Probing The Origin Of Neutrino Mass And Neutrino .
Probing the Origin of Neutrino Mass and NeutrinoProperties with Supernova Neutrinos †Ina SarcevicUniversity of Arizona Models of Neutrino Mass with a Low Scale Symmetry Breaking New Interactions of Supernova Relic Neutrinos Probing Neutrino Properties with Supernova Neutrinos Experimental Detection of the New Interactions via Light Scalar(HyperK, GADZOOKS, UNO, MEMPHYS) BBN and SN1987A Constraints on the Parameter Space of theNeutrino Mass Models†H. Goldberg, G. Perez and I. Sarcevic, JHEP 11, 023 (2006); J. Baker, H. Goldberg,G. Perez and I. Sarcevic, hep-ph/0630218.
Observation of neutrino flavor conversion from solar (SuperK,SNO), atmospheric (SuperK) and terrestrial (KamLand, K2K)neutrino data has provided firm evidence for neutrino flavorconversion. Recent SuperK data on the L/E-dependence of atmospheric neutrinoevents and the new spectrum data from terrestrial experiments (KamLand,K2K) is the first time evidence of the expected oscillatory behavior. Thisstrongly favors non-vanishing sub-eV neutrino masses.1.61.41.41.21.211RatioData/Prediction (null osc.)1.80.82.6 MeV promptanalysis thresholdKamLAND databest-fit oscillationbest-fit decaybest-fit decoherence0.80.60.60.40.40.20.200110102L/E (km/GeV)1031042030405060L 0/E ν (km/MeV)e7080
Neutrino Mass Models with Low Scale of Symmetry BreakingChacko, Hall, Okui and Oliver, PR D70 (2004)Chacko, Hall, Oliver and Perelstein, PRL 94 (2005)Davoudiasl, Kitano, Kribs and Murayama, PR D71(2005) Consider the effective Lagrangian below EWB scale and close tothe neutrino flavor symmetry breaking scale:LDν Lkin yν φνN V (φ)LMν Lkin yν φνν V (φ)ν is an active neutrino, V (φ) is the scalar potential (for the globalcase this contains interaction between φ and the additionalGoldstone bosons). After the symmetry breaking, neutrino gets the massmν yν f , where f φ and f MW .
Strongest limits on f come from cosmology and astrophysics:light scalars not to be in thermal equilibrium during big bangnucleosynthesis (BBN) gives a limit on f of approximatelyf 10 keV.Chacko et al., PRL 94 (2005)Davoudiasl et al., PRD 71 (2005) Similar bound is obtained by demanding that SN cooling not bemodified in the presence of these additional fields.Y. Farzan, PRD 67 (2003) Combining BBN bound and assuming that the heaviest neutrinomass, mhν 4 10 2 eV, we find that the strength of theinteraction between the scalar and the neutrinos yν is ratherweak,yν 10 5 ,
New Interactions of Supernova Relic NeutrinosH. Goldberg, G. Perez and I.S.,JHEP 11, 023 (2006). Dramatic modification ofthe supernova neutrinoflux (diffuse or burst)through interactions between SN neutrinos andthe cosmic backgroundneutrinos:ννGνννSN νCM B G νν Typical SRN energies are above solar neutrino energies and bellow theatmospheric ones likely to be observed by SuperK, GAZOOKS, HyperK,KamLand, UNO and MEMPHYS. Unique possibility of detecting the extra light degrees of freedomas well as cosmic background neutrinos!
10SRN10.11010.102040608010001
The Effect of New Interactions on SRN Flux SRN neutrino energies will be redistributed after theinteraction Significant distortion of the SRN flux as a result ofredistribution? SRN flux can have regions of depletion relative toflux without new interactions? SRN flux can have regions of enhancement relativeto flux without new interactions These modifications could be detected at large neutrinodetectors
SRN Flux with New Interactions Depletion of flux in region EνRes /(1 z) EνObs EνRes Replenishment of flux from 0 energy back up toEunscattered for each neutrino energy in resonance regiondF dEΝ Hcm-2 s-1 MeV-1 Lz 0.510.80.60.40.25101520EΝ HMeVL
Resonance Including Cosmological Expansion Consider the conditions on the coupling for which there is sizableresonant degradation of the original flux of supernova neutrinos. Probability that a neutrino, created at red shift z, with energy(1 z)E arrives unscattered at the detector with energy E isgiven by: Z z dz̄n(z̄) σνν φ (2mν (1 z̄)E) ,P (E, z) exp H(z̄)(1 z̄)0where n(z̄) (1 z̄)3 n0 is the background neutrino density atredshift z̄ and n0 ' 56 cm 3 . Large depletion of the initial SRN flux ifMG 8 yν 4 101 keV
Accumulative Resonance There will be resonant absorption of the original neutrino flux aswell as replenishment from neutrinos re-emitted in the decay of aG. A neutrino emitted with energy Ei E from a source at redshift zundergoes resonant scattering at redshift z̄ z, so that1 z̄E Ei1 z Neutrinos from the decay have flat energy distribution,E 0 f E , 0 f 1 , where f varies uniformly over the region [0,1]. The spectrum with absorption has a dip at E E , and is shifteddownward from the spectrum absent resonant absorption. Thecomplete effect of neutrinos emitted with non-resonant energies,passing through resonance, and then replenishing the flux atlower energies, is what we call accumulative resonance.
