Among the information provided by high energy neutrinos, a promising possibility is to analyze the effects of a Violation of Equivalence Principle (VEP) on neutrino oscillations. We analyze the recently released IceCube data on atmospheric neutrino fluxes under the assumption of a VEP and obtain updated constraints on the parameter space with the benchmark choice that neutrinos with different masses couple with different strengths to the gravitational field. In this case we find that the VEP parameters times the local gravitational potential at Earth can be constrained at the level of $10^{-27}$. We show that the constraints from atmospheric neutrinos strongly depend on the assumption that the neutrino eigenstates interacting diagonally with the gravitational field coincide with the mass eigenstates, which is not \textit{a priori} justified: this is particularly clear in the case that the basis of diagonal gravitational interaction coincide with the flavor basis, which cannot be constrained by the observation of atmospheric neutrinos. Finally, we quantitatively study the effect of a VEP on the flavor composition of the astrophysical neutrinos, stressing again the interplay with the basis in which the VEP is diagonal: we find that for some choices of such basis the flavor ratio measured by IceCube can significantly change.
High-energy atmospheric neutrinos observed by the IceCube Neutrino Observatory are extremely sensitive probes of Lorentz violation (LV). Here we report the result of analyzing two years of IceCube data in the search for LV. This analysis places some of the strongest constraints on LV when considering high-dimensional operators.
A recent proposal to associate 60~TeV to 2~PeV IceCube neutrino events with gamma-ray bursts~(GRBs) indicates the Lorentz violation of cosmic neutrinos and leads further to the $CPT$ symmetry violation between neutrinos and antineutrinos. Here we find that another 12 northern hemisphere track events possibly correlated with GRBs from three-year IceCube data satisfy the same regularity at a lower energy scale around 1~TeV. The combined fitting indicates a Lorentz violation scale ${E}_{\rm LV}=(6.4\pm 1.5)\times10^{17}~{ \rm GeV}$ and an intrinsic time difference ${Δ{t}_{\rm in}=(-2.8\pm 0.7)\ti…
Astrophysical high-energy neutrinos observed by IceCube are sensitive to small effects in a vacuum such as those motivated from quantum gravity theories. Here, we discuss the potential sensitivity of Lorentz violation from the diffuse astrophysical neutrino data in IceCube. The estimated sensitivity reaches the Planck scale physics motivated region, providing IceCube with real discovery potential of Lorentz violation.
The IceCube collaboration has recently announced the discovery of ultra-high energy neutrino events. These neutrinos can be used to probe their production source, as well as leptonic mixing parameters. In this work, we have used the first IceCube data to constrain the leptonic CP violating phase $δ_{cp}$. For this, we have analyzed the data in the form of flux ratios. We find that the fit to $δ_{cp}$ depends on the assumptions made on the production mechanism of these astrophyscial neutrinos. Consequently, we also use this data to impose constraints on the sources of the neutrinos.
The 6-year dataset of high-energy starting events (HESE) at IceCube indicates a spectrum of astrophysical neutrinos much softer than expected from the Fermi shock acceleration mechanism. On the other hand, IceCube's up-going muon neutrino dataset and Fermi-LAT's gamma-ray spectrum point to an $E^{-2}$ neutrino spectrum. If the HESE data above 200 TeV are fit with the latter flux, an excess at lower energies ensues, which then suggests a multicomponent spectrum. We show that the HESE dataset can be explained by a single $E^{-2}$ power-law neutrino flux from a muon-damped $pγ$ source if neutrino…
It has been speculated that Lorentz-invariance violation (LIV) might be generated by quantum-gravity (QG) effects. As a consequence, particles may not travel at the universal speed of light. In particular, superluminal extragalactic neutrinos would rapidly lose energy via the bremssthralung of electron-positron pairs (nu -> nu e+ e-), damping their initial energy into electromagnetic cascades, a figure constrained by Fermi-LAT data. We show that the two cascade neutrino events with energies around 1 PeV recently detected by IceCube -if attributed to extragalactic diffuse events, as it appears …
Lorentz invariance is a fundamental symmetry of spacetime underpinning the Standard Model (SM) and our understanding of high-energy phenomena in particle physics. However, beyond the quantum gravity scale, we expect the SM to be replaced with a more fundamental, covariant theory giving a quantum description of gravity. The effective theory arising from this theory can break Lorentz invariance and thus predicts observables that exhibit low-energy manifestations of Lorentz violation. In particular, these observables could be a subleading contribution to neutrino oscillations and could therefore …
