Leptoquark Solution for Both the Flavor and ANITA Anomalies

PHYSICAL REVIEW D 99, 095018 (2019)

Leptoquark solution for both the flavor and ANITA anomalies

Bhavesh Chauhan* Physical Research Laboratory, Ahmedabad 380009, India and Indian Institute of Technology Gandhinagar, Palaj 382355, India † Subhendra Mohanty Physical Research Laboratory, Ahmedabad 380009, India

(Received 31 January 2019; published 17 May 2019)

The ANITA experiment has seen anomalous Earth emergent showers of EeV energies which cannot be explained with Standard Model interactions. In addition, tests of lepton flavor universality in RðDðÞÞ and RðKðÞÞ have shown significant deviations from theoretical predictions. It is known that, among single leptoquark solutions, only the chiral vector leptoquark U1 ∼ ð3; 1; 2=3Þ can simultaneously address the discrepancies. In this paper, we show that the leptoquark motivated by flavor anomalies coupled to a sterile neutrino can also explain the ANITA anomalous events. We consider two scenarios, (a) the sterile neutrino, produced via resonant leptoquark mediated neutrino-nucleon interactions, propagates through the Earth without significant attenuation and decays near the surface to a τ lepton; and (b) a cosmogenic sterile neutrino interacts with the matter near the surface of Earth and generates a τ lepton. These two scenarios give significantly large survival probabilities even when regeneration effects are not taken into account. In the second scenario, the distribution of emergent tau energy peaks in the same energy range as seen by ANITA.

DOI: 10.1103/PhysRevD.99.095018

I. INTRODUCTION Similarly, collider experiments such as LHCb, Belle, and BABAR have observed hints of lepton flavor universality The ANtarctic Impulsive Transient Antenna (ANITA) violation (LFUV) in semileptonic decays of the B meson. instrument is designed to detect interaction of ultrahigh In particular, the ratios energy neutrinos via the Askaryan effect in ice. During its first and third flight, it also observed unexpected upward ¯ ðÞ − BRðB → D τ ν¯τÞ directed showers apparently emerging well below the R DðÞ ; 1 ð Þ¼ ¯ ðÞ − ð Þ horizon [1–3]. The observed signal is consistent with τ BRðB → D l ν¯lÞ induced showers. The essential details of the two anomalous ANITA events (AAEs) are given in Table I. The − BRðB¯ → K¯ ðÞμþμ Þ survival probability (ϵ) is estimated taking into account the RðKðÞÞ¼ ; ð2Þ BR ¯ → ¯ ðÞ þ − neutrino regeneration effects and τ energy losses in [4] ðB K e e Þ using only Standard Model (SM) interactions. The small survival probabilities within SM indicate that where l ¼ e, μ are known to have very weak dependence new physics scenarios should be invoked to explain these on hadronic form factors and provide excellent probes of events. In the past, the AAEs have been explained in the LFUV [10]. The experimentally measured value of the framework of sterile neutrinos [5,6], supersymmetry observables RðDðÞÞ [11,12] and RðKðÞÞ [13,14] is con- [4,7,8], and CPT symmetric universe [9]. However, each sistently below SM prediction and together are dubbed as of these explanations has their own limitations [7]. “flavor anomalies” in this paper. These discrepancies can

TABLE I. Properties of the anomalous events. *[email protected] † [email protected] Property AAE1 AAE2 0 6 0 4 0 56þ0.3 Published by the American Physical Society under the terms of Energy (Eτ) . . EeV . −0.2 EeV the Creative Commons Attribution 4.0 International license. Zenith Angle 117.4 0.3° 125.0 0.3° Further distribution of this work must maintain attribution to Chord Length (l⊕) 5740 60 km 7210 55 km ’ the author(s) and the published article s title, journal citation, ϵ 4.4 × 10−7 3.2 × 10−8 and DOI. Funded by SCOAP3. SM