Event Rates Consider the effect of the accumulative resonance on the total SRNdifferential flux. The differential flux of Supernova Relic Neutrinos is givenbyZ zmaxdFdN ( )dt RSN (z)(1 z)dz ,dEd dz0 (1 z)E where dNd ( ) is the neutrino energy spectrum, RSN is the (comoving) rate ofdtis the Jacobian given bysupernova formation and dz kmdt 100h (1 z)dzs Mpcpwith ΩM 0.3, ΩΛ 0.7 and h 0.7.ΩM (1 z)3 ΩΛ 1
The resulting differential flux, showing depletion in the incoming SRN fluxdue to the accumulative resonance effect (blue curve) and withoutresonance (red curve), integrated over redshift up to z 4.dF dEΝHcm-2 s-1 MeV-1 L21.751.51.2510.750.50.255MG 1.1 keV101520EΝ HMeVL2 There is a sharp dip at Eν E MG/2mν for all values of z.
Differential neutrino flux folded with the detection cross section (theinverse beta decay induced by ν̄e capture in the detector):Σ dF dEΝ Hevents yr-1 MeV-1 L0.3SuperK, GADZOOKSMG 1.1 keV0.250.20.150.10.051020304050EΝ HMeVL The shape of the differential rate is modified due to the energy dependenceEe pe 10 42 cm2 .of the cross section, i.e. σν̄e p e n 0.0952 1MeV 2 The main features of the effect due to the accumulation resonancesuch as the location of the dip and its width remain unmodified.
Theoretical Models for Neutrino Spectrum from SupernovaExplosion The neutrino spectrum is well fitted by a simple formula: β ν1 βν(1 βν )dNνLν Eν (1 βν )Eν /Ēν edEνΓ(1 βν )Ēν2ĒνMassĒν̄eĒνxModel(M Lνeβνe(erg)(erg)3.81.84.9 10525.0 3.62.2———15.415.74.22.5——
1010110.10.10102030405060010Supernova Relic Neutrino Flux2030405060
Probing Neutrino Mass Hierarchy Consider three flavor neutrino mixingm2m2νeνµντm32solar 7 10 5eV2atmospheric 2 10 3eV2m22m12solar 7 10 5eV2?0m22m12atmospheric 2 10 3eV2m32?0
Flavor Composition of the Neutrino Flux that Emerges from aSupernova Because of the matter oscillation effects, neutrinos emerge from asupernova as coherent fluxes of mass eigenstates (Fνi )Dighe and Smirnov, PR D62, 033007 (2000) If neutrino evolution inside of the collapsing star is eitheradiabatic or fully non-adiabatic then the energy spectrum of eachneutrino mass eigenstates that leaves the surface of the starcorreponds to the original energy spectrum of some particularneutrino flavor eigenstate at emission from the neutrino sphereDighe and Smirnov, PR D62, 033007 (2000)
Fνe and Fν̄e Fluxes For normal hierarchy:22Fe Ph Ue2Fe0 (1 Ph Ue2)Fx022Fē Ue1Fē0 Ue2Fx̄0 For inverted hierarchy:22Fe Ue2Fe0 Ue1Fx022Fē Ph Ue1Fē0 (1 Ph Ue1)Fx̄022Ue1 cos2 θ12 , Ue2 sin2 θ12 ;Ph 0 for the adiabatic casePh 1 for non-adiabatic case.θ12 θ
sin2 θ13 & 10 3 (adiabatic, Ph 0)sin2 θ13 . 10 5 (non adiabatic, Ph 1)Normal HierarchyNormal & Inverted HierarchiesFνe Fν0xFν̄e cos2 θ Fν̄0e sin2 θ Fν0xFνe sin2 θ Fν0e cos2 θ Fν0xFν̄e cos2 θ Fν̄0e sin2 θ Fν0xInverted HierarchyFνe sin2 θ Fν0e cos2 θ Fν0xFν̄e Fν0x
Normal Hierarchy In the case of the normal hierarchy the neutrinos emerge fromthe supernova in mass eigenstates and carry information withthem about the original fluxes of different neutrino flavorsaccording toF1 Fν0µ F1̄ Fν̄0eF2 Fν0τ F2̄ Fν̄0µF3 Fν0e F3̄ Fν̄0τ Fν̄e flux seen at Earth is a mixture of the one-bar and two-barmass eigenstates (the mixing of the mass three eigenstate inelectron type neutrinos is small),Fν̄e cos2 θ Fν̄0e sin2 θ Fν̄0µ .
