Exploiting a future galactic supernova to probe neutrino magnetic moments

A core-collapse supernova (SN) offers an excellent astrophysical laboratory to test non-zero neutrino magnetic moments. In particular, the neutronization burst phase, which lasts for few tens of milliseconds post-bounce, is dominated by electron neutrinos and can offer exceptional discovery potential for transition magnetic moments. We simulate the neutrino spectra from the burst phase in forthcoming neutrino experiments like the Deep Underground Neutrino Experiment (DUNE), and the Hyper-Kamiokande (HK), by taking into account spin-flavour conversions of SN neutrinos, caused by interactions with ambient magnetic fields. We find that the neutrino transition magnetic moments which can be explored by these experiments for a galactic SN are an order to several orders of magnitude better than the current terrestrial and astrophysical limits. Additionally, we also discuss how this realization might shed light on three important neutrino properties: (a) the Dirac/Majorana nature, (b) the neutrino mass ordering, and (c) the neutrino mass-generation mechanism.


Introduction
The discovery of neutrino oscillations, driven by non-zero neutrino masses and mixing, provided the first robust evidence of physics beyond the Standard Model (SM) [1]. In order to account for the tiny neutrino masses and mixing, the SM must be extended. In these extensions, a generic outcome of mechanisms of neutrino mass generation is the existence of a non-zero neutrino magnetic moment (µ ν ) through quantum loop corrections. Thereby, a careful theoretical and experimental study of neutrino electromagnetic interactions may help shed some light on the underlying theory. Within the SM minimally extended to contain Dirac neutrino masses, neutrino magnetic moments are µ ν 10 −19 µ B [2], where µ B = e/(2m e ) is the Bohr magneton, e is the electron charge, and m e is the electron mass. On the other hand, the strength of transition neutrino magnetic moments, in case of Majorana scenario in the standard seesaw mechanism, is even smaller and of the order of ∼ 10 −23 µ B [3]. Such a small values µ ν is far beyond the reach of current experimental capabilities.
New symmetries and interactions [4][5][6][7][8] can change the above picture, and allow for larger values of µ ν , without getting into unrealistic values of neutrino masses (for a review, see Ref. [9]). Neutrino magnetic moments can either be flavour-diagonal and/or flavour off-diagonal, depending on the nature of the neutrino. Dirac neutrinos can have an intrinsic magnetic moment that gives rise to spin precession for a given flavour α, i.e. ν αL → ν αR (where L, R refer to left-handed helicity and right-handed helicity respectively) in the presence of sufficiently strong magnetic fields [2], as well as a transition magnetic moment (TMM) that induces flavour precession in addition to rotation of the spin, i.e., ν αL → ν βR [3,10,11]. For Dirac neutrinos, the latter processes would cause the resultant neutrinos to be invisible since they will have the wrong helicity to be detected through weak interactions. Within the minimally extended SM, such TMMs of Dirac neutrinos are small due to a cancellation as a result of the Glashow-Iliopolus-Maiani (GIM) mechanism. On the other hand, Majorana neutrinos can have only transition moments, and the resultant spin-flavour precession would convert a neutrino into an antineutrino of a different flavour, and vice-versa [10]. Furthermore, coherent forward scattering of neutrinos off the surrounding matter background can resonantly enhance these spin-flavour conversions, thereby termed as the resonant spin-flavour precession (RSFP) [12][13][14]. This is very similar to matter enhancement of neutrino oscillations due to the Mikheyev-Smirnov-Wolfenstein (MSW) effect [15,16].
