Double-beta decay and BSM physics: shell model nuclear ...Department of Physics, Central Michigan University, Mount Pleasant, Michigan 48859, USA !Support from NSF grant PHY-1404442

ACFI-FRIB M. Horoi CMU

Double-beta decay and BSM physics: shell model nuclear matrix elements for

competing mechanisms

Mihai Horoi Department of Physics, Central Michigan University, Mount Pleasant, Michigan 48859, USA

Ø Support from NSF grant PHY-1404442 and DOE/SciDAC grants DE-SC0008529/SC0008641 is acknowledged

Overview •  Neutrino physics within and beyond the

Standard Model (BSM) •  DBD mechanisms: light Majorana neutrino

exchange, right-handed currents, heavy neutrinos, SUSY R-parity violation,…

•  48Ca: 2v and 0v shell-model matrix elements – Beyond closure approximation

•  76Ge, 82Se, 130Te, and 136Xe results


Classical Double Beta Decay Problem


Adapted from Avignone, Elliot, Engel, Rev. Mod. Phys. 80, 481 (2008) -> RMP08

€

Qββ

A.S. Barabash, PRC 81 (2010)

€

136Xe 2.23 ×1021 0.020€

T1/ 2−1(2ν) =G2ν (Qββ ) MGT

2v (0+)[ ] 2

€

T1/ 2−1(0v) =G0ν (Qββ ) M

0v (0+)[ ] 2 < mββ >

me

%

& '

(

) *

2

€

mββ = mkUek2

k∑

2-neutrino double beta decay

neutrinoless double beta decay

Neutrino Masses


-  Tritium decay:

-  Cosmology: CMB power spectrum, BAO, etc,

€

Δm212 ≈ 7.5 ×10−5 eV 2 (solar)

Δm322 ≈ 2.4 ×10−3 eV 2 (atmospheric)

€

c12 ≡ cosθ12 , s12 = sinθ12 , etc

Two neutrino mass hierarchies

€

3H → 3He + e− +ν e

mν e= Uei

2mi2

i∑ < 2.2eV (Mainz exp.)

KATRIN (to takedata): goal mν e< 0.3eV

€

mii=1

3

∑ < 0.23eV

Goal : 0.01eV (5 −10 y)

€

PMNS −matrix

€

m02 = ?

€

Neutrino oscillations :− NH or IH ?− δCP = ?−Unitarity of UPMNS ?− Are there m ~ 1eV sterile neutrinos?

€

− Dirac or Majorana?− Majorana CPV α i = ?− Leptogenesis?→Baryogenesis

Neutrino ββ effective mass


€

T1/ 2−1(0v) =G0ν (Qββ ) M

0v (0+)[ ] 2 < mββ >

me

%

& '

(

) *

2€

mββ = mkUek2

k=1

3

∑

= c122 c13

2m1 + c132 s12

2m2eiφ 2 + s13

2m3eiφ 3

Cosmology constraint

€

φ2 = α2 −α1 φ3 = −α1 − 2δ

76Ge Klapdor claim 2006

The Minimal Standard Model


?

€

Local Gauge invariance of Lagrangian density L :

Dµ = I∂µ − igAµa (x)T a

T a ∈GA SM group : SU(3)c × SU(2)L ×U(1)Y

€

SM fermion masses :

ψ iLYijψ jRφ →Yij < φ >ψ iLψ jR = mD( )ijψ iLψ jR

€

→neutrino is sterile: Dµ = I∂µ

€

SU(2)Ldoublet

€

SU(2)Lsinglet

€

SU(2)Ldoublet

€

mν l

SM = 0 l = e, µ, τlepton flavor conserved

€

φ

Too Small Yukawa Couplings?


arXiv:1406.5503 Standard Model fermion masses

€

-L ⊃12ψ iLYijψ jRφ →

12mDijψ iLψ jR mDij =Yij v( )

€

-L ⊃12mLR # ν R

c # ν Lc

€

Majorana

€

Yν ≈10−10 −10−9Yt

arXiv:0710.4947v3

€

φ

€

φ

€

< φ >

€

< φ >

The origin of Majorana neutrino masses


€

-L ⊃

Type I see-saw

€

mLLν ≈

(100 GeV )2

1014GeV= 0.1eV

mLLν ≈

(300keV )2

1TeV= 0.1eV

$

% & &

' & &

€

12 " ν L " ν R

c( )0 mLR

mLRT 0

$

% &

'

( ) " ν Lc

" ν R

$

% &

'

( ) + h.c.

