Sterile Neutrinos S
LIGHT EXTENDED NEUTRINO SECTORS: FOUNDATIONS AND PHENOMENOLOGY
MINI-WORKSHOP ON NEUTRINO THEORY SEPTEMBER 22, 2O2O
BIBHUSHAN SHAKYA REFERENCES Neutrino masses and sterile neutrino dark matter from the PeV scale S. B. Roland, B. Shakya, J. D. Wells, 1412.4791
PeV neutrinos and a 3.5 keV X-ray line from a PeV scale supersymmetric neutrino sector S. B. Roland, B. Shakya, J. D. Wells, 1506.08195
Sterile neutrino dark matter from freeze-in B. Shakya, 1512.02751
Cosmological imprints of frozen-in light sterile neutrinos S. B. Roland, B. Shakya, 1609.06739
Sterile Neutrino Dark Matter with Supersymmetry B. Shakya, J. D. Wells, 1611.01517
Exotic Sterile Neutrinos and Pseudo-Goldstone Phenomenology B. Shakya, J. D. Wells, 1801.02640 …
2 PARAMETER SPACE FOR STERILE NEUTRINOS
from Roland, Shakya, Wells, 1412.4791 [hep-ph]
3 PARAMETER SPACE FOR STERILE NEUTRINOS
Sterile Neutrino Dark Matter: X-ray + Lyman-alpha rule out DM from Dodelson-Widrow (DW) production from Roland, Shakya, Wells, 1412.4791 [hep-ph] need alternate mechanism, e.g. freeze-in, that does not need active- Abazajian, 1705.01837 sterile mixing
4 PARAMETER SPACE FOR STERILE NEUTRINOS
Direct Searches rely on decay channels+lifetime dictated by active-sterile mixing from 1504.04855 5 NEED FOR “NEW” PHYSICS IN THE NEUTRINO SECTOR (WITH LIGHT STERILE NEUTRINOS)
“unnatural” parameters in the (sterile) neutrino sector:
• < GeV scale masses for sterile neutrinos
• tiny Yukawa couplings ( y < 10-7 )
• production of sterile neutrino DM beyond DW
Hints of an underlying structure?
additional structure? new particles? new symmetries? novel phenomenology?
6 Exotic Signals in the Sterile Neutrino Sector
Exotic SignalsPreliminary in notes the on Sterile the phenomenology Neutrino associated Sector with a light pseudo-Goldstone from a broken global U(1)0 (unrelated to lepton number) in the neutrino sector. Preliminary notes on the phenomenology associated with a light pseudo-Goldstone from a broken global U(1)0 (unrelated to lepton number) in the neutrino sector. MOTIVATION The U(1)B L is appealing but by no means the only Exotic Signals in the Sterile Neutrino Sector possibility. We consider instead a global symmetry U(1)0 Preliminary notes on the phenomenology associated with a light pseudo-Goldstone from a broken MOTIVATIONLight sterile neutrinos below the electroweakThe U(1)B scaleL is are appealingthat the butN byi (but no means none of the the only SM fields) are charged un- global U(1)0 (unrelated to lepton number) in the neutrino sector. well motivated by many argumentspossibility. (dark matter, We lepto- consider insteadder. This a global forbids symmetry the DiracU(1) as0 well as Majorana mass terms in the above equations. However, with an oppo- Light sterile neutrinosgenesis below the etc) electroweak and are being scale searched are that for the at aN varietyi (but none of of the SM fields) are charged un- MOTIVATION The U(1)B L is appealing but by no means the only experiments. The searches are performedder. This in the forbids tradi- the Diracsitely as charged well as Majorana, we can write mass down the higher dimen- well motivated by many arguments (dark matter, lepto- possibility. We consider instead a global symmetry U(1) tional decay channels induced by theterms mixing in of the the above active equations.sional operator However, with0 an oppo- genesis etc)Light and sterile are neutrinos being searched below the forelectroweak at a variety scale are of that the Ni (but none of the SM fields) are charged un- and sterile sectors as dictated by the seesaw mechanism. experiments.well motivated The searches by many are arguments performed (dark matter, in the lepto- tradi- der.sitely This charged forbids the , we Dirac can as write well as down Majorana the higher mass dimen-1 However, the natural mass scale oftermssional Majorana in theoperator above neutrinos equations. However, with an oppo- LhN (3) tional decaygenesis channels etc) and induced are being by searched the mixing for at of a the variety active of L ⇤ and sterileexperiments. sectors as The dictated searchesis at the by are UVthe performed seesaw cuto↵ scale in mechanism. the (GUT tradi- or Planck),sitely charged so if they, we can are write down the higher dimen- sional operator 1 However,tional the decay natural channels masslight, induced scale this by of is the Majorana indicative mixing of neutrinos the of active some deeper structure in the which,LhN once gets a vev, reproduces(3) the Dirac mass term. and sterile sectors as dictated by the seesaw mechanism. sterile neutrino sectors, such as some protecting symme- 1L Here⇤ ⇤ is some UV-cuto↵ scale. To keep things general, is at theHowever, UV cuto the↵ naturalscale (GUT mass scale or Planck), of Majorana so if neutrinos they are LhN (3) try that keeps their masses at a low scale. This structure ⇤ light, thisis at is the indicative UV cuto↵ scale of some (GUT deeper or Planck), structure so if they in are the which, once getsL a vev,we reproduces do not explicitly the Dirac write mass down term. a term that gives rise to sterile neutrinolight, this sectors, is indicative suchcan of also as some some give deeper protecting rise structure to other symme- in light the degreeswhich,Here of once⇤ freedomis somegets a in vev, UV-cuto the reproduces↵thescale. Majorana the Dirac To keep mass mass things term. term, general, and take the sterile neutrino try thatsterile keeps neutrino their masses sectors,neutrino at such a low as sector, some scale. protecting and This consequently structure symme- newHerewe decay⇤ dois not some channels explicitly UV-cuto for↵ writescale.mass down To keepM ato things term be that general, a free gives parameter rise to instead. Spontaneous can alsotry give that rise keeps to their other massessterile light at neutrinos, degrees a low scale. of whichfreedom This structure can in completely the we do change not explicitly their write phe- downbreaking a term that of the givesU rise(1)0 towith gives rise to a light pseudo- the Majorana mass term, and take the sterile neutrinoh i neutrinocan sector, also give and rise consequently to othernomenology. light new degrees We decay of would freedom channels like in theto for studythemass this Majorana possibility.M to mass be a term, free and parameterGoldstone take the sterile instead.