Neutrino Lines from Majoron Dark Matter

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PoS(NuFact2017)138 https://pos.sissa.it/ ∗ , whereas a coupling to photons is generated at two loops. The typically small couplings J 0 ` [email protected] → Speaker. Majorons are the Goldstone bosonsMajorana associated neutrino masses. to At lepton tree level, number itscharged and only fermions fermion thus arise couplings at closely are one-loop to level, connected neutrinos. including to lepton-flavor-violating Couplings` ones to that lead to decays make massive majorons a primetwo candidate mono-energetic neutrinos for is long-lived potentially dark detectableimportantly matter. for depends majoron on masses Its different above signature parameters MeV than decay and the most into visible decay channels. ∗ Copyright owned by the author(s) under the terms of the Creative Commons c Attribution-NonCommercial-NoDerivatives 4.0 International License (CC BY-NC-ND 4.0). The 19th International Workshop on Neutrinos25-30 from September, Accelerators-NUFACT2017 2017 Uppsala University, Uppsala, Sweden Julian Heeck Neutrino Lines from Majoron Dark Matter Service de Physique Théorique, Université LibreE-mail: de Bruxelles, CP225, 1050 Brussels, Belgium PoS(NuFact2017)138 L ], ], ≡ 2 5 | ≤ − 0 , K con- (1.1) (1.2) (1.3) 1 `` at the B † D resides K f | m J D , , we would m Julian Heeck ν . ). , D . With , parametrized 3 M 0 j q being the m h.c. `` ν symmetry results f ), which in partic- K + ` L σ v 2 1.1 − m ] (Sec. R 2 B . As shown in Ref. [ 1 √ ) ) and the connection to N π − R , / 1 0 2 λ ` f ( 6 , 16 M c R is an anomaly-free global m 0 and quarks λ U , implying that N charge 2, ` L 1 2 } ' = = and L † D 0 0 R + D `` m − S J S Jqq M D m H g B g R m , ν LyN 2 and M . Perturbativity sets an upper bound on { √ R − / ) M yv ν σ ( with physical meaning. M = 2 that carries V , ]; otherwise, it is induced at two-loop level and † D and lepton number have been measured already: the two mass split- D 1 6 √ − m 0 ν m / symmetry breaking then yields the famous seesaw B ) can easily be derived from Eq. ( D `` ) M L σ J to the light neutrino mass eigenstates below eV, this coupling is incredibly tiny. At one-loop K m ]. In the simplest realization, this majoron of the neutrino masses and can in particular be much iJ − µ j ) 4 B with + ). We suppressed flavor indices and details of the scalar f ∂ + , ) m bijectively onto ( 2 3 0 H 1 T D K † ( ( ( } ) σ tr m / R j ` 1 , L U σ 3 + − µ R M T m K 0 × j f , ∂ M tr `` is furthermore positive definite we have the inequalities ν D Y q δ D 5 ) 3 m + ( γ independent 1 = ( is anomaly free [ K T i m { ) 0 ( j R 0 3 ` L σ qq N ν v U with coefficients m δ 2 and we introduced the dimensionless hermitian coupling matrix 2 J µ − 2 ' − / × v ∂ π f + q 2 1 ν B µ L ) ` the heavy CP-even majoron partner. Further introducing three right-handed ) π 5 γ 16 m − M γ 2 8 m R 0 2 ( f = N σ 1 i ' ' , which are , and since u 0 0 3 SU f P J f † D + T . These fermion couplings are obviously crucial for majoron phenomenology and g `` / . m P J P Jqq v K − ) g + D g SM π , the Lagrangian reads tr ], the majoron also obtains couplings to charged leptons 2 σ . The majoron couplings to charged fermions are hence determined by the seesaw f m = R ( 1 ) L 1 ≤ , N ,` V S J f 0 6 v f = d ` 3 g ( 0 , ` T ( / 3 1 vanishes because L K ¯ † D f There is one more coupling of interest, that to photons. For a massless majoron, the coupling The difference between baryon number We start our discussion with a basic introduction to the majoron model, based on Refs. [ Five of the nine parameters encoded in The tree-level couplings of the majoron `` ˜ m F iJ of order 4 K D seesaw scale and active neutrino masses level [ in principle even offer aoff-diagonal new lepton avenue couplings, to which reconstruct will the lead to seesaw lepton parameters. flavor violation Note [ inJF particular the in a Goldstone boson called majoron [ ular include the couplings parameters before delving into the phenomenology of majorons as dark matter (Sec. symmetry of the Standard Model (SM); spontaneously breaking this with the SM lepton (scalar) doublet one can map the parameters as where m bigger than the naiveK one-generation expectation neutrino mass matrix Neutrino Lines from Majoron Dark Matter 1. Majoron couplings lepton flavor violation (Sec. in a singlet complex scalar potential tings and three mixing angles. However, even if we could measure all elements of √ breaking scale and still not be able to reconstruct the underlying seesaw parameters neutrinos tains precisely those nine seesawtrino parameters masses that and cannot be oscillations. determinedphenomenology As by of we measurements majorons, which will of endow neu- see below, this is a convenient parametrization for the PoS(NuFact2017)138 , 1 (1.5) (1.4) , . 1 1 breaking in Julian Heeck L ≤ > − x x B ) 1 for for ( , and electric charge f U 3 T 2 , and charged SM fermions 2 j