€

12 " ν L " ν R

c( )0 mLR

mLRT MRR

$

% &

'

( ) " ν Lc

" ν R

$

% &

'

( ) + h.c.

€

mLLν = −mLR

ν MRR−1mLR

ν

€

Aββ ∝Uei2mi

q2i∑ −

Sej2

M jj∑

mi <1eV <<1GeV <<Mi

-  ΣU2eimi term dominates in

most cases

-  TeV collider Majorana tests not relevant

T1/2−1(0v)∝ Aββ

2

€

mi, M1 <1eV <<1GeV <<Mi

arXiv:0710.4947v3

€

φ

€

φ

€

< φ >

€

< φ >

The origin of Majorana neutrino masses


€

-L ⊃

See-saw mechanisms

€

mLLν ≈

(100 GeV )2

1014GeV= 0.1eV

mLLν ≈

(300keV )2

1TeV= 0.1eV

$

% & &

' & &

€

12 " ν L " ν R

c( )0 mLR

mLRT 0

$

% &

'

( ) " ν Lc

" ν R

$

% &

'

( ) + h.c.

€

12 " ν L " ν R

c( )mLL mLR

mLRT MRR

$

% &

'

( ) " ν Lc

" ν R

$

% &

'

( ) + h.c.

€

< φ >

€

< φ >

€

φ

€

φ€

12 " ν L " ν R

c( )0 mLR

mLRT MRR

$

% &

'

( ) " ν Lc

" ν R

$

% &

'

( ) + h.c.

€

mLLν = −mLR

ν MRR−1mLR

ν

Left-Right Symmetric model

WR search at CMS arXiv:1407.3683

€

SU(2)L × SU(2)R ×U(1)B −L WR

Majorana neutrino masses


€

-L ⊃

€

12 " ν L " ν R

c( )mLL mLR

mLRT MRR

$

% &

'

( ) " ν Lc

" ν R

$

% &

'

( ) + h.c.

€

ʹ′ ν L

ʹ′ ν Rc

⎛

⎝ ⎜

⎞

⎠ ⎟ =W

νLNR

c

⎛

⎝ ⎜

⎞

⎠ ⎟ ≡

U ST V⎛

⎝ ⎜

⎞

⎠ ⎟ νLNR

c

⎛

⎝ ⎜

⎞

⎠ ⎟

WW + =1 UU + ≈1 VV + ≈1

S , T <<1 U ≈UPMNS

€

W + diag m1,m2,m3,M1,M2,…( )W

!νL → active flavor neutrinos!νRc = !ν sL → sterile neutrino combinations

ν, N→ mass eigenstates

Low-energy contributions to 0vββ decay


€

-L ⊃12

hαβT ν βL e α L( ) Δ

− − Δ0

Δ−− Δ−

⎛

⎝ ⎜

⎞

⎠ ⎟

eRc

−νRc

⎛

⎝ ⎜

⎞

⎠ ⎟ + hc

No neutrino exchange

€

η

€

λ

€

H W =GF

2jL

µ JLµ+ +κJRµ

+( ) + jRµ ηJLµ

+ + λJRµ+( )[ ] + h.c.

Left − right symmetric model

€

H W =GF

2jL

µJLµ+ + h.c.

€

jL /Rµ = e γ µ 1∓ γ 5( )ν e

Low-energy effective Hamiltonian

Contributions to 0vββ decay: no neutrinos


See-saw type III

GUT/SUSY R-parity violation

Squark exchange Gluino exchange

Hadronization /w R-parity v.

