Three Twin Neutrinos: Evidence from LSND and Miniboone

Home , SciBooNE

arXiv:1512.05357v1 [hep-ph] 16 Dec 2015 eest xeiet ihtertoo h oscillation the of energy, ratio neutrino the the over with distance SBL experiments Here, neu- (SM). to active Model three refers Standard the the of within framework explained trino experiments be oscillation cannot neutrino which (SBL) baseline short in ugsigoclain fteform in the again excesses of [3], oscillations events reporting neutrino suggesting signal, anti-electron and same electron the both for searched also qae pitns∆ mass splittings involving squared oscillations neutrino to sensitive are which ν ∆ oeatoshv locniee arypop decay ( prompt [16] fairly neutrinos considered sterile also of have authors constraint, some disappearance [15], the ameliorate LSND+KARMEN To and respectively. 14] [13, BooNE+SciBooNE 1 eot vdneo ¯ of evidence reports [1] with es nldn cieplus active 3 including eV. 1 cess, of scale additional mass of a suggestion at flavors tantalizing neutrino the “sterile” obser- to these Together, lead vations results. LSND the with consistent (¯ inshms(3+ schemes tion oue on focused l etio odcytruhteprocess the ster- through decay the state to enables light neutrinos which new ile [17–19]), a Majoron to form a neutrinos this (potentially of of decay coupling the a the within cases, requires neutrinos most In active to lengths. experimental neutrinos sterile of decay ipe31shm a rvd odfi othe to fit good a provide can scheme 3+1 simple hsdcycno xli h SDecs n ewill we and excess here. LSND it the consider not explain cannot decay this hl oeatoshv locniee easo the of decays considered also have form authors some While ν µ m µ h atdcd a enasre faoaisemerge anomalies of series a seen has decade past The ayshmshv encniee ofi h ex- the fit to considered been have schemes Many → 2 → ν ν µ ∼ s ν ν ¯ ¯ , e → e ν perneecse,teefisaei tension in are fits these excesses, appearance ) eV 1 silto 2.TeMnBoEcollaboration MiniBooNE The [2]. oscillation µ ν N and a atta etio aealre cteigcosscint section anti-n cross larger a scattering of larger observation MiniBooNE’s a for have explanation neutrinos constr that disappearance fact the satisfying simultaneously while h ig oo n a h ih re fmgiuet tted the 4 neutrino fit around to active at magnitude into fit, of lengths good electrow order a the experimental right provide of the the ratio t has within the to and decay be couplings s boson to twin neutrino Higgs predicted the the twin is parit angle and three twin mixing all Model a This controls Standard includes angle the which mixing in model, structures The Yukawa MiniBooNE. lepton and LSND at b a + 2 ecntutanurn oe ftreti etio nligh in neutrinos twin three of model neutrino a construct We and 1 = nttt eFıiaCruclr nvria eValencia de Universidad F´ısica Corpuscular, de Instituto swl sals rmtcecs for excess dramatic less a as well as , eateto hsc,Uiest fWsosnMdsn M Wisconsin-Madison, of University Physics, of Department he wnNurns vdnefo SDadMiniBooNE and LSND from Evidence Neutrinos: Twin Three .INTRODUCTION I. γ ν e N 2]t xli h iioN signal, MiniBooNE the explain to [20] iapaac osrit rmMini- from constraints disappearance ,wt oto h teto being attention the of most with ), m agBai, Yang ν 2 µ ∼ N i.e. → eV 1 31] hl vnthe even While [3–12]. 2 = ν ¯ m e N silto ossetwith consistent oscillation s 2 Γ h SDexperiment LSND The . a trl etiooscilla- neutrino sterile s a Lu, Ran ν ∼ µ L/E eV 1 → ν ν e 2 σ a oalwthe allow to ) ∼ n ¯ and ν ofiec ee,t h SDadMnBoEapaac data appearance MiniBooNE and LSND the to level, confidence s iaLu, Sida → m 1 ν ν µ ν µ / a → MeV, → + a ν ¯ ϕ ν e ϕ e od Salvado Jordi , . e stetreseienurns eas of Because neutrinos. identi- sterile be three of can the and out as massive fied become three neutrinos (VEV’s), six total values the expectation vacuum their r.Tepril otn nec etr sal denoted usually sector, each in A content particle The try. soitdwt pnaeu raigo napproximate an of global breaking (PNGB) spontaneous boson with the Goldstone model, pseudo-Nambu associated this a In is theory. field effective least Higgs the at of group, cutoff requiring gauge the SM so- without below the a problem under provides attractive charged hierarchy it particles An little new that is the sector. model to Higgs other lution Twin the the of to feature respect with sterile h rtoeao sdmninfieadrset ohthe both respects and Z sectors. dimension-five neutrino is the operator dimensional for first relevant higher The be to Two out turn structures. operators models flavor other similar to our applied with of be many can although studies framework, phenomenological Higgs Twin the within level. one-loop to at corrections mass divergent Higgs quadratically the no PNGB symmetry with the electroweak to breaking natural corrections allowing of potential, form Higgs the constrain to duced fteS ag ru n atcecnet ihcou- discrete with a content, by related particle sectors and two the group copy in partial gauge plings or SM full a the Higgs” contains model of “Twin Higgs [26– Twin the considered The been is have 30]. others type [21– One although 25], this content [24, consider. of model to particle model natural SM motivated becomes well scenario the 3+3 “mirrors” the 23], that within embedded How- model is sector adding fit. a neutrino 3+2 that sterile the the improve indication minimality when would ever, clear neutrino of no sterile interest third was a the there in because and mainly scheme, cillation aiNkgw-aaa(MS arxi eurdto required Pontecorvo- is usual matrix the to (PMNS) addition Maki-Nakagawa-Sakata in uni- angle one mixing only versal sectors, two the between alignment Yukawa 2 nti ae,w osrc + etiomodel neutrino 3+3 a construct we paper, this In eyltl teto a enfcsdo h + os- 3+3 the on focused been has attention little Very and and it.FrteMjrn etiocs,the case, neutrino Majorana the For aints. SU urn perneexcess. appearance eutrino B SU a ninurnspoie natural a provides anti-neutrinos han lsaln-ie aoo n can and Majoron long-lived a plus s b rnfrsudrisonguegopadis and group gauge own its under transforms , eSadr oe hre leptons. charged Model Standard he a cl vrtecmoiesaeof scale composite the over scale eak ftenurn perneexcesses appearance neutrino the of t 4 ymty twin A symmetry. (4) n e .Stefanek A. Ben and 4 ymtis fe h ig ed develop fields Higgs the After symmetries. (4) SC aeca401 Spain 46071, Valencia CSIC, cos sarsl,auniversal a result, a As ectors. t.Tehayti neutrinos twin heavy The ata. ,ntrlypeit identical predicts naturally y, dsn I576 USA 53706, WI adison, a Z 2 ymtyi intro- is symmetry Z Z 2 2 -enforced symme- 2 describe how the three sterile neutrinos interact with the suggests additional SU(4) breaking terms in the scalar SM charged leptons. This mixing angle θ is predicted potential. Minimizing the potential for the two Higgs to be the ratio of two Higgs VEV’s, v/f (0.1), and doublets with small Z2-breaking terms, the ratio of the has the right order of magnitude to fit the∼ SBL O excesses. two VEV’s is The second relevant operator is dimension-six, which is Z HA v 2-conserving and SU(4)-breaking. It is responsible for h i = (0.1) , (1) H f ∼ O coupling the Majoron to neutrinos and additionally for h B i providing mass to the light active neutrinos. We will with the electroweak VEV, v = 246 GeV. Later we will show that after satisfying various constraints, the three show that this ratio will be crucial to determine the heavy sterile neutrinos can decay into active neutrinos fermion mass spectrum in the twin sector. plus one Majoron with the decay distance within the The fermion Yukawa couplings explicitly break the experimental lengths. In what follows, we will analyze global SU(4) symmetry. The Z twin parity is required oscillation and decay of Dirac and Majorana sterile neu- 2 to ensure that there are no corrections to the SM Higgs trinos within the context of this 3+3 “Twin Neutrino” mass proportional to Λ2 at the one-loop level. There- model. We will show that promptly decaying sterile neu- fore, we keep the Yukawa couplings in both sectors to trinos in this model can provide a good fit to the LSND be exactly the same, both for charged leptons and neu- and MiniBooNE anomalies. trinos. For the charged leptons, the Z2-invariant and SU(4)-breaking Yukawa couplings in the Lagrangian are