The recent high-statistics high-energy atmospheric neutrino data collected by IceCube open a new window to probe new physics scenarios that are suppressed in lower energy neutrino experiments. In this paper we analyze the IceCube atmospheric neutrino data to constrain the Violation of Equivalence Principle (VEP) in the framework of three neutrinos with non-universal gravitational couplings. In this scenario the effect of VEP on neutrino oscillation probabilities can be parametrized by two parameters $Δγ_{21}\equiv γ_2-γ_1$ and $Δγ_{31}\equiv γ_3-γ_1$, where $γ_i$'s denote the coupling of neutr…
If weak equivalence principle is violated then different types of neutrinos would couple differently with gravity and that may produce a gravity induced oscillation for the neutrinos of different flavour. We explore here the possibility that very small violation of the principle of weak equivalence (VEP) can be probed by ultra high energy neutrinos from distant astrophysical sources. The very long baseline length and the ultra high energies of such neutrinos could be helpful to probe very small VEP. We consider a 4-flavour neutrino scenario (3 active + 1 sterile) with both mass-flavour and gra…
Charged Lepton Flavor Violation at Neutrino Telescopes
Washington University（华盛顿大学）；Harvard University（哈佛大学）；Johannes Gutenberg-Universität Mainz（美因茨约翰内斯·古腾堡大学）；Durham University（杜伦大学）；Indian Institute of Technology Bombay（孟买印度理工学院）
Among the information provided by high energy neutrinos, a promising possibility is to analyze the effects of a Violation of Equivalence Principle (VEP) on neutrino oscillations. We analyze the IceCube data on atmospheric neutrino fluxes under the assumption of a VEP and obtain updated constraints on the parameter space with the benchmark choice that neutrinos with different masses couple with different strengths to the gravitational field. In this case we find that the VEP parameters times the local gravitational potential at Earth can be constrained at the level of $10^{-27}$. We show that t…
The IceCube neutrino spectrum shows a flux which falls of as $E^{-2}$ for sub PeV energies but there are no neutrino events observed above $\sim 3$ PeV. In particular the Glashow resonance expected at 6.3 PeV is not seen. We examine a Planck scale Lorentz violation as a mechanism for explaining the cutoff of observed neutrino energies around a few PeV. By choosing the one free parameter the cutoff in neutrino energy can be chosen to be between 2 and 6.3 PeV. We assume that neutrinos (antineutrinos) have a dispersion relation $E^2=p^2 - (ξ_3/M_{Pl})~p^3$, and find that both $π^+$ and $π^-$ deca…
The IceCube observation of cosmic neutrinos with $E_ν > 60$ TeV, most of which are likely of extragalactic origin, allows one to severely constrain Lorentz invariance violation (LIV) in the neutrino sector, allowing for the possible existence of superluminal neutrinos. The subsequent neutrino energy loss by vacuum $e^+e^-$ pair emission (VPE) is strongly dependent on the strength of LIV. In this paper we explore the physics and cosmology of superluminal neutrino propagation. We consider a conservative scenario for the redshift distribution of neutrino sources. Then by propagating a generic neu…
The oscillation of neutrino flavors, due to its interferometry nature, is extremely sensitive to the phase differences developing during the propagation of neutrinos. In this paper we investigate the effect of the Violation of Equivalence Principle (VEP) on the flavor oscillation probabilities of atmospheric and cosmic neutrinos observed at neutrino telescopes such as IceCube. Assuming a general parameterization of VEP, dubbed extended parameter space, we show that the synergy between the collected data of high energy atmospheric and cosmic neutrinos severely constrains the VEP parameters. Als…
The symmetry of the theory of relativity under diffeomorphisms strongly depends on the equivalence principle. Violation of Equivalence Principle (VEP) can be tested by looking for deviations from the standard framework of neutrino oscillations. In recent works, it has been shown that strong constraints on the VEP parameter space can be placed by means of the atmospheric neutrinos observed by the IceCube neutrino telescope. In this paper, we focus on the KM3NeT neutrino telescope and perform a forecast analysis to assess its capacity to probe VEP. Most importantly, we examine the crucial role p…
We derive stringent constraints on neutrino speed, weak equivalence principle violation, Lorentz invariance violation, and dual lensing from the first high-energy astrophysical neutrino source: TXS 0506+056. Observation of neutrino (IceCube-170922A) and photons in a similar time frame and from the same direction is used to derive these limits. We describe ways in which these constraints can be further improved by orders of magnitude.
