neutrino physics - research group of ignacio taboada · phys 8803 – special topics on...

Phys8803–SpecialTopicsonAstropar7clePhysics–IgnacioTaboada

NeutrinoPhysics

Neutrinophysicsisattheinterfaceofpar7clephysicsandastrophysics.Manyexperimentsdesignedtoobserveneutrinoproper7es(e.g.SNO)havemadeastrophysicalobserva7ons,andmanydetectorsdesignedtouseneutrinosasastronomicalmessengershavecontributedtotheknowledgeofpar7clephysics(e.g.IceCube).•  Neutrino-maLerinterac7on•  Neutrinooscilla7ons•  Neutrinomass•  Sterileneutrinos•  CPviola7onandneutrinos

References:PDG Mar7n&Shaw,Par7clePhysics arXiv:0704.1800(bigreview)


Neutrino-ma2erinterac3on–lowenergy(incomplete)

Chargedcurrentinterac7onsNeutralcurrentinterac7onsElectronscaLering

n

W

p p n

W

p, n p, n

⌫l, ⌫̄l ⌫l, ⌫̄l

Z0

e� e�

⌫l, ⌫̄l ⌫l, ⌫̄lZ0

e�

e�W

⌫e

⌫e

⌫e e� e+⌫̄e


X

Neutrino-ma2erinterac3on–highenergy(incomplete)

Chargedcurrentinterac7onsNeutralcurrentinterac7ons

:baryonsandmesons

⌫l

n

W

l� ⌫̄l l+

p

W

p, n

⌫l, ⌫̄l ⌫l, ⌫̄l

Z0

X

X

X

Forenergieshighenough,neutrinosprobethestructureofnuclei,protonsandneutrons.


Whyareweakinterac3ons“weak”?

Thefinestructureconstantisα=1/137.Theweakconstantisαw≈1/240.(Recallα≈e2,andeachvertexgetsafactorofe).It’dwouldseemthatweakinterac7onsshouldbeofsimilarstrengthatE.M.Propagatorforphoton: ->CoulombPropagatorfor:->Yukawa-likepoten7al(Propagatorsaremissingfactors)

Effec7veweakrange~10-3fm(protonsize1fm).ZerophotonmassgivesE.M.infiniterange.

W±, Z0

1

q⌫q⌫1

q⌫q⌫ �m2c2! � 1

m2c2

m� = 0 mW = 80.4 GeV mZ = 91.2 GeV

V (r) = ge�r/r0

r


NeutrinoOscilla3ons

Flavoredneutrinos,,areweakeigenstates.TheyareNOTthefreeeigenstates.Thefreeeigenstatesare.Thegenericbase3-dimensionbasetransforma7oninQuantumMechanicsisoftheform(PMNSmatrix):Theanglesareknownasthe“mixingangles”.ThephaseallowsforCPviola7on.

⌫e, ⌫µ, ⌫⌧⌫1, ⌫2, ⌫3

0

@⌫e⌫µ⌫⌧

1

A = U

0

@⌫1⌫2⌫3

1

A U =

0

@Ue1 Ue2 Ue3

Uµ1 Uµ2 Uµ3

U⌧1 U⌧2 U⌧3

1

A

U =

0

@cos ✓12 sin ✓12 0

� sin ✓12 cos ✓12 0

0 0 1

1

A

0

@1 0 0

0 cos ✓23 sin ✓230 � sin ✓23 cos ✓23

1

A

0

@cos ✓13 0 sin ✓13ei�

0 1 0

� sin ✓13ei� 0 cos ✓13

1

A


NeutrinoOscilla3ons

Recentvaluesforthemixingangleare:Let’simagineabeamofflavorαandfixedmomentum.Forsimplicity,let’sassume2-flavorsonly.WhatistheprobabilityofobservingflavorβatadistanceLfromthesource?Theini7alstateis(In2-Donlyoneangleisneeded):Usingthe7meevolu7onoperatorwithafreeHamiltonian:

Par7cleDataGroup(2016)

e�iHt/~|⌫↵ >= cos✓ e�iE1t/~|⌫1 > +sin ✓e�iE2t/~|⌫2 >

|⌫↵ >= cos ✓|⌫1 > +sin ✓|⌫2 >

sin2 ✓12 = 0.304± 0.014

sin2 ✓23 = 0.51± 0.05

sin2 ✓13 = (2.19± 0.12)⇥ 10�12


NeutrinoOscilla3ons

TheprobabilityofobservingflavorβatadistanceLfromthesourceis:Thefinalstateis:Sometrigonometrylater:Notethattheneutrinomassisverysmall,soThus:

P (⌫↵ ! ⌫�) = | < ⌫� |e�iHt/~|⌫↵ > |2

|⌫� >= � sin ✓|⌫1 > +cos ✓|⌫2 >

E, cp >> m⌫c2

pm2c4 + c2|~p|2 ⇡ cp(1 +

m2c2

2p2)

P (⌫↵ ! ⌫�) = sin2 2✓ sin2(E2 � E1)L

2c~

E2 � E1 =q

m22c

4 + c2|~p|2 �qm2

1c4 + c2|~p|2

E ⇡ pc

E2 � E1 ⇡ m22 �m2

1

2p⇡ �m2

21

2E


NeutrinoOscilla3ons

FinallyOscilla7onsarepossibleonlyifatleastoneneutrinohasmass.Ingeneral,neutrinooscilla7onsdependonallparameters:Inmany–butnotall–experiments,the2flavoroscilla7oncaseisareasonabledescrip7on.Whether2-flavoroscilla7onsareagooddescrip7ondependsonL/Eontheflavorsproducedbythesourceandtheflavorsthatwanttobedetected.

P (⌫↵ ! ⌫�) = sin2 2✓ sin2�m2

21L

4c~E

�m221, �m2

13, ✓12, ✓13, ✓23, �


NeutrinoOscilla3ons

Themostrecentvaluesforthesquaredifferenceofmassesareshown:(pdg2016) Bydefini7on ,sowedon’tneedtomeasurethethirdvalue.Currentexperimentscan’tdis7nguishamonghierarchies.

�m221 +�m2

32 +�m213 = 0

⌫e

⌫µ

⌫⌧

Normal Inverted ?

0

m2

m22

m21

m23

m23

m22

m21

2.44⇥ 10�3 eV2 2.51⇥ 10�3 eV2

7.53⇥ 10�5 eV2

7.53⇥ 10�5 eV2


MSWeffect–Neutrinopropaga3oninma2er

Neutrinospropaga7ngthroughmaLerarenot“freely”propaga7ng.Theyaresubjecttoaneffec7vepoten7althatcanbecalculatedusingthediagramsshownabove.ThediagramontheleqappliestoALLneutrinosandan7neutrinosequally.Thecenterdiagramappliestoonly,andtherightdiagramappliestoonly.Thediagramsforandarerelatedby7mereversal.Theeffec7vepoten7alcanbere-interpretedasaddingatermtothemassoperator.

e�

e�W

⌫e

⌫ee� e�

⌫l, ⌫̄l ⌫l, ⌫̄lZ0

e� e�

W⌫̄e ⌫̄e

⌫̄e

⌫e⌫e⌫̄e


MSWeffect–2flavoroscilla3ons

Theequa7onofmo7onforfreeneutrinosinthefreebaseis:()Andinthisbase,theHamiltonianis:Recall:Addingapoten7alresultsin:VisNOTdiagonalinthe|ν1>,|ν2>base

~ = 1 c = 1

Hm =1

2E

✓m2

1 00 m2

2

◆

id

dt

✓⌫1⌫2

◆= Hm

✓⌫1⌫2

◆

H = Hm + V

Hm|⌫1 >= E1|⌫1 >⇠ (m21/2p+ p)|⌫1 >


MSWeffect–2flavoroscilla3ons

Inpar7cular,inthefreebase,thepoten7alis:Theplussignisforneutrinosandthenega7vesignforan7neutrinos.GFisFermi’sweakinterac7onconstant,andneistheelectrondensityinthematerial.DiagonalizingthenewHamiltonianResultsin:a)Newmasssquaredtermsb)New“maLer”eigenstates,i.e.newmixingangles

1

2E

✓m2

1 00 m2

2

◆+ U †

✓±p2GFne 00 0

◆U

U†V U = U†✓

±p2GFne 00 0

◆U


MSWeffect

MSWiscri7calforunderstandingsolarneutrinooscilla7ons.MSWisalsocri7calinunderstandingMeVsupernovaeneutrinos.TheMSWeffectmayhelpmeasurethehierarchy.Thisisbecausetheeffectisdifferentforand.Becausethediagramsarerelatedby7me-reversal,theeffec7vepoten7alchangessignwhengoingfromto

⌫e ⌫̄e

⌫e ⌫̄e


Vacuumoscilla3onsforastrophysicalobjects

Itiscommonforhigh-energyneutrinostobeproducedfrompiondecay:Andthekinema7csaresuchthatallthreeneutrinoshaveapproximatelythesameenergy.Thustheflavorfluxra7os,attheastrophysicalsourceare:Inthelimitofverylongbaseline(i.e.astrophysicalsources)SoatEarthwesee(easymatrix-vectormul7plica7on):Thereareexcep7ons,e.g.TKash7,EWaxmanPRL95(2005)181101

