∼1 eV)thantheStandardModelneutrinos,the mixing between νs and νe, in line with the hints from MiniBooNE signal could be explained. This explanation reactor and radioactive source experiments. Finally, we will 3 8σ would also be consistent with a similar . anomaly from the argue that decaying sterile neutrinos may avoid cosmo- logical constraints because the model automatically * endows sterile neutrinos with self-interactions (“secret [email protected] † ” [email protected] interactions [25,26]). ‡ [email protected] §[email protected] II. DECAYING STERILE NEUTRINO FORMALISM 1Here and in the following, when we say neutrino we mean also the corresponding antineutrinos. We extend the Standard Model by a sterile neutrino νs (a Dirac fermion) and a singlet scalar ϕ. The relevant Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to 2The latter class of experiments is usually referred to as the author(s) and the published article’s title, journal citation, “gallium experiments,” based on the active component of their and DOI. Funded by SCOAP3. target material. 2470-0010=2020=101(11)=115013(13) 115013-1 Published by the American Physical Society DENTLER, ESTEBAN, KOPP, and MACHADO PHYS. REV. D 101, 115013 (2020) ˆ ˆ interaction and mass terms in the Lagrangian of the basis, and Γ ¼ Γ4Π4 is the decay term, which contains the ˆ model are projection operator Π4 ¼jν4ihν4j onto the fourth, mostly X sterile, mass eigenstate as well as the decay width Γ4 of ν4 L ⊃− ν¯ ν ϕ − ν¯ ν ð Þ g s s mαβ α β: 1 in its rest frame. Similarly, Γϕ is the rest frame decay width a¼e;μ;τ;s of ϕ. The functional Rν½ρˆν; ρϕ;E;t describes the appear- ance of the daughter neutrinos from ν4 and ϕ decay. The neutrino flavor eigenstates να are linear combinations Neglecting the masses of ν1, ν2, and ν3,itisgivenby of the mass eigenstates νj (j ¼ 1, 2, 3, 4) according to the relation να ¼ Uα ν , where U is the unitary 4 × 4 leptonic j j Rν½ρˆν; ρϕ;E;t mixing matrix. The first term in Eq. (1) can thus be Z ∞ X Γlabðν → ν ϕÞ rewritten as ˆ d 4 k ¼ ΠF dE4 ρˆν;44ðE4;tÞ E 2 dEk 2 à 1−x k − ν¯ ν ϕ − j j ν¯ ν ϕ − ð ν¯ ν ϕ þ Þ ð Þ ϕ4 g F F g Us4 4 4 gUs4 4 F H:c: ; 2 Z X ∞ dΓlabðϕ → ν ν¯ Þ þ Πˆ ρ ð Þ k j ð Þ with F dEϕ ϕ Eϕ;t ; 6 k;j E dEk X3 where dΓlabðX → YÞ=dE are the differential decay νF ≡ Usiνi: ð3Þ k i¼1 widths for the various decays X → Y in the lab frame, and xϕ4 ≡ mϕ=m4. The projection operator We assume initially that the fourth, mostly sterile, mass ν ≃ ν Oð Þ 3 à eigenstate 4 s has a mass m4 between eV and jν ihν j X U U Oð100 Þ ϕ Πˆ ¼ F F ¼ P si sj jν ihν jðÞ keV , and that the mass of is of the same order, F jhν jν ij2 j j2 i j 7 F F ¼1 k Usk but smaller. The last term in Eq. (2) will then induce ν4 → i;j νF þ ϕ decays, while the first term is responsible for ϕ → ν þ ν¯ decays. When these decays occur in a neutrino isolates the specific combination of mass eigenstates that F F ν ϕ beam, they will produce lower-energy neutrinos at the appears in 4 and decays, and the integrals run over all expense of higher-energy ones, and they may also alter the parent energies E4, Eϕ that lead to daughter neutrinos of R ½ρˆ flavor structure of the beam. In particular, they can produce energy E. Analogously, ϕ ν;E;t describes the appear- ance of scalars from ν4 decay: excess low-energy νe in a νμ beam, as suggested by the MiniBooNE anomaly. Z E=x2 X Γlabðν → ν ϕÞ The phenomenology of the model depends mainly on ϕ4 d 4 k Rϕ½ρˆν;E;t¼ dE4 ρˆν;44ðE4;tÞ five new parameters. Besides m4 and mϕ, these are the E k dEϕ j j2 j j2 ν coupling g and the mixings Ue4 , Uμ4 between 4 and Γlabðν¯ → ν¯ ϕÞ þ ρˆ¯ ð Þ d 4 k ð Þ νe, νμ. We will assume the mixing with ντ to be zero and ν;44 E4;t : 8 dEϕ neglect the complex phases, as these parameters do not play an important role in explaining the MiniBooNE excess. For With the appearance terms Rν½ρˆν; ρϕ;E;t and Rϕ½ρˆν;E;t Γ practical purposes, it is convenient to quote m4 4 instead of defined, the equations of motion (4) and (5) can be solved g,asm4Γ4 appears directly in the laboratory frame decay ð Γ Þ analytically if we neglect matter effects. Neglecting fur- length E= m4 4 . Also, it is convenient to use the ratio thermore the small mass splittings between the three light mϕ=m4 instead of just mϕ because the ratio measures more neutrino mass eigenstates, the electron neutrino flux directly the kinematic suppression in ν4 decays. ϕeðL; EÞ appearing in a muon neutrino beam of energy The evolution in energy E and time t of a neutrino beam E after a distance L due to oscillations and decay is in our model can be described by a neutrino density matrix given by ρˆ ð Þ 4 4 ν E; x (a × matrix in flavor space), the corresponding ρˆ¯ ð Þ antineutrino density matrix ν E; x , and the scalar density 2 2 −m4Γ4L ϕ ðL;EÞ¼ϕμð0;EÞjU 4j jUμ4j 1 þ e E function ρϕðE; tÞ. The evolution equations are [27,28], e e 2 2 dρˆνðE;tÞ 1 m4 −m4Γ4L Δm41L 2 jhνejνFij ¼ − ½ ˆ ρˆ − Γˆ ρ þ R ½ρˆ ρ ðÞ − 2 2E þj j I i H; ν ; ν ν; ϕ;E;t 4 e cos 2 Uμ4 2 : dt 2 E E jhνFjνFij dρϕðE; tÞ mϕ ð9Þ ¼ − Γϕρϕ þ Rϕ½ρˆν;E;tð5Þ dt E Here, jνFi is the superposition of mass eigenstates into ˆ ¼ 1 ð0 Δ 2 Δ 2 Δ 2 Þ ν where H 2E diag ; m21; m31; m41 is the standard which the 4 decay [defined in Eq. (3)], and the decay neutrino oscillation Hamiltonian, written here in the mass integral I is given by 115013-2 DECAYING STERILE NEUTRINOS AND THE SHORT BASELINE … PHYS.
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