In the Light of LSND, Miniboone and Other Data

DAPNIA-SPhT Joint Seminar, 21 May 2007

Exotic Neutrino Physics in the light of LSND, MiniBooNE and other data

Marco Cirelli + Stéphane Lavignac SPhT - CEA/Saclay Introduction CDHSW

Neutrino Physics (pre-MiniBooNE): CHORUS NOMAD NOMAD NOMAD

0 KARMEN2 CHORUS Everything ﬁts in terms of: 10 LSND 3 neutrino oscillations (mass-driven) Bugey BNL E776 K2K SuperK CHOOZ erde 10–3 PaloV Super-K+SNO Cl +KamLAND ]

2 KamLAND [eV 2 –6 SNO

m 10 Super-K ∆

–9 10 νe↔νX νµ↔ντ νe↔ντ νe↔νµ

10–12 10–4 10–2 100 102 tan2θ http://hitoshi.berkeley.edu/neutrino Particle Data Group 2006 Introduction CDHSW

Neutrino Physics (pre-MiniBooNE): CHORUS NOMAD NOMAD NOMAD

0 KARMEN2 CHORUS Everything ﬁts in terms of: 10 LSND 3 neutrino oscillations (mass-driven) Bugey BNL E776 K2K SuperK Simple ingredients: CHOOZ erde 10–3 PaloV νe, νµ, ντ m1, m2, m3 Super-K+SNO Cl +KamLAND ]

θ12, θ23, θ13 δCP 2 KamLAND [eV 2 –6 SNO

m 10 Super-K ∆

–9 10 νe↔νX νµ↔ντ νe↔ντ νe↔νµ

10–12 10–4 10–2 100 102 tan2θ http://hitoshi.berkeley.edu/neutrino Particle Data Group 2006 Introduction CDHSW

Neutrino Physics (pre-MiniBooNE): CHORUS NOMAD NOMAD NOMAD

θ12, θ23, θ13 δCP 2 KamLAND

Simple theory: [eV 2 –6 SNO

m 10 |ν! = cos θ|ν1! + sin θ|ν2! Super-K ∆

−E1t −E2t |ν(t)! = e cos θ|ν1! + e sin θ|ν2! Ga 2 Ei = p + mi /2p 2 –9 ν ↔ν m L 10 e X 2 2 ∆ ν ↔ν P ν → ν θ µ τ ( α β) = sin 2 αβ sin ν ↔ν E e τ νe↔νµ

10–12 10–4 10–2 100 102 tan2θ http://hitoshi.berkeley.edu/neutrino Particle Data Group 2006 Introduction CDHSW

Neutrino Physics (pre-MiniBooNE): CHORUS NOMAD NOMAD NOMAD

θ12, θ23, θ13 δCP 2 KamLAND

Simple theory: [eV 2 –6 SNO

m 10 |ν! = cos θ|ν1! + sin θ|ν2! Super-K ∆

−E1t −E2t |ν(t)! = e cos θ|ν1! + e sin θ|ν2! Ga 2 Ei = p + mi /2p 2 –9 ν ↔ν m L 10 e X 2 2 ∆ ν ↔ν P ν → ν θ µ τ ( α β) = sin 2 αβ sin ν ↔ν E e τ ν ↔ν Simple phenomenology: e µ 2 solar ν → ν : ∆m21, θ12 10–12 e µ,τ 10–4 10–2 100 102 2 2 atmo ν µ → ν τ : ∆m32, θ23 tan θ 2 http://hitoshi.berkeley.edu/neutrino SBL ν e, µ → ν x : ∆m32, θ13 Particle Data Group 2006 Introduction CDHSW

Neutrino Physics (pre-MiniBooNE): CHORUS NOMAD NOMAD NOMAD

θ12, θ23, θ13 δCP 2 KamLAND

Simple theory: [eV 2 –6 SNO

m 10 |ν! = cos θ|ν1! + sin θ|ν2! Super-K ∆

−E1t −E2t |ν(t)! = e cos θ|ν1! + e sin θ|ν2! Ga 2 Ei = p + mi /2p 2 –9 ν ↔ν m L 10 e X 2 2 ∆ ν ↔ν P ν → ν θ µ τ ( α β) = sin 2 αβ sin ν ↔ν E e τ νe↔νµ But: LSND does not fit: –12 2 2 10 –4 –2 0 2 ∆mLSND ! 1 eV 10 10 10 10 tan2θ −3 θ ! 10 http://hitoshi.berkeley.edu/neutrino LSND Particle Data Group 2006 Introduction The LSND signal does not fit. add new flavours Complicate the simple picture: modify oscillation physics (more or less radically) Sterile neutrinos, CPT, Lorentz, MaVaNs, xDims, anomalous muon decay, neutrino decay...

Beyond resolving the LSND puzzle, this exotic neutrino physics might be justified by new physics beyond the SM, and might give rise to subleading effects in other neutrino experiments. Introduction The LSND signal does not fit. add new flavours Complicate the simple picture: modify oscillation physics (more or less radically) We will review aspects of: Sterile neutrinos, CPT, Lorentz, MaVaNs, xDims, anomalous muon decay, neutrino decay...

Beyond resolving the LSND puzzle, this exotic neutrino physics might be justiﬁed by new physics beyond the SM, and might give rise to subleading effects in other neutrino experiments. Why Lorentz and/or CPT Lorentz, CPT: - fundamental ingredients of ordinary Quantum Field Theories (including the SM) - have been tested with high precision (K0-K0 system, charged lepton sector...)

Why should they be violated in the neutrino sector? Why Lorentz and/or CPT Lorentz, CPT: - fundamental ingredients of ordinary Quantum Field Theories (including the SM) - have been tested with high precision (K0-K0 system, charged lepton sector...)

Why should they be violated in the neutrino sector? - neutrinos are “special”: no conserved charge, can be Majorana ⇑ requires new physics beyond SM 2 Mweak −4 - m ν ∼ e V suggests Λ n e w ∼ ∼ 1 0 M Pl : mν Quantum Gravity might violate Lorentz and/or CPT Still very speculative possibilities! Lorentz Basics Possible origin: - spontaneous breaking - non trivial background in x-dim - non-commutative ﬁeld theory - quantum gravity... In absence of an explicit model, parameterize as: Colladay, Kostelecky 1997 L = LSM + L(Lor(en(tz

for neutrinos (renormalizable case): Kostelecky, Mewes 2003 i ↔ L(Lor(en(tz = (a ) L¯ γµL + (c ) L¯ γµ Dν L µ ij i j 2 µν ij i j

⇑ aµ charged leptons interactions , c GeV µν must be tiny −17 but ∼ 1 0 is enough to affect neutrino propagation! Lorentz phenomenology 3 3 -Unusual energy dependence of ﬂa1 vor conversions: 1 0.51 1 1 GeV L 0.5 0.51 es 2003 instead of usual : L or L E 1 GeV w 0.5 0.5 Me E 1 , 10 GeV 0 0 -1 2 however conspiracies can reproduce 0.5 -1 -0.5 0 0.5 1 10 1 10 10 cos Θzenith 10 GeV 0 E (MeV)

0 ostelecky -1 2 the usual dependance at given energies: -1 -0.5 0 0.5 1 K 10 1 10 10 P P E FIG. 1: νµ→νµ averaged ovecroaszΘimzeuntithhal angle for the bicycle FIG. 3: ( νe→νe )adiabatic avera(MgeedVo)ver one year (solid) and model (solid) and for a conventional case with mass (dotted). at intervals between an equinox and a solstice (dashed). FIG. 1: Pν →ν averaged over azimuthal angle for the bicycle FIG. 3: (Pν →ν )adiabatic averaged over one year (solid) and -Direction dependence of ﬂavor conµ µversions: e e model (solid) and for a conventional case with mass (dotted). at intervals between an equinox and a solstice (dashed). 1 1

0.5 es 2003 atmospheric neutrinos at SK: 1 1 GeV w 1 Me

1 , 0.5 P ν → ν depends on azimuthal angle 0.5 µ µ 0.5 o 1 GeV 1 (Θzenith = 36 ) 10 GeV 0.5 0 ostelecky -1 2 0.5 S E N W S K 3 10 1 10 10 10 GeV E (1) ˆ X ˆ Y XX Y Y 0 (MeV) (Bs )ab = N N (cL)ab − (cL)ab FIG. 2: Pν →ν averaged over zenith angle for the bicycle -1 2 terrestrial experiments: S µ µ E 0.6 N W S 10 1 10 10 − Nˆ X Nˆ X − Nˆ Y Nˆ Y (c )XY , (11) ! L "abmodel (solid) and for a conventional case with mass (dotted). FIG. 4: (Pν →ν )adiabatic for some modiﬁed models. es 2004 e e E (1) 1 X X Y Y XX Y Y y (MeV) t ˆ ˆ ˆ ˆ w

P i (Bc )ab = − N N − N N (cL)ab − (cL)aPb ν →ν ν¯ →ν¯ !2 " FIG. 2: µ µ averl aged over zenith angle for the bicycle µ e changes due to Earth rotation i 0.4 b

