Whataretheconsequencesofparityviola:oninbetadecay?

h =!σ ⋅!p

phelicity

Theeigenvalueofhisv/c.Foramasslesspar:cle,theeigenvaluesofhcanbeonly+1or-1.Ingeneral,thepar:clewith•  h>0iscalled“right-handed”•  h<0iscalled“lem-handed”

Experimentally, h(νe ) ≈ −1, h(νe ) ≈ +1

left-handed or right-handed?

Beta decay: helicity

(helicityflipsunderparity)

Theglobalcharacteriza:onintermsofhandednessisnotmeaningfulforotherpar:cles,likeelectrons.Anelectroncouldhavespintotherightandbetravelingrightandthereforebeclassifiedasright-handed.Butfromthereferenceframeofsomeonetravelingfasterthantheelectron,itsvelocitywouldbetothelem,whileitsspinwouldbeunchanged.Thiswouldmeanthattheelectronisalem-handedpar:clewithrespecttothatreferenceframe.

hUp://hyperphysics.phy-astr.gsu.eduhUp://journals.aps.org/pr/abstract/10.1103/PhysRev.109.1015

Theoperatorsthatarescalars,pseudoscalarsandtensorsproduceleptonsofbothhelici:esunderaparitytransforma:on.OnlyvectoroperatorsVandaxialvectoroperatorsAcanaccommodatetheobservedresult.Furthermore,sinceVandAareofdifferentparity,theymustappearinalinearcombina:on.ThisleadstotheV-Atheoryofbetadecay.Inprinciple,bothVandApartsshouldbecharacterizedbydifferentcouplingconstants,GVandGA,respec:vely.Inthistheory,theweakinterac:onactsonlyonlem-handedpar:cles(andright-handedan:par:cles).Sincethemirrorreflec:onofalem-handedpar:cleisright-handed,thisexplainsthemaximalviola:onofparity.Thevectorcurrentisknowntobeaconservedquan:ty(CVChypothesis)

HowtorelateGVandGA?

€

gA ≡GA

GV

=fπ gπnMNc

2

pion decay constant pion-nucleon coupling constant

Goldberger-Treiman relation

Experimentally, gA=1.267(4). This value is very close, up to 3%, to the Goldberger-Treimanes:mate.Thisrela:oncanbeobtainedbyassumingtheso-calledpar:allyconservedaxial-vectorcurrent(PCAC)hypothesis.Nowwearereadytoes:matethenuclearoperator!

Beta decay: axial vector coupling constant

Vint ≈ gδ!rn −!rp( )δ !rn −

!re−( )δ !rn − !rυ( )O(n→ p) zero-range

Thenuclearoperatortransforminganeutronintoaprotonmustbeonebodyinnature.Henceitmustinvolvetheisospinraisingorloweringoperators.Inthenon-rela:vis:climit,thevectorpartmayberepresentedbytheunityoperator:mesτ±andtheaxial-vectorpartbyaproductofτ±andσ.(Aproperderiva:onrequiresmanipula:onwithDirac4-componentfunc:onsandγmatrices!)

Vint →GV τ ±( j)+ gA!σ ( j) ⋅ !τ ( j)[ ]

j=1

A

∑

Fermi decay, carries zero angular momentum

Gamow-Teller decay, carries one unit of angular momentum

Beta decay: nuclear matrix elements

GVdeterminedfromsuperallowedFermibetadecays!

FromtheexpressionforfT,itispossibletodeterminethestrengthgofthebeta-decayprocess,ifoneknowshowtodeterminethereducedmatrixelement.Forsuperallowed0+⇾0+Fermitransi:ons,thematrixelementis√2sothefTvaluesshouldbeiden:cal.

g = 0.88×10−4 MeV fm3

or,introducingthedimensionlessconstantG: G = g me2c!