⇡+ ! µ+ + ⌫µ ! e+ + ⌫e + ⌫µ + ⌫̄µ

⇡� ! µ� + ⌫̄µ ! e� + ⌫̄e + ⌫µ + ⌫̄µ

�⌫e+⌫̄e : �⌫µ+⌫̄µ : �⌫⌧+⌫̄⌧ = 1 : 2 : 0

sin2L�m2

ij

4E~ ! 1/2

�⌫e+⌫̄e : �⌫µ+⌫̄µ : �⌫⌧+⌫̄⌧ = 1 : 1 : 1

JLearned,SPakvasaAstropartPhys3(1995)267


Vacuumoscilla3onsforastrophysicalneutrinos

Forastrophysicalneutrinos(unprovenhere):Soforastrophysicalbaselines,oscilla7onsareindependentof.Withthecurrentknowledgeofmixingangles:Example:Imaginethatneutrinosareproducedvianeutrondecayinanastrophysicalsource(thisistrueforlowenergyGZKneutrinos),theEarthflavorfluxra7ois0.6:0.2:0.2

P (⌫↵ ! ⌫�) =X

i

|U↵i|2|U�i|2

�m2

60% 20% 20%

20% 40% 40%

20% 40% 40%

⌫e⌫µ⌫⌧

⌫e ⌫µ ⌫⌧


Neutrinomass–tri3umdecay

Neutrinomasscaninprinciplebemeasuredfromtheendpointofβ-decayspectrum.Thisistypicallydonewithtri7umFromourspecialrela7vitylecture:Currentlimit:2eV(Par7cleDataGroup2016)Whytri7um:lowhalflife(12.3yr),lowendpointenergy(18.57keV),atomicstatescalculableexactly,etc.Neutrinomasscanalsobeconstrainedcosmologicallyorastro-physically.

3H !3 He+ e� + ⌫̄e

Emax

e =M2

3H +m2

e � (M3He +m⌫̄)2

2M3Hc2


NeutrinoMass

Katrincanmeasuredownto0.35eVandlimittobelow0.2eV

Katrin’sSpectrometer

Figure:LutzBornscheinRecontroisdeBloisConf2012


Wait,doesn’ttri3umdecaymeasure?Strictlyspeakingdoesn’thaveamass.Sowhatisthatisbeingmeasuredintri7umdecay?WhatisbeingmeasuredisBecauseThentheketis:So

U =

0

@Ue1 Ue2 Ue3

Uµ1 Uµ2 Uµ3

U⌧1 U⌧2 U⌧3

1

A

m⌫̄e

m⌫̄e =< ⌫̄e|M |⌫̄e >

⌫̄e

0

@⌫̄e⌫̄µ⌫̄⌧

1

A = U

0

@⌫̄1⌫̄2⌫̄2

1

A

|⌫̄e >=X

i

Uei|⌫̄i >

< m⌫̄e >=X

i

X

j

< ⌫̄i|U⇤eiMUei|⌫̄j >


Wait,doesn’ttri3umdecaymeasure?

Sincethemassoperatorisdiagonalinthefreestatebase:Thenexperimentsthatlookattheendpointofbetadecay,measure: < m⌫̄e >

X

i

|Uei|2mi

m⌫̄e

< m⌫̄e > =X

i

X

j

U⇤eiUejmj < m⌫̄i |m⌫̄j >

=X

i

X

j

U⇤eiUejmj�ij


NeutrinomasslimitfromSN1987A

InFebruary1987acorecollapsesupernovawasobservedintheLMC.Atotalof~25neutrinoswerereportedby3detectors.Thesearethoughttobemostly.

⌫̄e


NeutrinomasslimitfromSN1987A

TheLMCisat52kpc.Atthespeedoflight,thetravel7meist0=5.3x1012s.Ifneutrinoshavemassm,thenyouexpectthetotaltravel7metobe .Assumingneutrinosareallproducedsimultaneously,there’sanenergydependentspreadinarrival7mes.Sincethiswasnotseen:

W.D.ArneL&J.LRosnerPhys.Rev.LeL.58,1906–1909(1987)

tobs

� tem

= t0

(1 +m2/2E2)

m⌫̄e < 12 eV


AtmosphericNeutrinosAirshowersproductofcosmicrayinterac7onswithnitrogenandoxygenintheupper(10-20km)atmosphereresultinatmosphericneutrinos.Neutrinosareproductofthedecayofpionsandheaviermesons,suchaskaonsThecontribu7onfromkaonsincreaseswithneutrinoenergy.Thedecaylengthofa1GeVµ±is6km–lessthantheatmosphereheight.So,µ±andmesonsdecaybeforetheyreachtheground.Itfollowsthattheflavorfluxra7ois1:2:0.π±interac7onlength()isshorterthanthedecaylength(γcτ)forεπ=115GeV.SoK±arethemajorsourceofathigherenergy.ForK±,interac7onismoreimportantthandecayaboveεK=850GeV.

