Fancy Neutrino Oscillometry -on Settling the Reactor Neutrino Anomaly)

EESFYE, Patras EESFYE, Patras April 14-16/2011April 14-16/2011

Fancy Neutrino Oscillometry-on Fancy Neutrino Oscillometry-on Settling the Reactor Neutrino Settling the Reactor Neutrino Anomaly)Anomaly)

(LOW ENERGY NEUTRINOS IN A BO(LOW ENERGY NEUTRINOS IN A BOX)X)

J.D. Vergados*, Y. Giomataris* and Yu.N. Novikov

*for the NOSTOS Collaboration: Saclay, APC-Paris, Saragoza, Ioannina, Thessaloniki, Dimokritos, Dortmund, Sheffield


NOSTOS:NOSTOS: SPHERICAL TPC’s SPHERICAL TPC’s (STPC) for detecting Earth or (STPC) for detecting Earth or sky neutrinossky neutrinos•A) LOW ENERGY NEUTRINOSA) LOW ENERGY NEUTRINOS IN A SPHERICAL BOX IN A SPHERICAL BOX

((electron recoils from low energy neutrinos)electron recoils from low energy neutrinos)

• B) B) Neutral Current Spherical TPC’s Neutral Current Spherical TPC’s

(nuclear recoils) (nuclear recoils)

• B1: For DedicatedB1: For Dedicated SUPERNOVA NEUTRINO SUPERNOVA NEUTRINO DETECTIONDETECTION

• B2: For exotic B2: For exotic neutrino Oscillometry neutrino Oscillometry (Reactor Neutrino (Reactor Neutrino

Anomaly)Anomaly)


NEUTRINO OSCILLATIONSNEUTRINO OSCILLATIONSNeutrino mass termsNeutrino mass terms1. Dirac +(heavy neutrino) Majorana type 1. Dirac +(heavy neutrino) Majorana type oror2. Light neutrino Majorana type2. Light neutrino Majorana type Result in all cases:Result in all cases: Neutrino mixingNeutrino mixing


Standard Parameterization of Standard Parameterization of Mixing Matrix Mixing Matrix (2 Majorana phases (2 Majorana phases not shown)not shown)

The mixing matrix is called PNMS The mixing matrix is called PNMS ((Pontecorvo–Maki–Nakagawa–Sakata matrix). ). It has not yet been derived from a basic It has not yet been derived from a basic theory. From neutrino oscillations we know theory. From neutrino oscillations we know that, unlike the C-M matrix for quarks, it that, unlike the C-M matrix for quarks, it has large off diagonal elements. Some has large off diagonal elements. Some models yield “bi-tri maximal” form models yield “bi-tri maximal” form consistent with consistent with ν-ν-oscillations, i.e. oscillations, i.e.


http://en.wikipedia.org/wiki/Neutrino_oscillation#Pontecorvo.E2.80.93Maki.E2.80.93Nakagawa.E2.80.93Sakata_matrix

http://en.wikipedia.org/wiki/Neutrino_oscillation#Pontecorvo.E2.80.93Maki.E2.80.93Nakagawa.E2.80.93Sakata_matrix


Massive Neutrinos Oscillate!Massive Neutrinos Oscillate!

• Flavor states: Flavor states: ννα α , α=, α=e,e,μ,τμ,τ..

• Mass eigenstates: : Mass eigenstates: : ννi i , i=1,2,3, i=1,2,3

• Flavor Flavor αα at time t=0, at time t=0, νναα ==ΣΣι ι UUααj j ννjj

• Flavor Flavor α α at a later time tat a later time t##0, 0, νναα==ΣΣι ι UUααj j

ννj j exp(iEexp(iEj j t)t)

• P(P(ννα α -->>ννββ) ) ==ΣΣjj ((UUββjj)* )* UUααjj exp(iEexp(iEj j t ) #t ) #δδαβαβ

Neutrino Oscillations (two Neutrino Oscillations (two ν ν types)types)L=ct, LL=ct, L00=oscillation length=oscillation length<-<->period>period Mixing matrixMixing matrix Q.M. Evolution EquationQ.M. Evolution Equation



Neutrino Oscillation ExperimentsNeutrino Oscillation ExperimentsEffectively analyzed as two Effectively analyzed as two generationsgenerations• Appearance Appearance

P(P(νναα-> -> ννββ, , αα≠β≠β))==sinsin2222θθ sinsin2 2 π(π(L/LL/L00))• DisappearanceDisappearance

