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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)
Phys8803–SpecialTopicsonAstropar7clePhysics–IgnacioTaboada
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
Phys8803–SpecialTopicsonAstropar7clePhysics–IgnacioTaboada
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.
Phys8803–SpecialTopicsonAstropar7clePhysics–IgnacioTaboada
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
Phys8803–SpecialTopicsonAstropar7clePhysics–IgnacioTaboada
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
Phys8803–SpecialTopicsonAstropar7clePhysics–IgnacioTaboada
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
Phys8803–SpecialTopicsonAstropar7clePhysics–IgnacioTaboada
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
Phys8803–SpecialTopicsonAstropar7clePhysics–IgnacioTaboada
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, �
Phys8803–SpecialTopicsonAstropar7clePhysics–IgnacioTaboada
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
Phys8803–SpecialTopicsonAstropar7clePhysics–IgnacioTaboada
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
Phys8803–SpecialTopicsonAstropar7clePhysics–IgnacioTaboada
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 >
Phys8803–SpecialTopicsonAstropar7clePhysics–IgnacioTaboada
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
Phys8803–SpecialTopicsonAstropar7clePhysics–IgnacioTaboada
MSWeffect
MSWiscri7calforunderstandingsolarneutrinooscilla7ons.MSWisalsocri7calinunderstandingMeVsupernovaeneutrinos.TheMSWeffectmayhelpmeasurethehierarchy.Thisisbecausetheeffectisdifferentforand.Becausethediagramsarerelatedby7me-reversal,theeffec7vepoten7alchangessignwhengoingfromto
⌫e ⌫̄e
⌫e ⌫̄e
Phys8803–SpecialTopicsonAstropar7clePhysics–IgnacioTaboada
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
Phys8803–SpecialTopicsonAstropar7clePhysics–IgnacioTaboada
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 ⌫⌧
Phys8803–SpecialTopicsonAstropar7clePhysics–IgnacioTaboada
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
Phys8803–SpecialTopicsonAstropar7clePhysics–IgnacioTaboada
NeutrinoMass
Katrincanmeasuredownto0.35eVandlimittobelow0.2eV
Katrin’sSpectrometer
Figure:LutzBornscheinRecontroisdeBloisConf2012
Phys8803–SpecialTopicsonAstropar7clePhysics–IgnacioTaboada
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 >
Phys8803–SpecialTopicsonAstropar7clePhysics–IgnacioTaboada
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
Phys8803–SpecialTopicsonAstropar7clePhysics–IgnacioTaboada
NeutrinomasslimitfromSN1987A
InFebruary1987acorecollapsesupernovawasobservedintheLMC.Atotalof~25neutrinoswerereportedby3detectors.Thesearethoughttobemostly.
⌫̄e
Phys8803–SpecialTopicsonAstropar7clePhysics–IgnacioTaboada
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
Phys8803–SpecialTopicsonAstropar7clePhysics–IgnacioTaboada
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
Phys8803–SpecialTopicsonAstropar7clePhysics–IgnacioTaboada
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
Phys8803–SpecialTopicsonAstropar7clePhysics–IgnacioTaboada
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)
Phys8803–SpecialTopicsonAstropar7clePhysics–IgnacioTaboada
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
Phys8803–SpecialTopicsonAstropar7clePhysics–IgnacioTaboada
DayaBayandNeutrinoOscilla3ons
Shortbaselineneutrinodetectors(~1km)withnuclearreactorneutrinos(afewMeV)aremostlysensi7vetoθ13.Thefirstnon-zeromeasurementofthismixinganglewasdonebyDayaBayandhasbeenconfirmedbyseveralotherexperiments.Oscilla7onsareobservedasadisappearanceofinthefardetector.Systema7csarecontrolledbymeasuringthera7oofneutrinosinthefartotheneardetector.
⌫̄e
Neardetector
Fardetector(s)
⌫̄e
Phys8803–SpecialTopicsonAstropar7clePhysics–IgnacioTaboada
DayaBayandNeutrinoOscilla3ons
Thisresultispar7cularlyinteres7ngbecauseitenablesCPviola7onwithneutrinos.
DayaBay.arXiv:1203.1669
Phys8803–SpecialTopicsonAstropar7clePhysics–IgnacioTaboada
Sterileneutrinos
LEPshowedthatthereareonly3flavorsofneutrinosthatcoupletoZ0.Anyaddi7onalneutrinomustbeeithersterile(onlygravita7onalinterac7on)orhaveamassAshortbaseline,targetexperiment,LSND,reportedtheobserva7onofexcessinabeamof.Onit’sownthisisbestinterpretedasoscilla7onswith.AnsterileneutrinoisrequiredifLSNDresultsareincludedintoallotheroscilla7onresults.LSNDhasbeenrepeatedforandbeamsbytheminiBoonecollabora7on.
m⌫ > mZ0
⌫̄e ⌫̄µ⌫̄µ ! ⌫̄e �m2 ⇠ 1 eV
⌫̄µ⌫µ
Phys8803–SpecialTopicsonAstropar7clePhysics–IgnacioTaboada
miniBooneresults
miniBoonearXiv:1207.4809
miniBoone(andLSND)useamuonneutrinobeamfrompiondecayproducedintargetexperimentsataccelerators.Aresidualfluxofelectronneutrinosisexpected.Thisresultisderivedfromanexcessof3.8σofelectronneutrinosandan7neutrinos.
Phys8803–SpecialTopicsonAstropar7clePhysics–IgnacioTaboada
miniBooneresultsCombinedandallowedregions.⌫̄e⌫e
miniBoonearXiv:1207.4809
Theseresultsusethefullneutrinoenergyrangeof200MeVto3GeV.
Phys8803–SpecialTopicsonAstropar7clePhysics–IgnacioTaboada
ButIceCubedoesn’tseeanything
PRL117(2016)071801
Combined
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