X Y XY Me ˆ ˆ , − 2N! N (cL)ab . "! model (sol(i1d"2)) and for a a conventional case with mass (dotted). Pν →ν b FIG. 4: ( e e )adiabatic for some modified models. o X Y Z atmospheric neutrinr os, which is a signal for Lorentz vi- ˆ Pˆ ˆ = 0.26% p 0.2 (plot: LSND, with daIn tyhe sae evxeragepressions, N ! , N ν ¯ µ, N→ aν¯ re d "i re c t io n a l f a ct o r s ) combination of effects produces ripples in the binned flux ostelecky containing information about the neutroinlao-tbieoanm.diFreocr- exampl% e, consider neutrinos propagating in K near the equinoxes, which might be detected in detailed tion with respect to the Earth. At the datethtmeectoohrsoplorhciazetoironinc,tanlepultarnineoosf,0twhheidcheteisctaors.igNneaultfroinroLsoorreingitnzavt-i- let θ be the angle between the beam and the vertical up- 0 5 10 15 202 ecxopmerbimineanttioanl aonfaelffyesecstsopf reoxdisutcinegs roirppfuletsurine dthaetab.inned flux oilnagtiforno.mFtohreeexaasmt oprlew, ecsotnhsaidveercnoseuΘTtr=in0o,s ∆prmopΘa=ga0t,inagndin ward direction, let φ be the angle between the beam and ⊕ (hours) Although detection of the semiannual variation would south measured towards the east, and ltehtheχenbhceeothrneizocoloantst-cailllpatlaionnes.ofInthceondtertaesctt,otrh.oNseeuentrtienroinsgotrhigeindaet-- near the equinoxes, which might be detected in detailed P itude of the detector. Then, the directional factors are FIG. 1: Variations of the percent probability 2ν¯µ→ν¯e over represent a definite positive signal for Lorentz violation, itnegctforormfrotmhetehaestnoorrthweosrtshoauvteh ceoxspΘeri=en0c,e∆ampseu=do0m, asnsd experimental analyses of existing or future data. given explicitly as 2 one2sidereal2day for three sample configurations wΘith averaged its absence cannot serve to eliminate this type of model. of ∆m = ∆mprob◦abciloitys !Pχν¯ .→ν¯ F" =ig0u.2r6%e: 2(C)e¯sµ¯h=# o0w(sdasthhede), (sAusr)e¯vµ¯ i=# val hence nΘo oscillati0ons. Inµcoentrast, those entering the de- Although detection of the semiannual variation would Nˆ X cos χ sin θ cos φ + sin χpcroos θbability ave0ra(dgotetded)o, vanedr(zC)ee¯nµ¯ i=th(Aas)ne¯µ¯g=# le0 a(ssoliad).function of az- Sriempprleesemnotdaifidceafitniointes opfotshiteivmeosdigenl aexl ifsotrtLhaotreenxthzibviitoslaimti-on, Nˆ Y = sin θ sin φ tector f.ro(m13)the north or south experience a pseudomass    imutha2l angle. A2lthou2gh this model predicts no east-west ilar overall behavior for solar and atmospheric neutrinos Nˆ Z − sin χ sin θ cos φ + cosoχfco∆s θm = ∆m ◦ cos χ. Figure 2 shows the survival its absence cannot serve to eliminate this type of model. Θ Th0ere are therefore a total of eight complex experiment- but have only a small semiannual variation. As an illus-    asymmetry beyond the usual case,(0n) orth-e(0a)st or (n0)orth- Simple modifications of the model exist that exhibit sim- probability averdeapgeneddenotvecoreffizecinenittsh: a(nAgs le)eµa,s (aAfcu)neµc,ti(oCn o)efµ,az- Z Any given short-baseline experiment is sensitive ¯¯ ¯¯ ¯¯ tration, consider the replacement of the coefficient (aL)eµ soµuth asymmetri(e1)s app(e1)ar. Si(1m) ilar (‘1c)ompa(1s)s’ asymme- ilar overall behavior for solar and atmospheric neutrinos to three complex combinations of (aimL) utchoeaffilcaientgs,le. (AAslth)e¯oµ¯,u(gAhc t)e¯hµ¯i,s(Bms o)ed¯µ¯e, l(Bpcre)e¯dµ¯i,c(tCs n)e¯oµ¯.eaAscto-mw-est T (0) (0) (0) tries are typicaplreihnenasilvle daniraleycsitsiofnt-hde eLpSNenDddeantatfomr tohde eablso.ve en- with a coefficient (aL)eµ of half the size. This has the ef- (As )ab, (Ac )ab, (C )ab, and five caomsyplmexmcoemtbrinya-beyond the usual case, north-east or north- but have only a small semiannual variation. As an illus- (1) (1) (1) ergy and sidereal dependence would in principle yield tions of (c )µν coefficients, (A ) , (A T) h, e(Bba)si,c features of solar-neutrino oscillations pre- fect of replacing the solid and dashed curves of Fig. 3 Z L s ab c ab s ab measurements of 16 of the possible 102 real degrees of tration, consider the replacement of the coefficient (aL)eµ (1) (1) south asymmetries appear. Similar ‘compass’ asymme- (Bc )ab, (C )ab. However, the directiodniacltdeedpenbdyenctehe fmreeoddomelinatrhee naelustorinocosemctopraotfitbhelemiwniimtahl SoMbEs.eWrvea- with those shown in FiTg. 4. The semiannual variations tries are typical in all direction-dependent models. with a coefficient (aL)eµ of half the size. This has the ef- implies that a combination of experimenttisotnes.tinOg abspeer-vedresmoalrakrinnpeausstinrginthoast pthreoipncalugsaiotneofina mthases-sEquaarrtedh’s in this type of model lie below existing statistical sen- cific oscillation mode νa → νb can provide access to all 2 fect of replacing the solid and dashed curves of Fig. 3 µ µν The basic femaatturirxe(sm˜ o)afb fsoor lnaeru-trnineous tinritnhoe poressecni◦tllfaortmioalnissm pisre- Z T components of (aL) and (cL) , providoedrbthietdailrepctlioannse, which lies at an angle η 23 relative to sitivities. Replacing also (aL)µτ with (aL)µτ is another ab ab straightforward. For example, i2n Eq. (15) it suffices to with those shown in Fig. 4. The semiannual variations of the associated neutrino beams differ.dicted by the model are also compatib!le wit−h1 ob2 s∗erva- the equatorial pexltaendet.heTdhefienivtiaonluoef (oC)fe¯µ¯ctoos(C)Θe¯µ¯ t=h(e2rEe)fo(rm˜e v)eaµr+ies option, which removes all orientation dependence in the For the special case of the transition mode relevant to ¯2¯ in this type of model lie below existing statistical sen- tion. Observed(Cs(o0)l)ar+nEe(uC(t1r))in.osIt pturronspoaugt athtaet tihne gtehneeraEl tawrot-h◦’s LSND, the probability takes the form from zero at the tweo¯µ¯ equinoxe¯µe¯ s to its maximum◦ of sin 23 model. Another example of a smZall modificatiTon is a 10% orbital plane, wgehneircahtiolniemsodaetl waitnh aamnagslse-sqηuared 2m3atrixrealnadtbiovteh to sitivities. ReplacTing also (aL)µτ with (aL)µτ is another at the two solsticeµs. Assuµmν ing adiaba2tic propagation in admixture of (aL)ee, which raises the survival probability L2 the equatorial p(alLa)nea.ndT(chLe) vacoleuffiecioenftschoass 4Θ1!detghreerseoffofreeedvoamr, ies option, which removes all orientation dependence in the Pν →ν # | (C)eµ while its rotation-invariant restriction has eight [12]. of 0.5 at low energies to about 0.6 without appreciably ¯µ ¯e (h¯c)2 ¯¯ the Sun, the average νe survival probability is 2 ◦ from zero at the tTwheopeuqbluisihnedoxreesuslttsofriotms LmSNaDxipmerummit tohef esxitnrac2- 3 amffeocdtienl.g Aonthoetrherreseuxlatms.plTehoef aensmsuainllgmsoudrvifiivcaaltiponroibsaabi1l-0% + (As)e¯µ¯ sin ω⊕T⊕ + (Ac)e¯µ¯ cos ω⊕T⊕ tion of a measurement for one combination of these de- T at the two solstices. Assu2ming2adiabatic2 prop2agation in admixture of (aL)ee, which raises the survival probability (Pν →ν 2 )adiagbreaetsicof=freseidnom.θ sInintheθe0xp+ericmoesnt,θcocpoiosusθn0u,mber(s5) ity in the adiabatic approximation is shown as the dot- + (Bs)e¯µ¯ sin 2ω⊕T⊕ + (Bc)e¯µ¯ cos 2ω⊕e T⊕ |e, of 0.5 at low energies to about 0.6 without appreciably the Sun, t(1h4e) avoef rν¯aµ gweerνe eprsoduurcvedi.vaAlnpexrcoebssaobf iν¯leitoyverisbackground ted line in Fig. 4. Other more complicated modifications was observed, which was interpreted as ν¯ oscillating where θ0 is the mixing angle at the core, giµven by re- thaffatecctoinugld obtehecrournesteunltasn.ceTdhbeutentshuaitngnosnuertvhievlaelssprreotbaainbil- where ω⊕ # 2π/(23 h 56 min) is the Earth’s sidereal into ν¯e. The 2correspo2nding oscilla2tion pro2bability is (Pν →ν )adiabatic = sin θ sin θ0 + cos θ cos θ0, (5) ity in the adiabatic approximation is shown as the dot- frequency and T⊕ is a standardized timpe l[2a3c].inTeghe tiem˚cEe wPiν¯tµh→ν¯e #˚cE0.2+6 ±G0.0F8n%e. /S√inc2e tihnis Epuqbl.ish(e4d).resuFltiginu-re the flavor of the simple model include allowing depen- variation is a direct consequence of the3dsirhecotiwonsa−l tdhe-e advoilavebsa−altliecvenptrsoirbreaspbeicltiivteyofasisderaealfutimnec,tiitorenpreosefntesn- dteendcelinoenindiFreicgt.io4n. sOotthheerrmthoaren cZom, oprliceavteend imntordoidfiuccaitnigons an average over the run time of the experiment. To a pendence. In the short-baseline approxwimhaetiroen, θw0e fiinsd the mixing angle at the core, given by re- that could be countenanµced butµ that nµonetheless rµeνtain ergy averaged goovdearpporonxeimayteioanr, .it caTn hbe tapkrenedasicretperdesenteinugttrhieno arbitrary coefficients (aL)ee, (aL)eµ, (aL)eτ , and (cL)ee , harmonics up to 2ω⊕, but more generally all higher har- √ monics can occur. pflluacxinisg ha˚clfEthweeixtpehexcptaet˚icoEnteodv+ervaGasliFduenereeaa/l tdayl2,o$wPiν¯nµe→nEν¯eeq%r#.gi0(e.42s6).±a0n.F0d8i%gd.uer-e wthhiechflayvieolrdsoaf tmhoedseilmwpilteh m21oddeelgrineecsluodfefraelelodwomin.g Mdeopreen- − Using −Eq. (14) and this result, we obtain a nonzero In Eq. (14), the complex factors 3c(Arsesh)ae¯oµs¯,ews(sAact)he¯µ¯he,igahdeirabenaetricgiepsr,ocboanbsiilsiteyntaswiathfuenxcisttioinng odfatean.- gdenenercael opnossdiibrielcittiieosnaslsoothexeristth[7a]n. WZe, coornecvluedne itnhtartodpuocs-ing (Bs)e¯µ¯, (Bc)e¯µ¯, and (C)e¯µ¯ are experiment-dependent lin- measurement for a combination of SME coefficients for µ µ µ µν µ ear combinations of the SME coefficeiAerngltssyo(aasLhv)oerwaangdeisdtLhoovereenartdz ivoainoblaeatitoyince: aprr.obaTbhileitypraetdaicptperdoxnimeuattreilnyo itairvbeitsriganryalcsofeoffir cLioenretnst(zaLvi)oelea,ti(oanL)ceoµu,ld(abLe)eτo,btaanidne(dcLb)yee , (c )µν for Lorentz violation. These combinations depend L flwuexekilsyhinatlfertvhaels ebxeptwecete|e(nCd)avn|2a+eluq1eu|(iAnato) xl|o2aw+nd1 e|(anAes)rogl|si2etiscea.nOdvdeer- dwethaiiclhedyfiietltdinsgaomf eoxdisetlinwgitehxp2e1ridmeegnrteaelsdoaftafr,ebedutomth.atMitore on the energy of the neutrinos. Their decomposition into e¯µ¯ 2 s e¯µ¯ 2 c e¯µ¯ cmreuacshesofathheigyheaer,einterregmieasi,ncs1onnesairstte2hnet1awvietrhag2eex.isTtihnegrediastaa. isgecnhearllaelnpgoinsgsibanilditipeserahlasposeexvisetn[7im].pWosesicbolencaltupdreetshenatt tpoos- energy-independent quantities takes a form analogous to + 2 |(Bs)e¯µ¯| + 2 |(Bc)e¯µ¯| that of Eq. (4): 2 Astlsronsghorewdnucistitohnenaedairaebaacthic(eh¯qpc)ur$oiPnbν¯oµa→xbν,¯eibl%iutyt tahteaapdpiraobxaitmicaatepl-y eixtcivluedseigtnhaelspofsosribLiloitryentthzatvitohlaetoiobnsecrovuedldnbeuetroibntoaionsecdil-by # 2 (0) (1) wpereokxliymianttieornvafalsilsbtehtwereeenbeacnauesqeLuoinscoixllaatnidonas scoelassteic, ea.nOd vsoer ladteitoanisleadrefidttuiengtooLf oerxeinsttiznagnedxCpePrTimveinotlatlidonatraa,tbhuert tthhaant it (C)e¯µ¯ = (C )e¯µ¯ + E(C )e¯µ¯, −19 2 (0) (1) mthuechtroufetshuervyievaarl,pirtorbeambai#liinty(s3 np±e1a) ×rks1t0hsheaaGrvpeeVlryatg.oe.unTihtye.r(e1T6)ihsea toismchaasslledniffgienrgenacnesd. perhaps even impossible at present to (As)e¯µ¯ = (As )e¯µ¯ + E(As )e¯µ¯, (0) (1) strong reductioSninnceetahre LeSaNcDhn!eeuqturinino oenxe,rgbyuliets tinht"eheardanigaeb1a0 tMiceVap- exclude the possibility that the observed neutrino oscil- (Ac)eµ = (A )eµ + E(A )eµ, ¯¯ c ¯¯ c ¯¯ < E < 50 MeV, this result corresponds to values of the (1) pr(1o)ximation fai∼ls th∼ere because oscillations cease, and so lations are due to Lorentz and CPT violation rather than (Bs)e¯µ¯ = E(Bs )e¯µ¯, (Bc)e¯µ¯ = E(Bc )e¯µ¯. (15) −19 the true survivaSMl pErcoebffiacibeniltistfoyr Lpoereanktzsvsiohlaatiropn loyf ortdoeru10nityG. eVThe to mass differences. Lorentz phenomenology 3 3 -Unusual energy dependence of fla1 vor conversions: 1 0.51 1 1 GeV L 0.5 0.51 es 2003 instead of usual : L or L E 1 GeV w 0.5 0.5 Me E 1 , 10 GeV 0 0 -1 2 however conspiracies can reproduce 0.5 -1 -0.5 0 0.5 1 10 1 10 10 cos Θzenith 10 GeV 0 E (MeV)

0.5 es 2003 atmospheric neutrinos at SK: 1 1 GeV w 1 Me

P i (Bc )ab = − N N − N N (cL)ab − (cL)aPb ν →ν ν¯ →ν¯ !2 " FIG. 2: µ µ averl aged over zenith angle for the bicycle µ e changes due to Earth rotation i 0.4 b