II. THE TWIN NEUTRINO MODEL ij ye HALA iEA j + HBLB iEB j + h.c. . (2) Motivated by the Twin Higgs model, we consider a Here, the indexes “i, j = 1, 2, 3” denote lepton flavors. global non-Abelian SU(4) symmetry in the electroweak After inputting the scalar VEV’s, we have the three twin parts of both the SM and twin sectors. The two charged-lepton masses exactly proportional to the SM ones: m i /m i = v/f. For instance, the twin electron Higgs doublets HA and HB, which transform under eA eB is anticipated to have a mass of m = (5 MeV). SU(2)A U(1)A and SU(2)B U(1)B gauge symme- eB O tries, can× be grouped together as× a quadruplet of SU(4): T = (HA,HB) . At the minimum of its SU(4) invari- antH potential, the quadruplet develops a VEV of = A. Majorana Neutrinos (0, 0, 0,f)T , spontaneously breaking SU(4) downhHi to its SU(3) subgroup. As a result, there are seven Nambu- In the neutrino sector, we will consider both Majo- Goldstone-bosons (NGB’s) in the low energy theory be- rana and Dirac neutrino cases and will only focus on the low the cutoff Λ 4πf. Turning on electroweak gauge spectrum with normal ordering, which is preferred for interactions in both∼ sectors, the quadruplet VEV breaks the Majorana case. In this subsection, we first study the the twin electroweak gauge symmetry SU(2)B U(1)B to Majorana neutrinos for both SM and twin sectors. Dif- a single U(1) with three NGB’s eaten by the× three mas- ferent from the charged-lepton sector, we can have the ± 1 Z sive gauge bosons WB and ZB. The remaining four following 2-invariant and SU(4)-conserving Majorana NGB’s can be identified as the SM Higgs doublet, H, mass operators which acquire mass and become PNGB’s after turning ij on SU(4) breaking gauge or Yukawa interactions. yν T T i j + h.c. (3) The little hierarchy problem can be alleviated by im- ΛS L HC H L posing an additional Z2 symmetry between the two sec- e eT ˜ T T T tors which forces all couplings to be the same. This is Here, (LA,LB) and H (HA , HB ) with HA,B LT ≡ ≡ ≡ because in the gauge sector, the one loop corrections to iσ2HA,B. The cutoff, ΛS, could be related to the some the Higgs mass which are quadratic in Λ have the form −heavy right-handed neutrinoe masses toe realize thee See- 2 2 2 † 2 † 2 2 2 † Saw mechanism. After Higgs doublets get their VEV’s, 9Λ /(64π )(gAHAH + gBHBH )=9Λ /(64π )g A B HH i i and are independent of the PNGB Higgs field. In ad- the linear combinations (vνA,L +fνB,L) are massive and dition, the logarithmically divergent part contributes to are approximately the three sterile neutrino states. To 4 the coefficient of the SU(4)-breaking operator κ ( HA + provide mass for other combinations, we introduce the 4 4 2 | | Z HB ) at the order of g /(16π ) log (Λ/gf), so the Higgs following 2-invariant and SU(4)-breaking dimension-six field| | mass is generically suppressed compared to the VEV operator f 1 TeV. To obtain the lighter Higgs boson mass at 125 ∼ ij GeV, the coefficient is needed to be around 1/4, which yν T T 2 φLA iHA HB LB j + h.c. (4) Λφ C Here, the new gauge-singlete e scalar φ carries both SM 1 An additional Higgs mechanism may be required to provide the and twin lepton numbers. Furthermore, one could define twin photon mass. a discrete symmetry in the twin sector with φ φ, ↔ − 3