Bounds on neutrino magnetic moments can be placed using neutrinos from a variety of terrestrial as well as astrophysical sources. The search for the neutrino magnetic moments began seven decades ago [17], even before the neutrino was discovered. However, it became a very popular topic three decades ago when the Chlorine experiment found an apparent time variation of solar neutrino flux in anti-correlation with the Sun-spot activity [18,19]. After that, several neutrino experiments (reactor-based experiments like KRASNOYARSK [20], ROVNO [21], MUNU [22], TEXONO [23], GEMMA [24] and CONUS [25]; solar neutrino experiment like Borexino [26]; accelerator-based experiments like LAPMF [27] and LSND experiment [28]) investigated neutrino magnetic moments by looking at ν e − e scattering in general. The best constraint from these lab-based experiments, coming from Borexino, sets µ ν < 2.8 × 10 −11 µ B [26]. The GEMMA [24] and CONUS [25] collaborations placed somewhat less stringent constraints on neutrino magnetic moments of the order of O(10 −11 ) µ B . Other terrestrial experiments mentioned above have shown sensitivity to neutrino magnetic moments of the order of O(10 −10 ) µ B .
The topic of neutrino magnetic moments started receiving renewed attention when the XENON1T experiment [29] observed an excess of low energy electron recoil events, which can be explained by a neutrino transition magnetic moment µ ν ∈ (1.4, 2.9) × 10 −11 µ B at 90% C.L.
Strong bounds on neutrino magnetic moment can arise from astrophysical setups as well [30][31][32]. The presence of a non-zero neutrino magnetic moment allows for a direct coupling between neutrinos and photons, thereby allowing for neutrino radiative decays, as well as plasmon decays to neutrino-antineutrino pairs. The strongest bounds usually arise from globular cluster stars, where plasmon decay can delay helium ignition, leading to anomalous cooling of stars. Absence of any such observational evidence leads to µ ν ≤ 3 × 10 −12 µ B [33]. For an updated bound, check [34]. Similar cooling bounds also exist from observations of neutrinos from SN1987A. The presence of a non-zero neutrino magnetic moment allows for ν L → ν R conversions, leading to further cooling, and hence a shorter duration of neutrino emission than observed. Constraining the amount of ν R produced, one arrives at µ ν ≤ 10 −11 µ B [35]. Cosmological constraints on neutrino magnetic moments arise from observation of the primordial abundances of elements during Big Bang Nucleosynthesis (BBN), which sets constraints of the order of O(10 −10 ) µ B [36].
The neutrino flux from a core-collapse supernova (SN) can be an excellent tool to constrain neutrino magnetic moments. Neutrino flavour evolution inside a SN is currently an unsolved problem in the realm of particle physics. The dense matter environment, coupled with strong magnetic fields, makes a SN ideal for studying flavour transitions due to RSFP [13,14]. This is specially relevant for Majorana neutrinos, where non-zero TMMs can lead to ν e →ν x , where ν x is linear combination of the non-electron flavours, ν µ and ν τ . Related studies were performed in [37][38][39][40], where this mechanism was shown to mix different neutrino flavours, causing spectral changes. A simple, effective two-flavour analysis of neutrino flavour evolution in the presence of non-zero TMMs identifies, in addition to the usual MSW resonances, two extra resonances: (i) the RSFP-H, associated with the atmospheric mass-squared difference (∆m 2 31 ), occurring at high densities, and (ii) the RSFP-L, associated with the solar mass-squared difference (∆m 2 21 ), occurring at lower densities. Ref. [40] studied the impact of such RSFP in a three-flavour setup and discussed an additional type of resonance, the RSFP-E (electron-type), which is present in a pure three-flavour analysis. The RSFP-E can result in converting ν e →ν x in the normal mass ordering (NO), while in the inverted mass ordering (IO), it would result in ν e → ν x . In all these cases, it was found that all the resonances associated with spinflavour precession depend very sensitively on the electron number fraction per nucleon, denoted by Y e . These results can be further complicated due to the presence of collective flavour oscillations, arising out of the non-linearity of the equations of motion associated with neutrino flavour evolution within a SN [41,42].
