Zee-Burst: a New Probe of Neutrino Nonstandard Interactions at Icecube

PHYSICAL REVIEW LETTERS 124, 041805 (2020)

Zee-Burst: A New Probe of Neutrino Nonstandard Interactions at IceCube

K. S. Babu ,1 P. S. Bhupal Dev ,2 Sudip Jana ,1 and Yicong Sui 2 1Department of Physics, Oklahoma State University, Stillwater, Oklahoma 74078, USA 2Department of Physics and McDonnell Center for the Space Sciences, Washington University, St. Louis, Missouri 63130, USA (Received 16 September 2019; published 31 January 2020)

We propose a new way to probe nonstandard interactions (NSI) of neutrinos with matter using the ultrahigh energy (UHE) neutrino data at current and future neutrino telescopes. We consider the Zee model of radiative neutrino mass generation as a prototype, which allows two charged scalars—one SUð2ÞL doublet and one singlet, both being leptophilic, to be as light as 100 GeV,thereby inducing potentially observable NSI with electrons. We show that these light charged Zee scalars could give rise to a Glashow-like resonance feature in the UHE neutrino event spectrum at the IceCube neutrino observatory and its high-energy upgrade IceCube-Gen2, which can probe a sizable fraction of the allowed NSI parameter space.

DOI: 10.1103/PhysRevLett.124.041805

Introduction.—The observation of ultrahigh energy 5.9 0.18 PeV [5,13], but has not been included in the (UHE) neutrinos at the IceCube neutrino observatory event spectrum yet [6]. The nonobservation of Glashow [1–6] has commenced a new era in neutrino astrophysics. events might be still consistent with the SM expectations Understanding all aspects of these UHE neutrino events, within the error bars, given the uncertainty in the source including their sources, energy flux, flavor composition, type (pp versus pγ), as well as (νe, νμ, ντ) flavor propagation, and detection, is of paramount importance to composition (1:2:0 vs 0:1:0) [14–18]. On the other hand, both astrophysics and particle physics communities [7,8]. the possibility of observing a Z-boson resonance (Z burst) A simple, single-component unbroken power-law flux at IceCube due to UHE antineutrinos interacting with −γ ΦðEνÞ¼Φ0ðEν=100 TeVÞ gives a reasonably good fit nonrelativistic relic neutrinos [19] is bleak, as the required to the high-energy starting event (HESE) component of incoming neutrino energy in this case turns out to be 2 23 the IceCube data, with the latest best-fit values of Φ0 ¼ Eν ¼ mZ=2mν ≳ 10 eV, well beyond the Greisen- 6 45þ1.46 10−18 −1 −2 −1 −1 γ 2 89þ0.20 ∼5 1019 ð . −0.46 Þ× GeV cm s sr and ¼ . −0.19 Zatsepin-Kuzmin cutoff energy of × eV for the at 1σ significance [9]. Any anomalous features in the UHE cosmic rays [20,21]—the most likely progenitors of observed event spectrum could potentially be used as a the UHE neutrinos (for related discussion, see Ref. [22]). probe of fundamental physics. One such anomalous feature An interesting alternative is the existence of secret neutrino could be in the form of a new resonance. The purpose of interactions with a light (MeV scale) Z0 [23–26] or light this Letter is to show that such a new resonance can arise neutrinophilic neutral scalar [27–29], in which case the naturally in the popular Zee model of radiative neutrino resonance could again fall in the multi-TeV to PeV range masses [10,11], which contains two charged scalars. We which will be accessible at IceCube. Heavy (TeV-scale) refer to this Zee-scalar resonance as the “Zee-burst.” resonances induced by neutrino-nucleon interactions Within the SM, the only resonance IceCube is sensitive mediated by exotic charged particles, such as leptoquarks to is the Glashow resonance [12], where electron antineu- [30–33], or squarks in R-parity violating supersymmetry trinos hitting the target electrons in ice could produce an [34–37]. have also been discussed. In this Letter, we − − on-shell W boson: ν¯ee → W → anything. The energy of propose the possibility of light charged scalar resonances the incoming neutrino required to make this resonance at IceCube, which are intimately related to neutrino mass 2 happen is fixed at Eν ¼ mW=2me ¼ 6.3 PeV. One candi- generation [10], as well as observable nonstandard inter- date Glashow event was identified in a partially contained actions (NSI) [38] (for a recent update, see Ref. [39]). PeV event (PEPE) search with deposited energy of As a prototypical example, we take the Zee model [10]— one of the most popular radiative neutrino mass models, which contains an SUð2ÞL-singlet charged scalar η and an SUð2ÞL-doublet scalar H2, in addition to the SM-like Higgs Published by the American Physical Society under the terms of doublet H1. The original version of the Zee model [10] is the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to fully consistent with neutrino oscillation data [40] (for the author(s) and the published article’s title, journal citation, explicit neutrino mass fits, see Ref. [11]), although the 3 and DOI. Funded by SCOAP . Wolfenstein version of the model [41], which assumes a Z2