The Black Box Theorem


J. Schechter and J.W.F Valle, PRD 25, 2951 (1982) E. Takasugi, PLB 149, 372 (1984) J.F. Nieves, PLB 145, 375 (1984)

M. Hirsch, S. Kovalenko, I. Schmidt, PLB 646, 106 (2006)

0νββ observed ó

at some level

(i) Neutrinos are Majorana fermions.

(ii) Lepton number conservation is violated by 2 units

€

(iii) mββ = mkUek2

k=1

3

∑ = c122 c13

2m1 + c132 s12

2m2eiφ 2 + s13

2m3eiφ 3 > 0

Regardless of the dominant 0νββ mechanism!

DBD signals from different mechanisms


arXiv:1005.1241

2β0ν rhc(η)

€

< λ >

€

t = εe1 −εe12

€

η

€

λ

The 0vDBD half-life


€

T1/ 20ν[ ]−1

= G0ν M jη jj∑

2

= G0ν M (0ν )ηνL + M (0 N ) ηNL +ηNR( ) + ˜ X λ < λ > + ˜ X η <η > +M (0 ' λ )η ' λ + M (0 ˜ q )η ˜ q +2

PRD 83, 113003 (2011)

€

T1/ 20ν[ ]−1 ≅G0ν M (0ν )ηνL + M (0N )ηNR

2≈G0ν M (0ν ) 2ηνL

2+ M (0N ) 2ηNR

2[ ] No interference terms!€

(i) ηNL neglijible in most models; (ii) η & λ ruled in /out by energy or angular distributions

€

" ν e L = UekνkLk

light

∑ + SekNkLk

heavy

∑

" ν e R = Tek*νkR

k

light

∑ + Vek*NkR

k

heavy

∑

%

&

' '

(

' '

€

+

€

λ =MWL

MWR

#

$ %

&

' (

2

UekTek*

k

light

∑ η = ζ UekTek*

k

light

∑ WR ≈ ζW1 +W2

€

ην L =mββ

me

ηNL = Sek2 mp

Mkk

heavy

∑

€

ηNR =MWL

MWR

#

$ %

&

' (

4

Vek2 mp

Mkk

heavy

∑

€

ν jL

Two Non-Interfering Mechanisms


€

ην =mββ

me

≈10−6

€

ηNR =MWL

MWR

#

$ %

&

' (

4

Vek2 mp

Mkk

heavy

∑ ≈10−8

Assume T1/2(76Ge)=22.3x1024 y

€

ην , ηNR ⇐GGe0νT1/ 2Ge

0ν[ ]−1

= MGe(0ν ) 2ην

2+ MGe

(0N ) 2ηNR2

GXe0νT1/ 2Xe

0ν[ ]−1

= MXe(0ν ) 2ην

2+ MXe

(0N ) 2ηNR2

&

' (

) (

Is there a more general description?


Long-range terms: (a) - (c )

€

Aββ ∝ T[L (t1)L (t2)]∝ jV −AJV −A+( ) jαJβ+( )

α, β :V − A, V + A, S + P, S − P, TL , TR

€

G010ν , G06

0ν , G090ν

Doi, Kotani, Takasugi 1983

Short-range terms: (d)

€

Jµν = u i2γ µ ,γν[ ] 1± γ 5( )d

€

Aββ ∝ L

Summary of 0vDBD mechanisms

•  The mass mechanism (a.k.a. light-neutrino exchange) is likely, and the simplest BSM scenario.

•  Low mass sterile neutrino would complicate analysis •  Right-handed heavy-neutrino exchange is possible, and

requires knowledge of half-lives for more isotopes. •  η- and λ- mechanisms are possible, but could be ruled

in/out by energy and angular distributions. •  Left-right symmetric model may be also (un)validated

at LHC/colliders. •  SUSY/R-parity, KK, GUT, etc, scenarios need to be

checked, but validated by other means. ACFI-FRIB M. Horoi CMU


2v Double Beta Decay (DBD) of 48Ca

€

f7 / 2€

p1/ 2

€

f5 / 2

€

p3 / 2

€

G

€

T1/ 2−1 =G2v (Qββ ) MGT

2v (0+)[ ] 2

€

48Ca 2v ββ# → # # 48Ti

€

Ikeda sum rule(ISR) = B(GT;Z →Z +1)∑ − B(GT;Z →Z −1)∑ = 3(N − Z)

Ikeda satisfied in pf !