2470-0010=2019=99(9)=095018(8) 095018-1 Published by the American Physical Society BHAVESH CHAUHAN and SUBHENDRA MOHANTY PHYS. REV. D 99, 095018 (2019) be explained in several extensions of SM, for example with energy. For example, if τ is produced through interaction of leptoquarks [15–29]. the incident neutrino such that Eτ ¼ Eν=4. Since the It was proposed in [4] that a long lived BSM particle, observed shower has energy in the range 0.1–1 EeV, one which is produced in ultrahigh energy (UHE) neutrino must integrate over 0.4–4 EeV. In general, ϵ depends on Eν nucleon interactions, propagates freely through the chord of and model parameters. Earth, and decays to a τ near the surface can explain the We now provide an order-of-magnitude estimate of the AAEs. A natural candidate for this is τ˜ (stau) in R-parity required ϵ taking δT ¼ 25 days. For the isotropic case, we conserving supersymmetry [4] and neutralino (mostly bino) assume that the source of EeV neutrinos is the Greisen- in R-parity violating supersymmetry [7]. In this paper, we Zatsepin-Kuzmin (GZK) mechanism. We approximate the consider two scenarios wherein a leptoquark, proposed as a GZK flux by the upper limit of its saturated value over the resolution to flavor anomalies, also explains AAEs. In the range 0.4–4 EeV as, first scenario, we extend the minimal leptoquark model of χ χ Φ¯ ≈ 10−25 2 −1 [15] with a heavy sterile neutrino ( ). The SM singlet is iso ðGeV cm ssrÞ ; ð5Þ produced in UHE neutrino-nucleon interactions mediated by the leptoquark. The sterile neutrino can travel inside which gives N ≈ 200ϵ. To get two events, one requires Earth without significant attenuation and decays near the ϵ ∼ 0.01. Similar estimates were also obtained in [7] which south pole. One of the decay products is the τ particle takes energy dependence into account albeit with larger whose shower is seen by ANITA. In the second scenario, an exposure time. With the Standard Model interactions, the ϵ ∼ 10−7 cosmogenic UHE sterile neutrino propagates freely through authors in [4] have estimated that SM for the two the chord of the Earth and produces a τ via leptoquark reported events. Thus the estimated number of anomalous mediated interaction. Interestingly, the same leptoquark events from GZK neutrinos with only SM interactions is, interaction also explains RðDðÞÞ through b → cτχ as N SM ∼ 2 10−5 shown in [18]. iso × ; ð6Þ In Sec. II, we estimate the number of AAEs for isotropic and anisotropic flux. In Sec. III, we provide details of the which makes observation of two events extremely unlikely. leptoquark model and discuss the two scenarios in detail One can relax the assumption that the source of EeV before we conclude in Sec. IV. neutrinos is the GZK flux. This allows us to postulate that such high energy neutrinos are coming from a localized II. ANITA ANOMALOUS EVENTS source in the sky. The upper limit on such anisotropic flux of EeV neutrinos is, In order to estimate the number of Earth emergent Φ¯ ≈ 3 2 10−20 2 −1 showers seen by ANITA, we evaluate the survival prob- aniso . × ðGeV cm ssrÞ ; ð7Þ ability ϵ (also called efficiency in [6]) which represents the fraction of incident flux Φ that is converted into τ near the which is several orders larger than the isotropic case. After surface. We use the expression accounting for the small solid angle one can similarly obtain, N ≈ 2.1 × 104ϵ. To get two events, one requires EZmax ϵ ∼ 10−4. Using SM interactions for the incident neutrinos, N ¼ A · δT · δΩ dEν · ϵ · ΦðEνÞ; ð3Þ N SM ∼ 2.1 × 10−3; 8 Emin aniso ð Þ where the effective area of ANITA A ≈ 4 km2 is estimated which again makes the two events very unlikely. In this using the Cherenkov angle [6], δT is the time period, and section, we have ignored the energy dependence of ϵ as δΩ is the acceptance angle. For a temporally continuous well as Φ. Even after taking those into account, the message ϵ source, δT ≈ 25 days is the combined exposure of ANITA-I will remain unchanged. The smallness of SM makes the (17.25 days) and ANITA-III (7 days) [1,2]. We have two event unlikely. ignored the contribution of ANITA-II (28.5 days) as it One must also check the compatibility of IceCube with was not sensitive to such events. For transient sources, δT ANITA observations. Even though IceCube has smaller will depend on the source and can be smaller. For isotropic effective area, the long duration of the experiment implies source, δΩ ≈ 2π sr. However, for anisotropic source, that the expected number of EeV scale up going τ-tracks N seen by IceCube ( IC) to be larger than expected anoma- N δΩ ≈ 2πð1 − cos δθÞ ≈ 0.0021 sr; ð4Þ lous events by ANITA ( AN). Using the relative expo- N ≈ 10 N sures, it has been estimated that IC × AN [6,7].In where δθ ∼ 1.5° is the angular uncertainty relative to parent [4], the authors identify three events in nine year neutrino direction [2]. The neutrino energy (Eν) is inte- (3142 days) IceCube data that may have origin similar N 0 3 grated over the range which gives correct range of shower to ANITA. This implies that AN ¼ . . Using Poisson