0031-9007=20=124(4)=041805(7) 041805-1 Published by the American Physical Society PHYSICAL REVIEW LETTERS 124, 041805 (2020) symmetry, thus making the diagonal entries of the neutrino According to Eq. (4), the product of the Yukawa couplings mass matrix vanishing, is excluded by oscillation data f and Y is constrained by the neutrino oscillation data, [42,43]. Furthermore, it was pointed out in Ref. [11] that which allow for only one of these couplings to be of order both the singlet and doublet charged scalar components can one. We will adopt the choice Y ∼ Oð1Þ and f ≪ 1, which be as light as ∼100 GeV, while satisfying all existing maximizes the neutrino NSI in the model [11]. theoretical and experimental constraints in both charged For the IceCube phenomenology, we are specifically and neutral scalar sectors. More interestingly, such light interested in the light charged scalar scenario. This is charged scalars can lead to sizable diagonal NSI of confronted with several theoretical and experimental con- neutrinos with electrons, with the maximum allowed values straints, such as charge breaking minima, electroweak pre- of the NSI parameters ðεee; εμμ; εττÞ¼ð8%; 3.8%; 43%Þ. cision tests, charged lepton flavor violation (cLFV), collider We show here that the possibility of having a resonance constraints from LEP and LHC, lepton universality tests, and feature with these light charged Zee scalars (Zee burst) monophoton constraints. It was shown [11] that both hþ and provides a new probe of NSI at high-energy IceCube, Hþ charged scalars can be as light as 100 GeV, while complementary to the low-energy neutrino oscillation and satisfying all these constraints. The main constraints for light scattering experiments. charged scalars come from direct searches at LEP, which are Light charged scalars in the Zee model.—In the Higgs applicable as long as Yαe ≠ 0 for any flavor α.Morestringent W basis [44], only the neutral component of H1 gets a vacuum limits from lepton universality tests in decays [45] will 0 Y ≠ 0 expectation value hH i¼v ≃ 246.2 GeV, while H2 is apply if ee , restricting the charged scalar masses to 1 pffiffiffi H Hþ; H0 iA0 = 2 above 130 GeV [11]. In what follows, we will consider the parametrized as 2 ¼½ 2 ð 2 þ Þ . The charged Y ≠ 0 Y ≠ 0 α e μ þ þ scenario where τe and ατ for ¼ or ,which scalars fH2 ; η g mix in the physical basis to give rise to satisfies all constraints for mhþ ¼ 100 GeV, and at the same the physical charged scalar mass eigenstates time, allows for the largest NSI effect. Signature at IceCube.—Expanding the last term in hþ φηþ φHþ; ¼ cos þ sin 2 Eq. (3), we get þ þ þ H ¼ − sin φη þ cos φH2 ; ð1Þ − − c LY ⊃ Yαβðh sin φ þ H cos φÞναlβ þ H:c: ð6Þ with the mixing angle φ given by For β ¼ e, this will induce neutrino-electron interactions pffiffiffi − − − 2vμ mediated by the charged scalars h and H .ForEν ¼ sin 2φ ¼ ; ð2Þ 2 − − m2 − m2 mh− H− =2me, this will lead to an h ðH Þ resonance Hþ hþ ð Þ (Zee-burst) at IceCube. There is no interference with the where μ is the dimensionful coefficient of the cubic term SM Glashow process (even for α ¼ e), because the Zee i j − burst involves only right-handed electrons. Thus, depend- μH1H2ϵijη in the scalar potential, with fi; jg being the ing on the mass spectrum of h− and H−, we would SUð2ÞL indices and ϵij being the SUð2ÞL antisymmetric expect either one or two additional resonance peaks in tensor. the IceCube energy spectrum. We will consider two bench- The leptonic Yukawa couplings are given by the mark scenarios: (i) mh− ≈ mH− , so that the two peaks are Lagrangian indistinguishable, i.e., contribute to the same energy bin, Δm ≡ m − − m − 30 −L ⊃ f Li Lj ϵ ηþ Y˜ H˜ i Lj lcϵ and (ii) h H h ¼ GeV, so that the two Y αβ α β ij þ αβ 1 α β ij peaks are distinguishable (i.e., their dominant contributions ˜ i j c þ YαβH2Lαlβϵij þ H:c:; ð3Þ fall in different energy bins). To estimate the modification to the event spectrum, we c i where fα; βg are flavor indices, l denotes the left-handed compute the number of events in a given energy bin as H˜ iτ H⋆ a 1 τ Z Z antilepton fields, and a ¼ 2 a ( ¼ , 2) with 2 being Emax X N T dΩ i dE Φ E A E; Ω : the second Pauli matrix. The neutrino mass is generated at i ¼ να ð Þ να ð Þ ð7Þ Emin the one-loop level and is given by i α