LA LA and LB LB, such that additional oper- In the charged-lepton mass-eigenstate basis, the diag- ators↔ for φ coupling↔ to − only SM leptons are forbidden. onalization unitary matrix can be written in terms of This discrete symmetry is important for our later discus- a tensor product U sion of φ-related phenomenology. The Yukawa couplings 6×6 = O2×2 U 3×3 , (9) are chosen to be identical for Eq. (3) and Eq. (4), which U ⊗ PMNS could originate from a UV theory at a much higher than 3×3 where UPMNS is the PMNS matrix in the SM (the exper- TeV scale. imental values are taken from Ref. [31]) and O2×2 is a 2 After φ develops a VEV with φ = fφ, the 6 6 rotation matrix neutrino mass matrix is h i × 2×2 cos θ sin θ 2 O = . (10) v v f fφΛS sin θ cos θ Λ Λ (1 + Λ2 ) S S φ 3×3 − M = 2 yν (5) 2 v f fφΛS f To the leading order of f Λ /Λ 1, the new mixing  (1 + 2 )  ⊗ φ S φ ΛS Λ ΛS ≪ φ angle between the SM and twin neutrino sectors is T  = diag mν1 ,mν2 ,mν3 ,mν1 ,mν2 ,mν3 . (6) v U a a a s s s U θ = (0.1) . (11) 2 ≈ f O In the leading order of fφΛS/Λφ 1 and v/f 1, the ≪ ≪ i three heavy (sterile) neutrino masses are Consequently, the three active neutrinos (νa) interact with the SM charged leptons with a strength propor- 2 i i f tional to cos θ, while the three sterile neutrinos (νs) have m i y¯ , (7) νs ν The sterile neutrino in- ≈ ΛS interactions suppressed by sin θ. teraction strengths with SM charged leptons are therefore i wherey ¯ν is the eigenvalue of the Yukawa matrix yν . Be- related to the fine-tuning problem for the SM Higgs boson. cause of flavor alignment in the SM and twin sectors, the In this model, there is a PNGB or Majoron [17–19] as- ratios of the neutrino masses satisfy sociated with the global symmetry breaking of U(1) LA × U(1)L U(1)L. The relevant Yukawa couplings for 2 B m i → iϕ/fφ mi νa fφΛS v the Majoron particle, ϕ, defined as φ fφe , in our r = 2 2 2 , (8) ≡ m m i Λ f models is flavor diagonal and are ≡ i+3 νs ≈ φ vf to the leading order of the small parameter, f Λ /Λ2 λi iϕνi T νi y¯i iϕνi T νi , φ S φ as a,L s,L ν 2Λ2 a,L s,L 1, in our model. For a normal ordering mass spectrum≪ C ≡ φ C of active neutrinos, m1 < m2 < m3, and from Ref. [31], i i T i i vf i T i 2 −5 2 2 2 λaa iϕνa,L νa,L θ y¯ν 2 iϕνa,L νa,L . (12) we have ∆m21 7.54 10 eV and ∆m ∆m31 C ≡ 2Λφ C 2 ≈ −3× 2 ≡ − ∆m21/2 2.43 10 eV . The twin neutrino masses are shown≈ in Fig.× 1 for two different values of r. The sterile neutrinos are not stable particles and have the decay widths of Γ[νi] = 2 Γ[νi νi (¯νi )+ ϕ] 105 s s → a a -6 i 2 3 2 3 m r = 10 (λ ) m i m i 6 I M as νs (λas) νs 104 = . (13) -6 2 m r = 10 ≈ 4π 4π m 3 5 I M νs 1000 L In our numerical study later, we will focus on the pa- eV

H 3 −2 3 −2 100 rameter region of λ = (10 ) ory ¯ = (10 ) and i as O ν O m Λφ = (10 √vf)= (TeV). = 10 m6 Hr 0.01L SinceO the mass operatorsO in Eq. (3) explicitly break the m Hr = 0.01L 1 5 U(1)L symmetry, we anticipate a non-zero mass for the m1 < m2 < m3 Majoron ﬁled, ϕ. The one-loop diagram mediated by LA m4 0.1 and LB generates a mass for ϕ 0.1 1 10 100 1000 104 105 4 4 m4 HeVL 2 1 v f † † mϕ 2 4 2 Tr(yν yν yν yν ) ∼ 16π ΛφΛS FIG. 1: The twin neutrino masses as a function of the lightest 1 3 2 2 2 twin neutrino mass. The normal ordering mass spectrum is (λas) θ mν3 . (14) ∼ 16π2 s assumed for the active neutrinos. For a normal ordering neutrino mass spectrum, we have 3 3 mϕ 1 eV for mνs 10 keV, θ = 0.1 and λas 0.01. The≈ Majoron decay width≈ is ∼ 2 2 3 2 m i 2 i θ (λas) νa We take the VEV of φ to be a real number. Its complex phase is i Γ(ϕ 2νa)= 2 mϕ Θ(mϕ 2mνa )(15). physical, but will not change our phenomenological study later. → 4π m 3 − i i νa X X 4

For a normal ordering neutrino mass spectrum, mϕ III. CONSTRAINTS FROM UNITARY, MESON 3 ≈ 1 eV, λas 0.01 and θ =0.1, the decay width at rest is DECAYS AND NEUTRINOLESS DOUBLE BETA Γ 8 10∼−8 eV. DECAY ϕ ≈ × For both the Majorana and Dirac neutrino models, we B. Dirac Neutrinos have the model parameters: m4, Γ4 (related to the cou- 3 pling λas), θ and r. In this section, we study the existing For the Dirac neutrino case, one need to introduce an constraints on our model parameters from unitarity of additional set of right-handed neutrinos in both the SM the active neutrino mixing matrix, neutrinoless double beta decay and meson decays. and twin sectors. The Z2-invariant and SU(4)-conserving Dirac mass operators are The mixing between active and twin neutrinos reduces the couplings of active neutrinos to charged leptons in the ij SM. The 6 6 mixing matrix, , is a unitary matrix in our yν (νA,R + νB,R) + h.c. (16) × U H L model, but the 3 3 mixing matrix, U, is not unitary and × 3 2 2 Furthermore, the following Z and SU(4)-breaking has the normalization property of i=1 Uℓi = cos θ. e 2 Using the results in Ref. [32] and neglecting| | the effects dimension-five operator is introduced to provide light P neutrino masses and decay couplings for the heavy neu- of sterile decay products, we have found that trinos sin θ . 0.20 , (25) ij yν φ HA LA νB,R + h.c. (17) at 2σ C.L. Λφ There are additional bounds on the sterile neutrino e decay widths from the pion and kaon three-body de- After φ develops a VEV with φ = f , the 6 6 h i φ × cay into the new Majoron state and the electron-muon neutrino mass matrix is universality tests of their total leptonic widths (see f Ref. [33] for a recent summary). Using the analysis in 1 v v(1 + φ ) Λφ 3×3 Ref. [34] and the measurement of π eν branching M = yν (18) → √2 " f f # ⊗ ratio [35, 36], the predicted deviation from e µ uni- 2 − T versality is Rπ = 1+157.5(g )ee with the experimental 1 2 3 1 2 3 = diag mνa ,mνa ,mνa ,mνs ,mνs ,mνs (19). U W value of Rπ = 0.9931 0.0049 (the updated value of ± with the left-handed rotation matrix as Rπ = 0.9993 0.0024 provides a similar bound), so the bound on our± model parameters is 6×6 2×2 3×3 = OL UPMNS . (20) 3 U ⊗ 32π Γ i i 2 νs→νa+ϕ T −5 (g )ee = c Uei Uie < 3.0 10 , (26) m i × Using the same parametrization in Eq. (11) and in the i=1 νs limit of fφ Λφ, we still have θ v/f = (0.1). The X mass ratios≪ for this Dirac neutrino≈ model isO at 90% C.L. Here, c = 1(2) for the Majorana(Dirac) neutrino case. In Fig. 2, we show the constraints on our mi mνi 1 fφ v r = a . (21) model parameters in the m4 Γ4 and m4 plane. m m i √ Λ f ≡ i+3 νs ≈ 2 φ For the Majorana neutrino case, searches for the neutrinoless double beta decay (ββ)0ν can also impose In the Dirac neutrino model, we also have a PNGB bounds on our model parameter space. The amplitude associated with the symmetry breaking of U(1)LA of (ββ) is proportional to the effective Majorana mass × 0ν U(1)νB,R U(1)L. The couplings of the Majoron, ϕ, → iϕ/fφ 6 3 parametrized by φ fφe are ≡ m m 2 = (r cos2 θ + sin2 θ) m U 2 (27). |h ββi| ≡ i Uei 3+i ei v i=1 i=1 i i i i i i λas iϕ νa,L νs,R y¯ν iϕ νa,L νs,R , (22) X X ≡ 2Λφ The CP -violating phases can affect the predicted effec- i i i i v i i λaa iϕ νa,L νa,R y¯ν iϕ νa,L νa,R . (23) tive Majorana mass. In our model, we have identical ≡ 2Λφ Majorana and Dirac phases for the SM and twin sectors. In Fig. 3, we show the allowed parameter space by al- The sterile neutrino decay widths are lowing arbitrary Majorana phases but fixed Dirac phase 3 of δCP = 0. We did not find additional processes like i 2 3 2 m i i i (λas) (λas) νs i 0ν2βϕ or 0ν2β2ϕ provide more stringent bounds than Γ[νs νa + ϕ] mνs = 2 . (24) → ≈ 32π 32π m 3 νs from 0ν2β and meson decays. 3 Because of the fairly large interaction strength (λas In our model, the active neutrinos from sterile neutrino 0.01) among sterile neutrinos, active neutrinos and the∼ decays are left-handed. Majoron particle, both sterile neutrinos and the Majoron 5