X Y XY Me ˆ ˆ , − 2N! N (cL)ab . "! model (sol(i1d"2)) and for a a conventional case with mass (dotted). Pν →ν b FIG. 4: ( e e )adiabatic for some modified models. o X Y Z atmospheric neutrinr os, which is a signal for Lorentz vi- In these expressions, Nˆ , Nˆ , Nˆ are directional factors p 0.2 combination of effects produces ripples in the binned flux ostelecky A very non-conventionalcontaining informa tphenomenologion about the neutroinlao-tbieoanm.diFreocr-ye,xampl% e, consider neutrinos propagating in K near the equinoxes, which might be detected in detailed tion with respect to the Earth. At the datethtmeectoohrsoplorhciazetoironinc,tanlepultarnineoosf,0twhheidcheteisctaors.igNneaultfroinroLsoorreingitnzavt-i- let θ be the angle between the beam and the vertical up- 0 5 10 15 202 ecxopmerbimineanttioanl aonfaelffyesecstsopf reoxdisutcinegs roirppfuletsurine dthaetab.inned flux very unlikely to fit all neutrinoo ilndata.agtiforno.mF tohreeexaasmt oprlew, ecsotnhsaidveercnoseuΘTtr=in0o,s ∆prmopΘa=ga0t,inagndin ward direction, let φ be the angle between the beam and ⊕ (hours) Although detection of the semiannual variation would south measured towards the east, and ltehtheχenbhceeothrneizocoloantst-cailllpatlaionnes.ofInthceondtertaesctt,otrh.oNseeuentrtienroinsgotrhigeindaet-- near the equinoxes, which might be detected in detailed P itude of the detector. Then, the directional factors are FIG. 1: Variations of the percent probability 2ν¯µ→ν¯e over represent a definite positive signal for Lorentz violation, itnegctforormfrotmhetehaestnoorrthweosrtshoauvteh ceoxspΘeri=en0c,e∆ampseu=do0m, asnsd experimental analyses of existing or future data. given explicitly as 2 one2sidereal2day for three sample configurations wΘith averaged its absence cannot serve to eliminate this type of model. of ∆m = ∆mprob◦abciloitys !Pχν¯ .→ν¯ F" =ig0u.2r6%e: 2(C)e¯sµ¯h=# o0w(sdasthhede), (sAusr)e¯vµ¯ i=# val hence nΘo oscillati0ons. Inµcoentrast, those entering the de- Although detection of the semiannual variation would Nˆ X cos χ sin θ cos φ + sin χpcroos θbability ave0ra(dgotetded)o, vanedr(zC)ee¯nµ¯ i=th(Aas)ne¯µ¯g=# le0 a(ssoliad).function of az- Sriempprleesemnotdaifidceafitniointes opfotshiteivmeosdigenl aexl ifsotrtLhaotreenxthzibviitoslaimti-on, Nˆ Y = sin θ sin φ tector f.ro(m13)the north or south experience a pseudomass    imutha2l angle. A2lthou2gh this model predicts no east-west ilar overall behavior for solar and atmospheric neutrinos Nˆ Z − sin χ sin θ cos φ + cosoχfco∆s θm = ∆m ◦ cos χ. Figure 2 shows the survival its absence cannot serve to eliminate this type of model. Θ Th0ere are therefore a total of eight complex experiment- but have only a small semiannual variation. As an illus-    asymmetry beyond the usual case,(0n) orth-e(0a)st or (n0)orth- Simple modifications of the model exist that exhibit sim- probability averdeapgeneddenotvecoreffizecinenittsh: a(nAgs le)eµa,s (aAfcu)neµc,ti(oCn o)efµ,az- Z Any given short-baseline experiment is sensitive ¯¯ ¯¯ ¯¯ tration, consider the replacement of the coefficient (aL)eµ soµuth asymmetri(e1)s app(e1)ar. Si(1m) ilar (‘1c)ompa(1s)s’ asymme- ilar overall behavior for solar and atmospheric neutrinos to three complex combinations of (aimL) utchoeaffilcaientgs,le. (AAslth)e¯oµ¯,u(gAhc t)e¯hµ¯i,s(Bms o)ed¯µ¯e, l(Bpcre)e¯dµ¯i,c(tCs n)e¯oµ¯.eaAscto-mw-est T (0) (0) (0) tries are typicaplreihnenasilvle daniraleycsitsiofnt-hde eLpSNenDddeantatfomr tohde eablso.ve en- with a coefficient (aL)eµ of half the size. This has the ef- (As )ab, (Ac )ab, (C )ab, and five caomsyplmexmcoemtbrinya-beyond the usual case, north-east or north- but have only a small semiannual variation. As an illus- (1) (1) (1) ergy and sidereal dependence would in principle yield tions of (c )µν coefficients, (A ) , (A T) h, e(Bba)si,c features of solar-neutrino oscillations pre- fect of replacing the solid and dashed curves of Fig. 3 Z L s ab c ab s ab measurements of 16 of the possible 102 real degrees of tration, consider the replacement of the coefficient (aL)eµ (1) (1) south asymmetries appear. Similar ‘compass’ asymme- (Bc )ab, (C )ab. However, the directiodniacltdeedpenbdyenctehe fmreeoddomelinatrhee naelustorinocosemctopraotfitbhelemiwniimtahl SoMbEs.eWrvea- with those shown in FiTg. 4. The semiannual variations tries are typical in all direction-dependent models. with a coefficient (aL)eµ of half the size. This has the ef- implies that a combination of experimenttisotnes.tinOg abspeer-vedresmoalrakrinnpeausstinrginthoast pthreoipncalugsaiotneofina mthases-sEquaarrtedh’s in this type of model lie below existing statistical sen- cific oscillation mode νa → νb can provide access to all 2 fect of replacing the solid and dashed curves of Fig. 3 µ µν The basic femaatturirxe(sm˜ o)afb fsoor lnaeru-trnineous tinritnhoe poressecni◦tllfaortmioalnissm pisre- Z T components of (aL) and (cL) , providoedrbthietdailrepctlioannse, which lies at an angle η 23 relative to sitivities. Replacing also (aL)µτ with (aL)µτ is another ab ab straightforward. For example, i2n Eq. (15) it suffices to with those shown in Fig. 4. The semiannual variations of the associated neutrino beams differ.dicted by the model are also compatib!le wit−h1 ob2 s∗erva- the equatorial pexltaendet.heTdhefienivtiaonluoef (oC)fe¯µ¯ctoos(C)Θe¯µ¯ t=h(e2rEe)fo(rm˜e v)eaµr+ies option, which removes all orientation dependence in the For the special case of the transition mode relevant to ¯2¯ in this type of model lie below existing statistical sen- tion. Observed(Cs(o0)l)ar+nEe(uC(t1r))in.osIt pturronspoaugt athtaet tihne gtehneeraEl tawrot-h◦’s LSND, the probability takes the form from zero at the tweo¯µ¯ equinoxe¯µe¯ s to its maximum◦ of sin 23 model. Another example of a smZall modificatiTon is a 10% orbital plane, wgehneircahtiolniemsodaetl waitnh aamnagslse-sqηuared 2m3atrixrealnadtbiovteh to sitivities. ReplacTing also (aL)µτ with (aL)µτ is another at the two solsticeµs. Assuµmν ing adiaba2tic propagation in admixture of (aL)ee, which raises the survival probability L2 the equatorial p(alLa)nea.ndT(chLe) vacoleuffiecioenftschoass 4Θ1!detghreerseoffofreeedvoamr, ies option, which removes all orientation dependence in the Pν →ν # | (C)eµ while its rotation-invariant restriction has eight [12]. of 0.5 at low energies to about 0.6 without appreciably ¯µ ¯e (h¯c)2 ¯¯ the Sun, the average νe survival probability is 2 ◦ from zero at the tTwheopeuqbluisihnedoxreesuslttsofriotms LmSNaDxipmerummit tohef esxitnrac2- 3 amffeocdtienl.g Aonthoetrherreseuxlatms.plTehoef aensmsuainllgmsoudrvifiivcaaltiponroibsaabi1l-0% + (As)e¯µ¯ sin ω⊕T⊕ + (Ac)e¯µ¯ cos ω⊕T⊕ tion of a measurement for one combination of these de- T at the two solstices. Assu2ming2adiabatic2 prop2agation in admixture of (aL)ee, which raises the survival probability (Pν →ν 2 )adiagbreaetsicof=freseidnom.θ sInintheθe0xp+ericmoesnt,θcocpoiosusθn0u,mber(s5) ity in the adiabatic approximation is shown as the dot- + (Bs)e¯µ¯ sin 2ω⊕T⊕ + (Bc)e¯µ¯ cos 2ω⊕e T⊕ |e, of 0.5 at low energies to about 0.6 without appreciably the Sun, t(1h4e) avoef rν¯aµ gweerνe eprsoduurcvedi.vaAlnpexrcoebssaobf iν¯leitoyverisbackground ted line in Fig. 4. Other more complicated modifications was observed, which was interpreted as ν¯ oscillating where θ0 is the mixing angle at the core, giµven by re- thaffatecctoinugld obtehecrournesteunltasn.ceTdhbeutentshuaitngnosnuertvhievlaelssprreotbaainbil- where ω⊕ # 2π/(23 h 56 min) is the Earth’s sidereal into ν¯e. The 2correspo2nding oscilla2tion pro2bability is (Pν →ν )adiabatic = sin θ sin θ0 + cos θ cos θ0, (5) ity in the adiabatic approximation is shown as the dot- frequency and T⊕ is a standardized timpe l[2a3c].inTeghe tiem˚cEe wPiν¯tµh→ν¯e #˚cE0.2+6 ±G0.0F8n%e. /S√inc2e tihnis Epuqbl.ish(e4d).resuFltiginu-re the flavor of the simple model include allowing depen- variation is a direct consequence of the3dsirhecotiwonsa−l tdhe-e advoilavebsa−altliecvenptrsoirbreaspbeicltiivteyofasisderaealfutimnec,tiitorenpreosefntesn- dteendcelinoenindiFreicgt.io4n. sOotthheerrmthoaren cZom, oprliceavteend imntordoidfiuccaitnigons an average over the run time of the experiment. To a pendence. In the short-baseline approxwimhaetiroen, θw0e fiinsd the mixing angle at the core, given by re- that could be countenanµced butµ that nµonetheless rµeνtain ergy averaged goovdearpporonxeimayteioanr, .it caTn hbe tapkrenedasicretperdesenteinugttrhieno arbitrary coefficients (aL)ee, (aL)eµ, (aL)eτ , and (cL)ee , harmonics up to 2ω⊕, but more generally all higher har- √ monics can occur. pflluacxinisg ha˚clfEthweeixtpehexcptaet˚icoEnteodv+ervaGasliFduenereeaa/l tdayl2,o$wPiν¯nµe→nEν¯eeq%r#.gi0(e.42s6).±a0n.F0d8i%gd.uer-e wthhiechflayvieolrdsoaf tmhoedseilmwpilteh m21oddeelgrineecsluodfefraelelodwomin.g Mdeopreen- − Using −Eq. (14) and this result, we obtain a nonzero In Eq. (14), the complex factors 3c(Arsesh)ae¯oµs¯,ews(sAact)he¯µ¯he,igahdeirabenaetricgiepsr,ocboanbsiilsiteyntaswiathfuenxcisttioinng odfatean.- gdenenercael opnossdiibrielcittiieosnaslsoothexeristth[7a]n. WZe, coornecvluedne itnhtartodpuocs-ing (Bs)e¯µ¯, (Bc)e¯µ¯, and (C)e¯µ¯ are experiment-dependent lin- measurement for a combination of SME coefficients for µ µ µ µν µ ear combinations of the SME coefficeiAerngltssyo(aasLhv)oerwaangdeisdtLhoovereenartdz ivoainoblaeatitoyince: aprr.obaTbhileitypraetdaicptperdoxnimeuattreilnyo itairvbeitsriganryalcsofeoffir cLioenretnst(zaLvi)oelea,ti(oanL)ceoµu,ld(abLe)eτo,btaanidne(dcLb)yee , (c )µν for Lorentz violation. These combinations depend L flwuexekilsyhinatlfertvhaels ebxeptwecete|e(nCd)avn|2a+eluq1eu|(iAnato) xl|o2aw+nd1 e|(anAes)rogl|si2etiscea.nOdvdeer- dwethaiiclhedyfiietltdinsgaomf eoxdisetlinwgitehxp2e1ridmeegnrteaelsdoaftafr,ebedutomth.atMitore on the energy of the neutrinos. Their decomposition into e¯µ¯ 2 s e¯µ¯ 2 c e¯µ¯ cmreuacshesofathheigyheaer,einterregmieasi,ncs1onnesairstte2hnet1awvietrhag2eex.isTtihnegrediastaa. isgecnhearllaelnpgoinsgsibanilditipeserahlasposeexvisetn[7im].pWosesicbolencaltupdreetshenatt tpoos- energy-independent quantities takes a form analogous to + 2 |(Bs)e¯µ¯| + 2 |(Bc)e¯µ¯| that of Eq. (4): 2 Astlsronsghorewdnucistitohnenaedairaebaacthic(eh¯qpc)ur$oiPnbν¯oµa→xbν,¯eibl%iutyt tahteaapdpiraobxaitmicaatepl-y eixtcivluedseigtnhaelspofsosribLiloitryentthzatvitohlaetoiobnsecrovuedldnbeuetroibntoaionsecdil-by # 2 (0) (1) wpereokxliymianttieornvafalsilsbtehtwereeenbeacnauesqeLuoinscoixllaatnidonas scoelassteic, ea.nOd vsoer ladteitoanisleadrefidttuiengtooLf oerxeinsttiznagnedxCpePrTimveinotlatlidonatraa,tbhuert tthhaant it (C)e¯µ¯ = (C )e¯µ¯ + E(C )e¯µ¯, −19 2 (0) (1) mthuechtroufetshuervyievaarl,pirtorbeambai#liinty(s3 np±e1a) ×rks1t0hsheaaGrvpeeVlryatg.oe.unTihtye.r(e1T6)ihsea toismchaasslledniffgienrgenacnesd. perhaps even impossible at present to (As)e¯µ¯ = (As )e¯µ¯ + E(As )e¯µ¯, (0) (1) strong reductioSninnceetahre LeSaNcDhn!eeuqturinino oenxe,rgbyuliets tinht"eheardanigaeb1a0 tMiceVap- exclude the possibility that the observed neutrino oscil- (Ac)eµ = (A )eµ + E(A )eµ, ¯¯ c ¯¯ c ¯¯ < E < 50 MeV, this result corresponds to values of the (1) pr(1o)ximation fai∼ls th∼ere because oscillations cease, and so lations are due to Lorentz and CPT violation rather than (Bs)e¯µ¯ = E(Bs )e¯µ¯, (Bc)e¯µ¯ = E(Bc )e¯µ¯. (15) −19 the true survivaSMl pErcoebffiacibeniltistfoyr Lpoereanktzsvsiohlaatiropn loyf ortdoeru10nityG. eVThe to mass differences. A Lorentz model for LSND de Gouvêa, Grossman 2006 - allow: massive neutrinos + Lorentz - drop: directional dependence - encode all Lorentz effects in the dispersion relation E = E ( p! ) : 2 2 2N m f(|p!| ) |p!| E ! |p!| + + and take f(|p!|) = 2E0 aN 2|p!| 2|p!| !E0 " |p!| ! m, f standard Lorentz ! " #

- assume Lorentz for one state only: |νL! = cos ζ cos θL |νe! + cos ζ sin θL |νµ! + sin ζ |ντ ! A Lorentz model for LSND de Gouvêa, Grossman 2006 - allow: massive neutrinos + Lorentz - drop: directional dependence - encode all Lorentz effects in the dispersion relation E = E ( p! ) : 2 2 2N m f(|p!| ) |p!| E ! |p!| + + and take f(|p!|) = 2E0 aN 2|p!| 2|p!| !E0 " |p!| ! m, f standard Lorentz ! " #