We present an explicit proof that a minimal model of rank-2 antisymmetric field with spontaneous Lorentz violation and a classically equivalent vector field model are also quantum equivalent, by calculating quantum effective actions of both theories. We comment on the issues encountered while checking quantum equivalence in curved spacetime.
We consider possible violations of the equivalence principle through the exchange of a light `dilaton-like' scalar field. Using recent work on the quark-mass dependence of nuclear binding, we find that the dilaton-quark-mass coupling induces significant equivalence-principle-violating effects varying like the inverse cubic root of the atomic number - A^{-1/3}. We provide a general parameterization of the scalar couplings, but argue that two parameters are likely to dominate the equivalence-principle phenomenology. We indicate the implications of this framework for comparing the sensitivities o…
We study Lorentz violation effects on flavor transitions of high energy astrophysical neutrinos. It is shown that the appearance of Lorentz violating Hamiltonian can drastically change the flavor transition probabilities of astrophysical neutrinos. Predictions of Lorentz violation effects on flavor compositions of astrophysical neutrinos arriving on Earth are compared with IceCube flavor composition measurement which analyzes astrophysical neutrino events in the energy range between $25~{\rm TeV}$ and $2.8~{\rm PeV}$. Such a comparison indicates that the future IceCube-Gen2 will be able to pla…
We discuss the derivation of the trace anomaly using a non-local effective action at one loop. This provides a simple and instructive form and emphasizes infrared physics. We then use this example to explore several of the properties of non-local actions, including displaying the action for the full non-local energy-momentum tensor. As an application, we show that the long-distance corrections at one loop lead to quantum violations of some classical consequences of the equivalence principle, for example producing a frequency dependence of the gravitational bending of light.
We study the equivalence principle and its violations by quantum effects in scalar-tensor theories that admit a conformal frame in which matter only couples to the spacetime metric. These theories possess Ward identities that guarantee the validity of the weak equivalence principle to all orders in the matter coupling constants. These Ward identities originate from a broken Weyl symmetry under which the scalar field transforms by a shift, and from the symmetry required to couple a massless spin two particle to matter (diffeomorphism invariance). But the same identities also predict violations …
We point out that equivalence principle violations, while not dynamically equivalent, produce the same kinematical effects as Lorentz invariance violations for particle processes in a constant gravitational potential. This allows us to translate many experimental bounds on Lorentz invariance violations into bounds on equivalence principle violations. The most stringent bound suggests that a postive signal in an Eötvös experiment may be at least seven orders of magnitude beyond current technology.
Neutrino flavour oscillations are analyzed in a model in which particles experience an effective Schwarzschild geometry modified by maximal acceleration corrections. These imply a quantum violation of the equivalence principle. The corresponding shifts in the phase of the neutrino mass eigenstates are calculated and discussed.
We show that the Abell Cluster A586 exhibits evidence of the interaction between dark matter and dark energy and argue that this interaction implies a violation of the Equivalence Principle. This violation is found in the context of two different models of dark energy-dark matter interaction. We also argue, based on the spherical symmetry of the Abell Cluster A586 that skewness is not the most general quantity to test the Equivalence Principle.
We have examined Lorentz invariance and equivalence principle violations in the neutrino sector as manifested in neutrinoless double beta decay. We conclude that this rare decay cannot provide a useful view of these exotic processes.
In this paper we consider the violation of supersymmetric equvalence among the R parity violating couplings $lamabda_{ijk}$ caused by widely split chiral supermultiplets. We find that if $λ^{\prime}_{2jk}=g$ and $λ^{\prime}_{1jk}=e$ then the violation of SUSY equivalence is of the order of $5-6%$ in heavy SQCD models. On the other hand if $λ^{\prime}_{3jk}=g$ and $λ_{ijk}=e$ then the violation of SUSY equivalence can be as large as 9.4% in 2-1 models.