Inverted Hierarchy In the case of the inverted hierarchy the neutrino masseigenstates carry information about the original fluxes of thedifferent types of neutrinos according toF1 Fν0µ F1̄ Fν̄0τF2 Fν0e F2̄ Fν̄0µF3 Fν0τ F3̄ Fν̄0e In this case the final electron antineutrino flux is given byFν̄e cos2 θ Fν̄0τ sin2 θ Fν̄0µ
The observed SRN spectrum depends on the neutrino masshierarchy, whether neutrinos are Majorana or Dirac and whetherthere is a heavy sterile neutrino. It also depends on how many ofthe mass eigenstates go through the resonance on their way tothe earth. After the interaction, the modified flux is given byf1̄ F1̄ F res P1 (F res F res F res F res F res F res )F1 1̄2 1̄3 1̄1̄1̄ 1̄2̄ 1̄3̄ 1̄where F1̄ is the original flux, F1̄res is the flux of one-bar neutrinosresthat go through resonance, and the Fi 1̄ are the contributionfrom the state i to the final one-bar flux after going through theresonance. P1 is the probability that a boson will decay into theone-bar mass eigenstate neutrino. For Dirac case a factor of 1/2 multiplies the third term. Different eigenstates, i, that give contribution to F1̄ go throughthe resonance at different energies for a given boson mass.
Similarly,f2̄ F2̄ F res P2 (F res F res F res F res F res F res )F2 2̄1 2̄3 2̄2̄2̄ 2̄1̄ 2̄3̄ 2̄ Mixing with the third eigenstate is small, thus the combinationf1̄ and Ff2̄ determines the observedof these modified fluxes, Fspectra. The modified flux of electron antineutrinos can then be written as22ffgFν̄e cos θ12 F1̄ sin θ12 F2̄ .
Neutrino Mass HierarchydF dEΝ Hcm-2 s-1 MeV-1 L3.532.5Inverted Hierarchy21.510.52.557.5 10 12.5 15 17.5 20EΝ HMeVL m1 ' m2 ' 0.05 eV, m3 ' 0.008 eV m1 and m2 neutrinos go through resonance at EνRes 12 MeV(MG 1 keV); m3 neutrino goes through resonance at EνRes 63 MeV The decay probabilities are P1 0.49, P2 0.49 and P3 0.02.
Folding dF/dE with ν̄e p n p Cross SectionΣ FHevents yr-1 MeV-1 L17.51512.5107.552.5510152025303540EΝ HMeVL Differential flux folded with the detection cross section(inverse beta decay induced by antineutrino capture inthe detector) Cross section for antineutrinos on protons is increasingfunction of the energy, leading to observed shapeMain features, i.e. dip location, remain unchanged
dF dEΝ Hcm-2 s-1 MeV-1 L3.532.5Normal Hierarchy21.510.52.5 57.5 10 12.5 15 17.5 20EΝ HMeVLm1 ' 0.002 eV, m2 ' 0.009 eV, m3 ' 0.05 eVTwo heavier neutrino mass eigenstates have dip at lower energies,E2Res 3 MeV and E3Res 0.5 MeV The probabilities are: P1 0.005, P2 0.025 and P3 0.97. Overall depletion because G decays with P3 into heaviest neutrinomass eigenstate, which does not contribute to electron antineutrinoflux.