However, flavour transitions due to RSFP will not be very effective if the spectra of different neutrino flavours are similar. This is mostly true of the cooling phase -a period existing for O(1 − 10)s post-bounce. However, the first O(30)ms post-bounce is dominated by the deleptonization epoch, also known as the neutronization burst (described in detail in the next section). This epoch is characterized by a pure ν e flux, with very little contamination ofν e and ν µ,τ . This phase is a robust feature of all hydrodynamic simulations, and hence acts as an excellent laboratory to test new neutrino properties. As a result, any new physics mechanism that ends up converting ν e s would cause a dramatic change in the ν e spectra. In particular, it was discussed in Ref [39,40]  In this work, we expand on this idea to utilize the neutronization burst from a future galactic SN to put some of the strongest constraints on neutrino TMMs. We simulate the neutrino spectra from the burst phase in upcoming neutrino experiments such as the Deep Underground Neutrino Experiment (DUNE) [43,44], and the Hyper-Kamiokande (HK) [45]. Since DUNE has maximum sensitivity to the ν e spectra, while HK can measure the ν e , both these experiments can be used to constrain TMMs of neutrinos using the neutronization burst spectra. The large sizes of these detectors and their detection channels make them ideal for probing the effect of TMM on the burst spectra. We find that the values of neutrino TMM that can be probed by these experiments for a SN occurring at 10 kpc are two or three orders of magnitude better than the current terrestrial as well as astrophysical constraints. We perform a parameterized study of the effect of neutrino TMM in this paper. In order to relate it to the fundamental parameters of a given model, we consider a simple model based on SU (2) H horizontal symmetry [6], which can give rise to large neutrino magnetic moments. We translate the bounds obtained from our analysis onto the model parameters.
The paper is structured as follows: in the next section, we briefly discuss the supernova neutronization burst. Then we analyze in detail the neutrino flavour conversion in the presence of neutrino magnetic moments. Subsequently, we analyze the discovery potential of neutrino magnetic moments in forthcoming experiments, and finally, we discuss the implications on neutrino properties before we conclude.

Supernova neutronization burst
The supernova neutronization burst is a period of deleptonization of the SN core, which lasts for about 30 ms after core-bounce [46]. During collapse, as the core stiffens and reaches nuclear densities, a shockwave is launched, which travels outwards dissociating the surrounding nuclei on its way into corresponding nucleons. Electron capture on protons leads to a large burst of ν e , which dominates the spectral content during this period, with subdominant contributions fromν e and ν µ,τ . The neutrino spectra from a SN can be parameterized using the "alpha-fit" spectra [47]: where L ν is the neutrino luminosity, E ν is the average energy of the neutrino, Γ(z) denotes the Euler gamma function, and the pinching parameter, α, defined as, is related to the spectral width. Fig. 1 shows the time-integrated (upto t = 50 ms) neutrino spectra during this period, obtained from a spherically symmetric simulation of a 15 M progenitor [48]. Evidently, this period is dominated by the ν e spectra for E ≤ 25 MeV, while the non-electron flavours dominate above that energy.
Deep inside the SN, the matter densities are high enough that the ν e is produced as the instantaneous Hamiltonian eigenstate associated with the largest eigenvalue. During evolution, the flavour eigenstates decohere, and hence can be treated as an incoherent superposition of mass eigenstates. Assuming adiabatic evolution inside the SN, the ν e flux at the Earth can be written as [49] F νe (E) = 1 where U eh is the corresponding flavour element of the PMNS matrix, and h denotes the heaviest mass eigenstate. In the NO, the ν e produced inside the SN comes out of it as a ν 3 , whereas in the IO, it comes out as a ν 2 . Since the other neutrino flavours are subdominant during this epoch, the flux in the NO is suppressed with respect to that in the IO by a factor of ∼ |U e3 | 2 /|U e2 | 2 0.1. In principle, this suppression of the flux in the NO as compared to the IO can be utilized to probe the neutrino mass ordering [49]. For antineutrinos, since the sign of the matter potential inverts, aν e produced will exit the SN as the lightest mass eigenstate. However, this entire picture changes as soon as neutrinos acquire a non-trivial magnetic moment, as we will discuss in the next section.