€

E0 =12Qββ + ΔM Z +1

AT−ZAX( )

The choice of valence space is important!

€

B(GT) =f ||σ⋅ τ || i

2

(2Ji +1)

Horoi, Stoica, Brown,

PRC 75, 034303 (2007) €

gAστquenched$ → $ $ $ 0.77gAστ

ISR 48Ca 48Ti pf 24.0 12.0

f7 p3 10.3 5.2


Double Beta Decay NME for 48Ca M. Horoi, PRC 87, 014320 (2013)

€

T1/ 22ν( )exp = 4.4−0.5

+0.6(stat) ± 0.4(syst)[ ] ×1019 yr

€

f7 / 2€

p1/ 2

€

f5 / 2

€

p3 / 2

€

G

Closure Approximation and Beyond in Shell Model


€

MS0v = ˜ Γ ( ) 0 f

+ ap+ ˜ a n( )

JJk Jk a # p

+ ˜ a # n ( )J

0i+

p # p n # n J k J

∑ p # p ;J q2dq ˆ S h(q) jκ (qr)GFS

2 fSRC2

q q + EkJ( )

τ1−τ2−

(

) * *

+

, - -

∫ n # n ;J − beyond

Challenge: there are about 100,000 Jk states in the sum for 48Ca

Much more intermediate states for heavier nuclei, such as 76Ge!!!

No-closure may need states out of the model space (not considered).

€

MS0v = Γ( ) 0 f

+ ap+a # p

+( )J

˜ a # n ˜ a n( )J$ % &

' ( )

0

0i+ p # p ;J q2dq ˆ S

h(q) jκ (qr)GFS2 fSRC

2

q q+ < E >( )τ1−τ2−

$

% &

'

( ) ∫ n # n ;J

as

− closureJ, p< # p n< # n p< n

∑

Minimal model spaces

82Se : 10M states 130Te : 22M states 76Ge : 150M states

€

M 0v = MGT0v − gV /gA( )2

MF0v + MT

0v

ˆ S =σ1τ1σ2τ 2 Gamow −Teller (GT)τ1τ 2 Fermi (F)

3( ! σ 1⋅ ˆ n )(! σ 2 ⋅ ˆ n ) − (! σ 1⋅! σ 2)[ ]τ1τ 2 Tensor (T)

⎧

⎨ ⎪

⎩ ⎪

€

many − body! " # # # # # # # $ # # # # # # #

€

two − body! " # # # # # # # # # # # # # $ # # # # # # # # # # # # #


1 2 3 4 5 6 7 8 9 10 11 12 13 14Closure energy <E> [MeV]

2.8

3

3.2

3.4

3.6

3.8pure closure, CD-Bonn SRCmixed, CD-Bonn SRCpure closure, AV18 SRCmixed, AV18 SRC

0 50 100 150 200 250N, number-of-states cutoff parameter

3.2

3.3

3.4

3.5

3.6mixed, <E>=1 MeVmixed, <E>=3.4 MeVmixed, <E>=7 MeVmixed, <E>=10 MeV

50 100 150 200 2500

0.5

1

1.5

2Er

ror [

%]

error in mixed NME

J=0 J=1 J=2 J=3 J=4 J=5 J=6 J=7 J=8 J=9Spin of the intermediate states

-0.2

0

0.2

0.4

0.6

0.8

1 GT, positiveGT, negativeFM, positiveFM, negative

82Se: PRC 89, 054304 (2014)

€

Mmixed (N) = Mno−closure (N) + Mclosure (N = ∞) −Mclosure (N)[ ]

GXPF1A FPD6 KB3G JUN450

0.5

1

1.5

2

2.5

3

3.5

4

Opti

mal

clo

sure

ener

gy [

MeV

]

