STERILE NEUTRINO DARK MATTER MODELS / THEORY
BIBHUSHAN SHAKYA
SNOWMASS CF1 MEETING SEPTEMBER 11, 2020
1 STERILE NEUTRINO DARK MATTER MODELS / THEORY AN (INCOMPLETE, RAPID) OVERVIEW
For greater details, see one of several reviews in the literature, e.g.
• Sterile Neutrino Dark Matter; Boyarsky+, 1807.07938
• A White Paper on keV Sterile Neutrino Dark Matter; Adhikari+, 1602.04816
• Sterile Neutrino Dark Matter from Freeze-in; Shakya, 1512.02751
• The Phenomenology of Right Handed Neutrinos; Drewes, 1303.6912
• keV Neutrino Model Building; Merle, 1302.2625
• …
2 WHY STERILE NEUTRINOS (AS DARK MATTER) ?
• Neutrino masses require BSM, most straightforward implementations feature right handed/sterile neutrinos
• Very weakly coupled to SM sector: small but non-negligible production in early Universe, as well as long lifetime, are “automatic”
• Relatively straightforward/predictive phenomenology: depends mostly on the sterile neutrino mass and mixing angle with SM neutrinos. Diverse signatures: extended neutrino sectors generally feature observable signals in indirect detection, cosmology, colliders, low energy (neutrino) experiments
• Hints of sterile neutrinos at several experiments (3.5 keV line, short baseline anomalies)
3 STERILE NEUTRINO AS DARK MATTER: CAVEATS (PROBLEMS / OPPORTUNITIES)
• MASS SCALE: The natural value of the mass of a singlet is at the cutoff scale of the theory (e.g. Planck or GUT scale), most of the viable DM candidates have much lower masses (sub-electroweak scale)
• Not a disaster: singlet fermion mass does not get large quantum corrections (unlike the higgs); Seesaw mechanism works across a wide range of mass scales (from keV to GUT scale) Nevertheless, need an explanation for the mass scale
4 STERILE NEUTRINO AS DARK MATTER: CAVEATS (PROBLEMS / OPPORTUNITIES)
• MASS SCALE: The natural value of the mass of a singlet is at the cutoff scale of the theory (e.g. Planck or GUT scale), most of the viable DM candidates have much lower masses (sub-electroweak scale)
• Not a disaster: singlet fermion mass does not get large quantum corrections (unlike the higgs); Seesaw mechanism works across a wide range of mass scales (from keV to GUT scale) Nevertheless, need an explanation for the mass scale
• MIXING ANGLE: sterile neutrinos that explain the observed neutrino masses via the seesaw mechanism cannot be dark matter for ANY mass - the mixing angles involved are too large. For dark matter, need a sterile neutrino essentially decoupled from the seesaw mechanism
• again, not a disaster: vanishing coupling with the SM (small Yukawa) is a technically
natural limit where the theory has an enhanced Z2 symmetry. Additional sterile neutrinos can generate neutrino masses via seesaw.
• Philosophical conundrum: what is the boundary between a sterile / right handed neutrino and a generic heavy neutral lepton / singlet fermion?