P(P(νναα-> ν-> ναα))==1-sin1-sin2222θθ sinsin2 2 π(π(L/LL/L00))• θθ the effective mixing angle the effective mixing angle• LL0 0 the oscillation Length =the oscillation Length =((44ππEEνν)/Δ)/Δmm2 2

oror

LL00==2.4762.476km {Ekm {Eνν/1MeV}/{/1MeV}/{ΔΔmm2 2 /10/10-3-3eVeV22}= }=

2.4762.476m {Em {Eνν/1keV}/{/1keV}/{ΔΔmm2 2 /10/10-3-3eVeV22}}• L is the source detector distanceL is the source detector distance

Two generation OscillationsTwo generation Oscillationsθ=π/4θ=π/4 (atmospheric), (atmospheric), θ=π/θ=π/5 5 (solar)(solar)



Table I: Best fit values from global Table I: Best fit values from global data (solar, atmospheric, reactor data (solar, atmospheric, reactor (KamLand and CHOOZE) and K2K (KamLand and CHOOZE) and K2K experiments)experiments)


InIn ((ννe e ,e) detector all flavors ,e) detector all flavors contributecontributeσσee(Ε(Ενν ,,L)=L)= σ(Ε σ(Ενν,,0) P0) P(Ε(Ενν,ν,νee-->-->ννee))• σσee(Ε(Ενν,,0) is the standard electron neutrino 0) is the standard electron neutrino

cross section in the absence of oscillation.cross section in the absence of oscillation.• The 3-generation oscillation probability The 3-generation oscillation probability

(after integration over the electron (after integration over the electron energies ) will appear as:energies ) will appear as:

• P(P(ννee -->>ννee)≈)≈1- 1- χ(Εχ(Ενν))

{{sinsin2 2 (2(2θθ1212) ) sinsin2 2 [π([π(L\LL\L1212)])]+ +

sinsin2 2 (2(2θθ1313) ) sinsin2 2 [π([π(L\LL\L1313)])]}}, , LL1313 = L= L2233

The The ννe e disappearancedisappearance probability probability EEνν=13=13keVkeV, ,

θθ1122 ==π/5π/5, ,

sinsin2222θθ1133=0.175,0.085,0.045=0.175,0.085,0.045 Detector close to the sourceDetector close to the source Detector far from the sourceDetector far from the source


More Exotic Neutrino More Exotic Neutrino Oscillation Experiments to Oscillation Experiments to extract more preciseextract more precise Neutrino Oscillation Neutrino Oscillation ParametersParameters•Very low energy neutrinos small

oscillation lengths

•The full oscillation takes place inside the detector (many standard experiments simultaneously)

•Due to thresholds available are only:

•neutrino electron and neutral current scattering are open


The NOSTOS Set Up The NOSTOS Set Up (the (the position is determined via a radial position is determined via a radial Electric field)Electric field)

The detectorThe detector The neutrino sourceThe neutrino source


The famous “sphere”The famous “sphere”


The number of events for a The number of events for a spherical gaseous detector (source spherical gaseous detector (source at the at the origin)origin)


Part I (Part I (ννee,, e) scattering e) scattering

• For measuring For measuring


sin2 (2θ13) and δm213

Some sources of low energy Some sources of low energy Monoenergetic Neutrinos for Monoenergetic Neutrinos for mesuring mesuring sinsin2 2 (2(2θθ1313)) and and δδmm22

1313


Event rate dN/dL(per m), Event rate dN/dL(per m), P=10Atm,P=10Atm,Ar target for m=0.2 and 0.3 kg of Ar target for m=0.2 and 0.3 kg of sourcesource sinsin2222θθ1133=0.175,0.085,0.045=0.175,0.085,0.045 T Tthth=0.1keV=0.1keVL=10m, EL=10m, Eνν=9.8=9.8 keV ( keV (157157Tb)Tb) L=50m, EL=50m, Eνν==50 keV (50 keV (193193Pt)Pt)

Neutrino20010 Neutrino20010 Athens 19/06/10Athens 19/06/10

L->mL->m

Part II:Part II: ((ννee,, e) scattering for e) scattering for oscillations to a Sterile oscillations to a Sterile Neutrino Neutrino measuring* measuring* sinsin2 2 (2(2θθ1144)) and and δδmm22

1144

• Motivated by Motivated by The reactor neutrino anomaly and LSND:The reactor neutrino anomaly and LSND:sinsin2 2 (2(2θθ1144)) =0.17±0.1(95%), =0.17±0.1(95%), δ δmm22

114 4 >1.5 eV>1.5 eV22

*Now *Now δδmm2 2 is larger ->The optimal is larger ->The optimal ν-ν-energy energy can be largercan be larger