⇢, which neutrino Spontaneous inherits the couplings of ; its mass neutrino sector, and consequently new decay channels for mass M to be a free parameter instead. Spontaneous sterile neutrinos, which canMotivate completely from change hidden their sectors. phe- Even if GUT scale see- depends on details of the underlying model (explicit soft sterile neutrinos, which can completely change their phe- breakingbreaking of the ofU the(1)Uwith(1)0 with gives risegives to a rise light to pseudo- a light pseudo- saw, if neutrino-like fields in hidden sectors exist,0 inte- term,h i or from quantum gravity), but for generality we nomenology.nomenology. We would We would like like to study to study this this possibility. possibility. GoldstoneGoldstone⇢, which⇢, which inherits inheritsh i the couplings the couplings of ; its mass of ; its mass grating out the GUT scale neutrinos generates a low en- MotivateWHYMotivate fromARE hidden from STERILE hidden sectors. sectors. Even NEUTRINOS Even if if GUT GUT scale scale see- see- LIGHT?dependsdepends on details on details of the of underlying thealso underlying take model this (explicit model mass soft (explicitm⇢ to be soft a free parameter. saw, ifsaw, neutrino-like if neutrino-like fieldsergy fields in e hidden in↵ective hidden sectors seesaw! sectors exist, exist, Plausible inte- inte- toterm, haveterm, additionalor or from from quantum struc- quantum gravity), gravity), but for but generality for generality we we grating out the GUTture scale there. neutrinos generates a low en- also take this mass m to be a free parameter. grating out the GUT scale neutrinos generates a low en- also take this mass⇢ m⇢ to be a free parameter. ergy e↵ergyective e↵ective seesaw! seesaw! Plausible Plausible to to have have additional additional struc- struc- PHENOMENOLOGY Whyture there. are the active (Standard Model) neutrinos light? ture there. PHENOMENOLOGY FRAMEWORK PHENOMENOLOGYThe phenomenology depends on four free parame- 1. symmetry protectionFRAMEWORK The phenomenology dependsters: on four , ⇤ free,m parame-⇢,M (other phenomenologically relevant FRAMEWORKThe operators traditionally associated with right- h i 2. mass partner is a singlet ters:The , ⇤ phenomenology,m⇢,M (other phenomenologically dependsparameters on are four relevantm freeand parame- its mixing with the SM Higgs, The operators traditionallyhanded, sterile associated neutrinos with right- are theparameters Dirach i and are Majoranam and its mixing with the SM Higgs, ters: , ⇤,m ⇢,M (otherbut phenomenologically these are only tangentially relevant relevant to neutrino phe- handed, sterile neutrinos are the Dirac and Majorana but theseh arei only tangentially relevant to neutrino phe- The operators traditionallymasses:y associated with right- parameters are m andnomenology its mixing with and wethe ignore SM Higgs, these for now). masses: ν
Exotic SignalsPreliminary in notes the on Sterile the phenomenology Neutrino associated Sector with a light pseudo-Goldstone from a broken global U(1)0 (unrelated to lepton number) in the neutrino sector. Preliminary notes on the phenomenology associated with a light pseudo-Goldstone from a broken global U(1)0 (unrelated to lepton number) in the neutrino sector. MOTIVATION The U(1)B L is appealing but by no means the only possibility. We consider instead a global symmetry U(1)0
Exotic Signals inMOTIVATION the SterileLight sterile Neutrino neutrinos Sector below the electroweakThe U(1)B scaleL is are appealingthat the butN byi (but no means none of the the only SM fields) are charged un- well motivated by many argumentspossibility. (dark matter, We lepto- consider insteadder. This a global forbids symmetry the DiracU(1) as0 well as Majorana mass Preliminary notes on the phenomenology associated with a light pseudo-Goldstone from a broken terms in the above equations. However, with an oppo- global U(1)0 (unrelatedLight to lepton sterile number) neutrinos in thegenesis below neutrino the etc) sector. electroweak and are being scale searched are that for the at aN varietyi (but none of of the SM fields) are charged un- well motivated by manyexperiments. arguments (dark The matter, searches lepto- are performedder. This in the forbids tradi- the Diracsitely as charged well as Majorana, we can write mass down the higher dimen- genesis etc) and are beingtional searched decay channels for at a induced variety ofby theterms mixing in of the the above active equations.sional operator However, with an oppo- MOTIVATION The U(1)B L is appealing but by no means the only and sterile sectors as dictated by thesitely seesaw charged mechanism. , we can write down the higher dimen- experiments. The searchespossibility. are performed We consider in the instead tradi- a global symmetry U(1)0 1 However, the natural mass scale ofsional Majorana operator neutrinos LhN (3) Light sterile neutrinos belowtional the decay electroweak channels scale inducedare that by the theN mixingi (but none of the of the active SM fields) are charged un- L ⇤ well motivated by many argumentsand sterile (dark sectors matter, as lepto- dictatedis atder. the by This UVthe forbidsseesaw cuto↵ scale the mechanism. Dirac (GUT as well or Planck), as Majorana so if mass they are 1 genesis etc) and are beingHowever, searched for the at naturala variety mass of light,terms scale this in of is the Majorana indicative above equations. neutrinos of some However, deeper with structure an oppo- in the which,LhN once gets a vev, reproduces(3) the Dirac mass term. sitely charged , we can write down the higher dimen- ⇤ experiments. The searchesis are at performed the UV cuto in the↵ scale tradi- sterile (GUT neutrino or Planck), sectors, so if they such are as some protecting symme- L Here ⇤ is some UV-cuto↵ scale. To keep things general, sional operator tional decay channels inducedlight, by the this mixing is indicative of the active oftry some that deeper keeps their structure masses in at the a low scale. This structure we do not explicitly write down a term that gives rise to and sterile sectors as dictated by the seesaw mechanism. which, once gets a vev, reproduces the Dirac mass term. can also give rise to other1 light degrees of freedom in the the Majorana mass term, and take the sterile neutrino However, the natural masssterile scale of neutrino Majorana sectors, neutrinos such as some protecting symme-LhN Here ⇤ is some(3) UV-cuto↵ scale. To keep things general, ⇤ is at the UV cuto↵ scale (GUTtry or that Planck), keeps so their if they masses are neutrino at a low sector, scale. and This consequentlyL structure newwe decay do not channels explicitly for writemass downM ato term be that a free gives parameter rise to instead. Spontaneous light, this is indicative of somecan alsodeeper give structure rise to in other the sterile light neutrinos, degrees of whichfreedom can in completely the change their phe- breaking of the U(1)0 with gives rise to a light pseudo- which, once gets a vev, reproduces thethe Dirac Majorana mass term. mass term, and take the sterile neutrinoh i sterile neutrino sectors, suchneutrino as some protecting sector, and symme- consequentlynomenology.Here ⇤ newis some We decay UV-cuto would channels like↵ scale. to for study To keepmass this things possibility.M general,to be a free parameterGoldstone instead.