(Andsimilarforπ-)⇡+ ! µ+ + ⌫µ; µ+ ! e+ + ⌫e + ⌫̄µ

⌫µ & ⌫̄µ

�⇡± ⇡ 62 g · cm�2


AtmosphericNeutrinos

TheenergyspectrumoftheprimarycosmicraysisE-α.Theinterac7onofmesonsintheatmospheresteepensthisspectrumtoE-(α+1).Atlowenergies,muonsarethemainsourceof.Athighenergiesit’s.Onceisdominant,theflavorfluxra7oofdecreasessignificantly.At~TeVenergies,theflavorfluxra7ois≈1:10:0Atevenhigherenergies(100TeV–1PeV),thedominantsourceofatmosphericneutrinosarecharmedmesons(e.g.D±mesons).Thesemesonshaveveryshortlife7me,hencetheseneutrinosarecalledprompt.Becausecharmedmesonsdonotinteractbeforedecaying,theneutrinospectrumgoesasE-α.

⌫e + ⌫̄eK0

L ! ⇡± + e⌥ + ⌫̄e(⌫e) K0L

⌫e + ⌫̄e


AtmosphericNeutrinos

Themuonneutrinofluxcanbeparameterized(Gaisser‘90)as:Detailedcalcula7onsby,e.g.Hondaetal.Phys.Rev.D75,043006(2007)

Kaons

Pions

Frac7onofduetopionsandkaons

dN⌫

dE⌫⇡ 0.0096E�2.7

⌫

"1

1 + 3.7E⌫ cos ✓115GeV

+0.38

1 + 1.7E⌫ cos ✓850GeV

#

Fluxof ⌫µ + ⌫̄µ⌫µ + ⌫̄µ

Eν(GeV) Eν(GeV)


Super-Katmosphericneutrinooscilla3ons.

Atmosphericneutrinos(intheGeVscale)aremostlysensi7vetoand

Black:dataRed:fittodatawithoscilla7onsBlue:Nooscilla7onsSub-G:<1GeV;Mul7-G:>1GeVe-like:νe;µ-like:νµ1-R:oneCherenkovringMul7-R:morethanoneCherenkovring

✓23 �m223

cosθ

Super-KPhys.Rev.D74:032002,2006


DayaBayandNeutrinoOscilla3ons

Shortbaselineneutrinodetectors(~1km)withnuclearreactorneutrinos(afewMeV)aremostlysensi7vetoθ13.Thefirstnon-zeromeasurementofthismixinganglewasdonebyDayaBayandhasbeenconfirmedbyseveralotherexperiments.Oscilla7onsareobservedasadisappearanceofinthefardetector.Systema7csarecontrolledbymeasuringthera7oofneutrinosinthefartotheneardetector.

⌫̄e

Neardetector

Fardetector(s)

⌫̄e


DayaBayandNeutrinoOscilla3ons

Thisresultispar7cularlyinteres7ngbecauseitenablesCPviola7onwithneutrinos.

DayaBay.arXiv:1203.1669


Sterileneutrinos

LEPshowedthatthereareonly3flavorsofneutrinosthatcoupletoZ0.Anyaddi7onalneutrinomustbeeithersterile(onlygravita7onalinterac7on)orhaveamassAshortbaseline,targetexperiment,LSND,reportedtheobserva7onofexcessinabeamof.Onit’sownthisisbestinterpretedasoscilla7onswith.AnsterileneutrinoisrequiredifLSNDresultsareincludedintoallotheroscilla7onresults.LSNDhasbeenrepeatedforandbeamsbytheminiBoonecollabora7on.

m⌫ > mZ0

⌫̄e ⌫̄µ⌫̄µ ! ⌫̄e �m2 ⇠ 1 eV

⌫̄µ⌫µ


miniBooneresults

miniBoonearXiv:1207.4809

miniBoone(andLSND)useamuonneutrinobeamfrompiondecayproducedintargetexperimentsataccelerators.Aresidualfluxofelectronneutrinosisexpected.Thisresultisderivedfromanexcessof3.8σofelectronneutrinosandan7neutrinos.


miniBooneresultsCombinedandallowedregions.⌫̄e⌫e

miniBoonearXiv:1207.4809

Theseresultsusethefullneutrinoenergyrangeof200MeVto3GeV.


ButIceCubedoesn’tseeanything

PRL117(2016)071801

Combined

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