103 we have both oscillation and decay, we will keep both Dirac (r = 10−6) effects for neutrino appearance and disappearance. For Majorana (r = 10−6) the short-baseline experiments, the differential probabil- 2 Dirac (r = 10−7) 10 ity for a neutrino of flavor α with energy Eνα converting Majorana (r = 10−7) into a neutrino of flavor β with energy in the interval of ) 2 (Eνβ , Eνβ + dEνβ ) is [16, 40] eV

( 101

4 2 6 2 Γ mi L miΓiL 4 dPνα→νβ (Eνα ) ∗ −i − 2Eνα 2Eνα

m = e dE UβiUαi νβ i=1 100 X δ(E E )+ W → να νβ Eνα Eνβ × − 2 2 ′ ′ L 6 m L m Γ L −1 c mj Γj −i j − j j 10 1 2 3 4 5 6 ′ ∗ 2Eνα 2Eνα 10 10 10 10 10 10 dL β(j−3) αj e (28). × 0 2 U U Eνα m4 (eV) Z j=4 s X

Here, the neutrino decay widths, Γi = 0 for i = 1, 2, 3 FIG. 2: The constraints on our model parameters from the and Γ = 0 for i = 4, 5, 6, are defined in the rest frame. e − µ universality of pion decays. The Dirac phase δ = 0. i CP c = 1(2)6 for the Majorana(Dirac) neutrino case. For the case of neutrino goes to neutrino, the energy spec- 2 trum function is WE →E =2Eν /E Θ(Eν Eν ). να νβ β να α − β mββ > 0.31 eV For the Majorana model, the helicity-flip formula for −6 r = 10 να νβ has only the second term (the decaying part) −7 → −1 r = 10 with a different energy spectrum function, W = 10 Eνα →Eνβ 2 2(Eνα Eνβ )/Eνα Θ(Eνα Eνβ ). For the case with initial anti-neutrinos,− one should− replace the elements of

θ by their complex conjugates. U

sin In our numerical studies, we will focus on the pure os- −2 10 cillation case as well as the case where the decay eﬀect dominates. For the pure oscillation case with Γi = 0 and 2 2 in the limits of m4,5,6 m1,2,3 and ∆m12 , ∆m23 E/L (the short-baseline≫ approximation),| the neutrino| | | ap- ≪ pearance probability is 10−3 102 103 104 105 106 3 j−1 m4 (eV) P (ν ν ) = 4 sin4 θ U U ∗ U ∗ U α → β | βj αj βk αk| j=2 k=1 m4 θ ν β X X FIG. 3: Constraints on and sin from 0 2 decay with 2 2 |hmββi| < 0.31 eV [37]. We have chosen a normal ordering ∆mjkL ∆mjkL sin 2 sin φβαjk 2 ,(29) mass spectrum for the three active neutrinos and the Dirac × 2 r E ! − 2 r E ! phase δCP = 0. ∗ ∗ for α = β. Here, the phase φβαjk arg(Uβj Uαj UβkUαk). The formula6 for the anti-neutrino≡ case can be obtained by a replacement of φ φ. In our model, only a single particles stay within the supernova core. Our model does Dirac CP phase enters→− both sectors. In the small mixing not have an additional energy loss problem for supernova angle limit of θ 1 and δ order of unity, we have 13 ≪ CP SN1987A. For sterile neutrinos with a mass below around φeµ21 = (θ13 sin δCP ), φeµ31 = φeµ32 = δCP + (θ13). 1 MeV, they contribute to additional relativistic degrees So, a largeO CP -violating phase can aﬀect− theO (anti- of freedom and are constrained from BBN [38, 39]. How- )neutrino appearance probabilities. The disappearance ever, to have a conclusive statement, additional analysis probability is independent of CP -violating phase and has or non-standard cosmology should be taken into account. We do not explore these directions here. 3 ∆m2 L P (ν ν )=1 sin2 (2θ) U 2 sin2 j+3,1 (30). α → α − | αj | 2 E j=1 ! X IV. NEUTRINO APPEARANCE AND Comparing Eqs. (29) and (30), one can see that the ap- DISAPPEARANCE pearance probability is suppressed by sin4 θ, while the disappearance is only suppressed by sin2 θ. We will later In this section, we write down general neutrino appear- show because of this fact it is challenging to only use ance and disappearance formulas for our model. Since oscillation to explain LSND and MiniBooNE anomalies. 6

For the case in which sterile neutrino decay effects are For the MiniBooNEν ¯µ ν¯e and νµ νe appear- 2 → → dominant and in the limit of ∆m45,56,46 Γj mj , the ance analysis based on initial anti-neutrino and neutrino appearance probability is | | ≫ fluxes [3], we use the data released by MiniBooNe collaboration [41] to derive the preferred contours in our dPν →ν (Eν ) c α β α = sin2 θ W model parameter space. We combine the two data sets Eνα →Eνβ dEνβ 2 in the (anti-)neutrino energy range of (200 MeV, 3 GeV). 3 Again, for the simplest 3 + 1 sterile neutrino model, we mj+3Γj+3L 2 2 − 4 U U 1 e Eνα + (sin θ) . (31) reproduce the contours in the MiniBooNE publication [3]. × | βj| | αj | − O j=1 For the constraints from (anti-)neutrino disappear- X ance, we use the combined SciBooNE and MiniBooNE For the Majorana model, the helicity-flip formula for analysis [13] for the anti-neutrino disappearance mea-