095018-2 LEPTOQUARK SOLUTION FOR BOTH THE FLAVOR AND ... PHYS. REV. D 99, 095018 (2019) distribution, the probability of observing two such events is It is assumed that the cross section for the process is around 0.03. The challenge for BSM scenarios is to get dominated by the resonant s-channel neutrino-quark inter- N ϵ AN of this order by enhancing as has been done in the actions. It has been pointed out in [31] that the gluon two scenarios studied in this paper. initiated process can also give significant contributions. However, this will give an Oð1Þ correction to survival III. LEPTOQUARK RESOLUTION OF AAE probability and has been neglected for the heavy sterile neutrino case. The production cross section can be approxi- As has been discussed [18,19], a vector leptoquark U1 mated in the narrow width limit as, 3 2 1 with SUð ÞC × SUð ÞL × Uð ÞY quantum numbers ð3; 1; 2=3Þ can simultaneously explain the flavor anoma- 3π 2 σ gx lies. It is also one of the handful models that admit LQðEνÞ¼ 2 2 g þ 1.08 leptoquark coupling to a sterile neutrino [30]. The inter- x Z 1 1 action of U1 with fermions in the mass basis is, 2 2 2 × dyy ðð0.11Þ fu þð0.5Þ fcÞ; ð12Þ 2MNEν 0 −L ⊃ ¯ i γμ νj ¯ i γμ j ðV · gLÞijuL U1;μ L þðgLÞijdL U1;μeL where f is the parton distribution function (PDF) of q ¯ i γμ j ¯ i γμ χ q ffiffiffi þðgRÞijdR U1;μeR þðgχÞiuR U1;μ R; ð9Þ 2 2 p evaluated at x ¼ MU= MNEν and Q ¼ MU y.Wehave where V is the Cabibbo-Kobayashi-Maskawa (CKM) used ManeParse [32] and NNPDF3.1(sx) [33,34] datasets matrix and the contribution of Pontecorvo-Maki- for the PDFs. The numerical factors (1.08, 0.11, and 0.5) Nakagawa-Sakata (PMNS) matrix is ignored. are obtained using the central value of CKM parameters [35]. Note that the PDFs are evaluated at small-x where the A. Heavy sterile neutrino quark and antiquark PDFs are similar and hence neutrino and antineutrino have a similar cross section. The inter- In this section, we assume that the sterile neutrino is action length is estimated as, l ¼ðρN σ Þ−1 where we sufficiently heavy so that its contribution to semi-leptonic B LQ A LQ have used ρ ≈ 4g=cm3 and N ¼ 6.022 × 1023 cm−3 in decays is kinematically forbidden. Even though the inter- A water-equivalent units. Even though the density is larger action of up-type quarks with a sterile neutrino can generate near the center of Earth, the approximation for density is dangerous scalar and pseudoscalar operators, their contri- valid for the chord lengths relevant for AAE. butions can be neglected and the conclusions in [19] remain As opposed to previous studies with three body decay of unchanged. The required texture of coupling matrices is, a singlet [7], in this paper we estimate the two body decay 0 1 00 0 width of the sterile neutrino to a pseudoscalar meson and B C the tau lepton. Since the decay width is being estimated in @ 0 A 0 0 0 gL ¼ gsμ gsτ gR ¼ . gχ ¼ð gx Þ: the rest frame of sterile neutrino of mass few GeV, one can 0 gbμ gbτ integrate out the heavy leptoquark and write the effective ð10Þ Lagrangian as,