3 Neutrino flavour Conversion in the presence of mag-

netic moments
Neutrinos can have Dirac and/or Majorana magnetic moments, which can be parameterized by the following interaction Lagrangians, where F ηδ is the electromagnetic field-strength tensor, and µ D and µ αβ denote the Dirac

Evolution equation
We consider a three-flavour setup, and study the evolution of neutrinos and antineutrinos in the presence of a finite transverse magnetic field intensity B ⊥ . Ignoring temporal variations, the Equation of Motion (EoM) in matrix form is given by, where r is the radial coordinate in the SN. The neutrino flavour dynamics is governed by the Hamiltonian, where U is the PMNS matrix, E is neutrino energy and ∆m 2 ij gives the mass square difference between vacuum eigenstates ν i and ν j , and V denotes the forward scattering potential due to coherent scattering of neutrinos on electrons and nucleons. Assuming equal number densities of electron and protons (n e = n p ), the potentials, at leading order, have the following form, where n e and n n represent the electron and neutron number densities, respectively. The corresponding Hamiltonian for the antineutrinos, Hν, only differs in the sign of the potential, such that Vν e = −V νe and Vν µ,τ = −V νµ,τ . Note that the relevant quantity for the flavour evolution is the difference of the ν e and ν µ,τ potentials, since an overall phase term can always be rotated away.
The matrix M contains the TMMs: own anti-particle, its diagonal moments must disappear. This does not preclude off-diagonal transition magnetic moments.
It is the B ⊥ M term that couples the neutrinos to the antineutrinos, and gives rise to RSFP conversions. Note that in this analysis, we neglect the neutrino self-interaction terms, which are known to cause collective oscillations among different flavours [50,51]. This is primarily because the negligible proportions ofν e and ν µ,τ suppresses collective oscillations during the neutronization epoch.
We rewrite the EoMs in terms of the electron number fraction per nucleon Y e = n e /(n p + n n ), such that the electron number density n e = Y e ρ/m N , where ρ is the matter density and m N is the nucleon mass. For our discussions with regards to resonant flavour conversions, the relevant potential difference for the MSW flavour conversion is whereas for the RSFP flavour conversions, it is Clearly, in order to proceed with the neutrino flavour evolution, it is important to know the matter profile ρ, as well as the electron number fraction, Y e . We use the static profile model for a progenitor mass 15M and solar metallicity as shown in Fig. 2 [52].
We focus on the almost isotopically neutral region where (1 − 2Y e ) is small.
The magnetic field within a SN can be parameterized as a dipole, where r 0 is the radius of the iron core, which is set to r 0 ≈ 0.0024R for a progenitor mass 15M [53]. The magnitude of the magnetic field at the equator of the iron surface is given by B 0 , and its value can be deduced from the observation of white dwarfs to be in the range 10 7 G B 0 10 10 G [53].

Level crossing scheme
To understand the neutrino flavour evolution, it is useful to work in the basis in which the ν µ − ν τ andν µ −ν τ subspaces are simultaneously diagonal. The flavour states in the new basis are primed: ν µ , ν τ ,ν µ andν τ . In addition, the magnetic moment elements in Eq. 9 alter accordingly to the change of basis and are called µ eµ and µ eτ . For simplicity, we set µ µτ = 0 as all our results are insensitive to it 2 .
We compute the energy levels of the instantaneous matter eigenstates of the Hamiltonian in Eq. 6 for both mass orderings and show them in Fig. 3. The values of the mixing parameters were artificially chosen for illustration purpose in where j = 3 for H and j = 2 for L. For RSFP-H(L), the corresponding resonance condition On the other hand, the RSFP-E only appears in a full three-flavour analysis [40].