γ γ π n . These neutrinos will not i ! f f 2 − 2 J / j -Goldstone boson. This could m m , isospin 4 x x 1 1 m f c − −

N 1 1 g f √ √ 2 pseudo 2 + − ) Q 1 1 a f x ]. 3 J 1 T √ [ f f c Z log N f x ∑ 1 arcsin 4

, with coupling ( j 2 3 J x 2 1 ] Z − ν , making v j 1 m J      ν 2 m 7 ) = , e.g. from the coupling to the Higgs or the right-handed π K → forest. In these cases, different production mechanisms 2 with color multiplicity tr J ( α f )]) ]. A prerequisite here is an explicit 2 4096 1 8 i j α n n , − 7 freeze-in ' x ( ) x γγ p x 2 4 → cold enough, which can naturally be found in inverse-seesaw majoron + J is given by J ( x g 2 Γ with the longitudinal component of J − J 1 [ ]. Here we will focus on DM masses above MeV for simplicity. log ( 11 ]. For majoron masses as low as keV one has to be careful not to violate structure- − , 9 Majoron decay into two photons as mediated by loops of neutrinos 10 ) is therefore a reasonable guess for the decay rate. ) = x ( 1.4 Assuming a massive singlet majoron to make up all of DM, the main signature then comes With the relevant majoron couplings at our disposal, we can start to discuss phenomenology. g . The loop function f , effectively mixing f the Lagrangian to generate a majoron mass The other two-loop diagrams are moreent complicated parameters to (and calculate, in but particular importantly notEq. depend on ( on quark differ- masses) and thus cannot fully cancel the amplitude. simply be an explicitoperator mass or term an in axion-like therequired anomaly-induced scalar to potential. potential, generate a the Furthermore,obvious gravity-generated observed mechanism a higher-dimensional to abundance use production here in mechanism is theneutrinos is early [ Universe.formation With constraints small from couplings, the the Lyman- from its eventual decaylevel into is SM into particles. neutrino mass As eigenstates, discussed above, the only decay channel at tree First off, we are goingis to motivated by study the the fact caseand that of stable it the enough generically majoron to has as form tiny a couplings DM dark to [ matter the (DM) SM, candidate. ensuring that This it is dark 2. Majoron dark matter are required that make models [ Figure 1: non-trivial to calculate. Considering only the gauge-invariant subset of diagrams shown in Fig. Neutrino Lines from Majoron Dark Matter we can however obtain the simple expression [ where the sum is over all SMQ fermions PoS(NuFact2017)138 1 com- eV 0.1 ]. For sub- Julian Heeck in 12 . mass α to reconstruct the ν for an illustration. ordering + 0.01 2 , making them ne ). For higher masses, neutrino νν 3 inverted → ], but are of course less of → p e lightest J 13 ) shows that the quark cou- 0.001 ν component of the ﬂux, because remains as a promising indirect 1.3 Μ e Τ e Ν Ν Ν ν 4 γγ ] (see Fig. - 1 component of the ﬂux [ 10 →