2g g l The left-handed coupling (g ) generates the desired Wilson L x q ¯ l¯ χ L eff ¼ 2 ½cPLq½ PR ; ð13Þ coefficients (i.e., δC9 ¼ −δC10 with the correct sign for MU b → sμμ and g > 0 for b → cτν). In this way, U1 is VL ∈ l ∈ μ τ one of the rare solutions that can simultaneously address both where q fs; bg and f ; g. We also use the expression, the anomalies. The right-handed coupling (gR) is severely constrained as it generates scalar and pseudoscalar operators 2 that are disfavored. The sterile neutrino χ can also couple to MP h0jq¯ 1γ5q2jPi¼i fP; ð14Þ other up-type right handed quarks, but we have neglected M1 þ M2 those couplings and their constraints for simplicity. In this P M f section, we will assume the mass of leptoquark U1 to be where is a pseudoscalar meson of mass P and P is the associated form factor. The rest frame partial width of the MU ¼ 1.5 TeV and the couplings to be, sterile neutrino is, gsμ ¼ −0.012;gbμ ¼ 0.2;gsτ ¼ 0.5;gbτ ¼ 0.5; ð11Þ 1 2 − þ gxgsτ Γτ ≡ Γðχ → τ D Þ¼ which can explain the flavor anomalies. Such a choice is s 16π M2 within the reach of future LHC searches but allowed from U 2 2 M þ present limits [19,20]. We treat the coupling gx and mass of Ds × f þ MχβðM þ ;Mτ;MχÞð15Þ Mχ Ds Ds the sterile neutrino ( ) as free parameters of the theory. Mc þ Ms The singlet is produced near the surface of Earth through neutrino-nucleon interaction mediated by the leptoquark. where the phase space factor is,

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FIG. 1. The Feynman diagrams for the process involved in Model A. Left: The s-channel neutrino quark interaction mediated by þ leptoquark U1 that produces sterile neutrino in final state is shown. Right: The decay mode of sterile neutrino to charged lepton and Ds is shown. The shaded circle represents the effective vertex. 2 2 1 2 a − b a þ b = interactions after propagating a distance l1. These neutrino βða; b; cÞ¼ 1 − 1 − : c c undergo leptoquark interactions with the matter and produce a sterile neutrino. The sterile neutrino propagates ð16Þ a distance of l⊕ − l1 − δ before it decays near the surface of Earth in the δ ≈ 10 km window that will produce the For numerical estimation we use, observed τ. In Fig. 2 we have shown the parameter space that gives f þ ¼ 257.86 MeV M þ ¼ 1.968 GeV ð17Þ −6 Ds Ds ϵ ϵ ϵ 1 10 LQ > SM, and LQ > × for the two values of l⊕. We find that the maximum survival probability in this and the quarks and lepton masses used are Mc ¼1.29GeV, scenario is of the order 4 × 10−6. It is understood that M ¼ 95 MeV, Mμ ¼ 105.66 MeV, and Mτ ¼ 1.77 GeV s ϵ respectively. The relevant Feynman diagrams for the neutrino regeneration effects can dramatically increase LQ production and decay are shown in Fig. 1. The associated decay length of χ in Earth’s frame is estimated as,