- assume Lorentz for one state only: |νL! = cos ζ cos θL |νe! + cos ζ sin θL |νµ! + sin ζ |ντ ! dν i α = H ν Neutrino oscillations are described by: dt αβ β 0 2 2 2 2N−1 c c c cθL sθL cζ sζ cθL 2 E ζ θL ζ ∆m21 † 2 2 2 H = UPMNS   U +a c c s c s c s s 2E PMNS N  ζ θL θL ζ θL ζ ζ θL  ∆ 2 'E0 ( 2 m31 c s c c s s s   ζ ζ θL ζ ζ θL ζ  2E    mass-induced oscillations Lorentz-induced oscillations A Lorentz model for LSND ∆m2 L ij ! 1 (A) LSND, SBL E : oscillations dominated by Lorentz 2N−1 ⇑ 4 2 −3 4 2 2 E L cos sin 2 10 Pµe ! cos ζ sin 2θL sin aN LSND ζ θL ! E0 2 ! " # $ 2N−1 4 2 −3 2 2 2 E L cos ζ sin 2θL < 1.1 10 Pµτ ! sin 2ζ sin θL sin aN E0 2 SBL 2 2 −4 ! " # $ sin 2ζ sin θL < 3.3 10 2 −3 choose: s in ζ = 0 and s in 2 θ L = 1 . 1 1 0 . de Gouvêa, Grossman 2006 1 ee P 0.9 7 P − (B) solar neutrinos + Kamland: ee V 0.8 0 e 5 6 1 − − M 0.7 5 2 / Lorentz effects must be suppressed, 0 0 1 V 2N−1 0.6 1 = e E 5 5 large N : ! 1 for E < E0 0.5 5 a !E0 " 0.4 a5 = 0 0.3 2 4 6 8 10 12 14 16 18 20 E (MeV) Eν (MeV) (C) atmospheric: with these choices, | ν L ! " | ν e ! ν F µI G .↔ 1 : Sν u τ rv oscillationsival probability ounafff solar ectedneutrino.s (Pee) as a function of the solar neutrino energy (E), for E0 = 15 MeV and diﬀerent values of aN . The diﬀerent curves correspond to N = 5 and

−5 2 −6 2 a5 = 0 (solid, black line), a5 = 5 10 eV /MeV (dashed, red line), a5 = 5 10 eV /MeV × × (dotted, green line), and 5 10−7 eV2/MeV (dashed-dotted, blue line). See text for details. ×

choices are made, KamLAND data is completely oblivious to LIV effects, given that relevant reactor neutrino energies are less than 10 MeV. Next we consider atmospheric neutrinos. For the values of N in which we are interested, LIV effects for E 100 MeV are very large and ν is basically decoupled from the other ≥ L two neutrinos. Thus, we are left with a standard effective two-flavor oscillation scheme

between these two states, governed by the oscillation frequency ∆13. Since we choose νL to

be mostly νe, the other two neutrinos are mostly linear combinations of νµ and ντ , such that ν ν oscillations proceed as if there were no LIV eﬀects. Eﬀects due to the deviation µ → τ of νL from a pure νe state can be readily computed, and turn out to be very small. We have checked that, for the parameter values considered here, such deviations are within the current experimental uncertainties.4 All considerations above constrain

2N−1 LSND −3 2 −6 E L Pµe 10 sin 2.54 10 , (10) ∼ ! × "15 MeV # "m#$ so that N is the only left-over parameter. Since we wish to avoid averaged-out oscillations for typical LSND energies and baselines (if at all possible), the best one can do is to choose the oscillation phase to be close π/2 for typical LSND parameters, L 30 m and E 50 MeV. ∼ ∼ This translates into 2N 1 = 9, or N = 5.5 This is far from providing a good ﬁt to the −

4 These eﬀects are indeed very small, and it is not clear whether one will be able to probe them in future atmospheric neutrino experiments. 5 For smaller values of N, there is “no hope” of reconciling solar and LSND data. A detailed discussion

8 A Lorentz model for LSND ∆m2 L ij ! 1 (A) LSND, SBL E : oscillations dominated by Lorentz 2N−1 ⇑ 4 2 −3 4 2 2 E L cos sin 2 10 Pµe ! cos ζ sin 2θL sin aN LSND ζ θL ! E0 2 ! " # $ 2N−1 4 2 −3 2 2 2 E L cos ζ sin 2θL < 1.1 10 Pµτ ! sin 2ζ sin θL sin aN E0 2 SBL 2 2 −4 ! " # $ sin 2ζ sin θL < 3.3 10 2 −3 choose: s in ζ = 0 and s in 2 θ L = 1 . 1 1 0 . de Gouvêa, Grossman 2006 1 ee P 0.9 7 P − (B) solar neutrinos + Kamland: ee V 0.8 0 e 5 6 1 − − M 0.7 5 2 / Lorentz effects must be suppressed, 0 0 1 V 2N−1 0.6 1 = e E 5 5 large N : ! 1 for E < E0 0.5 5 a !E0 " 0.4 a5 = 0 0.3 2 4 6 8 10 12 14 16 18 20 E (MeV) Eν (MeV) (C) atmospheric: with these choices, | ν L ! " | ν e ! ν F µI G .↔ 1 : Sν u τ rv oscillationsival probability ounafff solar ectedneutrino.s (Pee) as a function of the solar neutrino energy (E), for E0 = 15 MeV and diﬀerent values of aN . The diﬀerent curves correspond to N = 5 and

Bottom line: a highly non-trivial energy dependence−5 2 is needed −6 2 a5 = 0 (solid, black line), a5 = 5 10 eV /MeV (dashed, red line), a5 = 5 10 eV /MeV × × to ﬁt( dallott edata.d, gree n Evlinene), a nmord 5 e1 0so−7 eafterV2/Me VMiniBooNE(dashed-dotted, blu.e line). See text for details. ×

between these two states, governed by the oscillation frequency ∆13. Since we choose νL to

8 Sterile shortcuts in Extra Dimensions Sterile shortcuts in x-dims Päs, Pakvasa, Weiler 2005

Framework: a large extra dimension,HEINRICH PA¨ S,withSANDIP PaAKV waASA,vyAND THOMASbraneJ. WEILER PHYSICAL REVIEW D 72, 095017 (2005) On the other hand, in (x, y) coordinates, the brane is brane ν R sterile described by the periodic sine function, while the geodesic geodesic in the bulk follows a straight line along mean y, given by y 0; D t: (11) g g νactive A kx G, νs sin( ) Using Eqs. (6) and (7), the bulk geodesic equation (11) can 2 be transformed into the (u, z) system, FIG. 1 (color online). LSchematic− Lrepresentation ofAakperiodi- 5d 4d u A sin kt ; (12) cally curved brane! =in Minkowski spacetime."A coordinate trans- g ÿ formation leads to an equivalentL5ddescription as!a nondiagonal2 " metric with a flat brane, as described in the text. t f 2 2 2 zg 1 A k cos kt dt −E(t+∆t) 0 neutrino states evolution: |να! = e |να! Z p D x: (3) −Et g p1 A2k2 A2k2 ktf; ; (13) |νs! = e The geodesic|νs! for the active state on the brane is slightly k E s1 A2k2 more complicated: where p; q denotes the elliptic integral of the second x kind. E 2 2 2 2 2 2 ∆m Db dx dy 1 A k cos kx dx: (4) The bulk geodesic intersects the brane at u 0, which brane1 1 g H = U 2E U † +Z qE! Z p according to Eq. (12) occurs at the discrete times We use subscripts b and g to denote− the brane and bulk ! 0 " spaces, respecti2 vely.! 1 " n tint ; (14) In terms of the coordinate x, the parameter describing k the shortcut in the bulk is ∆m2 cos 2θ where n is an integer. However, if the size of the brane’s D D x fluctuations is small on the scale of an experimental detec- x bEÿ g =1 : (5) a resonance in the oscillation probability: res x 2 2 2 tor, then it is not required that the two geodesics be in Db ÿ!p1 A k2cos" kx dx intersection, and tint has no special significance. While mathematically correct,R thisdescriptionof the geo- From a comparison of the integrand in (13) to the result desics as functions of x has a shortcoming, in that x is not a of (10), one readily infers that zg > zb, which means that in coordinate easily identified in an experiment on the brane. a common time interval the bulk test particle seemingly It is useful to consider a more physical set of brane coor- travels farther in the physical z-coordinate than the brane dinates. They will lead to essentially the same parameter . particle. In other words, the specific metric (8) allows Consider the space-coordinate transformation apparent superluminal propagation. The shortcut in the bulk can be parametrized by u y A sinkx (6) ÿ zg zb ktf and tf ÿ 1 : z 2 2 g ÿ 1 A2k2 kt ; A k x f 1 A2k2 E z 1 A2k2cos2kx dx: (7) q p (15) Z p Under this transformation, the line element in (1) trans- We note that this and the one defined in Eq. (5) are forms into formally the same when the space-coordinate x is replaced by the physical time-coordinate t. 2 2 2 2 2Ak coskx z ds dt dz du du dz: The parameter depends very weakly on tf when many ÿ ÿ ÿ 1 A2k2cos2kx z fluctuations are traversed, i.e. when t 2=k. In fact, we f p (8) are free to choose tf according to Eq. (14). With this Note that in (u, z) coordinates, u 0 defines the location choice, the shortcut parameter depends only on the geome- of the brane, and z labels the physical distance along the try Ak of the brane fluctuation, according to brane. Consequently, a photon moving along the brane =2 (u 0) satisfies the equation 1 : (16) ÿ 1 A2k2 c ; A2k2 2 2 2 2 1 A2k2 ds dt dz ; (9) E ÿ p q and thus travels in time t the distance In the latter equation, we have used the relation n; q f E 2n c ; q ; the expression c ; q is called the complete z t : (10) E 2 E 2 b f elliptic integral. In the model developed here, an inference

095017-2 Sterile shortcuts in x-dims Päs, Pakvasa, Weiler 2005 Oscillation probability determined by neutrino energy. resonance HEINRICH PA¨ S, SANDIP PAKVASA, AND THOMAS J. WEILER PHYSICAL REVIEW D 72, 095017 (2005) HEINRICH PA¨ S, SANDIP PAKVASA, AND THOMAS J. WEILER PHYSICAL REVIEW D 72, 095017 (2005) Predictions for MiniBooNE: 1 m2 cos2 sin2 1 0 1 P 0.1 P θ H E : ~ µe E = 200 MeV µµ F ÿ 2 res 4E sin2 cos2 2 0 1 0.1 0.8 ÿ 2 0.08 (23) 300 MeV sin 0.01 0.6 0.06 The bulk term may beat against the brane term to give 0.001 400 MeV resonant mixing, i.e., for some energy Eres even a small 0.4 0.04 standard angle can become large or even maximal in the 0.0001 brane-bulk model. The resonance condition is that the two 0.2 0.00001 0.02 diagonal elements in HF be equal, which implies