In models with Large Extra Dimensions the smallness of neutrino masses can be naturally explained by introducing gauge singlet fermions which propagate in the bulk. The Kaluza-Klein modes of these fermions appear as towers of sterile neutrino states on the brane. We study the phenomenological consequences of this picture for the high energy atmospheric neutrinos. For this purpose we construct a detailed equivalence between a model with large extra dimensions and a (3 + n) scenario consisting of three active and n extra sterile neutrino states, which provides a clear intuitive understanding of …
This paper investigates the physics reach of the IceCube neutrino detector when it will have collected a data set of order one million atmospheric neutrinos with energies in the 0.1 \sim 10^4 TeV range. The paper consists of three parts. We first demonstrate how to simulate the detector performance using relatively simple analytic methods. Because of the high energies of the neutrinos, their oscillations, propagation in the Earth and regeneration due to τdecay must be treated in a coherent way. We set up the formalism to do this and discuss the implications. In a final section we apply the met…
In a recently proposed scenario, where the dilaton decouples while cosmologically attracted towards infinite bare string coupling, its residual interactions can be related to the amplitude of density fluctuations generated during inflation, and are large enough to be detectable through a modest improvement on present tests of free-fall universality. Provided it has significant couplings to either dark matter or dark energy, a runaway dilaton can also induce time-variations of the natural "constants" within the reach of near-future experiments.
Tree level unitarity violations of extra dimensional extensions of the Standard Model may become much stronger when the scalar sector is included in the bulk. This effect occurs when the couplings are not suppressed for larger Kaluza-Klein levels, and could have relevant consequences for the phenomenology of the next generation of colliders. We briefly review our formalism to obtain more stringent unitarity bounds when KK modes are present, as well as the generalization to extra dimensions of the Equivalence Theorem between Goldstone bosons and longitudinal gauge bosons
The joint realm of quantum mechanics and the general-relativistic description of gravitation is becoming increasingly accessible to terrestrial experiments and observations. In this essay we study the emerging indications of the violation of equivalence principle (VEP). While the solar neutrino anomaly may find its natural explanation in a VEP, the statistically significant discrepancy observed in the gravitationally induced phases of neutron interferometry seems to be the first indication of a VEP. However, such a view would seem immediately challenged by the atomic interferometry results. Th…
We study the non-relativistic limit of Dirac equation for mixed neutrinos. We demonstrate that such a procedure inevitably leads to a redefinition of the inertial mass. This happens because, in contrast to the case when mixing is absent, the antiparticle sector contribution cannot be neglected for neutrinos with definite flavor. We then show that, when a gravitational interaction is switched on, in the weak-field approximation the mass parameter which couples to gravity (gravitational mass) does not undergo the same reformulation as the inertial mass, thus leading to an apparent breakdown of t…
The theory of scalar gravity proposed by Nordström, and refined by Einstein and Fokker, provides a striking analogy to general relativity. In its modern form, scalar gravity appears as the low-energy effective field theory of the spontaneous breaking of conformal symmetry within a CFT, and is AdS/CFT dual to the original Randall-Sundrum I model, but without a UV brane. Scalar gravity faithfully exhibits several qualitative features of the cosmological constant problem of standard gravity coupled to quantum matter, and the Weinberg no-go theorem can be extended to this case as well. Remarkably,…
The Lorentz invariance and Einstein equivalence principle violating effects in the narrow 7.8 eV transition in 229Th nucleus may be 100 000 times larger than in atoms. This transition may be investigated using high precision laser spectroscopy methods, has a very small width, and suppressed systematic effects. Similar values of the effects are expected in 73 eV 235U nuclear transition which is coming within the reach of the laser spectroscopy. Mossbauer transitions give another possibility.