⇢, which Spontaneous inherits the couplings of ; its mass try that keeps their masses at a low scale. This structure Motivatewe do not from explicitly hidden write sectors. down a term Even that if GUT gives rise scale to see- sterile neutrinos, which can completely change their phe- breaking of the U(1)0 withdepends gives on rise details to a lightof the pseudo- underlying model (explicit soft can also give rise to other light degrees of freedom in the nomenology. We would likesaw,the to if study Majorana neutrino-like this mass possibility. term, fields and in hidden take theGoldstone sectors sterile neutrino exist,⇢, which inte- inheritsterm,h i the or couplings from quantum of ; its gravity), mass but for generality we neutrino sector, and consequently new decay channels for gratingmass outM to the be GUT a free scale parameter neutrinos instead. generates Spontaneous a low en- also take this mass m to be a free parameter. sterile neutrinos, which can completelyMotivate change from their hidden phe- sectors.breaking Even of the ifU GUT(1) with scale see-gives risedepends to a light on pseudo- details of the underlying model (explicit⇢ soft ergy e↵ective seesaw!0 Plausible to have additional struc- nomenology. We would likesaw, to study if neutrino-like this possibility. fields inGoldstone hidden⇢ sectors, which inherits exist,h inte-i the couplingsterm, of or; its from mass quantum gravity), but for generality we ture there. WHYMotivate ARE from STERILE hidden sectors.grating NEUTRINOS Even out if GUT the GUT scale see- scale LIGHT? neutrinosdepends on generates details of the a low underlying en- modelalso take (explicit this soft mass m⇢ to be a free parameter. saw, if neutrino-like fields inergy hidden e↵ective sectors seesaw! exist, inte- Plausibleterm, to or have from additional quantum gravity), struc- but for generality we PHENOMENOLOGY grating out the GUT scale neutrinosture there. generates a low en- also take this mass m⇢ to be a free parameter. ergy e↵ective seesaw! Plausible to have additional struc- FRAMEWORK PHENOMENOLOGYThe phenomenology depends on four free parame- Whatture if there. the same thing happens with a “sterile neutrino” ν’ ? ters: , ⇤,m ,M (other phenomenologically relevant PHENOMENOLOGY h i ⇢ FRAMEWORKThe operators traditionally associatedThe phenomenology with right- dependsparameters on are fourm freeand parame- its mixing with the SM Higgs, FRAMEWORK ν’ charged under somehanded, additional sterile neutrinos are the Dirac and Majorana The phenomenology depends on fourters: free parame-, ⇤,m⇢,M (otherbut phenomenologically these are only tangentially relevant relevant to neutrino phe- symmetry (U(1)’), masses:broken by the h i The operators traditionallyters: associated , ⇤,m⇢,M with(other right- phenomenologicallyparameters relevant are m andnomenology its mixing with and wethe ignore SM Higgs, these for now). The operators traditionally associatedvev with of an right- exotic higgsparameters φ h i are m and its mixing with the SM Higgs, handed, sterile neutrinos are the Dirac and Majorana ¯butc these are only tangentiallyIf m⇢ relevant Preliminary notes on the phenomenology associated with a light pseudo-Goldstone from a broken global U(1)0 (unrelated to lepton number) in the neutrino sector. MOTIVATION The U(1)B L is appealing but by no means the only possibility. We consider instead a global symmetry U(1)0 Light sterile neutrinos below the electroweak scale are that the Ni (but none of the SM fields) are charged un- well motivated by many arguments (dark matter, lepto- der. This forbids the Dirac as well as Majorana mass genesis etc) and are being searched for at a variety of terms in the above equations. However, with an oppo- experiments. The searches are performed in the tradi- sitely charged , we can write down the higher dimen- tional decay channels induced by the mixing of the active sional operator and sterile sectors as dictated by the seesaw mechanism. 1 However, the natural mass scale of Majorana neutrinos LhN (3) ⇤ is at the UV cuto↵ scale (GUT or Planck), so if they are L light, this is indicative of some deeper structure in the which, once gets a vev, reproduces the Dirac mass term. sterile neutrino sectors, such as some protecting symme- Here ⇤ is some UV-cuto↵ scale. To keep things general, try that keeps their masses at a low scale. This structure we do not explicitly write down a term that gives rise to can also give rise to other light degrees of freedom in the the Majorana mass term, and take the sterile neutrino neutrino sector, and consequently new decay channels for mass M to be a free parameter instead. Spontaneous sterile neutrinos, which can completely change their phe- breaking of the U(1)0 with gives rise to a light pseudo- nomenology. We would like to study this possibility. Goldstone ⇢, which inheritsh i the couplings of ; its mass Motivate from hidden sectors. Even if GUT scale see- depends on details of the underlying model (explicit soft saw, ifHEAVY neutrino-like NEUTRINO fields in hidden sectors PORTAL exist, inte- term, or from quantum gravity), but for generality we grating out the GUT scale neutrinos generates a low en- also take this mass m⇢ to be a free parameter. ergy e↵ectiveTO seesaw! A HIDDEN Plausible to have SECTOR additional struc- ture there. PHENOMENOLOGY FRAMEWORK The phenomenology depends on four free parame- ters: , ⇤,m ,M (other phenomenologically relevant h i ⇢ The operators traditionally associated with right- parameters are m and its mixing with the SM Higgs, handed, sterile neutrinos are the Dirac and Majorana but these are only tangentially relevant to neutrino phe- y y’ masses: ν neutrino sector extended with additional symmetries, particles: refer to these as N from hereon • sterile neutrinos (exotic fermions in a in particular: hidden sector, light because masses suppressed by N1=dark matter? the seesaw mechanism) • higgs boson (responsible for breaking the symmetry the sterile neutrinos are charged under) • Goldstone boson (if symmetry is global) • gauge boson(s) (if gauge symmetry) Do these lead to interesting physics? 10 WHAT IS THE SCALE OF U(1)’ BREAKING? m ν′ M ⟨ϕ⟩ Motivation Split keV-GeV GUT scale 100 TeV- 100 PeV Supersymmetry eV GUT scale few hundred GeV twin Higgs dark few hundred GeV keV-GeV 10^10 GeV matter+collider -TeV signatures + more… 11 2 3 6 1000 PeV are charged under a U(1)0, which are ubiquitous in string- 10 inspired modelsdark of nature. matter This abundance immediately is forbids consistent the with all existing con- 105 -5 terms in Eq. 2, and the traditional seesaw mechanism 10 straints [33]. W 3 does not work. Higher dimensional operators involving 104 n > W100 PeV t Resonant production: The presence of a lepton chem- DM = L W the SM and N fields can be obtained by coupling the N -10 n ÊÁ i i 3 10 > 10 -3 BBN ÊÁ‡· dark matter abundance is consistent with all existing con-10 - ÊÁ‡· ical potential in the plasma can lead tokeV resonantly5 am- to other fields charged under the U(1)0.Weintroduce H 10 straints [33]. s X 3 m 2 plified production of N1 [34], producing10 a colder non-Wn 10 PeV - an exotic field that carries the opposite charge under > W t Ray Resonant production: The presence of a lepton chem- DM -15 U(1) . -10 W ÊÁ 10 = 0 n q thermal distribution that can help evade1 the10 Lyman-> 10 -3 BBN ÊÁ‡· t ical potential in the plasmadark matter can abundance lead to resonantly is consistent witham-10 all existing con- -5 2 ÊÁ‡· = As motivated in the previous section, we are interested 10 Today alpha bounds,straints [33]. thereby accounting for all of dark mat- X plified production of N [34], producing a colder non- sin W - in a supersymmetric framework,1 motivated by a possible 1 n > W-20Ray 1 PeV t Resonant production: The presence of a lepton chem--15 10 DM = ter. This, however, requires fine-tuning of the10 order of -10 Wn ÊÁ thermal distribution that can help evade the Lyman- q 100 TeV> BBN common origin of the supersymmetry breaking scale and 10 10 -3 t ÊÁ‡·ÊÁ 11ical potential in the plasma can lead to resonantly2 am- = ‡· -3 -2 -1 Today thealpha mass scale bounds, that1 in thereby sets 10 thein accounting neutrino the mass masses for di↵ all (however,erence of dark between mat- 10 the two heav-10 10 X 1 plified production of N1 [34], producing a coldersin non- - -20 -15 -25 Ray thister. connection This, however,ier to supersymmetry sterile requires neutrinos fine-tuning is by in no order means of to the nec- generate order of the large10 lepton 10 ma eV 10 thermal distribution that can help evade the Lyman- q t 11 2 = essary).1 in We 10 thusinasymmetry the introduce massalpha di three↵ througherence bounds, chiral between therebyCP-violating supermultiplets accounting the two oscillations heav- for all of dark [35, mat- 36]. Today FIG. 1: Active-25 and sterilesin 10 neutrino-20 mass scales for various i forier the sterile sterile neutrinos neutrinos inter. and order aThis, chiral to however, generate supermultiplet requires the large fine-tuning , lepton of the order10 of H L -30 0 ‡· N DARK MATTER FREEZE-IN11 ˜ choices of y ,withM = MGUT10,tan =2(Hu = whoseasymmetry spin (0, 1/ through2)If components the CP-violating1 scalar in 10 are labelledinhas the oscillations mass additional (Ni,N di↵ierence) [35, and 36]. interactionsbetween the twoh (with heav-i the⇤ -3 -h2 i -1 1 2 3 155.6GeV),and0.001 1 Such operators have been studied in the context of supersymme- try [28–32], including the freeze-in production of sterile neutrino DM [33–35]. 4 This setup holds similarities with extended seesaw models [44– 2 For recent studies of right-handed neutrinos acting as portals to 48], which also employ a seesaw suppression for sterile neutrino ahidden/darksector,see[36–43]. masses to naturally accommodate an eV scale sterile neutrino. 3 5 We assume that the Ni sector is su ciently extended and general An explicit U(1)0 breaking Goldstone mass term is also possible. that one cannot rotate the L, L0 system to suppress couplings of Asmall⌘ mass is also generated from the Yukawa coupling [51], any particular L, L0 to the Ni sector. but is negligible for the parameters we are interested in. 4 FIG. 2: Parameter space with cold, warm, and hot dark mat- ter (black, blue, and red regions respectively). For all points 2 11 FIG. 4: Ne↵ for di↵erent N1 and N˜1 masses. Red, green, in the plot, ⌦h =0.12, m =10 GeV, A /m =10. blue, and black points denote Ne↵ in the ranges > 0.3, 0.1 0.3, 0.01 0.1, and < 0.01 respectively. For all points, N˜1 decays account for 1% of the dark matter abundance, while decays produce the rest of dark matter. green, blue, and black points represent Ne↵ in the ranges > 0.3, 0.1 0.3, 0.01 0.1, and < 0.01 respec- tively. Large contributions to Ne↵ comparable to cur- rent bounds are found to be possible while satisfying all the enforced constraints. The largest values are realized 9 12 for mN 0.01 1 MeV and m ˜ 10 10 GeV: for 1 ⇠ N1 ⇠ lighter N˜1 or heavier N1, the dark matter particles are not su ciently relativistic at BBN, whereas heavier N˜1 (which forces to be heavier) or lighter N1 both require FIG. 3: Cold, warm, hot dark matter (black, blue, and red larger x to maintain the correct dark matter abundance 6 regions respectively) for m =1MeVandm =10 GeV. (see Eq.6), which reduces the lifetime of N˜1. N1 N˜1 We emphasize that Figures 2, 3, and 4 are based on specific assumptions and values of parameters, and the more energetic, resulting in larger free streaming lengths. various regions in these plots can shift around as they are It should be clarified that regions where the full dark varied (such as having freeze in instead of maintaining matter relic density can be achieved extend beyond the equilibrium, a di↵erent mass hierarchy, or allowing rela- boundariesIMPRINTS of this plot. OF The HEAVY demarcation ofSTATES cold, warm, tivistic N1 to form more or less than 1% of dark matter.) and hot regions depends not only onB.m Shakya,and J. Wells,m 1611.01517but [hep-ph] N˜1 N1 • e.g.also in SUSY, on the sterile other neutrino parameters DM has (in a heavy particular, superpartner: the ones sterile that sneutrino • sterile sneutrinodetermine decaysN˜ 1mustlifetime); produce thisDM (effective point is Z_2 illustrated stabilizing in DM): Fig. 3,secondary DM DISCUSSION where we show that allproduction three possibilities mechanism can be realized • the twofor populations the same don't choice talk ofto meach other!and m [Freeze-in:(fixed DM to never 106 GeV “thermalizes”] N˜1 N1 In this paper, we have demonstrated that a supersym- • second population is hotter (sterile sneutrino is long-lived and decays out of equilibrium) and 1 MeV respectively) by varying m and A . metric extension of the widely studied sterile neutrino • single species mimics cold+hot DM setup Dark radiation: Next, we consider scenarios where dark matter framework with the basic features of dark extremely energetic N1 can contribute to Ne↵ dur- matter freeze-in, namely an underlying symmetry that ing BBN. Here we choose m 13 2 1 2 A vev for the exotic Higgs field , appropriately charged where we have defined ⇤e ↵ y /M , ye↵ yy0v0/M , and 2 2 ⌘ ⌘ under the lepton or B L symmetry, breaks the sym- Me↵ y0 v0 /M . Here, the first term accounts for the metry and produces sterile neutrino masses M x . 2 active⌘ neutrino masses y2v2/M from the primary seesaw i ⇠ h i If the symmetry is global, a physical light degree of involving integrating out the pure singlet neutrinos Ni. 1 2 A vev for the exotic Higgs field , appropriately chargedfreedom,where the Goldstonewe have defined boson,⇤e ↵ knowny /M as, ye the↵ majoron,yy0v0/M , and The latter two terms give a similar contribution to the ac- 2 2 ⌘ ⌘ under the lepton or B L symmetry, breaks the sym-emergesM [15,e↵ 16].y0 v0 /M . Here, the first term accounts for the tive neutrino masses from the secondary seesaw resulting metry and produces sterile neutrino masses M x . active⌘ neutrino masses y2v2/M from the primary seesaw i from integrating out the L fermions (note the analogy 3 If the symmetry is global, a physical light degree⇠ h In ofi thisinvolving paper, we integrating consider out instead the pure a global singlet symmetry, neutrinos N . i0 i between Eq. 4 and Eq. 1). freedom, the Goldstone boson, known as the majoron,for instanceThe lattera U(1) two0, that terms is give confined a similar to the contribution sterile neutri- to the ac- into (both active and sterile) neutrinos. For instance, emerges [15, 16]. nos andtive does neutrino not extend masses to from any SM the secondaryfield. Such seesaw a symme- resulting The mixing angle between the active neutrinos and 20 Age of Universe try forbids both terms in Eq. 1. However, a scalar field these hidden sector singlets L0 is approximately In this paper, we consider instead a global symmetry, from integrating out the Li0 fermions (note the analogy 2 carrying the opposite U(1) charge to N enables the 1 m⌫ for instance a U(1)0, that is confined to the sterile neutri- between Eq. 4 and Eq. 1).100 i f=109 GeV (⌘ ⌫⌫) m , (6) L 1 ye↵ v yv ma ⌘ s nos and does not extend to any SM field. Such a symme-higher dimensionalThe mixing operator angleê between⇤ LhN the,where active⇤ neutrinosis a UV- and sin ✓0 = = ! , ⇡ 8⇡ (5)f t ✓ ◆ 1 H ⇠ Me↵ y0v0 Me↵ these hidden sector singlets L0 is approximately try forbids both terms in Eq. 1. However, a scalarcuto field↵ scale. A vev breaks10 0 the U(1)0 and produces r BBN where m 0.1 eV is the active neutrino mass scale. For carrying the opposite U(1)0 charge to Ni enablesthe the Yukawa interaction term from Eq. 1 with the e↵ec- ⌫ Log 3 which is the relation expected from a seesaw framework. 