Sterile neutrinos inSterile neutrinos in ( (ννe e ,e) detector,e) detectorσσtottot(Ε(Ενν ,,L)=L)= σ(Ε σ(Ενν ,0) P ,0) P(Ε(Ενν ; ;ννee-->-->ννee))

Some sourcesSome sources (0.1 (0.1 kg) of low energy kg) of low energy Monoenergetic Neutrinos for Monoenergetic Neutrinos for

memeααsuring suring sinsin2 2 (2(2θθ1414)) and and δδmm2214 14

((electron recoils)electron recoils)To check the Reactor neutrino To check the Reactor neutrino anomaly anomaly sinsin2 2 (2(2θθ1414))= 0.17± 0.01, = 0.17± 0.01, δδmm22

1414≈1.5 eV≈1.5 eV22


Sterile neutrino oscillations: Sterile neutrino oscillations: RR00=4m,P=10 =4m,P=10 AtmAtm ΕΕν ν =747 keV=747 keV; ; full, dotted, full, dotted, dashed curve dashed curve sinsin22(2(2θθ1414))=0.27,0.17,0.07=0.27,0.17,0.07Oscillation Pattern (10d)Oscillation Pattern (10d) Expected Spectra (55d)Expected Spectra (55d)


Determination of Determination of θθ1144by by 4040Ar Ar ((ννee,e) detector:,e) detector: sinsin22(2(2θθ1144))=0.05 =0.05 (99%)(99%)

•The total number of events:The total number of events:

NN0 0 =A+B sin =A+B sin22 (2 (2θθ1144))

•For For 5151Cr (measuring for 55 Cr (measuring for 55 days):days):

A=1.59x10A=1.59x1044 , B=-7.56x10 , B=-7.56x1044


Part III:Part III: Neutral Current Neutral Current detectorsdetectors** for oscillations to a for oscillations to a Sterile NeutrinoSterile Neutrino measuring measuring sinsin2 2

(2(2θθ1144)) and and δδmm221144

• Motivated by Motivated by The reactor neutrino anomaly and LSND:The reactor neutrino anomaly and LSND:sinsin2 2 (2(2θθ1144)) =0.17±0.1(95%), =0.17±0.1(95%), δ δmm22

114 4 >1.5 >1.5 eVeV22 Now Now δδmm2 2 is larger ->The optimal is larger ->The optimal ν-ν-energy can be largerenergy can be larger

• *Expect large cross sections due to the N*Expect large cross sections due to the N22 dependence instead of Zdependence instead of Z for (for (ννee,, e) e)


Neutrino oscillations with NC Neutrino oscillations with NC interactions?interactions?


Some sourcesSome sources (0.1 (0.1 kg) of low energy kg) of low energy Monoenergetic Neutrinos for Monoenergetic Neutrinos for

memeααsuring suring sinsin2 2 (2(2θθ1414)) and and δδmm2214 14

((nuclear recoils)nuclear recoils)To check the Reactor neutrino To check the Reactor neutrino anomaly anomaly sinsin2 2 (2(2θθ1414))= 0.17± 0.01, = 0.17± 0.01, δδmm22

1414≈1.5 eV≈1.5 eV22


Unexpected snug: Threshold Unexpected snug: Threshold effect kills the benefit of large effect kills the benefit of large NN22 (large (large σ)σ) Large massLarge mass Small recoil Small recoil energyenergy


Sterile neutrino oscillations: Sterile neutrino oscillations: RR00=4m,P=10 =4m,P=10 AtmAtmΕΕν ν =1343 keV=1343 keV; ; (NC) full, dotted, (NC) full, dotted, dashed curve dashed curve sinsin22(2(2θθ1414))=0.27,0.17,0.07=0.27,0.17,0.07Oscillation PatternOscillation Pattern Expected SpectraExpected Spectra


Sterile neutrino oscillations: Sterile neutrino oscillations: RR00=4m,P=10 =4m,P=10 AtmAtmΕΕν ν =1343 keV=1343 keV; ; (NC) full, dotted, (NC) full, dotted, dashed curve dashed curve sinsin22(2(2θθ1414))=0.27,0.17,0.07=0.27,0.17,0.07 source:source:6565Zn; target Zn; target 2020NeNe source:source:6565Zn; target Zn; target 44HeHe


Sterile neutrino oscillations: Sterile neutrino oscillations: RR00=4m,P=10 =4m,P=10 AtmAtmAntineutrino (continuous) source Antineutrino (continuous) source ; ; (NC) (NC) NC cross section (no oscillation)NC cross section (no oscillation) Source spectrumSource spectrum