The observation by the IceCube Collaboration of a high-energy ($E \gtrsim 200$ TeV) neutrino from the direction of the blazar TXS 0506+056 and the coincident observations of enhanced $γ$-ray emissions from the same object by MAGIC and other experiments can be used to set stringent constraints on Lorentz violation in the propagation of neutrinos that is linear in the neutrino energy: $Δv = - E/M_1$, where $Δv$ is the deviation from the velocity of light, and $M_1$ is an unknown high energy scale to be constrained by experiment. Allowing for a difference in neutrino and photon propagation times …
We report a joint test of local Lorentz invariance and the Einstein equivalence principle for electrons, using long-term measurements of the transition frequency between two nearly degenerate states of atomic dysprosium. We present many-body calculations which demonstrate that the energy splitting of these states is particularly sensitive to violations of both special and general relativity. We limit Lorentz violation for electrons at the level of $10^{-17}$, matching or improving the best laboratory and astrophysical limits by up to a factor of 10, and improve bounds on gravitational redshift…
Massless neutrinos will mix if their couplings to gravity are flavor dependent, i.e., violate the principle of equivalence. Because the gravitational interaction grows with neutrino energy, the solar neutrino problem and the recent atmospheric neutrino data may be simultaneously explained by violations at the level of 1E-14 to 1E-17 or smaller. This possibility is severely constrained by present accelerator neutrino experiments and will be preeminently tested in proposed long baseline accelerator neutrino experiments.
Lorentz violation is a predicted phenomenon from the Planck scale physics. Although the three active massive neutrino framework with the Standard Model (SM), so-called the neutrino Standard Model (nuSM), is successful, series of signals not understood within the nuSM suggest neutrino physics may be the first place to see the physics beyond the SM, such as Lorentz violation. Especially, neutrino oscillations are the natural interferometer and they are sensitive to the Lorentz violation. The LSND oscillation signal was analyzed under the Standard Model Extension (SME) framework, and it was found…
We have updated the analysis for the solution to the solar neutrino problem by the long-wavelength neutrino oscillations induced by a tiny breakdown of the weak equivalence principle of general relativity, and obtained a very good fit to all the solar neutrino data.
The Lorentz violation~(LV) effect of ultra-relativistic particles can be tested by gamma-ray burst~(GRB) neutrinos and photons. The IceCube Collaboration has observed plenty of ultra-high energy neutrinos, including four events of PeV scale neutrinos. Recent studies suggested a possible energy dependent speed variation of GRB neutrinos in a similar way to that of GRB photons. Here we find that all four events of PeV neutrinos with associated GRB candidates can satisfy a regularity found from TeV neutrinos about a linear form correlation between the observed time difference and the LV factor. S…
We have found that long-wavelength neutrino oscillations induced by a tiny breakdown of the weak equivalence principle of general relativity can provide a viable solution to the solar neutrino problem.
We consider the pulsar velocity problem and relate it to some unconventional neutrino oscillation mechanisms based on a violation of the equivalence principle by neutrinos. We show that the observed pulsar velocities may be explained by violations at the level from 10^{-9} to 10^{-10} in the case of a non-universal tensor neutrino-gravity coupling, whereas there is no solution in the case of a non-universal scalar neutrino-gravity coupling. Neutrinos may remain massless and the requisite magnetic field strength is similar to that in the conventional mass oscillation mechanism.
New limits for the Violation of Equivalence Principle (VEP) are obtained considering the mass-flavor mixing hypothesis. This analysis includes observations of solar and reactor neutrinos and has obtained a limit for the VEP parameter $|Δγ|$ contributing to the $ν_e$ and $\barν_e$ disappearance channels of the order $|Δγ|<10^{-14}$, when it is assumed that neutrinos are mainly affected by the gravitational potential $φ\approx 10^{-5}$ due to the Great Attractor.
The violation of the equivalence principle (VEP) causing neutrino oscillations is of current interest. We study here the possibility of not only flavor oscillation but spin flavor oscillation of ultra high energy ($ \sim$ 1 PeV) neutrinos emanating from AGN due to VEP and due to the presence of a large magnetic field ($ \sim$ 1 Tesla) in AGN. In particular we look at the resonance spin flavor conversion driven by the AGN potential. Interesting bounds on the transition magnetic moment of neutrinos may therefore be obtained.