T T Here, T is the exposure time for which we use T0 ¼ 2653 Mν ¼ κðfMlY þ Y Mlf Þ; ð4Þ day, corresponding to 7.5 yr of live data taking at IceCube ffiffiffi ˜ p [6]; Ω is the solid angle of coverage and we integrate over where Ml ¼ Yv= 2 is the charged lepton mass matrix and the whole sky; E is the electromagnetic-equivalent depos- κ is a one-loop factor given by ited energy which is an approximately linear function of the   1 m2 incoming neutrino energy [46]; the limits of the energy κ 2φ hþ : integration Emin and Emax give the size of the ith deposited ¼ 16π2 sin log m2 ð5Þ i i Hþ energy bin over which the expected number of events is

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Φ E being calculated; να ð Þ is the differential astrophysical neutrino þ antineutrino flux for flavor α, for which we use a simple, single-component unbroken power law, isotropic −γ flux ΦðEνÞ¼Φ0ðEν=E0Þ with the IceCube best-fit −18 −1 −2 −1 −1 values of Φ0 ¼ 6.45 × 10 GeV cm s sr and γ ¼ 2 89 A . [9]; and να is the effective area per energy per solid angle for the neutrino flavor να, which includes the effective neutrino-matter cross section, number density of target nucleons or electrons and acceptance rates for the shower and track events. In the presence of new interactions as in Eq. (6), only the neutrino-electron cross section gets modified, which in turn affects the effective area. For FIG. 1. Reconstructed event spectra for the expected atmospheric the SM interactions only, we use the publicly available background (gray), SM best fit with a single-component astro- flavor-dependent effective area integrated over solid angle physical flux (red) and the Zee model with mhþ ≈ mHþ ¼ from Ref. [5] (for 2078 day of IceCube data), along with a 100 GeV, φ ¼ π=4, and Yτe ¼ 1, 0.5, 0.25 (light, medium, and 67% increase in the acceptance (for 2653 day of data) [47]. dark blue, respectively), all compared with the 7.5-yr IceCube data. In the presence of non-SM interactions as in Eq. (6),we The data points below 60 TeV (inside the vertical black-shaded rescale the effective area accordingly by taking the ratio of band) are not included in the IceCube HESE analysis we are the cross sections, assuming that the acceptance remains using here. the same. In the SM, neutrinos interact with nucleons via charged- contribution) and the 7.5 yr IceCube data [9]. The vertical and neutral-current processes. In the energy range of line at 60 TeV denotes the low-energy cutoff for the HESE interest, the corresponding deep inelastic scattering cross analysis, i.e., the bins below this energy are not considered sections can be approximated by [48] in the fitting process.   Now in the presence of light charged scalars, we E 0.4 ν¯ e− → X− → CC NC −36 2 ν expect a new resonance for α anything (where σ ≈ 3σ ≃ 2.7 × 10 cm : ð8Þ − − − νðν¯ÞN νðν¯ÞN GeV X ¼ h , H for the Zee model) with a cross section similar to Eq (9): In addition, there are subdominant antineutrino-electron σ s 8πΓ2 X− → ν¯ e− X− → interactions, except in the energy range of 4.6–7.6 PeV, Zeeð Þ¼ XBRð α ÞBRð allÞ − when the ν¯e − e interaction becomes important due to the s=m2 Glashow resonance [12]. In the vicinity of the resonance, X ; × s − m2 2 m Γ 2 ð10Þ the dominant piece of the cross section can be expressed by ð XÞ þð X XÞ P a Breit-Wigner distribution as [49]: 2 2 where ΓX ¼ αβ jYαβj sin φmX=16π is the total decay 2 − − − width of X. The factor of 1=3, compared to Eq. (9), is due to σ ðsÞ¼24πΓWBRðW → ν¯ee ÞBRðW → hadÞ Glashow the difference in the degrees of polarization between scalar s=m2 W ; and vector bosons. × 2 2 2 ð9Þ ðs − mWÞ þðmWΓWÞ In Fig. 1, we consider a benchmark case with mh− ≈ mH− ¼ 100 GeV, so that the two new resonances − − where s ¼ 2meEν and ΓW is the total width of the W boson due to h and H coincide, and thus, maximize the effect in W− →ν¯ e− 10 7% W− → 67 4% 2 with BRð e Þ¼ . and BRð hadÞ¼ . the bin containing the resonance energy Eν ¼ mh− =2me,as σ 6 3 [50]. At resonance, Eq. (9) gives GlashowðEν ¼ . PeVÞ¼ shown by the light, medium, and dark blue shaded histo- 3 4 10−31 2 σCC E Y 1 . × cm , about 240 times larger than νðν¯ÞNð ν ¼ grams corresponding to three illustrative values of τe ¼ , 6.3 PeVÞ ≈ 1.4 × 10−33 cm2. However, due to the narrow- 0.5, 0.25, respectively. The excess events due to this new −γ – ness of the resonance and the Eν nature of the astrophysi- resonance mostly populate the energy bins between 7.6 cal neutrino flux, the ratio of the reconstructed events 12.9 PeV, distinguishable from those dominated by the – between the resonance-induced ν¯e-e and nonresonant Glashow resonance bin (4.6 7.6 PeV), and the effect is νðν¯Þ-N interactions is not so pronounced in the event more pronounced for larger Yukawa couplings, as expected from Eq. (10). Here we have taken the maximal mixing spectrum, as shown by the red-shaded histograms in Fig. 1. − − E > 4 N =N ∼ 2 05 φ π=4 and BR h → ν¯τe 60%,BRh → ν¯βτ For instance, for ν PeV, Res non-Res . giving ¼ ð Þ¼ ð Þ¼ a total of about 0.3 events in the Glashow bin for the 40% (with β ¼ e or μ) for a fixed Yτe given above and IceCube best-fit flux. Also shown in Fig. 1 (gray shaded) accordingly chosen Yβτ, while all other Yukawa couplings are the total expected atmospheric background (from Yαβ are taken to be much smaller than 1 to satisfy the cLFV atmospheric muons and neutrinos, as well as the charm constraints [11]. Note that as we increase the mass