Sterile neutrino oscillations: Sterile neutrino oscillations: RR00=4m,P=10 =4m,P=10 AtmAtmAntineutrino (continuous) source ; Antineutrino (continuous) source ; (NC) (NC) full, dotted, dashed curve full, dotted, dashed curve sinsin22(2(2θθ1414))=0.27,0.17,0.07=0.27,0.17,0.07 source:source:3232P; target P; target 4040ArAr source:source:3232P; target P; target 2020NeNe


Determination of Determination of θθ1144 by NC by NC 2020Ne detector: Ne detector: sinsin22(2(2θθ1144))=0.1 =0.1 (99%)(99%)

•The total number of events:The total number of events:

NN0 0 =A+B sin =A+B sin22 (2 (2θθ1144))

•For For 6565Zn (measuring for 50 Zn (measuring for 50 days):days):

A=5.3 x10A=5.3 x1022 , B=-2.8x10 , B=-2.8x1022



Conclusions A Conclusions A (neutrino (neutrino oscillations):oscillations):• The discovery of neutrino oscillations gave neutrino The discovery of neutrino oscillations gave neutrino

physics and astrophysics a new momentum.physics and astrophysics a new momentum. • TheThe two mass square differences, except for a sign, two mass square differences, except for a sign,

are knownare known• The mixing angles The mixing angles θθ112 2 and and θθ2323 are understoodare understood. . • The angle The angle θθ1313 and the phase and the phase δδ1313 are unknown. are unknown.• Neutrino Oscillations like Neutrino Oscillations like double CHOOZE anddouble CHOOZE and

NOSTOS NOSTOS may help in determining the neutrino may help in determining the neutrino oscillation parameters, including oscillation parameters, including θθ1313, more , more precisely.precisely.

• The Reactor Neutrino Anomaly implies a fourth The Reactor Neutrino Anomaly implies a fourth (sterile?) neutrino. Neutrino oscillometry with the (sterile?) neutrino. Neutrino oscillometry with the gaseous STPC detector (nostos) is ideally suited to gaseous STPC detector (nostos) is ideally suited to resolve this issueresolve this issue

Questions that cannot be answered by Questions that cannot be answered by neutrino oscillations:neutrino oscillations: The mass scale The mass scale and the sign of and the sign of ΔΔmm22

3131 (normal vs (normal vs inverted hierarchy or almost inverted hierarchy or almost degenerate scenario)degenerate scenario)


Conclusions B (involving Conclusions B (involving neutrinos)neutrinos)The absolute scale of neutrino The absolute scale of neutrino mass is still elusive. mass is still elusive.

The combination neutrinoless double The combination neutrinoless double beta decay, triton beta decay, triton decay, astrophysics may provide the answerdecay, astrophysics may provide the answer

• We do not know whether the neutrinos are Dirac or We do not know whether the neutrinos are Dirac or Majorana type particles Majorana type particles (only neutrinoless double beta (only neutrinoless double beta decay can settle this issue)decay can settle this issue)

• Neutrinos may be the best probes for studying the Neutrinos may be the best probes for studying the deep sky and the interior of dense objects, like deep sky and the interior of dense objects, like supernovae. A network of cheap easily maintainable supernovae. A network of cheap easily maintainable and robust STPC detectors maybe a useful in and robust STPC detectors maybe a useful in supernova neutrino detection.supernova neutrino detection.

• Shall we ever see the neutrino background Shall we ever see the neutrino background radiation? Will we see it before the gravitational radiation? Will we see it before the gravitational background radiation?background radiation?


•THE ENDTHE END


The standard (The standard (νν,e) cross ,e) cross sectionsection((In the absence of neutrino In the absence of neutrino oscillations)oscillations)



II: Measure II: Measure the Weinberg anglethe Weinberg angle at very at very low momentum transfers low momentum transfers


III : At III : At low neutrino energieslow neutrino energies: : The The EM interaction competes with the EM interaction competes with the weakweak

• With With μμνν the neutrino magnetic moment and the neutrino magnetic moment and ξξ11

≈0.25≈0.25

• Thus we can obtain the limit: Thus we can obtain the limit: μμν ν ≤10≤10-12 -12 μμΒΒ

• (present limit: (present limit: μμν ν ≤10≤10-1-100 μμΒΒ))


Simulations: Simulations: sinsin2 2 (2(2θθ1313))=0.170 =0.170 (left)(left) , , sinsin2 2 (2(2θθ1313))=0.085 (right)=0.085 (right)

Current LimitsCurrent Limits



Neutrino mass terms-Neutrino mass terms- Dirac mass term Dirac mass term MMDD


Neutrino mass terms-Neutrino mass terms- Majorana mass terms M Majorana mass terms Mν ν &&