1 ye↵ v yv ma f=10 GeV ⇠ higher dimensional operator LhN ,where⇤ is a UV- sin ✓0 -10 = = , (5) the decay channels ⌘ Ni⌫ and ⌘ NiNi involving ⇤ tive Yukawa coupling y 1 /⇤; thus such an operator Therefore, light sterile neutrinos that appear! to satisfy ! 1 ⇠⇠ Mh e↵i y0v0 Me↵ the sterile neutrinos, m is replaced by m m and cuto↵ scale. A vev breaks the U(1)0 and producesalso provides a natural explanation for ther tiny Yukawas the seesaw relation could have exotic origins⌫ in a hid- p Ni ⌫ the Yukawa interaction term from Eq. 1 with the e↵ec- -20 m respectively. Fig.1 shows the ⌘ lifetime as a func- in termswhich of the is hierarchy the relation between expected the from two a scales seesaw framework.and den sector connected viaNi a high scale neutrino portal, tive Yukawa coupling y 1 /⇤; thus such an operator Therefore, light sterile neutrinos0 2 that appear4 h i to6 satisfy8 10 12 tion of m ,withM = 1 GeV and M = 7 keV, ⇠ h i ⇤. Next, we discuss a UV completion of this setup in with symmetries unrelated to⌘ the SM, andN2,N3 themselves N1 also provides a natural explanation for the tiny Yukawas the seesaw relation could have exotic originsLog inm aeV hid- for two di↵erent values of f. Depending on the scale f terms of singlet fermions from a hidden sector that10 cou-h obtain light masses via the seesaw mechanism. 4 We will in terms of the hierarchy between the two scales and den sector connected via a high scale neutrino portal, h iple to heavy right-handed seesaw neutrinos. henceforth ignore theand integrated the available out “true” decay right-handed channels, a range of interesting ⇤. Next, we discuss a UV completion of this setup in with symmetries unrelated to the SM, and themselves FIG. 1: Contours of lifetime Log (⌧ /s)withM = lifetimes are possible: ⌘ can decay before or after BBN terms of singlet fermions from a hidden sector that cou- obtain light masses via the seesaw mechanism. H4 Weê 10 willL ⌘ seesaw neutrinosN2,3 and work with the e↵ective field the- 1GeV, M = 7 keV for f =109 GeV (blue solid) and (and before/after Cosmic Microwave Background (CMB) ple to heavy right-handed seesaw neutrinos. henceforth ignore the integratedN1 out “true” right-handed ory (EFT) in Eq. 4, switching the notation Ni to refer f =103 GeV (red dotted). The horizontal lines represent decoupling), or live longer than the age of the Universe, “Sterileseesaw neutrinos” neutrinos from and work a hidden with the sector e↵ective with field a the- to these light sterile states L0, whose phenomenology we the age of the Universe (top) and the time of BBN (bottom). providing a potential DM candidate (for studies of ma- oryheavy (EFT) right-handed in Eq. 4, switching neutrino the portal notation N to refer will pursue in this paper. i joron DM, see [48, 49, 51, 58–63]). to these light sterile states L0, whose phenomenology+ GOLDSTONE we “Sterile neutrinos” from a hidden sector with a B. Shakya, J. Wells, 1801.02640 [hep-ph] will pursue in this paper. A pseudo-Goldstone coupling to neutrinos faces several heavy right-handed neutrino portal We start with the original seesaw motivation of pure much lighter that the sterile neutrinos. Furthermore, thisPseudo-Goldstoneconstraints [64–68]. Boson However, many of these constraints singlet, heavy (scale M, possiblyBroken close global to the symmetry GUT -> massless Goldstone η. scaling leads to specific relations between majoron cou- weaken/become inapplicable if the pseudo-Goldstone is We start with the original seesaw motivation of purescale) right-handed neutrinosPseudo-GoldstoneNot that the couple Majoron! Boson to SM The neutri- symmetry broken is not leptonheavy number… or can decay into sterile neutrinos. We remark singlet, heavy (scale M, possibly close to the GUT plings and sterile neutrino masses, which drivesThe spontaneous many of breaking of the global U(1)0 by nos through Yukawa terms yijLihNj.IftheNj also act that these constraints are generallyh i⌘ not very stringent in scale) right-handed neutrinos that couple to SM neutri- thecoupled constraints 2to neutrinos on majorons (both active [11, and 19, 52–55].sterile)f gives with rise strength to a massless proportional Goldstone to the boson, which we will as portalsThe to a spontaneous hidden sector breaking, this of the invokesneutrino global theU (1)masses generic0 by (similar to the Majoron) the parameter space of interest in our framework. nos through Yukawa terms yijLihNj.IftheNj also act In contrast, these energy scalesh arei⌘call distinct the ⌘ in-boson. the ⌘ It is conjectured that non-perturbative 2 prospectf ofgives an riseanalogous to a massless Yukawa Goldstone term yij0 boson,Li0 h0N whichj,where we will Cosmology: In the early Universe, GeV scale sterile as portals to a hidden sector , this invokes the generic framework: the symmetry breaking scalegravitationalf (i.e., the scale e↵ects explicitly break global symmetries, Li0 h0 is acall singlet the ⌘ combination-boson.explicit It is conjecturedbreaking of hidden of sector thatglobal non-perturbative fields symmetry anal- from nonperturbative gravitationalneutrinos effects:N (but not the DM2 candidate N ,which prospect of an analogous Yukawa term yij0 Li0 h0Nj,where leading to a pseudo-Goldstone boson2,3 mass of order m 1 gravitational eof↵ectsU(1) explicitly0 breaking) break is independent global symmetries, of the breaking of lep- ⌘ ogous to Lih. Integrating out the Ni produces the fol- 5 ⇠ Li0 h0 is a singlet combination of hidden sector fields anal- 2 3 has suppressed couplings to neutrinos)5 are in equilibrium leading to a pseudo-Goldstoneton number (at boson the mass much of higher order m realf seesaw/MPl scalevia anM operator) of the form [49, 50]. For lowing dimension-5 operators connecting the visible and ⌘ MPl ogous to Lih. Integrating out the Ni produces the fol- 5 ⇠ with the thermal bath due to their mixing with active 3 3 and is also distinct from the sterile5 neutrino mass scale hidden sectorsf /MPl via: an operator of the form [49, 50]. For generality, we treat m⌘ as a free parameter, but this ap- lowing dimension-5 operators connecting the visible and 2 MPl a pseudo-Goldstone boson neutrinos, decouple while relativistic at T 20 GeV [27], 3 (Me↵ f /M ), which, as discussed above,proximate is suppressed mass scale should be kept in mind. ⇠ hidden sectors : generality, we treat m⇠⌘ as a free parameter, but this ap- can grow to dominate the energy density of the Universe, 1proximate2 2 massRecall1by scale a seesawthat should “sterile mechanism. be kept neutrinos”1 in2 mind. The themselves2 ability toareNext, vary light them we(m~ draw f2 in-/M) the because distinction of a seesaw between the ⌘-boson and y (Lh) + yy0(Lh)(L0h0)+ y0 (L0h0) . (3) and decay before BBN [27, 69, 70]. 