1 Eχ 1 Eν lD ¼ γcτ ¼ ≈ ; ð18Þ Γτ Mχ Γτ 2Mχ where the last approximation is true for the range of energies involved. In this scenario, Eτ ¼ Eν=4 and hence for shower energy ∼0.5 EeV, one requires the incident neutrino to have energy Eν ∼ 2 EeV. With only SM interactions, one can estimate the bare −l⊕=l0 survival probability ϵ0 ¼ e where l⊕ is the length of path traversed by neutrino inside Earth and for EeV neutrinos, l0 ∼ 275 km [4]. However, this is severely modified when one takes neutrino regeneration effects during propagation. In [4], the probability is obtained using simulations and mentioned in Table I. We denote these ϵ probabilities with SM. Due to the additional leptoquark interactions, the survival probability of the neutrino flux can be estimated using,

− Zl⊕ l⊕Z l1 Zl1 −l2=l −l1=l e D e LQ dl3 −l3=l0 ϵ ϵ ϵLQ ¼ dl1 dl2 1− e FIG. 2. The parameter space that gives LQ > SM (blue), and l l l0 −6 D LQ ϵ > 1 × 10 (dark blue) for l⊕ ¼ 7210 km is shown. Similar 0 l⊕−l1−δ 0 LQ projections for l⊕ ¼ 5740 km is shown by red curves. The gray þ ð19Þ shaded region is conservatively ruled out from Bc decays and the limits for various Bl are shown. The top part is excluded using pffiffiffiffiffi The above expression can be understood as follows. The the perturbativity limit gx ≤ 4π. The neutrino energy is fixed to parentheses denote the fraction neutrinos that survives SM be 2 EeV. The benchmark point considered in the text is shown.

095018-4 LEPTOQUARK SOLUTION FOR BOTH THE FLAVOR AND ... PHYS. REV. D 99, 095018 (2019) similar to SM. However, complete estimation requires one is willing to give up simultaneous explanation of both simulation of neutrino propagation which is beyond the flavor anomalies, another interesting possibility opens up, scope of this work. Moreover, we find that the precision i.e., light sterile neutrino. þ measurement of Bc decay modes can probe the most interesting part of the parameter space. We evaluate the þ þ B. Light sterile neutrino branching fraction Bl ¼ BrðBc → l χÞ for l ∈ fμ; τg to be, In [18], it is shown that U1 leptoquark coupled to a light sterile neutrino can also explain the flavor anomalies. 2 2 2 ðÞ τ þ M þ However, as opposed to [19], RðD Þ is explained via Bc gxgbl Bc Bl f þ ðÞ ¼ 2 Bc right-handed couplings and RðK Þ via left-handed ones. 4πM þ M M þ M Bc U c b It is seen that a simultaneous explanation in this scenario is in 2 − 2 − 2 β × ðM þ Ml MχÞ ðMχ;Ml;MBþ Þ; ð20Þ ðÞ Bc c tension with big bang nucleosynthesis but RðD Þ can be explained successfully. The Lagrangian for the leptoquark is, f þ 0 43 M þ 6 275 where Bc ¼ . GeV [18] and Bc ¼ . GeV [35]. Since the typical branching ratio of leptonic mode is very 1 † μν † a aμν 2 † μ L ¼ − UμνU − ig κUμT UνG þ M UμU small, we take the conservative limit of Bl ¼ 10% for both LQ 2 s U μ and τ modes to constrain our parameter space. We also ¯ μ μ þ gbτbRγ U1;μτR þ gxc¯Rγ U1;μχR; ð22Þ show limits for Bl ¼ 1% which will be accessible in future B-factories and can test the model. κ 0 1 In this model, for the parameter space that we are where gs is the strong coupling constant and ¼ ð Þ for a interested in, the only kinematically allowed choice for minimally coupled (gauge) theory. The excess can be þ explained with the following choice of coupling and lep- the final state meson is Ds . The model also allows for − þ toquark mass, χ → μ Ds however this decay mode is suppressed due to smallness of jgsμj ∼ 0.012 as compared to jgsτj ∼ 0.5 as − 2 seen in Eq. (11). We also have χ → ν X but to get emergent MU jg g τj ∼ 0.62 : ð23Þ τ one needs to account for another interaction in (19) which x b 1 TeV makes it less probable. This mode will be important when regeneration effects are evaluated using simulation and is Considering the LHC constraints on the model, we chose beyond the scope of this paper. MU ¼ 1.5 TeV which is close to the lightest allowed mass To estimate the number of events, we consider the for κ ¼ 1. To a good approximation, gbτ ∈ f1.1; 1.4g which benchmark scenario translates to gx ∈ ð1.0; 1.25Þ using (23). In this limit, the model has signatures in future 300 fb−1 analysis. These 4 0 0 8 Mχ ¼ . GeV gx ¼ . ð21Þ limits are considerably weakened for κ ¼ 0. One can refer to [18] for detailed discussion of the model and other Γ 4 64 10−16 for which τ ¼ . × GeV and the survival fraction constraints. ϵ ∼ 1 5 − 2 0 10−6 is LQ ð . . Þ × . This gives the expected num- To explain AAE, we assume a flux of light sterile ber of AAE per direction to be 0.03 using the saturated neutrinos (χ) incident on Earth. These sterile neutrinos anisotropic flux. can pass through the Earth almost unattenuated, however, a In this scenario, larger values of the coupling gx seem to fraction of them can interact with the matter in Earth and be preferable. However, they would be constrained from produce a τ near the surface. In this section, we consider future measurements of Bμ. One can avoid these constraints both χ-quark and χ-gluon interactions. The relevant ðÞ if gbμ ¼ 0, but then the model cannot explain RðK Þ.If Feynman diagrams are shown in Fig. 3.