να νβ is similar but using WEν →Eν . The disap- surement, which provides more stringent constraints → α β pearance has contributions from both terms in Eq. (28) than the ones from the neutrino disappearance measure- and is ment [14]. We use the publicly available data [42] to constrain our model parameter space. We have also dP (E ) να→να να = checked additional constraints from appearance searches ′ dEνα by KARMEN [43] but found them to be less stringent, 3 and we will not report them here. mj+3Γj+3 L 2 2 2 − E 1 2 sin θ + sin θ Uαj e να δ(Eν Eν′ )  − | |  α − α 100 j=1 m4 = 1.4 eV, δCP = π/2 X MiniBooNE νe + ν¯e LSND ν¯e 1σ 3 MiniBooNE νe + ν¯e LSND ν¯e 2σ  mj+3Γj+3 L c − MiniBooNE νe + ν¯e LSND ν¯e 3σ 2 4 Eνα +WEν →E ′ sin θ Uαj 1 e (32), MiniBooNE+SciBooNE ν¯µ 90% C.L. α να × 2 | | − j=1 − X 10 1 ignoring additional terms suppressed by sin4 θ. One can see that for the decay case both appearance and disap- r pearance are suppressed by the same power of sin θ. This − fact will make the decay model a better ﬁt to LSND and 10 2 MiniBooNE data.

V. FIT TO LSND, MINIBOONE AND 10−3 SCIBOONE DATA 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 sinθ In this section, we will consider both cases for inter- preting short-baseline experimental data with or without FIG. 4: The MiniBooNE plus LSND preferred contours for sterile neutrino decays. For the first case without ster- the purely oscillation case in our model. The vertical dashed line at sin θ = 0.20 is the constraint line from unitarity of the ile neutrino decays, the energy spectrum of the neutrinos three active neutrinos. The yellow star is the best fit point of near the far detector follows the initial injected neutrino our model. spectrum. On the other hand, for the second case with sterile neutrino decays, additional care should be taken to account for the energy spectrum change. In Fig. 4, we show the LSND and MniBooNE preferred contours in terms of our model parameters: sin θ and r by fixing m4 = 1.4 eV and assuming δCP = π/2, which A. Oscillation without decay provides a better fit than no CP violation with δCP = 0. From a three-dimensional parameter scan, we have found To interpret the LSND event excess of anti-neutrino the point with the smallest χ2 at sin θ = 0.4, r = 0.011 2 appearance,ν ¯µ ν¯e [1] (we will ignore the less sig- and m4 = 1.4 eV. This is an improvement by ∆χ = 25 nificant excess in→ the neutrino appearance observed by compared to the no oscillation fit. Unfortunately, the dis- LSND [2]), and to derive the preferred model param- appearance constraints from SciBooNE and MiniBooNE eter space, we follow Ref. [6] to account the energy exclude all the 3σ appearance-data-preferred region. Fur- spectrum as well as the conversion of the neutrino en- thermore, the constraints from unitarity of the three ac- ergy spectrum to measured positron energy spectrum, tive neutrinos also exclude the LSND and MniBooNE + Ee = Eν¯e + mp mn, from the inverse neutron de- preferred contours. This can be understood by the for- − + cay processν ¯e + p n + e . The measured positron mulas in Section IV, which show that the appearance energy has the range→ of (20 MeV, 60 MeV). For the sim- probabilities for the pure oscillation case have an addi- plest 3 + 1 sterile neutrino model, we have reproduced tional sin2 θ with respect to the disappearance proba- the LSND contours in Ref. [6]. bilities. The tension for appearance and disappearance 7 data is a general feature even for a general 3 + 2 global theoretical L/Eν oscillation probability. For the decay fit [12, 44]. case at hand, the energy spectra of the initial neutrino flux at the source and the final flux at the detector are different. To compare to the LSND and MiniBooNE L/Eν B. Oscillation with decay data plots, we use the following probability

P exp. (ν ν + ν )(E ) = For the second case with the decay effects dominant, model α → β β νβ dP → dP → we need to know more information about the detec- Φ c να νβ σ +Φ c να νβ σ να 1 dEν νβ να 2 dEν νβ tors. The first important piece of information is to know ⊗ β ⊗ ⊗ β ⊗ .(34) whether the sterile neutrinos generated at the source lo- Φνα σνβ ⊗ cation have already decayed or not. It can be seen from Here, the symbol “ ” means function convolution. For Eq. (31) that in order to have a larger appearance prob- ⊗ ability, it is preferable to have all sterile neutrinos de- the Majorana model, we have c1 = 1,c2 = 0 for LSND cay within the experimental lengths. Taking the Lorentz and c1 =1,c2 = 1 for MiniBooNE. For the Dirac model, boost into account, this means Γ4m4 > Eν /L. LSND has we have c1 =1,c2 = 0 for both LSND and MiniBooNE. the distance range of (26, 34) m and the energy range For the initial anti-neutrino experiments, one just makes the interchange of ν ν . In deriving the above of (20, 60) MeV; MiniBooNE has the distance around α,β ↔ α,β 540 m and the energy range of (200, 3000) MeV; Sci- equation, we have also made the quasi-elastic approxima- BooNE has the distance around 100 m and the energy tion with the outgoing electron(positron) energy equal to range of (300, 1900) MeV for the disappearance analy- the incoming neutrino(anti-neutrino) energy. 2 sis [13]. Altogether, if Γ4m4 & 1 eV , the majority of Based on Eqs. (33)(34), there is an interesting obser- sterile neutrinos have already decayed before reaching the vation about our Majorana model prediction for Mini- detector. We also note that for large values of Γ4m4, all BooNE. Under the approximation of the same energy spectra of the initial fluxes, Φ Φ , one has sterile neutrinos decay promptly and only θ and Γ4m4 να ∝ να are relevant parameters for both appearance and disap- P MiniBooNE(ν ν + ν ) < P MiniBooNE(ν ν + ν )(35), pearance experiments. Majorana α → β β Majorana α → β β Both LSND and MiniBooNE are able to generate νµ or ν initial fluxes. On the other hand, for the appeared simply from the fact that the neutrino quasi-elastic cross µ section is larger than the anti-neutrino one. electron neutrino or anti-neutrinos in the detectors, the LSND detectors are different from MiniBooNE and Sci- 0.015 r −6 m m 2 BooNE. The LSND experiment can distinguish νe and = 10 , 4 = 4keV, sinθ = 0.15, 4Γ4 = 1.0eV Majorana ν¯ → ν¯e νe because after νe interacts via inverse beta decay in µ Dirac ν¯µ → ν¯e the mineral oil target of LSND, both a prompt positron LSND ν¯e and a correlated 2.2 MeV photon from neutron capture 0.010 ) e ¯ appear. This twofold signature is not true for νe. On ν the other hand, the MiniBooNE and SciBooNE can not → µ