Furthermore, note that the RSFP-H(L) happen at higher densities than MSW-H(L), because the former is driven by (1 − 2Y e ) 10 −3 , whereas the latter is governed only by Y e ≈ 0.5, hence the densities need to be higher in RSFP-H(L).
The corresponding adiabaticity parameter for the MSW and RSFP resonances are and where β = µ for L and β = τ for H. Eqs. (16) and (17) must be evaluated at the resonance point and adiabaticity is guaranteed for γ 1. When neutrinos encounter an adiabatic resonance, the transitions between different energy levels in Fig. 6 are negligible. If adiabaticity is not met, a instantaneous matter eigenstate follows the dashed lines in Fig. 6 and hops from its energy level to a close one with probability, where γ res assumes the form in Eqs. (16) or (17) with the subscript res referring to the specific resonance. In the non-adiabatic limit, γ res 1, the hopping probability in (18) approaches unity and the matter eigenstates corresponding the two energy levels involved in the resonance exchange their previous fluxes. For lack of precise analytical expression for the adiabaticity of RSFP-E [40], we rely on numerical numerical calculations. In what follows, we discuss these resonances in detail for both mass orderings.

Normal mass ordering (NO)
The analysis is simplified because of the adiabaticity of the MSW-H and MSW-L resonances. We find, numerically, for the RSFP-L and RSFP-E are completely non-adiabatic. On the other hand, the RSFP-H can transit from completely non-adiabatic to adiabatic in the interval The closer µ ν B 0 is to 10 −2 µ B G, the more adiabatic is the RSFP-H, whereas for values 10 −2 µ B G, adiabaticity at RSFP-H saturates to a maximum. The probability that transitions happen between energy levels of neutrinos due to non-adiabaticity of the RSFP-H is given by p H (i.e., p H = P RSFP-H , see Eq. (18)).
The energy levels of matter eigenstates in case of NO are given in the top panel of Fig. 3.
The coloured lines indicate the evolution of the matter eigenstates (solid for neutrinos, dashed for antineutrinos), whereas the dashed black lines track the flavour content. We find that in the presence of non-zero magnetic moment deep inside the star, the ν e state coincides with initialν 2 , andν µ with ν 3 , therefore Fν 2 = F 0 νe , whereas F ν 3 = F 0 ν µ . As the non-adiabatic RSFP-E resonance is hit, the flux associated with the matter eigenstates ν 2 and ν 3 switch, thereby F 0 νe = F ν 3 and F 0 ν µ = Fν 2 . The next resonance encountered by Theν e is produced deep inside as a ν 2 , whereas the ν τ is produced mainly as a ν 1 . As these states evolve, they encounter the RSFP-H, where the ν 2 can flip to the ν 1 and vice versa with a probability p H . At this stage, the ν 2 and ν 1 fluxes can be written as an admixture of the initialν e flux and the ν τ flux. As these states propagate, the ν 2 crosses adiabatic MSW-H and MSW-L resonances, therefore F ν 2 remains unchanged, and finally exits the SN as Meanwhile, after the RSFP-H, the ν 1 flux can be written as F ν 1 = p H F 0 νe +(1−p H )F 0 ν τ . As it propagates outwards, it encounters two resonances as well, the non-adiabatic RSFP-L, and the adiabatic MSW-L (check inset plot). At the RSFP-L point, transition happens between ν 1 andν 1 . Since initialν 1 flux deep inside the SN is Fν 1 = F 0 ν µ , after encountering the RSFP-L resonance, one has Finally, as theν 3 is not affected by any of the resonances, we have Therefore, the ν e and theν e fluxes at the Earth are Now, if the neutrino magnetic moment were zero, there would be no RSFP, and the flux arriving at the Earth can be obtained by setting p H = 1 in the above equations. Thus, in the limit where all the non-electron neutrino fluxes are set equal (F ν µ = F ν τ = Fν µ = Fν τ = F νx ), one can write Eq. 28 as where F M SW ν = F ν (p H = 1).