5 STERILE NEUTRINO DARK MATTER: A THEORIST / MODEL BUILDER’S CHECKLIST
✓ Motivate the mass scale ✓ Suitable production mechanism to obtain the correct relic density while ensuring sufficiently long lifetime ( minimal mechanism now ruled out; see next slide) ✓ Acceptable momentum distribution (ie should not be too warm, be consistent with all cosmological data) ✓ Embed the candidate into a broader well motivated framework that addresses the issue of neutrino masses
6 2
6 1000 PeV be obtained by coupling the Ni to other fields charged 10 under the U(1) . Introducing an exotic field that car- 0 105 ries the opposite charge under U(1)0, one is allowed the 4 100 PeV following higher dimensional operators in the superpo- L 10 tential: 3
keV 10 H y c x c c s 2 10 PeV W LHuN + N N . (3) 10 M M m ⇤ ⇤ 101 Here x and y are dimensionless (1) couplings (neglect- O 1 1 PeV ing possible flavor structure for now), and M is the scale 100 TeV at which this e↵ective theory needs to be UV⇤ completed 10-3 10-2 10-1 1 with new physics, such as the scale of grand unification MGUT or the Planck scale MP . Here we have ignored the ma eV 2 (LHu) /M term that is of the same order as it is not large enough⇤ to produce the active neutrino mass scale, FIG. 1: Active and sterile neutrino mass scales for various 0 choices of y ,withM = MGUT ,tan =2(Hu = but we note that it can provide the dominant contribu- h i ⇤ H L h i tion to the mass of the lightest active neutrino. 155.6GeV),and0.001 7 PARAMETER SPACE FOR STERILE NEUTRINOS: BEYOND THE MINIMAL FRAMEWORK • Plenty of parameter space for sterile neutrino dark matter (does not have to be confined to the keV scale!) with a satisfactory production mechanism 8 STERILE NEUTRINOS: BEYOND THE MINIMAL FRAMEWORK Sterile no more: Sterile neutrino dark matter need not be a complete singlet, could be charged under symmetries beyond the SM! Occurs very naturally in well motivated BSM frameworks, e.g.: • Grand unified theories (essentially, left-right theories) • Theories with gauged (or global) lepton number or B-L • Secluded/hidden/dark sectors with symmetries completely unrelated to the SM • Extended sectors that somehow mimic the SM (e.g. neutral naturalness) Such extensions feature additional particles+symmetries/interactions that can • produce sterile neutrino dark matter in the early Universe • modify observable properties of sterile neutrino dark matter • produce correlated signals at other experiments (colliders, neutrino experiments, cosmological probes) 9 BEYOND MINIMAL: DARK MATTER PRODUCTION FREEZE-OUT • SM dark matter can thermalize with the SM bath and undergo canonical freezeout if it has significant interactions (tends to occur, e.g., in left-right models) • Tends to freeze out while relativistic and overproduce dark matter, requires significant (more than an order of magnitude) entropy dilution. • Momentum distribution is thermal 10 BEYOND MINIMAL: DARK MATTER PRODUCTION FREEZE-OUT • SM dark matter can thermalize with the SM bath and undergo canonical freezeout if it has significant interactions (tends to occur, e.g., in left-right models) • Tends to freeze out while relativistic and overproduce dark matter, requires significant (more than an order of magnitude) entropy dilution. • Momentum distribution is thermal FREEZE-IN • Can be produced through “feeble” interactions, never thermalized • In particular, through decays of some heavy particle while it is part of the thermal bath, as well as after it has frozen out. MANY candidates: usually, scalar that breaks the symmetry that the sterile neutrinos are charged under. also: charged scalars, additional gauge/Goldstone bosons, superpartners, other fermions…[see aforementioned review papers for references] • Momentum distribution can be extremely nontrivial; could be cold (DM produced earlier, more time to redshift) or warm (if produced through late out of equilibrium decays) 11 Exotic Signals in the Sterile Neutrino SectorExotic Signals in the Sterile Neutrino Sector Preliminary notes on the phenomenology associated with a light pseudo-Goldstone from a broken 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.