¯ 0.005 ν distinguish ν and ν. In order to compare to the Mini- ( BooNE and SciBooNE data, we need to add both ν and . exp model ν. Furthermore, we also note that the quasi-elastic cross P 0.000 sections for ν and ν interacting with CH2 in MiniBooNE are different. Using the cross sections in GENIE [45] and for the relevant energy range of (200, 3000) MeV at −0.005 MiniBooNE, we have 0.0 0.5 1.0 1.5 2.0 L/Eν¯ (meters/MeV) σquasi−elastic > σquasi−elastic , (33) ν+CH2 ν+CH2 FIG. 5: A comparison of the decay model prediction and the which is mainly due to σ(νn ℓ−p) > σ(νp ℓ+n) LSND anti-neutrino appearance data. from a negative axial-vector form→ factor [46].→ We will show later that because of different scattering cross sections the Majorana and Dirac models have different fea- In Fig. 5, we show a comparison of a benchmark model −6 tures for fitting appearance data. point with r = 10 , m4 = 4 keV, sin θ = 0.15 and 2 Before we present our results, we also want to comment m4 Γ4 = 1.0 eV , to the LSND data. The Dirac model on the fact that the LSND or the MiniBooNE measured has probabilities higher than the Majorana model sim- neutrino transition probability is not simply Eq. (28) for ply by a factor of two. Note that the starting points of the sterile neutrino decay case. They have the mea- the model curves are higher than the actual data start- meas. sured probability for each energy bin to be Pi = ing point. This is due to the approximation of using the (datai bkgndi)/(fully oscillated)i [47]. For the full oscil- shortest distance L = 26 m and the maximal neutrino en- lation− model, their measured probability matches to the ergy of 52.6 MeV from muon decays at rest [6]. Similarly 8

0.025 101 −6 2 −6 r = 10 , m4 = 4keV, sinθ = 0.15, m4Γ4 = 1.0eV Majorana: r = 10 ,m4 = 4 keV MiniBooNE νe ν¯e LSND ν¯e 1σ Majorana νµ → νe + ν¯e + → MiniBooNE νe + ν¯e LSND ν¯e 2σ 0.020 Majorana ν¯µ νe + ν¯e → 0 MiniBooNE νe + ν¯e LSND ν¯e 3σ Dirac νµ νe + ν¯e 10 MiniBooNE+SciBooNE ν¯µ 90% C.L. Dirac ν¯µ → νe + ν¯e

) MiniBooNE ν → νe ν¯e e µ + ¯ ( ) ν 0.015 MiniBooNE ν¯µ → νe + ν¯e ) 2 10−1 → µ (eV

¯ 0 010

( ) . ν 4 ( Γ −2 4 . 10 m exp

model 0.005 P

−3 0.000 10

−0.005 10−4 0.0 0.5 1.0 1.5 2.0 2.5 0.05 0.10 0.15 0.20 0.25 0.30 L E / ν (meters/MeV) sinθ

FIG. 6: A comparison of the decay model prediction and the FIG. 7: The allowed Majorana model parameter space in MiniBooNE neutrino and anti-neutrino appearance data. sin θ and m4Γ4 for fixed values of r and m4. The vertical dashed line at sin θ = 0.20 is the constraint line (its left side is allowed) from unitarity of the three active neutrinos. The yellow star is the best fit point of our model, which has ∆χ2 = 22.5 compared to the no twin neutrino assumption. for MiniBooNE, in Fig. 6 we show both Majorana and Dirac model predictions for the same benchmark model point. As we argued before, the Majorana model has a larger excess for the initial νµ run than the initial νµ particle for both experiments. run at MiniBooNE. For the Dirac model, there is also For the Dirac neutrino case, we show the allowed pa- some difference between the initial νµ and νµ runs, which rameter region in Fig. 8 for fixed values of r = 10−6 comes from the slightly different energy spectra for the and m4 = 4 keV. The best fit point is at sin θ = 0.073 initial fluxes. 2 2 and m4Γ4 = 0.34 eV with ∆χ = 18.7 (a probabil- In Fig. 7 and for the Majorana model, we show the ity of 8.7 10−5 or 3.9σ) compared to the fit without contour plot for the two most relevant model parameters, the three× twin neutrinos. The Dirac model provides a sin θ and m4Γ4, to fit the MiniBooNE and LSND appear- slightly worse fit than the Majorana model, because the ance data. Also shown in this plot is the 90% C.L. con- Majorana model has a higher model prediction for the straints from MiniBooNE plus SciBooNE. Different from anti-neutrino appearance probability than the neutrino the pure oscillation case in Fig. 4, the constraint from one. We also note that the anti-neutrino disappearance the disappearance data is not stringent enough to rule constraint from MiniBooNE plus SciBooNE for the Dirac out the best fit region for appearance data. For r = 10−6 model is more stringent than for the Majorana model. and m4 = 4 keV (allowed from the neutrinoless double This is simply due to the larger scattering cross section beta decay constraints in Fig. 3), the smallest χ2 to fit of neutrinos than anti-neutrinos. both MiniBooNE (using their Monte Carlo samples) and LSND (using their energy resolution) has sin θ = 0.097 2 and m4Γ4 =0.55 eV . Compared to the fit without new VI. DISCUSSION AND CONCLUSIONS physics, the difference is ∆χ2 = 22.5. For two degrees of freedom this means that the background-only fit has The twin neutrino scenario is very predictive. The neu- a χ2-probability of 1.3 10−5 (or 4.4σ) relative to our × trino mixing matrix is fixed by the usual PMNS matrix twin neutrino decay model. and the ratio of the Higgs VEV’s in the two sectors. Ad- For the best fit point of the Majorana neutrino model, ditionally, the signals observed by LSND and MiniBooNE 2 2 the six neutrino masses are 0.004 eV, 0.0096 eV, 0.050 eV, dictates either m4 or m4Γ4 to be around 1 eV . In the 4 keV, 9.56 keV, 50.0 keV. The three sterile neutrino Majorana sterile neutrino decay scenario, the model also widths are Γ4 = 0.0001 eV, Γ5 = 0.0019 eV and Γ6 = requires a normal ordering mass spectrum for the three 0.27 eV. The decay Yukawa coupling defined in Eq. (12) active neutrinos to avoid the 0νββ decay constraint. Be- is λ3 0.008. As a result, the Majoron receives a loop- cause the SM and twin sectors are closely related by as ≈ generated contribution to its mass with a value of around the twin Z2 symmetry, the number of free parameters 3 eV, which means that the Majoron can decay into all is greatly reduced. The next generation neutrino experi- three active neutrinos. For the typical neutrino energy of ments probing the twin sector neutrinos can also provide 30 MeV at LSND (500 MeV at MiniBooNE), the Majoron information about the SM active neutrino sector. Com- travels far enough that it can be treated as an invisible bining the experimental information from both sectors, 9