0.50 0.20 0.10 0.05 0.02

Α J Ν per fraction decay Majoron ν are indeed all unavoidably induced at loop γγ , ¯ q q allows us to search for these neutrino lines with , 3 0 ¯ ` 1 ` νν decay into the different neutrino ﬂavors → → J J , the off-diagonal couplings can be approximately writ- J 0 ` -suppressed electron component; for inverted hierarchy, the m 13 eV 0.1 θ MeV. Above MeV, on the other hand, these experiments could in ∼ ` can still be derived from cosmology [ J m mass m νν ordering 0.01 MeV–100GeV region, one can indeed obtain strong constraints on the → ]. neutrino Branching ratios of J = normal 14 J , 8 m lightest 0.001 channel, making it impossible to directly compare these channels. In other words, Figure 2: Μ Τ e ]. For normal hierarchy, this implies only a small Ν Ν Ν 1 4 νν . In the - 10 →

]. For sub-MeV majoron masses, only the decay

0.02 0.10 0.05 0.50 0.20

Α Ν decay Majoron per fraction J 1 Majoron DM can thus be used to motivate neutrino line searches all the way down to MeV en- Going back to the majoron couplings to fermions of Eq. ( Knowing the flavor composition of matrix elements from the visible channels, without invalidating our conclusion about neutrino level in the singlet majoronof model. the However, they all depend on parameters that are independent plementary K lines [ the DM decay into visible channels probes different parameters than neutrino energy with good accuracy. Due toto the detect kinematic threshold neutrino of lines this below process it is not possible indeed be sensitive to a dark-matter induced neutrino flux [ ergies, far below what is typically considered.neutrino A fluxes natural are question to compatible ask withconstrained. here is As limits whether shown from above, observable the visible decays DM decay channels, which are far more 3. Lepton flavor violation the heaviest neutrino only has a tiny Super-K becomes most sensitive andMeV can masses, also limits utilize on the a smoking-gun signature for majoron DM. detection signature [ plings are diagonal atstrong one-loop lepton level, mass whereas hierarchy, the lepton couplings are not. Due to the rather majoron decays into the two heaviest neutrinos,flux; which in results the in quasi-degenerate roughly regime, 50% all electron flavors flavor are in equally the probable. See Fig. oscillate, so the flavor contenteigenstates of [ the monochromatic neutrino flux follows simply from the mass neutrino detectors. Borexino and KamLAND use inverse beta decay Neutrino Lines from Majoron Dark Matter PoS(NuFact2017)138 , . ) γ 0 → 3 ` − ` 10 → ( ` O Julian Heeck . | ` τ 2 K | , 10 5 −

SK , .

1 , assuming a quasi-degenerate invisible |

e ® µ νν

10 J K ]. Channels with more tagging |

→

Cosmology 16

J anisotropy

from

Μ Ν

Μ L Ν Μ 10 . Ν + Μ ]. atm GeV Ν 1 H , are also promising and can severely improve ) J 1 4 from DM decay e - Ν m f

10 e SK Ν visible

→

e KamLAND Ν J 2 ( 0 - `

. Current limits translate into

e 0 Borexino Ν ` 10 QD NH breaking scale → ν ` ` L ν 0 − ` or

γ h.c., which can induce the lepton-ﬂavor-violating two-body decays L H - → J 0 + ` 9 8 ` 0 10 15 14 13 12 11 10 ` L → 10 10