1. 10 6 0 0 20 40 60 80 100 120 1 5 10 50 100 500 1000 200 400 600 800 1000 2 m cos2 below resonance above resonance Eν (MeV) Eres : (24) E [MeV] D [m] s2 Bugey LSND CDHS E [MeV] FIG.standar2. Oscillationd oscillationsamplitude sin22~ as asupprfunctionessedof the oscill E ! E FIG. 6 (color online). The muon-neutrino survival probability Since the value of is unknown, the resonance energy neutrinochooseenergy E small, for a resonanceθes energy oforEres any40θMeVµs . FIG. 5 (coloroscillationonline). Bulk-shortcut peakoscillation at probabilities r e s . The different curves correspond to different values for the for MiniBooNE as a function of the neutrino energy. Shown is versus distance, for a monochromatic neutrino-beam energy of could have almost any value, a priori. However, if 1, 2 2 2 standard angle, sin 2 0:2, 0.1, 0.01, 0.001 (from above). a scenario withandsin no2 signal0:1; sin22 at 0 E:45>; mE2 res0:8 eV2. 30 MeV from stopped pions. The solid curves are parametrized as we assume, then we have the result m Eres. Still, The resonance energy isvaried, E 200, 300, 400MeV, from by resonance energies 33, 100, 200 (identical for 300 and there is much parameter space available for resonance. Our res aim is to accommodate the LSND result in a four-neutrino left to right (light to dark). For comparison, the expectation for a 400 MeV), in order of decreasing depletion. The dashed curve m2 E 2 2 2 2 is the result with no bulk shortcut. The low-energy parameters framework, and so we will restrict the resonance energy 2 2 standard oscillation solution (m 0:8 eV, sin 2LSND H sin 2 cos 2 1 : (27) 2 2E s ÿ Eres 0:006) for LSND is displayed (dashed line). The vertical line for the 33 MeV resonance are chosen as in Fig. 3: sin 0:01; with this in mind. It is worth noting that according to (24), 2 2 2 2 indicates the energy threshold of MiniBooNE. sin 2 0:9; m 0:7 eV ; while the parameters for the a determination of Eres fixes , if m and cos2 can be 2 2 The width of the resonance is easily derived from the other curves are chosen as in Fig. 4: sin 0:1; sin 2 independently determined. One way to independently de- 2 2 termine m2 and cos2 is to observe the active-sterile 1 2 ~ 0:45; m 0:8 eV . The vertical lines indicate the range of classical amplitude in Eq. (26). Fig. 2 shows sin 2 for Fig. 5 for resonance energies of 200, 300, and 400 MeV. As oscillation parameters far below resonance, where the different values of sin22 as a function of energy. possible source to near/far detector distances. oscillations are described by the standard formulas. Note For E E , the sterile state decouples from the active can be seen, the strongly enhanced oscillation probability res that knowledge of , when available, yields the shape- state, as sin22~ 0. Although the example presented in is unmistakable. ! On the other hand, if E lies below the MiniBooNE the SNS source for stopped pions, there is the possibility of parameter Ak of the brane fluctuation, according to this section contains a single sterile state and a single active res a high-intensity ‘‘proton driver’’ at Fermilab which would Eq. (17). threshold energy, then active-sterile mixing is strongly state, the decoupling of the sterile state(s) from the active also include stopped pions on its physics agenda. Detector The value of Eres naturally divides the energy domain state(s) is a general feature. suppressed for MiniBooNE. At energies E Eres, one into three regions. Below the resonance, oscillation pa- uses Eq. (26) in Eq. (41) to approximate distances at either site would be under 100 m from the pion source. Thus, the D=E is sufficiently small that only the rameters reduce to their standard values and give the IV. ACCOMMODATING THE LSND RESULT familiar oscillation results. At resonance, the mixing angle 1 E 8 LSND m2 can affect neutrino flavor change. sin 22~ sin22 tan42 ÿ : (43) attains a maximum (but the effect on the oscillation proba- As the sterile neutrino mass is not protected by the gauge MiniBooNE The amplitude for -survival is given by Eq. (35), and ’ 16 Eres bility can be reduced by a compensating factor in the m2 symmetry of the standard model, it is natural to assume it the term oscillating with distance is sin2 HD=2 , with H to be larger than the masses of the active neutrinos. We thus term). Above resonance, the oscillations are suppressed. Thus a null result is predicted for MiniBooNE in the case given in Eq. (27). The effects predicted for the stopped- Our strategy to accommodate the LSND data in a four- focus here on a 3 1 neutrino spectrum [14], i.e. three pion source at the SNS are shown in Fig. 6. The neutrino framework will be to set the resonant energy well active neutrinos are separated by the LSND mass-squared of a resonance energy (as in our 33 MeV example) below 2 the MiniBooNE threshold of 100 MeV. depletion of the beam due to substantial low-energy below the CDHS data to suppress oscillations for this gap mLSND from the dominantly sterile state 4 s. 2 O experiment, but at or above the LSND energies, so as to In the present model, m~ differs from the standard However, if Eres is too low for an observable effect in sterile-active mixing is considerable. For E E , or for LSND res not suppress (or even, to enhance) the LSND signal. formalism by the square-root factor in (27). If the new MiniBooNE, a distortion in the LSND spectrum is ex- near maximal, the oscillation length is insensitive to Eres. To find the new eigenvalue difference H and the new pected (see Fig. 3). A strong disappearance signal This explains the nearly common distance for the various mixing angle ~ affected by the bulk, one diagonalizes the 1A short calculation gives the Full Width in energy at a also is predicted for an experiment using neutrinos from minima in the figure. 2 2 system. In terms of the new H and ~ one obtains the fraction f of Maximum (FWfM) as stopped pions, being proposed for the Spallation Neutron We note that the large -depletion in Fig. 6 is specific usual expression for the flavor-oscillation probability Source (SNS). This we discuss next. E FWfM 1 f 1=2 to the parameters we have chosen, and so should be inter- 1 tan2 ÿ preted as illustrative only. Smaller mixing leads to smaller 2 ~ 2 Eres sf Pas sin 2sin HD=2 ; (25) F. Muon-neutrino disappearance at the SNS depletion. If a component were added to the a state, the 1 f 1=2 1 tan2 ÿ ; (28) -depletion may be less. Nevertheless, observable deple- ÿ ÿ f While the sterile neutrino effectively decouples from the with new values given in terms of standard values by s active sector at the CDHS energy and above, there is no tion of ’s from stopped pions is one of the more robust 1 f suppression of the active-sterile mixing at and below the predictions of the brane-bulk model. sin22 which, for small reduces to 2 ÿ . Thus, the resonance is 2 ~ f sin 2 2 2 ; (26) very narrow for a small standard angle. For example, Full Width resonance. Therefore, a significant effect is predicted for 2 2 E q sin 2 cos 2 1 at Half Max is E FWHM 2Eres for small angle. For a disappearance at lower energies. ÿ Eres V. FURTHER IMPLICATIONS FOR larger standard angle, the resonance becomes less dramatic. Just such a lower energy disappearance experiment ASTROPHYSICS AND COSMOLOGY has been proposed [20] at the Spallation Neutron Source (SNS) being built at Oak Ridge. The neutrino source would A. BBN 095017-4 be stopped ’s, which undergo two-body decay to pro- Successful big bang nucleosynthesis (BBN) puts severe duce a monochromatic beam at 30 MeV. In addition to constraints on the equilibration between active neutrinos

095017-8 CPT Basics CPT is conserved in any local, Lorentz invariant QFT.

(1) CPT can be induced by Lorentz (see above discussion)

(2) CPT can manifest itself in m != m ¯ (requires non-locality): Origin: non-perturbative effects in strings, quantum gravity... In the neutrino sector, the main motivation is LSND. From other sectors, there are strong bounds: −18 (mK0 − mK¯ 0 ) < 10 mK −9 (me+ − me− ) < 10 me Phenomenological approach: assume that CPT couples dominantly to neutrinos ¯ and use new parameters m ¯ i != m i and θij != θij CPT version 1 Murayama, Yanagida 2001 neutrinos anti-neutrinos_ Baremboim et al. 2001 m3

2 2 - solar ν e oscillate with ∆m21 ≡ ∆mSun LSND _ } ν ν¯ m m - atmospheric µ and µ with 3 2 2 2 2 ∆m31 = ∆m¯ 31 ≡ ∆matm _ Legend:_

atmospheric 2 2 } } atmospheric !e !e m2 m1 - LSND_ ν¯ µ → ν ¯ e with ∆m¯ 31 ≡ ∆mLSND !µ _!µ solar } m1 !" !"

Figure 1: Possible neutrino mass spectrum in the case of maximal CP T violation. Al- though the figure Butshows a:n Kamlandexample of la:rg e m(2002)ixing, our approach is agnostic about the mixing matrix. 2 2 ν¯ e disappear with ∆ m ¯ consistent with solar ∆ m ; energy effective field theory wthisill in hCPTerit C Pscenario:T invarianc edisfafrom tvhoure CPedT s.ymmetry of the underlying worldsheet dynamics. However it has been suggested that nonperturbative string effects may violate CP T directly, and it is also plausible that the choice of string vacuum may violate CP T spontaneously in the low energy four dimensional effective field theory [9]. We now observe that, in braneworld models of string phenomenology, the neutrino sector is the most likely messenger of CP T violation to the rest of the Standard Model. This is because the source of dynamical or spontaneous CP T violation will lie in the bulk, and the Standard Model effects will only be visible via couplings of Standard Model fields (assumed to reside on branes) to suitable bulk messengers. The generic candidates for the bulk fields which act as the messengers of CP T are (i) gravity and (ii) the right-handed neutrinos (i.e., the SU(2)L singlet neutrinos Ni). If the extra dimensions are not large enough, gravity effects are difficult to observe, while the right-handed neutrinos can still have easily observable Dirac mass couplings. These are precisely the braneworld scenarios

6 CPT version 2 neutrinos anti-neutrinos Baremboim et al. 2002 Strumia 2002

atmospheric , LSND - atmospheric ν µ oscillate with ∆m2 ≡ ∆m2 atmospheric 31 atm 2 2 KamLAND - atmospheric ν¯ µ with ∆m¯ 31 ≡ ∆mLSND solar 2 - Kamland ν¯ e disappear with ∆ m ¯ 2 Figure 2: Possible neutrino mass spectrum with almost no electron content in t h econsistentheavy with solar ∆m state. Although the figure shows an explict mixing pattern, there is a whole family of mixing matrices that can do an equally good job. The flavor content is distributed as follows: electron flavor (red), muonAflav odedicatedr (brown) and tau flav orglobal(yellow) fit is needed. differences but a much slighter effect in the mixing matrix. This is seen in Fig. 2 where the flavor distribution in the neutrino and antineutrino spectra is rather similar. The most distinctive feature of this family of solutions is its θ23, which lives far away from maximal mixing, or in other words which has a large component of antitau neutrino in the heavy state. The small antimuon neutrino component in the heavy state is not bounded by the non observation of muon neutrino disappearance over short baselines in the CDHS experiment[15], as the antineutrino component in this experiment was minimal.

KamLAND could have observed an oscillation signal driven by the smaller antineutrino mass splitting and interpreted it as LMA oscillations. To explicitly see how this might have happened, we will choose two sample points in our parameter space and calculate the transition probabilities for it. Let us emphasize that we have not performed a chi-squared ﬁt and therefore the points we are selecting (by eye and not by chi) are not optimized to give the best ﬁt to the existing data. Instead, they must be regarded as two among the many equally good sons in this family of solutions.

6 2 where terms proportional to ∆m¯ 21 which are irrelevant for LSND distances and energies have been neglected. In Eq. (257):

2 2 2 2 2 ¯ ∆mLSND = ∆m¯ 31 , sin 2θLSND = s¯23 sin 2θ13 . (258)

For the neutrino sector relevant information arises from solar neutrino experiments and the K2K and MINOS LBL experiments. The relevant probabilities are given in Eq. (76) for solar neutrinos and Eq. (79) for K2K and MINOS.

Finally, the analysis of atmospheric neutrino data involves oscillations of both neutrinos and anti-neutrinos, and, in the framework of 3ν + 3ν¯ mixing, matter effects become relevant and its effect has to be quantified by numerically solving the evolution equations for neutrinos and antineutrinos.

The basic approach to test the status of the scheme in Fig. 47 as a possible explanation of the LSND anomaly together with all other neutrino and antineutrino oscillation data is as follows. First, one performs a global analysis of all the relevant data, but leaving out LSND data. The goal of this analysis 2 2 is to obtain the allowed ranges of parameters ∆mLSND and sin 2θLSND as deﬁned in Eq. (258) from this all-but-LSND data set. We one compares these allowed regions to the corresponding allowed parameter region from LSND, and quantify at which CL both regions become compatible.

In this approach one starts by deﬁning the most general χ2 for the all-but- LSND data set:

2 2 2 2 2 ¯ ¯ ¯ χall-but-LSND(∆m21, ∆m31, θ12, θ13, θ23 ∆m¯ 21, ∆m¯ 31, θ12, θ13, θ23) = 2 2 | 2 2 χsol(∆m21, θ12, θ13) + χK2K(∆m31, θ23, θ13) 2 2 2 ¯ ¯ + χBugey+CHOOZ+KLAND(∆m¯ 21, ∆m¯ 31, θ12, θ13) + χ2 (∆m2 , ∆m2 , θ , θ , θ ∆m¯ 2 , ∆m¯ 2 , θ¯ , θ¯ , θ¯ ) . (259) atm 21 31 12 23 13| 21 31 12 23 13 In order to test the status of the CPT interpretation of the LSND signal using data independent of the “tension” between LSND and KARMEN results [310] CPTthe cons trglobalaints from the non-obs ervfitation of ν¯µ ν¯e transitions at KARMEN → have not been includedGonzalez-Gar. cia, Maltoni, Schwetz 2003 updated in Gonzalez-Garcia, Maltoni 2007 Using all the data described above except from the LSND experiment we find First: all data but LSND:the follbestowing afitll-b uist-L vSNerDyb eclosest fit poi ntot: CPT conserving 2 5 2 2 5 2 ∆m21 = 6.8 10− eV , ∆m¯ 21 = 7.9 10− eV , 2 × 3 2 2 × 3 2 ∆m31 = 2.7 10− eV , ∆m¯ 31 = 1.8 10− eV , | 2 | × | 2 | × sin θ12 = 0.30 , sin θ¯12 = 0.31 or 0.69 , (260) 2 2 sin θ13 = 0 , sin θ¯13 = 0 , 2 2 sin θ23 = 0.46 or 0.54 , sin θ¯23 = 0.5 .

0.5 1 1

Then: how much CPT 0.4 0.8 138

0.3 ! ! 0.6 0.1 23 13 12 ! ! ! ! 2 2 is allowed by 2 ! sin sin sin 0.2 0.4 all-but-LSND data: 0.1 0.2 0.01 0 0 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 0.01 0.1 1 2 2 2 sin !12 sin !23 sin !13 5 4 3

] ! ! ] 2 2 2 eV 10 eV -5 -3 ! [10 [10 2 21 2 31 -2 m m " " ! ! -3 -4 1 -5 1 10 -10 -1 1 10 2 -5 2 2 -3 2 "m21 [10 eV ] "m31 [10 eV ]

Fig. 48. Allowed regions for neutrino and anti-neutrino mass splittings and mixing angles in the CPT violating scenario. Diﬀerent contours correspond to the two-dimensional allowed regions at 90%, 95%, 99% and 3σ CL. The best ﬁt point is marked with a star.

2 10

1 LSND 10

0 10

2 31 -1

m 10 "

-2 10

All-but-LSND -3 10

-4 10 -3 -2 -1 0 10 10 10 10 2 sin 2!LSND

2 2 Fig. 49. 90%, 95%, 99%, and 3σ CL allowed regions (ﬁlled) in the (∆m¯ 31 = ∆mLSND, 2 sin 2θLSND) plane required to explain the LSND signal together with the corresponding allowed regions from our global analysis of all-but-LSND data. The con- tour lines correspond to ∆χ2 = 26 and 30 (4.7σ and 5.1σ, respectively).