101 the ν twin partner has a larger scattering cross section −6 µ Majorana: r = 10 ,m4 = 4 keV MiniBooNE νe + ν¯e LSND ν¯e 1σ than νe. Our explanation for the larger νµ run excess MiniBooNE νe + ν¯e LSND ν¯e 2σ does not require CP violation, which is necessary for the 100 MiniBooNE νe + ν¯e LSND ν¯e 3σ MiniBooNE+SciBooNE ν¯µ 90% C.L. pure oscillation explanation. Future experiments like MicroBooNE [48] (see also ) 2 10−1 Ref. [49] for other interesting proposals) may provide

(eV decisive tests for the LSND and MiniBooNE excesses. 4

Γ −2 Their results will not just cover our twin neutrino de- 4 10

m cay scenario, but also the pure oscillation interpretation. We also note that the IceCube collaboration is finalizing 10−3 their (eV) sterile neutrino searches. Some preliminary resultsO have shown significant improvement on constrain- ing oscillation parameters [50, 51]. The IceCube bound 10−4 is based on oscillation effects with a dramatical enhance- 0.05 0.10 0.15 0.20 0.25 0.30 sinθ ment of the oscillation amplitude due to matter effects at TeV energies. Although our twin neutrino decay scenario is unlikely to be constrained by the IceCube search, it is FIG. 8: The same as Fig. 7 but for the Dirac neutrino model. 2 interesting to explore how to search for the three twin The best fit point has ∆χ = 18.7 compared to the no twin neutrinos at large cosmic-ray neutrino experiments. neutrino assumption. In summary, motivated by the LSND and MiniBooNE excesses, we have constructed an interesting neutrino model to link the sterile neutrino phenomenology to the it is very likely that we can completely determine all the new TeV-scale physics associated with electroweak sym- parameters in the neutrino sector. metry breaking. The decay sterile neutrino scenario provides a novel explanation to the LSND and MiniBooNE anomalies. De- Acknowledgments. We would like to thank Vernon pending on whether neutrinos are Dirac or Majorana, one Barger, Josh Berger and Lisa Everett for useful discus- could have either only νe or both νe and νe to be decay sion and comments. This work is supported by the products of the twin neutrino components in νµ. For the U. S. Department of Energy under the contract DE- Majorana case, the MiniBooNE νµ run can have a larger FG-02-95ER40896. Jordi Salvado is also supported by excess than the νµ run. This is because νe as a product of FPA2011-29678 and FPA2014-57816-P.

[1] LSND Collaboration, A. Aguilar-Arevalo et al., [arXiv:1010.1395]. Evidence for neutrino oscillations from the observation [7] A. E. Nelson, Effects of CP Violation from Neutral of anti-neutrino(electron) appearance in a Heavy Fermions on Neutrino Oscillations, and the anti-neutrino(muon) beam, Phys. Rev. D64 (2001) LSND/MiniBooNE Anomalies, Phys. Rev. D84 (2011) 112007, [hep-ex/0104049]. 053001, [arXiv:1010.3970]. [2] LSND Collaboration, C. Athanassopoulos et al., [8] J. Kopp, M. Maltoni, and T. Schwetz, Are there sterile Evidence for muon-neutrino → electron-neutrino neutrinos at the eV scale?, Phys. Rev. Lett. 107 (2011) oscillations from pion decay in flight neutrinos, Phys. 091801, [arXiv:1103.4570]. Rev. C58 (1998) 2489–2511, [nucl-ex/9706006]. [9] J. Fan and P. Langacker, Light Sterile Neutrinos and [3] MiniBooNE Collaboration, A. A. Aguilar-Arevalo Short Baseline Neutrino Oscillation Anomalies, JHEP et al., Improved Search for ν¯µ → ν¯e Oscillations in the 04 (2012) 083, [arXiv:1201.6662]. MiniBooNE Experiment, Phys. Rev. Lett. 110 (2013) [10] E. Kuflik, S. D. McDermott, and K. M. Zurek, Neutrino 161801, [arXiv:1207.4809]. Phenomenology in a 3+1+1 Framework, Phys. Rev. [4] J. M. Conrad, W. C. Louis, and M. H. Shaevitz, The D86 (2012) 033015, [arXiv:1205.1791]. LSND and MiniBooNE Oscillation Searches at High [11] J. Huang and A. E. Nelson, MeV dark matter in the ∆m2, Ann. Rev. Nucl. Part. Sci. 63 (2013) 45–67, 3+1+1 model, Phys. Rev. D88 (2013) 033016, [arXiv:1306.6494]. [arXiv:1306.6079]. [5] G. Karagiorgi, A. Aguilar-Arevalo, J. M. Conrad, M. H. [12] J. Kopp, P. A. N. Machado, M. Maltoni, and Shaevitz, K. Whisnant, M. Sorel, and V. Barger, T. Schwetz, Sterile Neutrino Oscillations: The Global Leptonic CP violation studies at MiniBooNE in the Picture, JHEP 05 (2013) 050, [arXiv:1303.3011]. (3+2) sterile neutrino oscillation hypothesis, Phys. Rev. [13] SciBooNE, MiniBooNE Collaboration, G. Cheng D75 (2007) 013011, [hep-ph/0609177]. [Erratum: Phys. et al., Dual baseline search for muon antineutrino Rev.D80,099902(2009)]. disappearance at 0.1eV2 < ∆m2 < 100eV2, Phys. Rev. [6] C. Giunti and M. Laveder, Short-Baseline ν¯µ → ν¯e D86 (2012) 052009, [arXiv:1208.0322]. Oscillations, Phys. Rev. D82 (2010) 093016, [14] SciBooNE, MiniBooNE Collaboration, K. B. M. 10