With this information, we can calculate the changes in the neutronization fluence due to the presence of a non-zero TMM. From Fig. 1, note that for E 20 MeV, F 0 νe ≈ F 0 νx , and hence the effect due to a non-zero TMM cancels out. On the other hand, for E 20 MeV, we have F 0 νx > F 0 νe . This ends up reducing the ν e flux, and increasing theν e flux received at the Earth. We estimate that in case of complete adiabaticity of the RSFP-H resonance (p H = 0), for E = 25 MeV, one has

Inverted mass ordering (IO)
A similar argument can be applied if the mass ordering is inverted (see bottom panel of Fig. 3). At very high densities, we have F ν 1 = F 0 νe and F ν 2 = F 0 ν τ . As the neutrinos propagate, a RSFP-H causes a flip between a ν 1 and ν 2 with probability p H . Since the MSW-L resonance is adiabatic, the ν 2 finally emerges as On the other hand, the ν 1 , with flux F ν 1 = (1 − p H )F 0 νe + p H F 0 ν τ just after RSFP-H, goes through the adiabatic MSW-H and the non-adiabatic RSFP-E, where it flips completely toν 1 , and vice-versa. To get the final ν 1 flux, we need to track the flavour evolution of ν 1 . Theν 1 is produced deep inside as aν e , whileν 3 is produced as a ν µ . At RSFP-L,ν 1 andν 3 exchange fluxes so that Fν 1 = F 0 ν µ and Fν 3 = F 0 νe . Theν 3 flux remains unchanged and exits the SN as On the other hand, theν 1 exchanges flux with ν 1 at RSFP-E and reaches the surface of the star as whereas the ν 1 is emitted as Theν 2 and ν 3 have relatively trivial dynamics, and they are emitted as Collecting these fluxes, the ν e andν e fluxes at the Earth are given by In terms of the pure MSW fluxes (which is obtained by setting p H = 1 in Eqs. (38-39)), we get where all the non-electron neutrino fluxes are set equal Thus, the RSFP signal for inverted ordering will be more relevant at E 20 MeV once

Sensitivity in upcoming experiments
In this section, we study the impact of RSFP in the neutronization burst signal at upcoming neutrino detectors. As discussed in the previous sections, the effect of the RSFP is to reduce the ν e flux, and increase theν e . Depending on the mass ordering, the effect can be quite large. As a result, sensitivity can be maximised using a combination of detectors sensitive to the ν e and theν e flux. We focus on the Deep Underground Neutrino Experiment (DUNE), which can detect ν e , and the Hyper-Kamiokande (HK) which is mainly sensitive to theν e flux. The number of events of species ν α detected per unit energy is with N tar the number of targets in the detector material, R the distance of the supernova from the Earth, F να is the ν α flux that reaches the detector, σ α is the relevant neutrino interaction cross section and W is the Gaussian energy resolution function with width σ E that depends on that experimental setup. E t is the actual value of neutrino energy, while E r is the experimentally reconstructed energy. For the analysis presented in this paper, we choose a fiducial distance of R = 10 kpc. For the neutrino oscillation parameters, we assume the best fit values in [55].
We consider the following cases: 1. both µ eµ and µ eτ are equal, set to µ ν , and considered free parameters.
3. µ eµ = µ ν is considered a free parameter, while µ eτ = 0.    We perform a χ 2 analysis to study the sensitivity of DUNE and HK to the presence of neutrino TMM, using the signals from a future galactic SN. We use the Poissonian χ 2 estimator, where F i is the number of events predicted for a specific non zero value of µ ν B 0 and D i is the expected number of events assuming µ ν B 0 = 0. The subscript i refers to the i-th bin and n is the number of bins of the experiment.