Folding dF/dE with ν̄e p n p Cross SectionΣ FHevents yr-1 MeV-1 L17.51512.5107.552.5510152025303540EΝ HMeVL Differential flux folded with the detection cross section(inverse beta decay induced by antineutrino capture inthe detector) Cross section for antineutrinos on protons is increasingfunction of the energy, leading to observed shapeMain features, i.e. dip location, remain unchanged
Dirac vs. Majorana Neutrinos?dF dEΝ Hcm-2 s-1 MeV-1 L3.532.5Inverted Hierarchy21.510.52.557.5 10 12.5 15 17.5 20EΝ HMeVL If neutrinos are Majorana particles (red), each bosondecay produces a νν or ν̄ ν̄ If neutrinos are Dirac particles (blue) then the bosoncan decay to ν N̄ or to N ν̄Overall factor of 1/2 for Dirac vs. Majorana particles
Determining Neutrino MassesdF dEΝ Hcm-2 s-1 MeV-1 L21.75Normal Hierarchy1.51.2510.750.50.252.557.5 10 12.5 15 17.5 20EΝ HMeVL Two neutrinos could visibly go through resonance, i.e.two light nearly degenerate neutrino masses, oneneutrino mass approximately 0.05 eV Ratio of peak positions leads to determination ofneutrino masses, E1Res 12 MeV, E2Res 16 MeV
Folding dF/dE with ν̄e p n p Cross SectionΣ FHevents yr-1 MeV-1 L17.5Normal Hierarchy1512.5107.552.5510152025303540EΝ HMeVL Differential flux folded with the detection cross section(inverse beta decay induced by antineutrino capture inthe detector) Cross section for antineutrinos on protons is increasingfunction of the energy, leading to observed shapeMain features, i.e. dip location, remain unchanged
Bounds on Neutrino Mass Models from BBNConstraints The minimal model: Majorana neutrinos with Abeliansymmetry. The symmetry breaking scale, f , is below the BBNtemperature of about 1 MeV. During the BBN epoch we cannotseparate the Goldstone and the scalar (higgs) as they are a singleentity, a complex scalar field. The BBN bound on the number ofneutrinos is N 3.24 1.2 at 95%. The complex scalar adds 8/7(neutrino) degrees of freedom, so this additional degree offreedom can be accommodated with the BBN bound above. In the non-Abelian Majorana models, typically several complexscalars are present, which are not permitted to be by BBNconsiderations. Thus, in this case yν must be bounded fromabove to ensure decoupling. We have considered all the processesthat would produce G’s. Recoupling via the 2 1 process νν Gtakes place as the temperature falls to some value Trec determined
by equating the decay rate at Trec to the Hubble expansion rate:r22MG y ν MG8π 5 g Trec ,23Trec 16π45 MP lwhere g is the number of degrees of freedom at Trec . By requiringTrec TBBN we find 7yν 6 10 (keV/MG ) For the Dirac case, the absence of a negligible population ofright-handed (sterile) neutrinos (N ) in the bath disallows thereaction νN G, so that G’s can only be produced viaνL νL G G (via t channel N exchange). Requiring that thisprocess be out of equilibrium at TBBN yields a BBN bound of 5.1 10yν The s-channel process requires a chirality flip which makes thebound weaker. Note that this bound in independent of theGoldstone mass.
Non-Resonance Processes Two Goldstones production through scalar exchange, theoff-resonance process. For sMφ2 ,σGG yν2 f 2m4φ yν2f2 yν4m2ν . To have a substantial scattering, λnon res H 'Hm2νTν3 yν41. This yields a lower bound on yν (independent of MG ):yν Hm2νTν3 1/4 10 6 mν 1/20.05 eV Dramatic effect on the SRN flux: If MG 2mν and there issufficient optical depth, all the SRN will be transformed intoinvisible Goldstones and the signal is lost. If MG 2mν then theprocess can effectively be characterized as ν 4ν, implying asubstantial shifting of the entire SRN spectrum to lower energies.
Bounds from SN1987A For a point source at distance , the condition for sufficientoptical depth is 1/43000 Mpcyν 3.3 10 6 where l is the distance travelled by the SRN. For SN1987A, 50 kpc. SN1987A neutrinos observed with undegraded energy, implyingan independent upper bound on yνyν 5.5 10 5which is comparable to the cosmological one.
yΝ10-4Excluded10-610-8Couplingtoo weak10-10101001000MG HeVL10000The region above the red line is excluded by the BBN constraint (for the Dirac case), SNcooling (for Majorana case) and due to the observation of (undegraded) SN1987A neutrinos.In the region below the blue line the mean free path is too long for the resonance to occur.The region above the green line, which is relevant only for the non abelian Majorana case, isthe region excluded by the BBN constraint. The region above the black dashed line is theregion of the future experimental sensitivity to the observation/non-observation of the SRNneutrinos due to the the non-resonant processes.
Summary Interactions between the SRN and CνB neutrinos via lightbosons can result in a dramatic change of the SRN neutrino flux Measurements of these effects could shed light on? Symmetry structure of neutrino mass generation? Presence of the CνB? Neutrino mass hierarchy? Possibility to distinguish between Dirac and Majorananeutrinos? Absolute values of the neutrino masses Measurements of these effects are well within reach of futureneutrino experiments (GADZOOKS, HyperK, UNO,MEMPHYS)
Ina Sarcevic University of Arizona Models of Neutrino Mass with a Low Scale Symmetry Breaking New Interactions of Supernova Relic Neutrinos Probing Neutrino Properties with Supernova Neutrinos Experimental Detection of the New Interactions via Light Scalar (HyperK, GADZOOKS, UNO, MEMPHYS) BBN and SN1987A Constraints on the Parameter Space of the
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