We consider the effect of a long range, flavor changing tensor interaction of possible gravitational origin. Neutrino mixing experiments provide the most sensitive probe to date for such forces---testing the equivalence principle at levels below $10^{-20}$. Here we justify and generalize a formalism for describing such effects. The constraints from neutrino mixing experiments on gravitationally induced mixing are calculated. Our detailed analysis of the atmospheric neutrino data confirms a remarkable result: the atmospheric neutrino data implies the same size force as does the solar neutrino d…
Experimental discovery of the dilaton would provide strong evidence for string theory. A light dilaton could show up in current tests of the inverse square law for gravity at sub-millimeter distances. In the large extra dimension scenario, Kaluza-Klein excitations of the dilaton can also contribute to the cooling of supernovae. In order to quantify these effects we compute the couplings of a low energy dilaton to matter. These predominantly arise from the fundamental dilaton coupling to the gluon field strength, which receives a sizable enhancement from QCD scaling. We show that detection of t…
We explore a version of the cosmological dilaton-fixing and decoupling mechanism in which the dilaton-dependence of the low-energy effective action is extremized for infinitely large values of the bare string coupling $g_s^2 = e^ϕ$. We study the efficiency with which the dilaton $ϕ$ runs away towards its ``fixed point'' at infinity during a primordial inflationary stage, and thereby approximately decouples from matter. The residual dilaton couplings are found to be related to the amplitude of the density fluctuations generated during inflation. For the simplest inflationary potential, $V (χ) =…
New sub-GeV vector bosons with couplings to muons but not electrons have been discussed in order to explain the muon's magnetic moment, the gap of high-energy neutrinos in IceCube or the proton radius puzzle. If such a light Z' not only violates lepton universality but also lepton flavor, as expected for example from the recent hint for $h\toμτ$ at CMS, the two-body decay mode $τ\to μZ'$ opens up and for $M_{Z'} < 2 m_μ$ gives better constraints than $τ\to 3μ$ already with 20-year-old ARGUS limits. We discuss the general prospects and motivation of light vector bosons with lepton-flavor-violat…
Cosmic rays are the highest energy particles available for our study and as such serve as excellent probes of the effects of Lorentz Invariance Violations, which are expected to increase with energy. This general paradigm is investigated in this paper by studying the effects of such violations within the Coleman-Glashow model in which each particle species may have its own maximum attainable velocity, even exceeding that of light \textit{in vacuo}. The particular focus here is that the muon neutrino may have the maximum speed exceeding that of light. We show that such an assumption leads to th…
In this Brief Report, a non-standard solution to the solar neutrino problem is revisited. This solution assumes that neutrino flavors could have different couplings to gravity, hence, the equivalence principle is violated in this mechanism. The gravity induced mixing has the potential of accounting for the current solar neutrino data from several experiments even for massless neutrinos. We fit this solution to the total rate of neutrino events in the SuperKamiokande detector together with the total rate from other detectors and also with the most recent results of the SuperKamiokande results f…
Violation of equivalence principle predicts that neutrinos of different flavor couple differently with gravity. Such a scenario can give rise to gravity induced flavor oscillations in addition to the usual mass flavor neutrino oscillations during the neutrino propagation. Even if the equivalence principle is indeed violated, their measure will be extremely small. We explore the possibility to probe the violation of equivalence principle (VEP) for the case of long baseline (LBL) neutrinos in a 4-flavor neutrino framework (3 active + 1 sterile) where both mass and gravity induced oscillations ar…
Tensor-scalar theory is a wide class of alternative theory of gravitation that can be motivated by higher dimensional theories, by models of dark matter or dark ernergy. In the general case, the scalar field will couple non-universally to matter producing a violation of the equivalence principle. In this communication, we review a microscopic model of scalar/matter coupling and its observable consequences in terms of universality of free fall, of frequencies comparison and of redshifts tests. We then focus on two models: (i) a model of ultralight scalar dark matter and (ii) a model of scalariz…
A number of different effects of the violation of the Equivalence Principle (VEP), taken as sub-leading mechanism of neutrino flavor oscillation, are examined within the framework of the DUNE experiment. We study the possibility of obtaining a misleading neutrino oscillation parameter region caused by our unawareness of VEP. Additionally, we evaluate the impact on the measurement of CP violation and the distinction of neutrino mass hierarchy at DUNE. Besides, limits on VEP for a wide variety of textures of the matrix that connects neutrino gravity eigenstates to flavor eigenstates are imposed.…
The SNO result on charged current deuteron disintegration, the SuperKamiokande 1258-day data on electron scattering, and other solar neutrino results are used to revisit the model of neutrino oscillations driven by a violation of the equivalence principle. We use a chisq minimization technique to examine oscillation between the nu(e) and another active neutrino, both massless, and find that within the Standard Solar Model the fit to the SNO and SuperKamiokande spectra are moderately good while a very good fit is obtained when the absolute normalizations of the 8B and hep neutrino fluxes are al…