140 0.5 1 1

0.4 0.8

0.3 ! ! 0.6 0.1 23 13 12 ! ! ! ! 2 2 2 ! sin sin sin 0.2 0.4

0.1 0.2 0.01

0 0 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 0.01 0.1 1 2 2 2 sin !12 sin !23 sin !13 5 4 3

] ! ! ] 2 2 2 eV 10 eV -5 -3 ! [10 [10 2 21 2 31 -2 m m " " ! ! -3 -4 1 -5 1 10 -10 -1 1 10 2 -5 2 2 -3 2 "m21 [10 eV ] "m31 [10 eV ]

Fig. 48. Allowed regions for neutrino and anti-neutrino mass splittings and mixing CPTangles i n tglobalhe CPT violating sc enfitario. Different contours correspond to the two-dimensional allowed regiGonzalez-Garons at 90%, 95%cia,, 99% Maltoni,and 3σ C SchwL. Theetzbe s2003t fit point is marked with a star. updated in Gonzalez-Garcia, Maltoni 2007

2 Finally: compare with LSND: 10

1 LSND disagreement mainly due to 10 2 −2 2 ∆ m ¯ 3 1 < 1 0 e V (at 3 σ ) 0 agreement is possible 10

> 4.7σ 2 31 -1 .1σ at only m 10 5 " 4.7σ

-2 10

All-but-LSND -3 10

-4 10 -3 -2 -1 0 10 10 10 10 2 sin 2!LSND

140 0.5 1 1

0.4 0.8

0.3 ! ! 0.6 0.1 23 13 12 ! ! ! ! 2 2 2 ! sin sin sin 0.2 0.4

0.1 0.2 0.01

0 0 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 0.01 0.1 1 2 2 2 sin !12 sin !23 sin !13 5 4 3

] ! ! ] 2 2 2 eV 10 eV -5 -3 ! [10 [10 2 21 2 31 -2 m m " " ! ! -3 -4 1 -5 1 10 -10 -1 1 10 2 -5 2 2 -3 2 "m21 [10 eV ] "m31 [10 eV ]

2 Finally: compare with LSND: 10

1 LSND disagreement mainly due to 10 2 −2 2 ∆ m ¯ 3 1 < 1 0 e V (at 3 σ ) 0 agreement is possible 10

> 4.7σ 2 31 -1 .1σ at only m 10 5 " 4.7σ

-2 CPT cannot account for 10 All-but-LSND -3 LSND + all-but-LSND. 10

-4 10 -3 -2 -1 0 10 10 10 10 2 sin 2!LSND

2 2 CPT + one sterile neutrino??Fig. 49. 90%, 95%,Barger99%, a,n Marfatia,d 3σ CL a Whisnantllowed reg i2003ons (ﬁlled) in the (∆m¯ 31 = ∆mLSND, 2 sin 2θLSND) plane required to explain the LSND signal together with the corre- viable mass schemesspon dexist;ing allo wnoted r eaffgionecteds from oburyg lMiniBooNEobal analysis of a l lν- b u data.t-LSND data. The con- 2 MiniBooNE ν¯ channeltour lin ecoulds corresp discriminateond to ∆χ = 26 a nbetwd 30 (4een.7σ a nthem.d 5.1σ, respectively).

140 Sterile Neutrinos Basics The SM provides 3 neutrinos ⇑ 2 independent ∆m2 (m1, m2, m3) ∆m2 = 8+0.3 · 10−5 eV2 ∆m2 = 2.5+0.2 · 10−3 eV2 Sun −0.3 , Atm −0.2

∆m2 = ∆m2 If anything requires ! Sun,Atm 1 extra neutrino with no SM interactions (Z-width): “sterile”

LSND is such a case. Okada, Yasuda 1996, Bilenky et al 1998, Barger 2000... But also: - r-process nucleosynthesis G.Fuller >2000, G.McLaughlin 2006 - pulsar kicks A.Kusenko >1997 - solar ﬂux modulation Caldwell, Sturrock 2005 - ... Basics From the theory point of view: any fermion with no SM gauge interactions is a sterile neutrino SM + right handed ν . “mirror world” mirror fermion string theory modulino global sym in SuSY goldstino ......

Nothing forbids its mixing with active neutrinos M m L ⊃ ν2 + D ν LH 2 s v s effectively parameterized by its mass and mixing angle(s)

νe ν1  ν   ν  µ = V · 2  ντ   ν3       νs   ν4  Steriles and LSND Mass schemes: “3+1” “2+2” sterile in LSND (3+1) sterile in solar (2+2) sterile in atmospheric (2+2)

νs νµ ντ νµ νs atm atm

νµ ντ νµ νs LSND

νµ ντ LSND LSND mass

w a atm vie e

νe νµ ντ νe νs νe νsτ Vissani r sun sun sun

νe νµ ντ νe νs νe ντ Strumia, disfavoured excluded excluded Steriles and LSND Mass schemes: “2+2” νs has a role in sterile in LSND (3+1) sterile in solar (2+2) sterile in atmospheric (2+2) solar: excluded by SNO νe → νµ,τ νs νµ ντ νµ νs atm atm atmo: excluded by SK νµ ντ νµ νs ν → ν LSND µ τ Quantitatively: 40

νµ ντ LSND (a) LSND mass (b) (c)

2 w global $ a 30 30 PG vie

atm e KamLAND + atm + LBL

2 s s solar νe νµ ντ νe ν2 νe ντ Real $PC sun sun 20 sun 20 Maltoni r 2 #$

atm cia, s χ νe νµ ντ νe ν νe ντ Restricted atm ∆ atm + LBL 3 3 3 disfavoured excluded 10 % excluded + 10 + % % LBL LBL + SBL Gonzalez-Gar

0 0 0.2 0.4 0.6 0.8 10 0.2 0.4 0.6 0.8 10 0.05 0.1 0.15 2 2 2 2 “sterile fraction”2 in solar2 neutrinos2 2 " 2 " 2 2 " " " " d = |V | + |V | = s !s = |Vs1| + |Vs2| = c23 c24 !s = |Vs1| + |Vs2| = c23 c24 µ µ1 µ2 23

Fig. 46. ∆χ2 as a function of the active-sterile admixture η = V ν 2 + V ν 2 and the s | s1| | s2| parameter d = V ν 2 + V ν 2 from the analysis of solar+KamLAND data (green µ | µ1| | µ2| line) and atmospheric+LBL data (blue lines) in (2+2)-schemes. In the left panels we show the atmospheric+LBL χ2 for the restricted (θ = 0), real (δ = 0, π ) 23 23 { } and general cases. The red line in the central panel show the increase in the χ2 once the solar+KamLAND and atmospheric+LBL data are combined together.

in χ2 for the analysis of solar (+ KamLAND) neutrino data as a function of the active-sterile admixture η = V ν 2 + V ν 2 = c2 c2 . From the ﬁgure we s | s1| | s2| 23 24 conclude that the solar data favour pure νe νa oscillations but sizable active- sterile admixtures are still allowed. In this→curve the 8B ﬂux allowed to take larger values than in the SSM which, as discussed above so the active-sterile bound is as model independent as possible.

Similar analysis can be performed for the atmospheric neutrino data [297] to 2 2 obtain the allowed regions for the oscillation parameters ∆m43 and tan θ34 from the global analysis for diﬀerent values of θ23 and θ24 (or, equivalently, ν 2 ν 2 ν 2 ν 2 of the projections dµ = Vµ1 + Vµ2 and ηs = Vs1 + Vs2 ). The global minimum corresponds to| alm| ost |pur|e atmospheri|c ν| ν| o|scillations and µ − τ the allowed regions become considerably smaller for increasing values of the mixing angle θ23, which determines the size of the projection of νµ over the 2 neutrino states oscillating with ∆m43, and for increasing values of the mixing angle θ24, which determines the active-sterile admixture in which the almost- νµ oscillates. Therefore the atmospheric neutrino data give an upper bound on both mixings which further implies a lower bound on the combination ν 2 ν 2 2 2 ηs = Vs1 + Vs2 = c23c24. The same combination is limited from above by the so|lar|neut|rino| data.

In the left panel of Fig. 46 we show the shift in χ2 for the analysis of the atmospheric (+ LBL) data as a function of the active-sterile admixture ηs = ν 2 ν 2 2 2 Vs1 + Vs2 = c23c24, in the general case (in which the analysis is optimized | | | | ν 2 ν 2 2 with respect to both the parameter dµ = Vµ1 + Vµ2 = s23 and the Dirac phase δ ) as well as the real case (when| onl|y th|e va|lues δ = 0, π are 23 23 { } considered, as in our previous analyses) and the restricted case (θ23 = 0).

134 Steriles and LSND Mass schemes: ν¯µ → ν¯s → ν¯e 2 “3+1” “2+2” 2 2 2 ∆mLSNDL P = sin 2θ sin 2θes sin sterile in LSND (3+1) sterile in solar (2+2) µsterilee in atmospheric (2+2) µs ! 4Eν "

νs νµ ντ 1constraints02 νµ ν son individual angles Chapter 9. Unconﬁrmed anomalies atm from disaatmppearance experiments apply: νµ ντ νµ νs LSND 102 102 Karmen 99% CL (2 dof)

mass CCFR νµ ντ LSND LSND 10

1 excluded 2

a 2 atm LSND eV

eV LSND CDHS -1 in in 10 1 2

s m s 2 LSND νe νµ ντ νe ν νe ντ " sun sun sun m LSND 10-2 " νe ν ν νe νs νe ν Bugey µ τ τ #1 10 allowed disfavoured excluded 10-3 excluded CHOOZ 90% CL (2 dof) excluded #2 10-4 10 10-4 10-3 10-2 10-1 1 10#4 10#3 10#2 10#1 1 2 2 sin 2! sin 2!LSND Strumia (2000)

Figure 9.2: Collection of data in the νe, νµ Figure 9.3: 3+1 oscillations. The region 2 2 sector. The mixing angle θ on the hori- of the (∆m , sin 2θeµ) plane favored by LSND zontal axis is different for the different ex- is compared with the combined constraint from periments. Bound from Karmen and LSND cosmology and ν experiments (continuos lines). region (shaded) for ν ν . Bounds Dropping the cosmological bound on ν masses µ → e from Bugey and Chooz (ν¯e disappearance), (horizontal line), the dashed line shows the CDHS (ν¯µ disappearance), CCFR (νµ disap- constraints from the ν data in fig. 9.2 and SK. pearance). All at 90% CL (2 dof). All at 99% CL (2 dof).

Various future experiments plan to test the claim of [15]. In our view, a discussion of what should be considered as a convincing evidence for 0ν2β, is useful, because any experiment (past and future) needs to confront with this issue. Observing 0ν2β with diﬀerent nuclei seems really advisable for two reasons: to be fully sure that the signal is not faked by a spurious line, and in view of theoretical uncertainties on 0ν2β matrix elements.

9.2 LSND

In the LSND [12] and Karmen [13] experiments, a proton beam is used to produce π+, that decay as π+ µ+ν , µ+ e+ν ν¯ → µ → e µ generating ν¯µ, νµ and νe neutrinos. The resulting neutrino beam also contains a small ν¯e contami- −3 + + nation, about ν¯e/ν¯µ < 10 . In Karmen both π and µ decay at rest, so that the SM prediction for the neutrino ener∼gy spectra can be easily computed: νµ have an energy of 29.8 MeV, while νe + + and ν¯µ have a continuos spectrum up to 52.8 MeV. In LSND π and µ decay at rest produce + most of the neutrinos. Decay-in-ﬂight of π produce some ﬂux of νµ with higher energy, that has been used for ν ν searches. µ → e Steriles and LSND Mass schemes: ν¯µ → ν¯s → ν¯e 2 “3+1” “2+2” 2 2 2 ∆mLSNDL P = sin 2θ sin 2θes sin sterile in LSND (3+1) sterile in solar (2+2) µsterilee in atmospheric (2+2) µs ! 4Eν "

νs νµ ντ constraintsνµ ν son individual angles atm from disaatmppearance experiments apply: νµ ντ νµ νs LSND 102 excluded by SBL 101 experiments mass ν ν 2 LSND LSND µ τ eV in $ 100

a 2 LSND

atm m $ # LSND 10!1 νe νµ ντ νe νs νe νsτ sun sun sun 10!2 νe ν ν νe νs νe ν µ τ 10!5 10!4 10!τ3 10!2 10!1 100 2 sin 2ΘLSND disfavoured excluded excluded LSND islands barely survive

(bad goodness of ﬁt (more later)) Steriles and cosmology Cosmology constrains number and masses of neutrinos.

from (nuclear rates, n lifetime, CMB weak cross sections) Steriles and cosmology Cosmology constrains number and masses of neutrinos. BigBang Nucleosynthesis:

Nν BBN (T~MeV) 4He n/p ratio D/H 3He 6Li

Ωb from n from (nuclear(nuclear rates, rates, lifetime, n lifetime, CMB CMB weak crossweak crosssections) sections) (i) more neutrinos ⇑ faster expansion more He (ii) ν e → ν s deplete ν e modiﬁed weak rates more He − (e.g. Γ ( n ν e ← → p e ) ) Steriles and cosmology Cosmology constrains number and masses of neutrinos. BigBang Nucleosynthesis:

2 ∆ms , θs BBN (T~MeV) 4He n/p ratio D/H 3He 6Li

102 excluded by SBL experiments 1 10 having taken 2

eV conservatively in $ 0 4 10 ex He = 0.25 ± 0.01

2 LSND cluded by BBN Particle Data Group 2006 m $ # LSND 10!1 from (nuclear rates, n lifetime, CMB weak cross sections)

10!2 10!5 10!4 10!3 10!2 10!1 100 2 sin 2ΘLSND Cirelli, Marandella, Strumia, Vissani 2004 Di Bari et al. 2000 Steriles and cosmology Cosmology constrains number and masses of neutrinos. Galaxy Surveys:

from (nuclear rates, n lifetime, CMB weak cross sections)

2dF Galaxy Redshift Survey Steriles and cosmology Cosmology constrains number and masses of neutrinos. Galaxy Surveys:

6000 105

3 ν

" massless h ! m = 1 eV 5000 # 4 ν 2 10 K Μ Mpc

4000 ! ! in 3 ! 10 in TT !