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 isMOTIVATION appealing but by no means the only The U(1)B L is appealing but by no means the only possibility. We consider instead a global symmetry U(1)possibility.0 We consider instead a global symmetry U(1)0 that the N (but none of the SM fields) are charged un- Light sterile neutrinos below the electroweak scale areMOTIVATIONthatLight the sterileNi (but neutrinos none below of the the SM electroweak fields)The U(1) areB scale chargedL is are appealing un- but byi no means the only der. This forbids the Dirac as well as Majorana mass well motivated by many arguments (dark matter, lepto- wellder. motivated This forbids by many the arguments Dirac aspossibility. (dark well as matter, Majorana We lepto- consider mass instead a global symmetry U(1)0 terms in the above equations. However, with an oppo- genesis etc) and are being searched forLight at sterile a variety neutrinos of genesis belowterms the etc) in electroweak the and above are being equations.scale searched are However,that for the at aN withvarietyi (but an none of oppo- of the SM fields) are charged un- sitely charged , we can write down the higher dimen- experiments. The searches are performedwell motivated in the by tradi- manyexperiments. argumentssitely charged (dark The matter,, searches we can lepto- are write performed downder. This the in the higher forbids tradi- dimen- the Dirac as well as Majorana mass tional decay channels induced by the mixing of the active sional operator tional decay channels induced by thegenesis mixing etc) of the and active are beingsional searched operator for at a variety of terms in the above equations. However, with an oppo- and sterile sectors as dictated by thesitely seesaw charged mechanism. , we can write down the higher dimen- and sterile sectors as dictated by theexperiments. seesaw mechanism. The searches are performed in the tradi- 1 However, the natural mass scale1 ofsional Majorana operator neutrinos LhN (3) However, the natural mass scale oftional Majorana decay neutrinos channels induced by the mixing of the activeLhN (3) L ⇤ and sterile sectors as dictatedis at the by UVthe seesaw cuto↵ scale mechanism. (GUT⇤ or Planck), so if they are is at the UV cuto↵ scale (GUT or Planck), so if they are L 1 However, the natural masslight, scale this of is Majorana indicative neutrinos of some deeper structure in the which,LhN once gets a vev, reproduces(3) the Dirac mass term. light, this is indicative of some deeper structure in the ⇤ is at the UV cuto↵ scalesterile (GUTwhich, neutrino or once Planck), sectors,gets so a if vev, they such reproduces are as some protecting the Dirac symme- mass term.L Here ⇤ is some UV-cuto↵ scale. To keep things general, sterile neutrino sectors, such as somelight, protecting this is indicativesymme- oftryHere some that⇤ deeper keepsis some their structure UV-cuto masses in at↵ the ascale. low scale.which, To keep This once things structure gets general, a vev,we reproduces do not explicitly the Dirac write mass down term. a term that gives rise to try that keeps their masses at a low scale.sterile This neutrino structure sectors, suchcanwe also as do some not give explicitly protecting rise to other write symme- light down degreesHere a term of⇤ freedomis that some gives in UV-cuto the rise to↵thescale. Majorana To keep mass things term, general, and take the sterile neutrino can also give rise to other light degreestry of that freedom keeps their in the massesneutrinothe at a Majorana low sector, scale. and mass This consequently structure term, and new takewe decay do the not channels sterile explicitly neutrino for writemass downM ato term be that a free gives parameter rise to instead. Spontaneous neutrino sector, and consequently newcan decay also give channels rise to for othersterilemass light neutrinos, degreesM to of be whichfreedom a free can inparameter completely the instead. change their Spontaneous phe- breaking of the U(1)0 with gives rise to a light pseudo- the Majorana mass term, and take the sterile neutrinoh i sterile neutrinos, which can completelyneutrino change sector, their and phe- consequentlynomenology.breaking new of We decay the wouldU(1) channels0 likewith to for studygivesmass this rise possibility.M toto a lightbe a pseudo- free parameterGoldstone instead.