=1.026×10−5

correctedfornuclearstructureeffects(isospinmixing)andradia:vecorrec:ons

Superallowed0+→0+betadecaybetweenT=1analogstates

!"#$%&'()*'(+$,-&.'('-&

!"##!

$"!!!

$"!$!

$#%& $#%% $##' $##( '!!! '!!& '!!%

|Vud|2+

|Vus|2+

|Vub|2

)*+,

-. -/ -0

nuclear meson decay

20

30

40

10

NUMBER OF NEUTRONS 20 30 40 50 6010

0 , 1

0 , 1+

+

BR

t1/2

Q EC

Superallowed ! emitters

NU

MBE

R O

F PR

OTO

NS

Superallowed Fermi 0+ →0+ β-decay studies

Kobayashi and Maskawa (2008): … for "the discovery of the origin of broken symmetry, which predicts the existence of at least three families of quarks in nature."

Impressive experimental effort worldwide

Hardy and Towner survey (Feb. 2015) http://journals.aps.org/prc/abstract/10.1103/PhysRevC.91.025501

Beta decay: allowed transitions

Fermi transitions J fM fTfT0 f T∓ JiMiTiT0i = Ti (Ti +1)−T0i (T0i ∓1)δJiJ fδMiM f

δTiTfδT0 i∓1T0 f

Inreality,isospinisviolatedbytheelectromagne:cforce,buttheviola:onisweak.

J f = Ji ΔJ = 0( )Tf = Ti ≠ 0 ΔT = 0, but Ti = 0→Tf = 0 forbidden( )T0 f = T0i ∓1 ΔT0 =1( )Δπ = 0 no parity change

Gamow-Teller transitions Thematrixelementstronglydependsonthestructureofthewavefunc:on!

ΔJ = 0,1 but Ji = 0→ J f = 0 forbidden

ΔT = 0,1 but Ti = 0→Tf = 0 forbidden

T0 f = T0i ∓1 ΔT0 =1( )Δπ = 0 no parity change

TheabsolutevaluesofGTmatrixelementsaregenerallysmallerthanthoseforFermitransi:ons.

fT = constF 2

+ gA2 GT 2

Superallowed Gamow-Teller decay of the doubly magic nucleus 100Sn

Hinke et al., Nature 486, 341 (2012)

Number distribution of log(ft) values for allowed β-transitions (obeying the selection rules).

Forbidden transitions Forbiddentransi:onsinvolveparitychangeandaspinchangeofmorethanoneunit.Theycomefromthehigher-ordertermsintheexpansionofelectronandneutrinoplanewavesintosphericalharmonics.ForbiddendecaysareclassifiedintodifferentgroupsbytheL-valueofthesphericalharmonicsinvolved.

Systema:cUncertain:esintheAnalysisoftheReactorNeutrinoAnomalyA.Hayesetal.,PRL112,202501(2014)"...thecorrec:onsarenuclear-operatordependentandthatanundeterminedcombina:onofmatrixelementscontributestonon-uniqueforbiddentransi:ons.”Also:r-processsimula:ons….

Beta decay: electron capture

Electroncaptureleadstoavacancybeingcreatedinoneofthestrongestboundatomicstates,andsecondaryprocessesareobservedsuchastheemissionofX-raysandAugerelectrons.AugerelectronsareelectronsemiUedfromoneoftheouterelectronshellsandtakeawaysomeoftheremainingenergy.Captureismostlikelyfora1s-stateelectron.TheK-electronwavefunc:onattheoriginismaximalandisgivenby

ψe−(0) = 1

πZmee

2

!2"

#$

%

&'

3/2

WEC = Ev2 M fi

' 2g2

π 2!4c3Zmee

2

!2!

"#

$

%&

3

Theelectroncaptureprobabilityisthusgivenby:

hUp://www.nndc.bnl.gov/chart/reCenter.jsp?z=4&n=3Example

Manipula:nglife:mesinstoragerings:hUp://www.sciencedirect.com/science/ar:cle/pii/S0146641013000744