C 3000 ! " 2 1 10 ∆P mν " 2000 ! ! ! −8 spectrum ! ! 2 2 ! 1 P 93 eV Ωmh 1000 10 Power 0 200 400 600 800 1000 1200 1400 10$2 10$1 100 Multipole Wavenumber !k! in h! Mpc ! massive neutrinos free stream out of the forming structures, i.e. smoothen small inhomogeneities,# i.e. suppress power on small scales Steriles and cosmology Cosmology constrains number and masses of neutrinos. Galaxy Surveys:

6000 105

3 ν

" massless h ! m = 1 eV 5000 # 4 ν 2 10 K Μ Mpc

4000 ! ! in 3 ! 10 in TT !

C 3000 ! " 2 1 10 " 2000 ! spectrum ! !

! 1 1000 10 Power 0 200 400 600 800 1000 1200 1400 10$2 10$1 100 Multipole Wavenumber !k! in h! Mpc ! m a bound on ! ν , including sterile# neutrinos! m < 0.73 eV Cirelli, Strumia 2006 conservatively ! ν (99.9% C.L.) + many others Steriles and cosmology Cosmology constrains number and masses of neutrinos. Galaxy Surveys: 102 excluded by SBL experiments 101

2 excluded

eV by Galaxy in $ 100 Surveys umia, Vissani 2004 2 LSND tr m $ # LSND 10!1

10!2 Cirelli, Marandella, S 10!5 10!4 10!3 10!2 10!1 100 2 sin 2ΘLSND

m < 0.73 eV Cirelli, Strumia 2006 conservatively ! ν (99.9% C.L.) + many others Steriles and cosmology Cosmology constrains number and masses of neutrinos. Q. Are these bounds here to stay? Steriles and cosmology Cosmology constrains number and masses of neutrinos. Q. Are these bounds here to stay? In standard cosmology, Yes. Steriles and cosmology Cosmology constrains number and masses of neutrinos. Q. Are these bounds here to stay? In standard cosmology, Yes. Examples of non-standard cosmologies: - low TRH scenarios (the Universe exited from inﬂation very late) Gelmini et al. 2004 - exotic neutrino interactions (all neutrinos in the Universe decayed into scalars) Beacom et al. 2003 2 10 ! 10 ! - large leptonic asymmetry 4 excluded n − n¯ by Galaxy ν ν 101 Surv L = eys ν !10 !4 n 2 γ eV in Foot, Volkas 1995 $ 100 2 LSND m $ # LSND 10!1 L = 10−4 ! ν 10 2 Chu, Cirelli 2006 10!4 10!3 10!2 10!1 100 2 sin 2ΘLSND Steriles and cosmology Cosmology constrains number and masses of neutrinos. Q. Are these bounds here to stay? In standard cosmology, Yes. Examples of non-standard cosmologies: - low TRH scenarios (the Universe exited from inﬂation very late) Gelmini et al. 2004 - exotic neutrino interactions (all neutrinos in the Universe decayed into scalars) Beacom et al. 2003 2 10 ! 10 ! - large leptonic asymmetry 4 excluded n − n¯ by Galaxy ν ν 101 Surv L = eys ν !10 !4 n 2 γ eV in Foot, Volkas 1995 $ 100 2 LSND m $ # LSND 10!1 L = 10−4 ! ν 10 2 Chu, Cirelli 2006 10!4 10!3 10!2 10!1 100 2 sin 2ΘLSND Q. Do they carry an uncertainty? Yes (statistical & methodological). The discussed limits are conservative. Future data will reduce all errors. Steriles and LSND Mass schemes: ν¯µ → ν¯s → ν¯e 2 “3+1” “2+2” 2 2 2 ∆mLSNDL P = sin 2θ sin 2θes sin sterile in LSND (3+1) sterile in solar (2+2) µsterilee in atmospheric (2+2) µs ! 4Eν "

νs νµ ντ 9.2.constraintsLSNDνµ and νMiniBo son individualone angles 105 atm + MiniBooNE:atm νµ ντ νµ νs LSND 102 102 Karmen Global ﬁt: 99% CL (2 dof) 10 CCFR νµ ντ LSND LSND mass 2 10

1 χ = 24.7excluded (2 dof) MiniBoone 2 a 2

atm eV

eV LSND CDHS -1 incompatiblein in 10 1 2

s m s 2 LSND νe νµ ντ νe ν νe ντ at ! 4. σ " sun sun sun m LSND 10-2 " e e s e Bugey ν νµ ντ ν ν ν ντ -1 10 allowed disfavoured excluded 10-3 excluded CHOOZ Maltoni, Schwetz 2007 90% CL (2 dof) excluded (0705.0107)-2 10-4 10 10-4 10-3 10-2 10-1 1 10-4 10-3 10-2 10-1 1 2 2 sin 2! sin 2!LSND Strumia, Vissani review

Figure 9.2: Data in the νe, νµ sector. The Figure 9.3: 3+1 oscillations. The region 2 2 mixing angle θ on the horizontal axis is dif- of the (∆m , sin 2θeµ) plane favored by LSND ferent for the diﬀerent experiments. Bound is compared with the combined constraint from from MiniBoone, Karmen and LSND region cosmology and ν experiments (continuos lines). (shaded) for νµ νe. Bounds from Bugey Dropping the cosmological bound on ν masses → ( ) and Chooz (ν¯e disappearance), CDHS ( ν µ (horizontal line), the dashed line shows the disappearance), CCFR (νµ disappearance). constraints from ν experiments only. All at All at 90% CL (2 dof). 99% CL (2 dof).

2.2 MeV γ line obtained when n is captured by a proton). These experiments are more sensitive to oscillations than older experiments, that used higher neutrino energy (see table 9.1). LSND finds an evidence for ν¯ ν¯ , that ranges between 3 to 7σ depending on how data are µ → e analyzed (the final publication claims a 3.8σ excess in the total number of ν¯e events; our analyses 2 2 2 are made with the ‘official’ χ provided by the LSND collaboration, where χbest fit χno oscillation 52). This happens because LSND has a poor signal/background ratio: choosing− the selection≈ cuts as in [91] the LSND sample contains 1000 background events and less than 100 signal events, distinguished only on a statistical basis. The statistical significance of the LSND signal depends on how cuts are chosen, and relies on the assumption that all sources of background have been correctly computed. The main backgrounds are cosmic rays and νe misidentification. The final LSND results for the average oscillation probabilities are reported in table 9.1. The LSND anomaly can be interpreted as due to oscillations. Fitting LSND data alone in a two-flavour context gives the best-fit regions shown in fig. 9.3a. Karmen finds 15 events versus an expected background of 15.8 events. Karmen has a few times less statistics than LSND and has a pulsed beam, allowing to reduce the cosmic ray background (Karmen also has a better shield) and νe misidentification (due to a nuclear decay with a life-time different than the one characteristic of n capture). Furthermore Karmen has a baseline somewhat shorter than LSND. At the end Karmen excludes a significant part, but not Steriles and LSND Mass schemes: sterile in LSND (3+1) “3+2” sterile in solar (2+2) sterile in atmospheric (2+2) Sorel, Conrad, Shaevitz (2004) 2 2 !s !µ∆m!" ! 22!µ eV !s atm 15 atm 2 2 !µ∆m!" ! 0.!9µ eV!s LSND 14

nd ν sterile in LSND (3+1) sterileNot in solar (2+2)a bigsterile impr in atmosphericovement: (2+2) the 2 sterile adds disappearance channel for e, µ , tension with Bugey, Chooz etc is exacerbated. !µ !" LSND LSND mass Perez, Smirnov 2000 νs ν ν ν νs µ τ µ Even more so after MiniBooNE. atm atm a atm Maltoni, Schwetz 2007 νµ ντ νµ νs LSND !e !µ !" !e !s !e !s" sun sun sun

!e !µ !" !e !s !e !" νµ ντ LSND LSND mass disfavoured excluded excluded a atm

νe νµ ντ νe νs νe νsτ sun sun sun

νe νµ ντ νe νs νe ντ

disfavoured excluded excluded Steriles and LSND Mass schemes: sterile in LSND (3+1) “3+2” sterile in solar (2+2) sterile in atmospheric (2+2) Sorel, Conrad, Shaevitz (2004) 2 2 !s !µ∆m!" ! 22!µ eV !s atm 15 atm 2 2 !µ∆m!" ! 0.!9µ eV!s LSND 14

“3+2” ﬁt LSND mass + MiniBooNE νµ ντ LSND LSND disfavoured excluded the extraexcluded CP phase δ allows ν ¯ (LSND) != ν (MiniBooNE) 2 a atm ∆m L ( ) ( ) 54 P ν → ν ∝ cos ∓ δCP µ e # E $ ! " νe νµ ντ νe νs νe νsτ Maltoni, Schwetz 2007 sun sun sun

νe νµ ντ νe νs νe ντ

νe νµ ντ νe νs νe ντ The bounds from standard cosmology apply + apply. disfavoured excluded excluded Mass Varying Neutrinos Basics ∆m2 ! 8 10−3 eV Scale of neutrino masses: ! Sun −3 Dark Energy current density: √4 ρde 2 10 eV " Maybe they are coupled, maybe they “track” each other: m ! m Fardon, Nelson, Weiner 2003 ν ν (A) Hung 2000 - Gu,Wang,Zhang 2003 Acceleron, a scalar ﬁeld responsible for the Dark Energy, i.e. the acceleration of the Universe (a.k.a. Quintessence)

Basics ∆m2 ! 8 10−3 eV Scale of neutrino masses: ! Sun −3 Dark Energy current density: √4 ρde 2 10 eV " Maybe they are coupled, maybe they “track” each other: m ! m Fardon, Nelson, Weiner 2003 ν ν (A) Hung 2000 - Gu,Wang,Zhang 2003 Acceleron, a scalar ﬁeld responsible for the Dark Energy, i.e. the acceleration of the Universe (a.k.a. Quintessence) Potential energy of the system: Vtot = Vde + Vcνb Vcνb = mν (A) ncνb V 4 tot Vde = Λ log(µ/mν ) minimization: V Λ4 cνb dV m ⇑ tot( ν ) ≡ m = Vde dm 0 ν n ν cνb mν (A) Mass Varying! Basics Kaplan, Nelson, Weiner 2003 A may couple also to ordinary matter, Barger et al. 2005 ν ↔ similar but different from MSW, mediating an effective matter coupling e.g. not energy dependent Basics Kaplan, Nelson, Weiner 2003 A may couple also to ordinary matter, Barger et al. 2005 ν ↔ similar but different from MSW, mediating an effective matter coupling e.g. not energy dependent

Potential energy of the system:

Vtot = Vde + Vcνb + Vmatter Vcνb = mν (A) ncνb 4 Vde = Λ log(µ/mν ) 2 λm ρmmD Vtot Vmatter = MPl mν

Vcνb Vde Vmatter mν (A) Basics Kaplan, Nelson, Weiner 2003 A may couple also to ordinary matter, Barger et al. 2005 ν ↔ similar but different from MSW, mediating an effective matter coupling e.g. not energy dependent

Potential energy of the system:

Vtot = Vde + Vcνb + Vmatter Vcνb = mν (A) ncνb 4 Vde = Λ log(µ/mν ) 2 λm ρmmD Vtot Vmatter = MPl mν

minimization: Vcνb Vde mν ∝ ρm Vmatter Mass Varying mν (A) MaVaNs and LSND Naïve observation: Bugey, Chooz, null oscillation searches in vacuum/air: Karmen... solar, Kamland, positive oscillation signals occur in matter: atmo, LSND MaVaNs and LSND Naïve observation: Bugey, Chooz, null oscillation searches in vacuum/air: Karmen... solar, Kamland, positive oscillation signals occur in matter: atmo, LSND Naïve proposal: Kaplan, Nelson, Weiner 2003 2 −3 2 in vacuum/air ∆m23 ! 10 eV 2 −1 2 in matter ∆m23 ! 10 eV (with θ 1 3 != 0 ) MaVaNs and LSND Naïve observation: Bugey, Chooz, null oscillation searches in vacuum/air: Karmen... solar, Kamland, positive oscillation signals occur in matter: atmo, LSND 102 Chapter 9. Unconﬁrmed anomalies Naïve proposal: Kaplan, Nelson, Weiner 2003 2 −3 2 in vacuum/air ∆m ! 10 eV 102 102 23 Karmen 99% CL (2 dof) 2 −1 2 ∆m ! 10 eV 10 in matter 23 CCFR 10

1 excluded θ13 = 0 2

(with ! ) 2 LSND eV

eV LSND CDHS -1 in in 10 1 explains LSND 2 m 2 LSND

m LSND

-2 " 10 Bugey #1 10 allowed 10-3 CHOOZ 90% CL (2 dof) excluded #2 10-4 10 10-4 10-3 10-2 10-1 1 10#4 10#3 10#2 10#1 1 2 2 sin 2! sin 2!LSND Strumia (2000)

9.2 LSND

In the LSND [12] and Karmen [13] experiments, a proton beam is used to produce π+, that decay as π+ µ+ν , µ+ e+ν ν¯ → µ → e µ generating ν¯µ, νµ and νe neutrinos. The resulting neutrino beam also contains a small ν¯e contami- −3 + + nation, about ν¯e/ν¯µ < 10 . In Karmen both π and µ decay at rest, so that the SM prediction for the neutrino ener∼gy spectra can be easily computed: νµ have an energy of 29.8 MeV, while νe + + and ν¯µ have a continuos spectrum up to 52.8 MeV. In LSND π and µ decay at rest produce + most of the neutrinos. Decay-in-flight of π produce some flux of νµ with higher energy, that has been used for ν ν searches. µ → e MaVaNs and LSND Naïve observation: Bugey, Chooz, null oscillation searches in vacuum/air: Karmen... solar, Kamland, positive oscillation signals occur in matter: atmo, LSND Naïve proposal: Kaplan, Nelson, Weiner 2003 2 −3 2 in vacuum/air ∆m23 ! 10 eV 2 −1 2 in matter ∆m23 ! 10 eV (with θ 1 3 != 0 ) explains LSND explains atmo deficit

SK collaboration

FIG. 21. Zenith angle distribution of SuperKamiokande 1289 days data samples. Dots, solid line and dashed line correspond to data, MC with no oscillation and MC with best ﬁt oscillation parameters, respectively.