⇢, which Spontaneous inherits the couplings of ; its mass Motivate from hidden sectors.h i Even if GUT scale see- nomenology. We would like to studysterile this possibility. neutrinos, which canGoldstone completely⇢, change which their inherits phe- thebreaking couplings of of the U;(1) its0 masswithdepends gives on rise details to a lightof the pseudo- underlying model (explicit soft saw, if neutrino-like fields in hidden sectors exist, inte- term,h i or from quantum gravity), but for generality we Motivate from hiddenAN sectors. EXAMPLE: Evennomenology. if GUT scale We would see- likedepends to study on this details possibility. of the underlyingGoldstone model⇢, (explicit which inherits soft the couplings of ; its mass saw, if neutrino-like fields in hidden sectorsMotivate exist, from inte- hiddengrating sectors.term, out or Even from the if GUT GUT quantum scale scale neutrinos see- gravity),depends generates but for on a generality details low en- of the wealso underlying take this model mass (explicitm⇢ to be soft a free parameter. ergy e↵ective seesaw! Plausible to have additional struc- gratingHEAVY out the PORTALS GUT scale neutrinos TO Asaw, generates HIDDEN if neutrino-like a low SECTOR en- fieldsalso in hidden take this sectors mass exist,m to inte- be a freeterm, parameter. or from quantum gravity), but for generality we ture there. ⇢ grating out the GUT scale neutrinos generates a low en- also take this mass m⇢ to be a free parameter. ergy e↵ective seesaw! Plausible to have additional struc- PHENOMENOLOGY Replicateture there. the seesaw mechanism in a hiddenergy esector↵ective to seesaw! get light Plausible “sterile to have additional struc- neutrinos” in the same way asture light there. SM neutrinos PHENOMENOLOGY FRAMEWORK PHENOMENOLOGYThe phenomenology depends on four free parame- (explains the low (sub-EW) mass scale with high (above EW) scale dynamics) ters: , ⇤,m⇢,M (other phenomenologically relevant FRAMEWORK The phenomenology depends on four free parame- h i FRAMEWORKThe operators traditionally associatedThe phenomenology with right- dependsparameters on are fourm freeand parame- its mixing with the SM Higgs, handed,ters: sterile, ⇤,m neutrinos⇢,M (other are the phenomenologically Dirac and Majorana relevantbut these are only tangentially relevant to neutrino phe- h i ters: , ⇤,m⇢,M (other phenomenologically relevant The operators traditionally associated with right- masses:parameters are m and its mixing withh i the SM Higgs,nomenology and we ignore these for now). The operatorsU(1)’ traditionally associated with right- parameters are m and its mixing with the SM Higgs, handed, sterile neutrinos are the Dirachanded, and sterile Majorana neutrinosbut are these the Dirac are only and tangentially Majorana relevantbutc these to are neutrino only tangentially phe- If m⇢ relevant 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- boundaries of this plot. The demarcation of cold, warm, tivistic N1 to form more or less than 1% of dark matter.) andEXOTIC hot regions COSMOLOGICAL depends not only on m IMPRINTSand m but N˜1 N1 also on the other parameters (in particular, the ones that • Can have multiple sources of production. e.g. if the underlying theory is supersymmetric, determine N˜ lifetime); this point is illustrated in Fig. 3, DISCUSSION decays of the1 DM superpartner, the sterile sneutrino can produce DM where we show that all three possibilities can be realized • the two populations don't talk to each other! [Freeze-in: DM never6 “thermalizes”] for the same choice of m ˜ and mN (fixed to 10 GeV • second population is hotter (sterile sneutrinoN1 is long-lived1 and decays out of equilibrium)In this paper, we have demonstrated that a supersym- and 1 MeV respectively) by varying m and A . • single species can mimic cold+hot DM setup metric extension of the widely studied sterile neutrino 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 14 TAKE-AWAY MESSAGES • Sterile neutrino dark matter continues to be extremely well motivated • Our thinking has traditionally been dominated by a keV scale candidate produced via the Dodelson Widrow mechanism, but the possibilities are far richer. • From a grander viewpoint, it is likely that sterile neutrinos (especially if light) are not truly sterile, but are part of extended BSM frameworks involving additional particles and symmetries • This opens several possibilities for sterile neutrino dark matter cosmology (new production mechanisms, do not need to rely on the keV scale or active-sterile mixing) as well as phenomenology • An X-ray line remains the smoking gun signal, but not guaranteed (mixing angle might be tiny); however, other observables are possible, including cosmological imprints (e.g. nontrivial momentum distributions, dark radiation components) • Such theoretical considerations are also crucial to draw correlations with potential signals of new physics at high intensity / neutrino experiments (signals of other heavy neutral leptons) and colliders (probing heavier scalars/gauge bosons responsible for producing the observed relic density) 15