1 2 2 1 1 2 2 L M Next, we drawMdependently the distinction opens betweenM up phenomenologically the ⌘-bosonmechanism and the interesting more familiar re- majoron [15–21]. For both, couplings y (Lh) + yy0(Lh)(L0h0)+ y0 (L0h0) . (3) ⌘ couples appreciably only to the sterile neutrinos, and L M M M the more familiargions majoron of parameter [15–21]. space. For both, Furthermore, couplings to the (both sterile active neu- and sterile) neutrinos are proportional to In the above we have ignoredPseudo-Golstone flavor structure 2and sterile and neutrinos at the same massis producedscale if via sterile neutrino annihilation NiNi ⌘⌘ to (both activetrino and sterile) masses neutrinosMe↵ aref /M proportionalcan be to comparablethe neutrino to mass the suppressed by the scale of symmetry ! In the above we have ignored flavor structure and ⇠ (see Fig.2 (a)) or decay (if kinematically open). The an- droppedthe indices neutrino for mass simplicity,⌘-boson suppressed mass assumingm by2 thef all3 scale/Myij( ofy(ifij symmetry)f are M 2 /M ); this coin- dropped indices for simplicity, assuming all y (y ) are ⌘ Pl breaking,Pl as expectednihilation for Goldstone process, bosons, despite hencep-wave sev- suppression, is e cient ij ij roughlybreaking, the same, as so expectedcidence that the for of above mass Goldstone scales terms⇠ bosons, can should carry hence only important⇠ sev- implications roughly the same, so that the above terms should only eral phenomenological bounds on the majoron symmetry interesting for cosmology? at high temperatures T & mN2,3 . The magnitude of f for be takeneral as phenomenological approximate.for cosmology If the bounds hidden and on the DM, sector majoron as scalar we symmetry will ac- see later.breaking scale [11, 19, 52–55] are also applicable to ⌘. be taken as approximate. If the hidden sector scalar ac- breaking scale [11, 19, 52–55] are also applicable to ⌘. such annihilations to be rapid can be estimated by com- quires a vev v0, the above can be rewritten as However, the majoron is associated with the breaking of quires a vev v0, the above can be rewritten as However, the majoron is associated with the breaking of paring the annihilation cross section [71, 72] with the lepton number — a symmetry shared by the SM leptons lepton number — a symmetryHubble rate shared at T bym the SM leptons 1 2 N2,3 1 2 (Lh) + y LhL0 + M L0L0 (4) as well as the sterile neutrinos — and the⇠ sterile neutrino (Lh) + ye↵LhL0 + Me↵L0L0 (4) as well as the sterile neutrinose↵ — ande↵ the sterile neutrino14 ⇤ L ⇤e↵ FRAMEWORK AND PHENOMENOLOGY L e↵ mass scale approximately coincides with the scale of lep- mass scale approximately coincides withm4 the scale ofm lep-2 n v H Ni m Ni f m3/4M 1/4. ton number breaking. This results in the majoron being ton number breaking. ThisNi results in the4 majoronNi being Ni Pl ⇠ ) f ⇠ MPl ) ⇠ We focus on the low-energy e↵ective theory containing (7) 1 Such operators have been studied in the context of supersymme-1 Such operators have beenthree studied sterile in the neutrinos context of (which supersymme- we have reset to the la- 5 For mN2,3 GeV, this process is e cient for f . 10 try [28–32], including the freeze-in production of sterile neutrinotry [28–32], including the freeze-in production of sterile neutrino ⇠ 4 bel Ni rather than L0), and the pseudo-Goldstone boson GeV, and produces an ⌘ abundance comparable to the DM [33–35]. DM [33–35].This setup holds similarities with extended seesaw models [44– 4 This setup holds similarities with extended seesaw models [44– 2 ⌘. We treat m ,f, and m as independent parameters. 5 For recent studies of right-handed neutrinos acting as portals2 For to recent48], studies which of also right-handed employ a seesaw neutrinos suppressionNi acting for as sterile⌘portals neutrino to 48], which also employN a2, seesaw3 abundance. suppression For forf> sterile10 neutrinoGeV, the annihilation pro- ahidden/darksector,see[36–43]. masses to naturallyWe assume accommodatemNi an eVGeV scale sterile scale, neutrino. and yij are correspond- 3 ahidden/darksector,see[36–43].5 masses to naturally accommodatecess is feeble, an eV and scale a small sterile neutrino.⌘ abundance will accumulate We assume that the Ni sector is su ciently extended and general3 An explicit U(1)0 breaking Goldstone⇠ mass term is also possible. 5 We assume that the Niinglysector small is su ciently in a natural extended way and that general matchesAn the explicit measuredU(1)0 breakingvia the Goldstone freeze-in mass process term is also instead possible. [73, 74]. that one cannot rotate the L, L0 system to suppress couplings of Asmall⌘ mass is also generated from the Yukawa coupling [51], that one cannot rotate the L,2 L0 system to suppress couplings of Asmall⌘ mass is also generated from the Yukawa coupling [51], any particular L, L0 to the Ni sector. but is negligible form⌫ theand parameters mixings we among are interested the light in. active neutrinos. We Dark Matter Production: ⌘ can also mediate any particular L, L to the N sector. but is negligible for the parameters we are interested in. 0 will consideri the interesting and widely studied possibil- N N N N interactions between the sterile neutri- i i ! j j ity that the lightest sterile neutrino N1 is DM, which is nos (Fig.2 (b)), which enables a novel DM production especially appealing given recent claims of a 3.5 keV X- mechanism NiNi N1N1. One can analogously esti- ray line [56, 57] compatible with decays of a 7 keV sterile mate the scale f !below which this process [75] is e - neutrino DM particle. We also assume f v;theU(1) 1/4 0 cient: f pmN (MPlmN ) . This would generate an ⇠ 1 2,3 breaking singlet scalar is then decoupled and irrelevant N1 abundance comparable to relativistic freezeout, which for phenomenology. generally overcloses the Universe, hence this scenario is Lifetime: The ⌘ lifetime is controlled by decay rates best avoided. Likewise, ⌘ decays can also produce DM 4 109 Ni η Ni Nj 8 η 10 N Decays to η dominant i 107 Ni η Ni Nj 6 GeV 10 ê f (a) (b) 105 Decays before BBN 4 10 rapid Ni annihilation to ηη FIG. 2: Sterile neutrino annihilation processes involving the 1000 pseudo-Goldstone boson ⌘. 