113 MaVaNs and LSND Naïve observation: null oscillation searches in vacuum/air: Bugey, Chooz, 39 -1 Number of events only -1 Spectrum shape only sible by the inKarmen...ventiveness and the diligent eﬀorts of the

10 ] 10 ] 2 2 KEK-PS machine group and beam channel group. We [eV [eV 2 2 m

m gratefully acknowledge the cooperation of the Kamioka " " solar, Kamland, -2 -2 positive oscillation10 signals10 occur in matterMining and:Smelting Company. This work has been sup- ported by the Ministatmory of Edu, caLSNDtion, Culture, Sports, Science and Technology of the Government of Japan, -3 -3 10 10 the Japan Society for Promotion of Science, the U.S.

68% 68% DepartmeKant oplan,f Ene rNelson,gy, the Ko rWeaeinerResear c2003h Foundation, Naïve proposal: 90% 90% the Korea Science and Engineering Foundation, NSERC -4 99% -4 99% 10 10 0 0.25 0.5 0.752 1 0 0.25−30.5 0.75 2 1 Canada and Canada Foundation for Innovation, the Is- in vacuum/air ∆m sin2(2!) ! 10 eVsin2(2!) tituto Nazionale di Fisica Nucleare (Italy), the Minis- 23 terio de Educaci´on y Ciencia and Generalitat Valen- FIG. 46: Allowed region of oscillation parameters evaluated rec 6

2 ] with the number of even2ts only (left) and t−he E1ν spectrum in mattershape only (ri∆ght).mBo2th3info!rmatio1n 0allow the ecoVnsistent 2 region on the parameters space. eV 5 (with θ 1 3 != 0 ) -3

-1 K2K-I only -1 K2K-II only [10 2 ]

] 10 10 2 2 4 m [eV [eV 2 2 " m explains LSNDm " " -2 -2 explains atmo10 deﬁcit 10 3 -3 -3 10 10 2 68% 68% K2K 68% 90% 90% -4 99% -4 99% K2K 90% However: 10 10 0 0.25 0.5 0.75 1 0 0.25 0.5 0.75 1 2 2 1 K2K 99% sin (2!) sin (2!) incompatible with SK high-E and K2K SK L/E 90% ⇑ FIG. 47: Allowed region of oscillation parameters evaluated 0 with partial data of K2K-I-only (left)/K2K-II-only (right). 0.2 0.4 0.6 0.8 1 DoesBot hnotdata allow thwe conork.sistent region on the parameter space. K2K collaboration 2006 sin2(2!)

FIG. 48: Comparison of K2K results with the SK atmo- a statistical fluctuation with no neutrino oscillation is spheric neutrino measurement [2]. Dotted, solid, dashed and 0.0015% (4.3σ). In a two flavor oscillation scenario, the dash-dotted lines represent 68%, 90%, 99% C.L. allowed re- allowed ∆m2 region at sin2 2θ = 1 is between 1.9 and gions of K2K and 90% C.L. allowed region from SK atmo- 3.5 10−3 eV2 at the 90 % C.L. with a best-fit value of spheric neutrino, respectively. 2.8 × 10−3 eV2. ×

XI. ACKNOWLEDGMENT ciana (Spain), the Commissariat `a l’Energie Atomique We thank the KEK and ICRR directorates for their (France), and Polish KBN grants: 1P03B08227 and strong support and encouragement. K2K is made pos- 1P03B03826.

[1] Y. Ashie et al. (Super-Kamiokande), Phys. Rev. D71, hep-ex/0103001. 112005 (2005), hep-ex/0501064. [6] Y. Fukuda et al., Nucl. Instrum. Meth. A501, 418 (2003). [2] Y. Ashie et al. (Super-Kamiokande), Phys. Rev. Lett. 93, [7] Y. Yamanoi et al., KEK-preprint 97-225 (1997). 101801 (2004), hep-ex/0404034. [8] Y. Yamanoi et al., KEK-preprint 99-178 (1999), prepared [3] M. H. Ahn et al. (K2K), Phys. Rev. Lett. 90, 041801 for 16th International Conference on Magnet Technology (2003), hep-ex/0212007. (MT-16 1999), Tallahassee, Florida, 29 Sep - 1 Oct 1999. [4] E. Aliu et al. (K2K), Phys. Rev. Lett. 94, 081802 (2005), [9] M. Kohama, Master’s thesis, Kobe University (1997), in hep-ex/0411038. Japanese. [5] S. H. Ahn et al. (K2K), Phys. Lett. B511, 178 (2001), [10] T. Maruyama, Ph.D. thesis, Tohoku University (2000). MaVaNs and LSND 3+1 MaVaNs model?? Barger, Marfatia, Whisnant 2006 MaVaNs and LSND 3+1 MaVaNs model?? Barger, Marfatia, Whisnant 2006 Simpliﬁed sketch: in matter in vacuum/air (explains LSND) (avoids Chooz, Bugey) sterile in LSND (3+1) sterile in solar (2+2) sterile in atmospheric (2+2)

νs νµ ντ νµ νs atm atm

νµ ντ νµ νs LSND sterile in LSND (3+1) sterile in solar (2+2) sterile in atmospheric (2+2)

!s !µ !" !µ !s

atm mass atm νµ ντ LSND LSNDThe model is more complicated: !µ f!or" technical!µ r!seasons, requires a atm LSND - null MiniBooNE, o νe νµ ντ νe νs νe νsτ θ ∼ sun sun sun - large 1 3 ( 1 5 ) , only in matter !µ !" LSND LSND mass νe νµ ντ νe νs νe ντ (null DChooz, signal in Daya Bay, LBL) a atm disfavoured excluded excluded

!e !µ !" !e !s !e !s" sun sun sun

!e !µ !" !e !s !e !"

disfavoured excluded excluded A summary for LSND model ( = xotic) standard 3 active

ε sterile (2+2, 3+1, 3+2...) MaVaNs CPT Lorentz muon decay ... 2 ε sterile MaVaNs sterile CPT sterile N-std cosmo sterile decay sterile x-dim shortcuts A summary for LSND model mainly killed by standard 3 active (never born)

ε sterile (2+2, 3+1, 3+2...) solar, atmo, (SBL), std cosmo, MaVaNs SK, K2K CPT solar + Kamland + atmo Lorentz tension with SBL, other data muon decay Karmen ... 2 ε sterile MaVaNs sterile CPT sterile N-std cosmo sterile decay sterile x-dim shortcuts MiniBooNE A summary for LSND model mainly killed by standard 3 active (never born)

ε sterile (2+2, 3+1, 3+2...) solar, atmo, (SBL), std cosmo, MiniBooNE MaVaNs SK, K2K CPT solar + Kamland + atmo Lorentz tension with SBL, other data muon decay Karmen ... 2 ε sterile MaVaNs sterile CPT sterile N-std cosmo MiniBooNE sterile decay MiniBooNE sterile x-dim shortcuts MiniBooNE A summary for LSND model mainly killed by future? standard 3 active (never born)

ε sterile (2+2, 3+1, 3+2...) solar, atmo, (SBL), std cosmo, MiniBooNE MaVaNs SK, K2K CPT solar + Kamland + atmo MiniBooNE Lorentz tension with SBL, other data muon decay Karmen ... 2 ε sterile MaVaNs DChooz, DayaBay, LBL sterile CPT MiniBooNE ν¯ sterile N-std cosmo MiniBooNE cosmology itself sterile decay MiniBooNE sterile x-dim MiniBooNE low E ν shortcuts Conclusions The LSND puzzle prompted theorists to investigate many scenorios of exotic neutrino physics, most of which now disfavoured. In a more general perspective: The exotic physics stimulated by LSND - opens to interesting sectors of new physics - may appear as subleading effect in other ν exp’s Neutrino Physics - is the physics of the least tested particles in SM - has discovered new physics in the latest 15y Back-up slides , . , . . . . . , - r - . 3 e n . d 5 G . 1 20 ly 0 - m o h e ng . ma 89 for 0 t ion t i 433 u 1 i 51 . ul hei g 2 . EK r 10 r Res t 0 m 02) n s ng-8, t Phys Phys Phys Phys Nucl n t , 0 i i or i 8 s , , , ef B 7 . K et r Y d 0 , . . . nt 1 (1983) by ossible Phys n l l l . 6 Ha . e (20 L l M Science Science ds I e t 4 . p a a a osiu , end ra 20 rat n 9 for J a . AR h romot , 0 p 4 (SP y v et . 2 C t g , , g n ho U supp .jp/present s Phys et et et e P 4 . y t m L , ) . et s N es 2 R y e . 0 . of ng-8, 97 orea it pla i ioka A or , S ds . kek 9 week i 0 Met i J Nucl . made uda uda uda s for W r 0 K s o h t m 19 . k k k Energ t 1 ho Phys t orat , been Sp B223 versit . n i is nd . y 3 a u 482 u u Ish (20 Phys 1 i e l , m n SP . . , Phys a ct 1 s f F F F Meissner for h a , u n K . , Z e U of , . t A . o r . . . e Met . y l T r n re 65 t l ef . 2K ciet S ha . Y Y h , u e a f 1 s G u /02030 , . a et t t , , , roups o l Phys . apa h ct n . , K //neut x Di by t m J a I : g S . i et e U . 379 et . og ult of u p ion h - 41 Japa Se k ion ion ion . , t nolog – r V d - ment n ohok n C 453 u t , t h igent n of nd . . T 98) h s ht work l r c , of a nel Nucl hep a i ngs n A A mad e A . , 377 i I s one n , Nucl d T i Suz , . . h i ICRR l (19 d Res . . Japa r d see . ion laborat , ion i p /02060 h . Hyogo ct laborat laborat laborat . . d A ng, 98) H n . p x he hesis, ) n a . ion Depa . cha s, A a T ion ely rh , cee ragement t t . e he nd ment , Se 0 S a Y y 153 02) - t Q Col o . , . . Col Col Col a (19 , n , 0 erat Nucl r . d , , y , . Sehga aylor a Phys ion S D m 98) p ducat n y . 1 K n P , 97) T . y mat Cit . (20 . o K hep a i b h e ion l (20 E .- U iat ver ion . ds undat ion nde nde nde n . M Res o , P 19 E a S , encou (19 R i o roup L U . Elouad o bea . oundat 6 c 1562 l . .ps . 79 A41 , , , ho . fﬁl 7 K F . of L G R F 9 1 G . 1 a , den d 02) n . Science he l d et a L r , E e nd rch t ioka ioka ioka , 1 n , , A n a g 02) E , ma y 8 a nd h . a eness y et D Compa a , laborat . nd ) r m m m n he t Phys or Met (20 laborat approx . laborat a y v t Ga i t rd 1 a t rget T et a a a R i rch 451 Japa ct . 433 539 eau t b n 0 g (20 m at rent 1 a d uya i t ist i i , e K K K n ds or r . e t na n Col m T r M r k r dek R e , - - - Col A 1 Se n B B Col i u L n Resea ent u K a i n , dge i (20 n , . c ho . . neer nolog E r er er er Gluck ct resses021 . v . t t Iei . 95) a i Bo Rei K K K o M v t t Ma J Ber Swa r h ct n 8 M st 130 . . h 2 2 2 L le . . Resea e e . i supp c . . 7 1 s t n . . iﬁc wle e Res J SNO 1 M Acceler Science Hyogo T K Met K I A Sup L 0 K add Sup Re Sup L G28 B V D (19 J M Se e e Smelt *Fo Eng e T h col on mach h no t ] ] ] t Science W 1 W d d d s 6] 6 4] 0] [1 rong [ orea [3] [5] [7] [8] [4] [2] [9] n n n [1 [1 [1 [1 E [15] [12] [13] ha prot st by PS ack a by a Scient of K a I V . , l - - - - - E s e e e d d y d l ic e e of e n v h h he e is- nd b no ds a ers i v ce R t t i v ua 1 a me i a d i θ T pre r d

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