041805-3 PHYSICAL REVIEW LETTERS 124, 041805 (2020) difference Δmh ≡ mH− − mh− , the two peaks start populat- Here again we have taken the maximal mixing case with ing different bins, but because of the falling power-law flux, φ ¼ π=4 to get the largest possible NSI. The shaded the effect is more pronounced in the smallest resonance regions are all excluded: blue shaded by direct LEP energy bin. Also note that we cannot make Δmh exactly searches [51,52] and lepton universality (LU) tests in tau zero, otherwise the neutrino mass vanishes [cf. Eq. (5)]. decays [50]; green shaded by LEP dilepton searches From Fig. 1, it is clear that for a given charged scalar [45,53]; purple shaded (dashed) by LEP monophoton mass mh− , the Yukawa coupling Yτe cannot be made searches off (on) Z pole [54,55]; red shaded by arbitrarily large without spoiling the best fit to the observed BOREXINO [56], orange shaded by global fit to neutrino IceCube HESE data. We can use this fact to derive new oscillation plus COHERENT data [57], and brown shaded IceCube constraints in the mh− − Yτe plane, as shown in by IceCube atmospheric neutrino data [58,59]. For more Fig. 2 by the thick black contours. The curve labeled “IC details on these exclusion regions, see Ref. [11]. Note that 1T0” represents the parameter set which would give rise to the atmospheric neutrino data only constrain jεττ − εμμj < one event when summed over the last three bins considered 9.3% [58,59], which in the Zee model is equivalent to a by IceCube best-fit (4.6

FIG. 2. IceCube sensitivity (corresponding to one expected event in the resonance energy bins combined) for the parameter space relevant for εττ are shown by thick black curves, for different exposure times (in terms of the current exposure T0 ¼ 2653 day). The left panel is for mhþ ≈ mHþ and the right panel is for mHþ − mhþ ¼ 30 GeV. The predictions for εττ are shown by the thin dotted contours. The shaded regions are excluded; see text for details.

041805-4 PHYSICAL REVIEW LETTERS 124, 041805 (2020) feature in the future IceCube HESE data could provide a for warm hospitality, where part of this work was done. complementary probe of the allowed NSI parameter space, B. D. and Y. S. also thank the Department of Physics at which can even supersede the future DUNE sensitivities Oklahoma State University for warm hospitality, where this (shown by the upper and lower blue solid lines for 300 and work was completed. 850 kt MWyr exposures, respectively [60]). We note here that an exposure of 10T0 does not necessarily require 75 yr of IceCube running, as a number of factors could improve the conservative projected IceCube limits shown here in a [1] M. G. Aartsen et al. (IceCube Collaboration), First Obser- nonlinear fashion. For instance, the future data in all the vation of PeV-Energy Neutrinos with IceCube, Phys. 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