(a) (b) (c)

FIG. 3. The Feynman diagrams for χ-nucleon interaction. (a) The dominant s-channel χ-quark interaction. (b) The κ-dependent χ- gluon interaction. (c) The κ-independent χ-gluon interaction.

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quark initiated processes. The cross section depends on κ as evident from Fig. 3(b). In Fig. 4, we show the variation of σq and σg with incident sterile neutrino energy. We also show the relative strength for κ ¼ 0 and 1. The fraction of incident χ that interact with matter in Earth is given by,

l⊕ Z − l e l1= q=g ϵq=g ¼ dl1 ð26Þ lq=g l⊕−δ −1 where lq=g ¼ðρNAσq=gÞ . One must note that, for χ-quark interactions Eτ ¼ Eχ=2 whereas for χ-gluon interaction 4 FIG. 4. The variation of cross section σ ðσ Þ with incident Eτ ¼ Eχ= . By uniformly varying Eχ, we show the q g ϵ ϵ ϵ sterile neutrino energy is shown in blue (red). The inset shows the variation of ¼ q þ g with energy of emergent tau in difference in magnitude of σg for κ ¼ 0 and 1 in arbitrary units. Fig. 5. An interesting result of this scenario is that the distribution peaks for tau energy in the same range as seen by ANITA. The χ-quark interaction is dominated by the s-channel In order to estimate the number of events, one needs to resonant contribution and the cross section can be know the flux of incident χ on Earth. It is clear from the estimated by discussion in Sec. II that this scenario cannot explain AAE 3π g2g2 with isotropic flux. We assume anisotropic flux from point- σ ¼ σðχc → τbÞ¼ x bτ q 2 g2 þ g2 like sources in the sky and parametrize the incident flux as, Z x bτ 1 1 2 −γ × dyð1 − yÞ f : ð24Þ −20 Eχ 2 −1 2 c Φ ¼ ϕ0 × 10 ðGeV cm ssrÞ ; ð27Þ MNEν 0 EeV y RR The difference in - dependence is due to the nature of γ interaction as opposed to LR in the previous case. On the where the spectral index is unknown. The number of events other hand, the χ-gluon interaction cross section can be is then given by, estimated using, max 2ZEτ −γ 1800 Eχ N ≈ ϕ ϵ σ σ χ → τ ¯ ≈ σ χ → → τ¯ × 0 × dEχ · qðEχÞ · g ¼ ð g cbÞ ð g cU1Þ ×BrðU1 bÞ: ð25Þ EeV EeV min 2Eτ

max We implemented the model in FEYNRULES [36,37] and the 4ZEτ −γ cross section is calculated using CALCHEP [38].Aswas Eχ þ dEχ · ϵ ðEχÞ · ; ð28Þ shown in [31], the gluon initiated process are significant for g EeV min large energies and of the same order of magnitude as the 4Eτ