0.001 0.01 0.1 1 mN GeV FIG. 3: Solid blue: Symmetry breaking scale f below which if m > 2m . By comparing rates, we find that produc- ê ⌘ N1 the exotic decay N ⌘⌫ dominates over the standard sterile tion from such decays dominates over the annihilation neutrino decay channels! imposed by seesaw relations. Be- process provided m >m3 /f 2, which generally holds ⌘ N2,3 low the dashed red line, this decay channel causes the ster- over most of our parameter space. Additional DM pro- ile neutrinos to decay before BBN. Below the dotted green duction processes, such as ⌘ annihilation and N2,3 decays line, sterile neutrino - pseudo-Goldstone interactions are suf- via an o↵-shell ⌘, are always subdominant and therefore ficiently rapid to thermalize the two populations in the early neglected. The novel production processes discussed here Universe. do not rely on N1 mixing with active neutrinos, which is particularly appealing since this canonical (Dodelson- Ignoring phase space suppression, the decay rate is Widrow) production mechanism [76] is now ruled out by various constraints [9, 77–84]. + GOLDSTONE 1 mNi m⌫ (Ni ⌘⌫) mN . (9) COSMOLOGY/DARK Next,MATTER/ we discuss DIRECT various cosmological SEARCH histories ASPECTS that are ! ⇡ 416⇡ f 2 i possible within this framework.B. Shakya, OurJ. Wells, purpose 1801.02640 is not [hep-ph] to provide a comprehensive survey of all possibilities,109 but If su ciently large, this exotic decay channel can com- Ni η Ni Nj pete with the standard sterile neutrino decay channels simply to highlight some novel and interesting108 features that can be realized.η Since available decay channels and induced by active-sterile mixing [91]. In Fig. 3, we plot Ni New production7 Decays to η dominant 5 10 (blue curve) the scale f below which this channel dom- lifetimes are crucial to the cosmologicalmechanism history, we for findsterile it Ni η Ni Nj 6 GeV 10 ê inates (assuming standard seesaw relations). In this re- useful to organize our discussion into the followingf three Here, DM (N1) is produced from lateneutrino decays dark of heavier matter sity of Cincinnati and thanks the CERN and DESY the- (a) di↵erent regimes. (b) 105 gion, theDecays traditionally before searched-for decay modes are sup- • Presence of Goldstoneparticles introduces (⌘ newand interactions.N2,3) and can be warm. Such late pro- ory groups,BBN where part of this work was conducted, for 4 10 pressed, renderingrapid N thei sterile neutrinos invisible at detec- duction of warm DM can carry interesting cosmological hospitality.annihilation This work to ηη was performed in part at the As- FIG. 2: Sterile neutrinoHeavy annihilation regime: processesm⌘ >m involvingNi the 1000 tors such as at DUNE [92] and SHiP [93] (unless N1 also pseudo-Goldstonesignatures boson ⌘. and structure formation implications,0.001 which0.01 decayspen Center0.1 in the for detector,1 Physics, as which can occur is supported if it is not by DM). National Goldstone decay can be a viableAll ⌘ sourcedecay channels of sterile to neutrino sterile neutrinosdark matter are open, and lie beyond the scope of this paper. SciencemN GeV Foundation grant PHY-1066293. N2,3 are generally required to decay before BBN due ⌘ decays rapidly, long before BBN. If NiNi ⌘⌘ is rapid, ! to constraints from several recombination era observables ⌘ maintains an equilibrium distributionFIG. at 3:T Solidm blue:⌘, and Symmetry breaking scale f below which if m⌘ > 2mN . ByLight comparing regime: rates,m weNi find>m that⌘ >m produc-⌫ & ê 1 the exotic decay N ⌘⌫ dominates[94–96], over necessitating the standard sterile⌧N2,N3 . 1 s and consequently tion from such decaysthe dominates decay ⌘ overN1N the1 generates annihilation a freeze-in abundance! of All sterile neutrinos! can now decay intoneutrino⌘. In decay particu- channels imposedmN2,N by3 seesaw(100) relations. MeV inBe- the standard seesaw formal- New sterileprocess neutrino provided decaym channelN>m1, estimated3 N/f ->2, ην which to, giving be generally [33, a 3 35,ν state holds 74, 85–90] with no gamma ray & ⌘ N2,3 low the dashed red line, this decay channelO causes the ster- lar, a new, very long-lived DM decay channel N1 ⌘⌫ ism. The new decay channel Ni ⌘⌫, if dominant, counterpart;over interesting most of for our neutrino parameter telescopes? space. Additional DM pro- ile neutrinos to! decay before BBN.[1] P. Below Minkowski, the dotted Phys. green Lett. 67B!,421(1977). emerges. Since ⌘ subsequently decays into2 two neutrinos, can reduce the sterile neutrino lifetime, allowing lighter duction processes, such as ⌘ annihilation and N2,3 decays line, sterile neutrino - pseudo-Goldstone interactions are suf- MPl mN1 [2] R. N. Mohapatra and G. Senjanovic, Phys. Rev. Lett. Will also affectvia anheavy o↵-shell sterile⌘this, are neutrino can always provide subdominantlifetime distinctYeq and and 0decay.1 signatures therefore channel: atficiently affects neutrino. rapidbounds/ to detec- thermalize(8) masses the two populationsto be compatible in the early with BBN. In Fig. 3, the red ⇠ m f 44,912(1980). prospects fromneglected. past (BBN) The novel torsand present suchproduction as (direct) IceCube, processes searches Borexino, discussed for⌘ HNLs here✓ KamLAND,◆Universe. and Super- dashed line shows the scale f below which the sterile neu- [3] R. N. Mohapatra and G. Senjanovic,6 Phys. Rev. D23, do not rely on Kamiokande.N1 mixing with Note active that, neutrinos, unlike which the standard N ⌫ trino decays before BBN. For f . 10 GeV, even lighter The observed DM abundance is produced, for instance,1 165 (1981). is particularly appealing since this canonical (Dodelson- ! (MeV[4] T. scale) Yanagida, sterile neutrinos Prog. Theor. are Phys.compatible64,1103(1980). with the see- decaywith channel,f 105 thisGeV, hasm no gamma10 GeV, ray andIgnoring counterpart.m phase10 keV. space suppression, the decay rate is Widrow) production mechanism⇠ [76] is now⌘ ruled⇠ out by N1 ⇠ saw[5] asM. well Gell-Mann, as BBN constraints, P. Ramond, andin stark R. Slansky, contrast Conf. to the Proc. various constraintsUnlike [9,If 77–84]. the previousN N scenarios,⌘⌘ annihilation⌘ is extremely process is long-lived, feeble, a i i standard1 mC790927Ni m seesaw⌫ ,315(1979),1306.4669. requirements. and if su ciently! light, can contribute measurably (Ni to⌘⌫) mN . (9) Next, we discuss variousfreeze-in cosmological abundance15 histories of ⌘ is that generated are instead, and its! de- ⇡ 16[6]Depending⇡ J.f Schechter2 oni parameters, and J. W. F.⌘ can Valle, decay Phys. before Rev. orD22 after,2227 dark radiation at BBN or CMB [71, 97, 98]. A Gold- possible within thiscays framework. produce Our a small purpose abundance is not to of N1.TheN1 yield is BBN(1980). (Fig. 1), but its dominant decay channel is to the provide a comprehensivestone that survey freezes of all out possibilities, above 100 but MeV contributesIf su ciently large,0.39 this exotic decay channel can com- suppressed by the branching fraction BR(⌘ N1N1)= DM[7] candidateT. Asaka,⌘ S.N Blanchet,1N1.IfN and2,3 decay M. Shaposhnikov, dominantly into Phys. 2 pete with! the⇠ standard sterile neutrino decay channels simply to highlightto N somee ↵(⌘at novelN CMBN ) and [99]; interestingm thisN is the features case if the sterile neutrino ! 