Figs. 6 and 7 show χ 2 as a function of µ ν B 0 for NO and IO, respectively. The null hypothesis is that neutrinos undergo pure MSW flavour conversions, and there is no RSFP involved. As discussed before, the results are sensitive to the magnitude of the product µ ν B 0 , and it is not possible to disentangle one effect from the other. DUNE shows very little sensitivity to RSFP for NO, as we show in Fig. 6. On the other hand, for IO (see where the subscripts refers to specific cases 1, 2 and 3 respectively.
Due to its large size, HK will be sensitive to both the mass orderings. For the NO, HK can exclude, at 95% C.L., The best sensitivity to TMM comes from HK in case of IO, and it can exclude, at 95% C.L., As discussed, for a given B 0 , these bounds above can be translated into bounds on the TMM of neutrinos. Table I summarizes the derived sensitivities to µ ν assuming B 0 = 10 10 G.
Uncertainties may affect the derived sensitivity. However, such impact need not be drastic as the neutronization burst is a robust feature of all SN simulations with a relatively weak dependence on progenitor mass and/or specific traits of the models [57][58][59][60]. Indeed, other studies show that different progenitor models and neutrino emission parameters yield changes that are smaller than the statistical uncertainties for current water Cherenkov detectors [57]. For this reason, we do not perform a dedicated study about the influence of uncertainty in the fluence parameters on the expected sensitivities to µ ν B 0 .
Systematic uncertainties can also impact the above sensitivities, but owing to energy dependent spectral distortion of the neutrino signal in case of nonzero µ ν B 0 , only mild changes are expected. To see how systematics affect the χ 2 , we modify Eq. (44) as where ξ is nuisance parameter and σ an overall normalization error that we assume to be 50%. ξ is allowed to vary in the 3σ range and we minimize the χ 2 over it. We focus on case 1 and summarize new exclusion limits at 95% C.L. below with no sensitivity from DUNE in case of normal ordering.
A final comment on the adiabaticity of the RSFP-E resonance is in order. For µ ν B 0 > 10 −2 µ B G, the RSFP-E starts to be partially adiabatic. This can end up affecting the energy spectra in both the mass orderings. We checked that it is possible for the event spectra in the NO even to mimic that of the IO in certain cases. We do not comment on these cases further and leave the analysis to a future study.

Implications on neutrino properties
In this section, we mull over the possible impact of our results on the uncharted territories of neutrino physics. To do so, we first briefly summarize the experimental constraints and theoretical predictions on neutrino magnetic moments, along with our results, in Fig. 8.  • Neutrino mass generation mechanism: Due to similar chiral structure of the neutrino magnetic moment and neutrino mass operator, while removing the photon line from the loop diagram that yields the neutrino magnetic moment, a neutrino mass term is generated, and µ ν generally becomes proportional to m ν . One can estimate m ν originating from such diagrams as where Λ is the mass scale of the heavy particle inside the loop diagram. Experimental searches generally prefer charged particles with masses heavier than 100 GeV [65]. Without extra symmetries (and in the absence of severe fine-tuning), this implies that neutrino mass m ν must be ∼ 0.