FIG. 5. The variation of ϵq, ϵg, and ϵ is shown in blue, red, and black respectively. The solid curve is for κ ¼ 1 and the dashed curve for κ ¼ 0. The chord length l⊕ is fixed to be 5740 km (left) and 7210 km (right). We fix gx ¼ 1.2 for both the plots. The region shown in green is the observed shower energy for the two events.

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TABLE II. The required value of ϕ0 to get N ¼ 1 for various Another possibility is the absorption of active neutrino choices of spectral index and chord lengths (A ≡ 5740 km and flux by cosmic sterile neutrino background [40], cosmic B ≡ 7210 km). neutrino background [41], or dark matter [42].In[43],a γ 0 γ 1 γ 2 γ 3 flux of boosted right handed neutrinos was obtained ¼ ¼ ¼ ¼ through decay of dark matter. ABABABAB ϕ 0 0.19 0.41 0.31 0.71 0.37 1.04 0.33 1.30 IV. CONCLUSION Since the observation of AAEs, many BSM scenarios where the limits of integration are determined by the 1σ range have been invoked to explain the discrepancy. In this paper of observed τ energy. Note that the limits and ϵ depend on we have proposed two models that can significantly q=g τ the chord length in consideration. Keeping N ¼ 1,onecan enhance the survival probability while simultaneously addressing the flavor anomalies. In the first scenario, we obtain the required value of ϕ0 for various choices of γ.The results have been summarized in Table II. It can be seen that have extended chiral vector leptoquark model which these values are compatible with the upper bounds mentioned explains RðDðÞÞ and RðKðÞÞ [15] by a sterile neutrino. in Sec. II. Note that, for γ ¼ 0, one expects more number of The cosmogenic UHE neutrinos interact with the matter in events with shower energies higher than the ones observed by Earth and produce a sterile neutrino that propagates freely ANITA. Hence, higher values of spectral index is preferred. inside Earth and decays near the surface to a τ. The precise → τχ We briefly comment regarding the source of such high measurement of BrðBc Þ, which is possible in upcom- energy sterile neutrinos. They can either be produced via ing B factories, will provide a good test of this model. the leptoquark interactions, via oscillation of active neu- In the second scenario, a cosmogenic UHE sterile trinos near the source, or via interactions during propaga- neutrino passes through the Earth almost unattenuated tion. If the sterile neutrinos are produced due to oscillation and interacts with the matter in Earth to produce an from the active ones, then the flux is proportional to the observable τ. The same interactions and parameters also square of the mixing angle. For large mixing, the cross explain the RðDðÞÞ anomaly [18]. The interesting result is section will dominated by SM interactions and the sterile that the distribution of emergent τ energy peaks in the same neutrino will be significantly attenuated by Earth. For small regime as observed by ANITA. This model has observable mixing, albeit the sterile neutrino propagates freely, the signatures in 300 fb−1 LHC searches. incident flux is smaller and constraints from active neutrino In summary, the observation of lepton flavor universality flux becomes important. On the other hand, if a flux of τ active neutrinos encounters large magnetic fields during violation and Earth emergent with EeV energy can be propagation, it can convert to sterile neutrinos via the explained in a common framework. Moreover, it has transition magnetic dipole moment [39]. In this scenario, testable signatures in upcoming experiments. Future obser- one anticipates both fluxes to be of the same order of vations by IceCube Gen-II and data from ANITA-IV magnitude and offers a lucrative testable explanation. should be able to shed more light on such BSM hypotheses.

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