48Ca

46Ca

44Ca

76Ge

82Se

New Approach to calculate NME: New Tests of Nuclear Structure

ACFI-FRIB M. Horoi CMU I=0 I=1 I=2 I=3 I=4 I=5 I=6 I=7 I=8 I=9Spin of the neutron-neutron (proton-proton) pairs-3

-2

-1

0

1

2

3

4

5

6

7

GT, positiveGT, negativeFM, positiveFM, negative

Brown, Horoi, Senkov

arXiv:1409.7364,


136Xe ββ Experimental Results Publication Experiment T2ν

1/2 T0ν1/2(lim) T0ν

1/2(Sens)

PRL 110, 062502 KamLAND-Zen > 1.9x1025 y 1.1x1025 y

PRC 89, 015502 EXO-200 (2.11 0.04 0.21)x1021 y Nature 510, 229 EXO-200 >1.1x1025 y 1.9x1025 y

PRC 85, 045504 KamLAND-Zen (2.38 0.02 0.14)x1021 y €

±

€

±

€

±

€

±

€

Mexp2ν = 0.0191− 0.0215 MeV −1

EXO-200

arXiv:1402.6956, Nature 510, 229


136Xe 2νββ Results

€

στ →0.74στ quenching

0g7/2 1d5/2 1d3/2 2s5/2 0h11/2 model space

0h11/2

2s5/2

1d3/2

1d5/2

0g7/2

0h9/2

0g9/2

0h11/2

2s5/2

1d3/2

1d5/2

0g7/2

0h9/2

0g9/2

0h11/2

2s5/2

1d3/2

1d5/2

0g7/2

0h9/2

0g9/2

€

136Xe(0+)

€

136Cs(1+)

€

136Ba(0+)

€

M 2ν = 0.064 MeV −1

€

Mexp2ν = 0.019 MeV −1

€

B(GT;Z →Z +1)∑ − B(GT;Z →Z −1)∑ = 52

Ikeda: 3(N − Z) = 84

0g9/2 0g7/21d5/2 1d3/2 2s5/2 0h11/2 0h9/2

€

B(GT;Z →Z +1)∑ − B(GT;Z →Z −1)∑ = 84

Ikeda: 3(N − Z) = 84

New effective interaction,

0h11/2

2s5/2

1d3/2

1d5/2

0g7/2

0h9/2

0g9/2

np - nh

n (0+) n (1+) M(2v)

0 0 0.062

0 1 0.091

1 1 0.037

1 2 0.020


S. Vigdor talk at LRP Town Meeting, Chicago, Sep 28-29, 2014

€

T1/ 2 >1×1026 y, after ? years

€

T1/ 2 > 2.4 ×1026 y, after 3 years

€

T1/ 2 >1×1026 y, after 5 years€

T1/ 2 >1×1026 y, after 5 years

€

T1/ 2 > 2 ×1026 y, after ? years€

T1/ 2 > 6 ×1027 y, after 5 years! (nEXO)

€

Goals (DNP14 DBD workshop) :

IBA-2 J. Barea, J. Kotila, and F. Iachello, Phys. Rev. C 87, 014315 (2013).

QRPA-En M. T. Mustonen and J. Engel, Phys. Rev. C 87, 064302 (2013).

QRPA-Jy J. Suhonen, O. Civitarese, Phys. NPA 847 207–232 (2010).

QRPA-Tu A. Faessler, M. Gonzalez, S. Kovalenko, and F. Simkovic, arXiv:1408.6077

ISM-Men J. Menéndez, A. Poves, E. Caurier, F. Nowacki, NPA 818 139–151 (2009). SM M. Horoi et. al. PRC 88, 064312 (2013), PRC 89, 045502 (2014), PRC 90, PRC 89, 054304 (2014), in preparation, PRL 110, 222502 (2013).


IBA-2 J. Barea, J. Kotila, and F. Iachello, Phys. Rev. C 87, 014315 (2013).

QRPA-Tu A. Faessler, M. Gonzalez, S. Kovalenko, and F. Simkovic, arXiv:1408.6077

SM M. Horoi et. al. PRC 88, 064312 (2013), PRC 90, PRC 89, 054304 (2014), in preparation, PRL 110, 222502 (2013).