MMΝΝ


Generic Models of neutrino Generic Models of neutrino mass – See-saw mass – See-saw


Majorana neutrino massMajorana neutrino mass


The Mass HierarchiesThe Mass Hierarchies - Flavor - Flavor ContentContent


(1):Astrophysics Mass Limit(1):Astrophysics Mass Limit ΣΣkkmmk k == mmastroastro=0.71eV=0.71eV


Astrophysics bound: Astrophysics bound: 0.71 eV, 0.71 eV,

Log(0.71)=-0.15 Log(0.71)=-0.15 blackblack ΣΣmmk k , , greengreenmm3 3 green green mm11

dotted dotted mm11,, redred m m22 dotted dotted mm3 3 ,, redredmm22


(2): (2): Triton decay mass limitTriton decay mass limit mmdecaydecay=2.2eV=2.2eV


Triton decay limit:Triton decay limit: mmdecaydecay=2.2eV,=2.2eV,

Log(2.2)=0.34 Log(2.2)=0.34 KATRINKATRIN0.2 eV, Log(0.2)=-0.7; 0.2 eV, Log(0.2)=-0.7;

BlackBlackmmdecaydecay(m(m11)), ,

greengreenmm3 3 mm1 1 ≈≈ mm2 2 ≈≈ mmdecaydecay

dotted dotted mm11,, redred m m22 dotted dotted mm3 3 ,,


Majorana Mass MechanismMajorana Mass Mechanism((νν))cc =e=eiiφ φ νν , φ=α, φ=ακκ (Majorana (Majorana condition)condition)


Effective neutrino mass Effective neutrino mass <m<mνν>> encountered in encountered in 0ν ββ- 0ν ββ-decaydecay [ [αα==αα22-α-α11, β, β==αα33-α-α11+2δ+2δ13 13 , , α1α1 , α, α2 , 2 , αα33 Majorana phases Majorana phases]]Mass scale: Mass scale: mm1 1 (normal);(normal); mm3 3

(inverted)(inverted)

lower mlower mee ee bound from 0bound from 0ν ββν ββ-decay-decay(From J Valle)(From J Valle) Normal hierarchy Normal hierarchy InvertedInverted


The (The (νν,e) scattering cross ,e) scattering cross sectionsection


Minimal set of Neutrino Minimal set of Neutrino ParametersParameters


CAST:Another “Greek” CAST:Another “Greek” CollaborationCollaboration• Probing eV-scale axions with CAST

• E. Arik , , S. Aune , , D. Autiero , , K. Barth , , A. Belov , , B. Beltrán , , S. Borghi , , G. Bourlis , , F.S. Boydag , , H. Bräuninger , , J.M. Carmona , , S. Cebrián , , S.A. Cetin , , J.I. Collar , , T. Dafni , , M. Davenport , , L. Di Lella , , O.B. Dogan , , C. Eleftheriadis , , N. Elias , , G. Fanourakis , , E. Ferrer-Ribas , , H. Fischer , , P. Friedrich , , J. Franz , , J. Galán , , T. Geralis , , I. Giomataris , , S. Gninenko , , H. Gómez , , R. Hartmann , , M. Hasinoff , , F.H. Heinsius , , I. Hikmet , , D.H.H. Hoffmann , , I.G. Irastorza , , J. Jacoby , , K. Jakovčić , , D. Kang , , K. Königsmann , , R. Kotthaus , , M. Krčmar , , K. Kousouris , , M. Kuster , , B. Lakić , , C. Lasseur , , A. Liolios , A. Ljubičić , G. Lutz , G. Luzón , D. Miller , J. , A. Ljubičić , G. Lutz , G. Luzón , D. Miller , J. Morales , T. Niinikoski , A. Nordt , A. Ortiz , T. Papaevangelou , M.J. Morales , T. Niinikoski , A. Nordt , A. Ortiz , T. Papaevangelou , M.J. Pivovaroff , A. Placci , G. Raffelt , H. Riege , A. Rodríguez , J. Ruz , I. Pivovaroff , A. Placci , G. Raffelt , H. Riege , A. Rodríguez , J. Ruz , I. Savvidis , Y. Semertzidis , P. Serpico , R. Soufli , L. Stewart , K. van Savvidis , Y. Semertzidis , P. Serpico , R. Soufli , L. Stewart , K. van Bibber , J. Villar , J. Vogel , L. Walckiers and K. Zioutas Bibber , J. Villar , J. Vogel , L. Walckiers and K. Zioutas

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Fancy Neutrino Oscillometry -on Settling the Reactor Neutrino Anomaly)

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