and it can be as large as ∼ 10 −20 µ B . In the standard seesaw scenario, where neutrinos are Majorana particles, the transition magnetic moments as a result of Standard Model interactions are given by [3] The strength of transition neutrino magnetic moment is even smaller and of the order of ∼ 10 −23 µ B in this scenario. In the minimal Left-Right symmetric model, neutrino magnetic moment can be comparatively enhanced due to non-standard interactions via W ± R gauge boson [9]. However, the current experimental limit on the mixing angle between W ± R and W ± does not permit the strength to be greater than ∼ 10 −14 µ B . Similar strength of neutrino magnetic moment can be achievable in R-parity-violating supersymmetric extensions [67]. It was recently systematically analyzed and demonstrated in Ref. [6] that if neutrino magnetic moments are measured at the current experimental sensitivity O(10 −11 ) µ B level, neutrinos are most likely Majorana particles, and the models based on SU (2) H symmetry [5,6,68] fit well within this category. Neutrino mass models [65,69,70] based on spin-symmetry mechanism [7] can accommodate neutrino transition magnetic moments as large as O(10 −12 ) µ B [6]. All these predictions on neutrino magnetic moments in different neutrino mass models [6,9,71] are shown in green coloured lines in Fig. 8. It is quite interesting to see that the investigation of neutrino magnetic moments can be an excellent tool in searching for the theory underlying the neutrino mass generating mechanism. Any UV complete model of large neutrino magnetic moments is expected to provide a more extensive phenomenology. For completeness of our study, we consider the recently studied in a different context [6,72]. Following similar conventions and the same Lagrangian structure from Ref. [6], we summarize the different phenomenological implications in the SU (2) H model parameter space in Fig. 9. The transition magnetic moments of neutrino arise through charged Higgs induced quantum loop corrections. Due to SU(2) H symmetric limit, the contributions from two loop diagrams add up for neutrino magnetic moments, whereas it subtracts for neutrino mass contributions. In Fig. 9, h + denotes the responsible charged scalar field, and f is the relevant Yukawa term contributing to the neutrino magnetic moments. The colour shaded regions are excluded from current experimental searches: the light blue shaded region is excluded from charged Higgs searches at LEP experiment; the red shaded region is excluded from Borexino NSI searches [73]; NSI from the global fit to neutrino oscillation data [74] constrains dark green shaded region, IceCube atmospheric data [75] on NSI imposes bound as indicated by light green shaded region; the yellow shaded region is bounded from τ lifetime constraints [6]; the gray shaded region is excluded from neutrino magnetic moment searches at Borexino experiment [26]. There is an LEP mono-photon search limit [76] as well; however, we find that it is comparatively less constrained than the above-mentioned scenarios. We also project the future DUNE sensitivity [77] from NSI searches by the blue dashed line. The brown dashed line represents the future sensitivity from IceCube by looking at Glashowlike resonance features [78,79] induced by charged scalars in the ultrahigh-energy neutrino event spectrum. The gray dashed line is the astrophysical constraint originating from red giant and horizontal branch stars |µ ν | ≤ 1.5 × 10 −12 µ B (95% CL) [34,80,81]. However, it has been recently pointed out that this astrophysical limit can be relaxed by considering "neutrino trapping mechanism" [6,72]. The red dashed lines indicate the future sensitivities on neutrino magnetic moments at DUNE and HK experiments based on our analysis and setting magnetic field strength B 0 = 10 10 G. We can see that a large region of the SU (2) H model parameter space can be explored by looking at imprints of neutrino magnetic moments on supernova neutrino signal at DUNE and HK.

Conclusions
The neutronization burst from a future galactic SN has the potential to provide a wealth of information on neutrino transition magnetic moments (TMM). The neutrino spectra during this phase is usually dominated by a large fraction of ν e with sub-dominantν e and ν µ,τ . However, the presence of a non-zero neutrino TMM can change this picture completely. The combination of spin-flavour conversions due to a TMM, and resonant flavour conversions due to mass-mixings, can lead to a suppression of the ν e , while simultaneously enhancing theν e spectra in this epoch. This tell-tale signature can be used to put strong bounds on neutrino TMMs using the spectra from a future galactic SN. With immense experimental effort underway in the detection of neutrinos from a future galactic SN, it is timely to analyze the impact of neutrino TMM on the signal.
In this work, we have studied the neutrino flavour evolution inside a SN in the presence of a finite TMM, and considered the effect it has on the spectra from the burst phase.
By simulating the event spectra in upcoming neutrino experiments like as DUNE and Hyper-Kamiokande, we have found that the neutrino TMMs that may be probed by these experiments for a SN happening at 10 kpc are two or three orders of magnitude and extrapolated our bounds onto the model parameter space. We have found that in such models, a large section of the parameter space can be explored using the neutrino signal from a future galactic SN.