Mahn et al., Dual baseline search for muon neutrino [34] V. D. Barger, W.-Y. Keung, and S. Pakvasa, Majoron disappearance at 0.5eV2 < ∆m2 < 40eV2, Phys. Rev. Emission by Neutrinos, Phys. Rev. D25 (1982) 907. D85 (2012) 032007, [arXiv:1106.5685]. [35] D. I. Britton et al., Measurement of the π+ → e+ [15] J. M. Conrad and M. H. Shaevitz, Limits on Electron neutrino branching ratio, Phys. Rev. D49 (1994) 28–39. Neutrino Disappearance from the KARMEN and LSND [36] PiENu Collaboration, A. Aguilar-Arevalo et al., νe - Carbon Cross Section Data, Phys. Rev. D85 (2012) Improved Measurement of the π → eν Branching Ratio, 013017, [arXiv:1106.5552]. Phys. Rev. Lett. 115 (2015), no. 7 071801, [16] S. Palomares-Ruiz, S. Pascoli, and T. Schwetz, [arXiv:1506.05845]. Explaining LSND by a decaying sterile neutrino, JHEP [37] P. Guzowski, L. Barnes, J. Evans, G. Karagiorgi, 09 (2005) 048, [hep-ph/0505216]. N. McCabe, and S. Soldner-Rembold, Combined limit [17] Y. Chikashige, R. N. Mohapatra, and R. D. Peccei, on the neutrino mass from neutrinoless double-β decay Spontaneously Broken Lepton Number and Cosmological and constraints on sterile Majorana neutrinos, Phys. Constraints on the Neutrino Mass Spectrum, Phys. Rev. Rev. D92 (2015), no. 1 012002, [arXiv:1504.03600]. Lett. 45 (1980) 1926. [38] V. Barger, J. P. Kneller, H.-S. Lee, D. Marfatia, and [18] Y. Chikashige, R. N. Mohapatra, and R. D. Peccei, Are G. Steigman, Effective number of neutrinos and baryon There Real Goldstone Bosons Associated with Broken asymmetry from BBN and WMAP, Phys. Lett. B566 Lepton Number?, Phys. Lett. B98 (1981) 265. (2003) 8–18, [hep-ph/0305075]. [19] G. B. Gelmini and M. Roncadelli, Left-Handed Neutrino [39] Planck Collaboration, P. A. R. Ade et al., Planck 2015 Mass Scale and Spontaneously Broken Lepton Number, results. XIII. Cosmological parameters, Phys. Lett. B99 (1981) 411. arXiv:1502.01589. [20] S. N. Gninenko, The MiniBooNE anomaly and heavy [40] M. Lindner, T. Ohlsson, and W. Winter, A Combined neutrino decay, Phys. Rev. Lett. 103 (2009) 241802, treatment of neutrino decay and neutrino oscillations, [arXiv:0902.3802]. Nucl. Phys. B607 (2001) 326–354, [hep-ph/0103170]. [21] I. Yu. Kobzarev, L. B. Okun, and I. Ya. Pomeranchuk, [41] http://www-boone.fnal.gov/for_physicists/data_ On the possibility of experimental observation of mirror release/nue_nuebar_2012/. particles, Sov. J. Nucl. Phys. 3 (1966), no. 6 837–841. [42] http://www-sciboone.fnal.gov/data_release/joint_ [Yad. Fiz.3,1154(1966)]. numubar_disap/. [22] Z. G. Berezhiani and R. N. Mohapatra, Reconciling [43] KARMEN Collaboration, B. Armbruster et al., Upper present neutrino puzzles: Sterile neutrinos as mirror limits for neutrino oscillations muon-anti-neutrino → neutrinos, Phys. Rev. D52 (1995) 6607–6611, electron-anti-neutrino from muon decay at rest, Phys. [hep-ph/9505385]. Rev. D65 (2002) 112001, [hep-ex/0203021]. [23] R. Foot, H. Lew, and R. Volkas, A model with [44] C. Giunti, M. Laveder, Y. F. Li, and H. W. Long, fundamental improper spacetime symmetries, Physics Pragmatic View of Short-Baseline Neutrino Letters B 272 (1991), no. 1 67 – 70. Oscillations, Phys. Rev. D88 (2013) 073008, [24] Z. Chacko, H.-S. Goh, and R. Harnik, The Twin Higgs: [arXiv:1308.5288]. Natural electroweak breaking from mirror symmetry, [45] C. Andreopoulos, C. Barry, S. Dytman, H. Gallagher, Phys. Rev. Lett. 96 (2006) 231802, [hep-ph/0506256]. T. Golan, R. Hatcher, G. Perdue, and J. Yarba, The [25] N. Craig, A. Katz, M. Strassler, and R. Sundrum, GENIE Neutrino Monte Carlo Generator: Physics and Naturalness in the Dark at the LHC, JHEP 07 (2015) User Manual, arXiv:1510.05494. http://www. 105, [arXiv:1501.05310]. genie-mc.org. [26] R. Barbieri, T. Gregoire, and L. J. Hall, Mirror world at [46] J. A. Formaggio and G. P. Zeller, From eV to EeV: the large hadron collider, hep-ph/0509242. Neutrino Cross Sections Across Energy Scales, Rev. [27] R. Foot and R. R. Volkas, Natural electroweak Mod. Phys. 84 (2012) 1307, [arXiv:1305.7513]. symmetry breaking in generalised mirror matter models, [47] MiniBooNE Collaboration, A. A. Aguilar-Arevalo Physics Letters B 645 (2007), no. 1 75 – 81. et al., Using L/E Oscillation Probability Distributions, [28] R. Foot and R. R. Volkas, Implications of mirror arXiv:1407.3304. neutrinos for early universe cosmology, Phys. Rev. D61 [48] MicroBooNE Collaboration, M. Soderberg, (2000) 043507, [hep-ph/9904336]. MicroBooNE: A New Liquid Argon Time Projection [29] F. del Aguila, The standard model with mirror fermions, Chamber Experiment, AIP Conf. Proc. 1189 (2009) Annals of Physics 165 (1985), no. 1 237 – 258. 83–87, [arXiv:0910.3497]. [30] R. Foot and R. R. Volkas, The Exact parity symmetric [49] B. Dutta, Y. Gao, R. Mahapatra, N. Mirabolfathi, L. E. model and big bang nucleosynthesis, Astropart. Phys. 7 Strigari, and J. W. Walker, Sensitivity to oscillation (1997) 283–295, [hep-ph/9612245]. with a sterile fourth generation neutrino from ultra-low [31] Particle Data Group Collaboration, K. A. Olive threshold neutrino-nucleus coherent scattering, et al., Review of Particle Physics, Chin. Phys. C38 arXiv:1511.02834. (2014) 090001. http://pdg.lbl.gov/2015/reviews/ [50] C. A. Argüelles Delgado, New physics with atmospheric rpp2014-rev-neutrino-mixing.pdf. neutrinos. PhD thesis, University of [32] S. Parke and M. Ross-Lonergan, Unitarity and the Wisconsin-Madison, 2015. Three Flavour Neutrino Mixing Matrix, [51] B. J. P. Jones, Sterile Neutrinos in Cold Climates. PhD arXiv:1508.05095. thesis, MIT, 2015. [33] A. de Gouvêand A. Kobach, Global Constraints on a Heavy Neutrino, arXiv:1511.00683.