10 10 10 10 10 10 ¯

` ` , which has to be searched for on top of the continuous energy spectrum from Lower GeV f on limit 0 J ` 0 `` ]. We stress that lepton flavor violation with majorons depends on a different com- K 17 v ` 2 π Lower limit on the im 8 ]. If the majoron is massless or decays invisibly, the only signature of this decay is the 1 − , The singlet majoron model inherits some nice properties from the seesaw Lagrangian, namely 6 [ J 0 sensitivity [ potential, such as mono-energetic the SM decay channel bination of seesaw parameters than the more commonly studied heavy-neutrino induced small Majorana neutrino masses anddle. leptogenesis, while The providing loop-induced a majoron newparameters phenomenological couplings that han- to are impossible charged to particles determineple are from allow precisely the us given neutrino to mass by reconstruct matrix, the thetiny which seesaw without seesaw could with fine-tuning, in a low-energy princi- measurements. massive majoron Sincewith makes the signature for decay couplings a into can promising mono-energetic be unstable neutrinos, dark potentiallyWith matter detectable few candidate, for new parameters, energies above which MeV. are furthermoreare linked simple to the extensions seesaw of mechanism, the majoron Standard models Model that still provide rich phenomenology. 4. Conclusion Figure 3: ` with good prospects for improvement at Mu3e and Belle [ These channels are therefore complementary and should both be investigated. ten as Neutrino Lines from Majoron Dark Matter (solid) or normal-hierarchy neutrino spectrum (dashed) [ PoS(NuFact2017)138 , . , Phys. (1993) . , (2008) JHEP , , D49 , (2017) Julian Heeck B318 B665 D96 (2017) 102 (2017) 218–220 Phys. Rev. 05 , 1710.02062 , Phys. Lett. Phys. Lett. , (2016) 101–105 , Phys. Rev. ]. , JHEP 287-288 , B758 X-ray photons from late-decaying ]. 1606.02073 Phys. Lett. . , ,[ ]. . MC study for the lepton flavor violating tau Cold light dark matter in extended seesaw models ]. Are There Real Goldstone Bosons Associated with Nucl. Part. Phys. Proc. , 5 0805.2372 (2016) 036 ,[ A fresh look at linear cosmological constraints on a 13th Patras Workshop on Axions, WIMPs and WISPs, Planck scale symmetry breaking and majoron physics (1981) 265–268 ]. 1608 1709.07670 Sub-GeV dark matter as pseudo-Goldstone from the seesaw , in 1107.4564 ]. B98 hep-ph/9301213 ,[ JCAP ,[ (2008) 013 The KeV majoron as a dark matter particle , 2017, , ]. Neutrino Decay and Spontaneous Violation of Lepton Number Lepton Flavor Violation with Displaced Vertices Neutrino Lines from Majoron Dark Matter 0808 Determining seesaw parameters from weak scale measurements? Phys. Lett. ]. , Cold keV dark matter from decays and scatterings JCAP ]. (2011) 021026 . , hep-ph/9308258 Model-Independent Bound on the Dark Matter Lifetime ,[ (1993) 725–748 X1 hep-ph/0104076 ]. ]. . ,[ Astrophysical and terrestrial constraints on singlet Majoron models B403 hep-ph/9309214 Lepton flavor violation with light vector bosons Phenomenology of Majorons (1982) 774 1706.09909 ,[ 0712.1937 collaboration, T. Yoshinobu and K. Hayasaka, ,[ Phys. Rev. ,[ , D25 (2001) 013 ELLE 1602.03810 1701.07209 50–53 scale decay into a lepton and an undetectable particle [ 1709.07283 [ Thessaloniki, Greece, May 15-19 360–366 035018 Nucl. Phys. decaying dark matter component Broken Lepton Number? Rev. 09 (1994) 2398–2404 majoron dark matter I thank the NUFACT organizers for inviting me to this interesting and stimulating confer- [8] V. Berezinsky and J. W. F. Valle, [4] J. Schechter and J. W. F. Valle, [5] S. Davidson and A. Ibarra, [6] A. Pilaftsis, [7] I. Z. Rothstein, K. S. Babu and D. Seckel, [9] M. Frigerio, T. Hambye and E. Masso, [2] J. Heeck, [3] Y. Chikashige, R. N. Mohapatra and R. D. Peccei, [1] C. Garcia-Cely and J. Heeck, [17] J. Heeck and W. Rodejohann, [16]B [11] S. Boulebnane, J. Heeck, A. Nguyen and D. Teresi, [10] J. Heeck and D. Teresi, [12] S. Palomares-Ruiz, [13] V. Poulin, P. D. Serpico and J. Lesgourgues, [14] F. Bazzocchi, M. Lattanzi, S. Riemer-Sørensen and J. W. F. Valle, [15] J. Heeck, ence, as well as Camilo Garcia-Celysupported for by the collaboration F.R.S.-FNRS. on the work presented here. This work was References Neutrino Lines from Majoron Dark Matter Acknowledgments