1 1 1 ⌘, or ifLett.N1 B631thermalizes,151(2005),hep-ph/0503065. with N2,3,theN1 relic density is that can be realized. ( Since⌘ !N availableN ) = decaym channels. The resulting and induced abundance by active-sterile is much mixing [91]. In Fig. 3, we plot annihilation2,3 to2,3 ⌘ is eN 2,3cient or if sterile neutrinos decay [8] T. Asaka and M. Shaposhnikov, Phys. Lett. B620,17 ! (blue curve) the scale f belowoverabundant which this for channel DM. Viable dom- regions of parameter space lifetimes are crucialdominantly tosmaller the cosmological than to ⌘Y.Ifeq from history,⌘ decays Eq. we 8 andfind after it cannot neutrino account decoupling, for all of (2005), hep-ph/0505013. useful to organize our discussion into the following three inates (assuming standardinstead seesaw involve relations). a small In this fraction re- of N2,3 decaying into ⌘, DM unless mN1 mN2,N3 . [9] T. Asaka, M. Laine, and M. Shaposhnikov, JHEP neutrinos from its decays⇠ provide additionalgion, the radiation traditionally en- searched-forwhich subsequently decay modes decays are sup- to N . In this case, N ac- di↵erent regimes. 01, 091 (2007), [Erratum:1 JHEP02,028(2015)],1 hep- ergy density in the CMB [75]. pressed, rendering the sterilecounts neutrinos for the invisible observed at detec- DM abundance (for mN2,3 =1 Intermediate regime: mN2,3 >m⌘ >mN1 ph/0612182. Heavy regime: m >m tors such as at DUNE [92] and SHiP [93] (unless N alsom Finally,⌘ Ni if ⌘ is su ciently long-lived and heavy, it can GeV)[10] K. for N.f Abazajian109 GeV et1 al.N (2012),1 . For 1204.5379. instance, m =7 In addition to annihilation processes,decays⌘ can in the now detector, also as can occur if it⇡ is not DM). GeV N1 All ⌘ decay channelsalso account to sterile for neutrinos part or are all ofopen, DM. and The phenomenology in [11] M. Drewes et al.,6 JCAP 1701,025(2017),1602.04816. be produced directly from heavy sterileN2 neutrino,3 are generally decay. requiredkeV to requires decay beforef 10 BBNGeV.q due ⌘ decays rapidly,this long case before is BBN. similar If N toiN thati ⌘⌘ ofis the rapid, majoron [48, 49, 51, 58– [12] E. Ma, Mod. Phys. Lett. A32,1730007(2017), ! to constraints from several recombination era⇠ observables ⌘ maintains an63], equilibrium with neutrino distribution lines at T as& anm⌘ interesting, and signal [55]. 1702.03281. [94–96], necessitating ⌧N2,N3 . 1 s and consequently the decay ⌘ N1N1 generates a freeze-in abundance of [13] T. Alanne, A. Meroni, and K. Tuominen, Phys. Rev. ! mN2,N3 (100) MeV in the standard seesaw formal- N1, estimated to be [33, 35, 74, 85–90] & ism. TheO new decay channel D96N ,095015(2017),1706.10128.⌘⌫, if dominant, [14] J.i Sayre,! S. Wiesenfeldt, and S. Willenbrock, Phys. Rev. 2 DISCUSSION can reduce the sterile neutrino lifetime, allowing lighter MPl mN D72,015001(2005),hep-ph/0504198. Y 0.1 1 . (8) masses to be compatible with BBN. In Fig. 3, the red eq ⇠ m f [15] Y. Chikashige, R. N. Mohapatra, and R. D. Peccei, ⌘ ✓ ◆ dashed line shows the scale f below which the sterile neu- Phys.6 Lett. 98B,265(1981). We studied the phenomenology of atrino pseudo-Goldstone decays before BBN. For f . 10 GeV, even lighter The observed DMboson abundance⌘ associated is produced, with for a instance, spontaneously(MeV broken scale) sterile global neutrinos[16] areG. compatible B. Gelmini with and the M. see- Roncadelli, Phys. Lett. 99B,411 with f 105 GeV, m 10 GeV, and m 10 keV. (1981). symmetry⌘ in a light (GeVN1 scale) sterilesaw neutrino as well as sector. BBN constraints, in stark contrast to the ⇠ ⇠ ⇠ [17] H. M. Georgi, S. L. Glashow, and S. Nussinov, Nucl. If the NiNi The⌘⌘ presenceannihilation of sterile process neutrinos is feeble, a and standard⌘ at similar seesaw mass requirements. freeze-in abundance! of ⌘ is generated instead, and its de- Phys. B193,297(1981). scales gives rise to several novel possibilitiesDepending for cosmol- on parameters, ⌘ can decay before or after cays produce a small abundance of N1.TheN1 yield is BBN (Fig. 1), but its dominant[18] J. decay Schechter channel and is to J. the W. F. Valle, Phys. Rev. D25,774 ogy, DM, and direct searches. Primary among these are suppressed by the branching fraction BR(⌘ N1N1)= DM candidate ⌘ N1N1.IfN2(1982).,3 decay dominantly into 2 ! (⌘ N N ) mN ! 1 1 novel1 sterile neutrino DM production⌘ mechanisms, or if N1 thermalizes from with[19]N2,G.3,the B.N Gelmini,1 relic density S. Nussinov, is and M. Roncadelli, Nucl. (⌘ !N N ) = m . The resulting abundance is much ! 2,3 2,3 ⌘-mediatedN2,3 scattering or decay, andoverabundant new decay for chan- DM. Viable regionsPhys. ofB209 parameter,157(1982). space smaller than Y from Eq. 8 and cannot account for all of eq instead involve a small fraction[20] M. of N Lindner,decaying D. Schmidt, into ⌘, and T. Schwetz, Phys. Lett. DM unless m nelsm for heavy. sterile neutrinos, which can alleviate BBN 2,3 N1 N2,N3 B705,324(2011),1105.4626. bounds⇠ and suppress standard searchwhich channels subsequently at direct decays to N1. In this case, N1 ac- [21] M. Escudero, N. Rius, and V. Sanz, JHEP 02,045 counts for the observed DM abundance (for mN2,3 =1 Intermediate regime:search experiments,mN2,3 >m⌘ >m orN1 provide distinct DM signals at m (2017), 1606.01258. GeV) for f 109 GeV N1 . For instance, m =7 In addition toneutrino annihilation detectors. processes, Likewise,⌘ can now⌘ alsocan contribute measur-⇡ GeV[22] A. Maiezza, M. Nemevek,N1 and F. Nesti, Phys. Rev. Lett. be produced directlyably from to dark heavy radiation sterile neutrino at BBN decay. or CMB,keV requires injectf a late106 GeV.q ⇠ 115,081802(2015),1503.06834. population of SM neutrinos from its late decays, or ac- [23] M. Nemevek, F. Nesti, and J. C. Vasquez, JHEP 04, count for DM. We have only touched upon a few inter- 114 (2017), 1612.06840. esting phenomenological possibilities in this framework, [24] A. Maiezza, G. Senjanovi, and J. C. Vasquez, Phys. Rev. and several directions, such as the e↵ect of ⌘ on leptoge- D95,095004(2017),1612.09146. [25] P. S. B. Dev, R. N. Mohapatra, and Y. Zhang, Nucl. nesis [7–9, 72, 100], or di↵erences in the flavor structure Phys. B923,179(2017),1703.02471. and mixing angles from the hidden sector interpretation [26] W.-Y. Keung and G. Senjanovic, Phys. Rev. Lett. 50, compared to the canonical seesaw mechanism, could be 1427 (1983). worthy of further detailed study. [27] T. Asaka, M. Shaposhnikov, and A. Kusenko, Phys. Lett. B638,401(2006),hep-ph/0602150. Acknowledgements: The authors are supported in [28] G. Cleaver, M. Cvetic, J. R. Espinosa, L. L. Everett, part by the DoE under grants DE-SC0007859 and DE- and P. Langacker, Phys. Rev. D57,2701(1998),hep- SC0011719. BS acknowledges support from the Univer- ph/9705391. SUMMARY LIGHT EXTENDED NEUTRINO SECTORS: FOUNDATIONS AND PHENOMENOLOGY • light sterile neutrinos likely part of extended sectors with additional symmetries, particles (higgs, Goldstone/gauge bosons) • additional structure can be much heavier; sterile neutrinos can be the lightest in the new sector (seesaw mechanism in the hidden sector) DARK MATTER/COSMOLOGY • freeze-in production of sterile neutrino dark matter • nonthermal population can have nontrivial momtum distributions carrying imprints of heavy states, contribute to Neff DIRECT SEARCHES • new decay modes of light sterile neutrinos, signatures different from expectations from active-sterile mixing • modifies constraints on light sterile neutrinos from BBN/cosmology COLLIDER • heavier states (Higgs, gauge bosons) can be within reach of higher energy experiments (LHC) • colliders can probe sterile neutrino final states for both SM and exotic Higgs decays 16