€

CD − Bonn SRC→

€

AV18 SRC→

Take-Away Points


Black box theorem (all flavors + oscillations)

Observation of 0νββ will signal New Physics Beyond the Standard Model.

0νββ observed ó

at some level

(i) Neutrinos are Majorana fermions.

(ii) Lepton number conservation is violated by 2 units

€

(iii) mββ = mkUek2

k=1

3

∑ = c122 c13

2m1 + c132 s12

2m2eiφ 2 + s13

2m3eiφ 3 > 0

Regardless of the dominant 0νββ mechanism!


€

T1/ 2−1(0v) =G0ν (Qββ ) M

0v (0+)[ ] 2 < mββ >

me

%

& '

(

) *

2

€

φ2 = α2 −α1 φ3 = −α1 − 2δ

Take-Away Points The analysis and guidance of the experimental efforts need accurate Nuclear Matrix Elements.

€

mββ ≡ mv = c122 c13

2m1 + c132 s12

2m2eiφ 2 + s13

2m3eiφ 3


€

Σ = m1 +m2 +m3 from cosmology€

mββ = c122 c13

2m1 + c132 s12

2m2eiφ 2 + s13

2m3eiφ 3

Take-Away Points Extracting information about Majorana CP-violation phases may require the mass hierarchy from LBNE, cosmology, etc, but also accurate Nuclear Matrix Elements. €

φ2 = α2 −α1 φ3 = −α1 − 2δ


Take-Away Points Alternative mechanisms to 0νββ need to be carefully tested: many isotopes, energy and angular correlations.

These analyses also require accurate Nuclear Matrix Elements.

€

T1/ 20ν[ ]−1

= G0ν M jη jj∑

2

= G0ν M (0ν )ηνL + M (0 N ) ηNL +ηNR( ) + ˜ X λ < λ > + ˜ X η <η > +M (0 ' λ )η ' λ + M (0 ˜ q )η ˜ q +2

€

ην , ηNR ⇐GGe0νT1/ 2Ge

0ν[ ]−1

= MGe(0ν ) 2ην

2+ MGe

(0N ) 2ηNR2

GXe0νT1/ 2Xe

0ν[ ]−1

= MXe(0ν ) 2ην

2+ MXe

(0N ) 2ηNR2

&

' (

) (

SuperNEMO; 82Se


2 3 4 5 6 7 8 9 10Closure energy <E> [MeV]

3

3.2

3.4

3.6

3.8

4pure closure, CD-Bonn SRCmixed, CD-Bonn SRCpure closure, AV18 SRCmixed, AV18 SRC

76Ge

J=0 J=1 J=2 J=3 J=4 J=5 J=6 J=7 J=8 J=9Spin of the intermediate states

-0.2

0

0.2

0.4

0.6

0.8

1


I=0 I=1 I=2 I=3 I=4 I=5 I=6 I=7 I=8 I=9Spin of the neutron-neutron (proton-proton) pairs-3

-2

-1

0

1

2

3

4

5

6

7


€

Mmixed (N) = Mno−closure (N) + Mclosure (N = ∞) −Mclosure (N)[ ]

Take-Away Points Accurate shell model NME for different decay mechanisms were recently calculated.

The method provides optimal closure energies for the mass mechanism.

Decomposition of the matrix elements can be used for selective quenching of classes of states, and for testing nuclear structure.

Experimental info needed


Σ B(

GT)

0

0.5

1

Energy (KeV)0 500 1,000 1,500 2,000 2,500

B(GT

)

0

0.05

0.1

0.15

Energy (KeV)0 500 1,000 1,500 2,000 2,500

ExperimentalTheoretical

Collaborators:

•  Alex Brown, NSCL@MSU •  Roman Senkov, CMU and CUNY •  Andrei Neacsu, CMU •  Jonathan Engel, UNC •  Jason Holt, TRIUMF


Documents

Double-beta decay and BSM physics: shell model nuclear ...Department of Physics, Central Michigan University, Mount Pleasant, Michigan 48859, USA !Support from NSF grant PHY-1404442