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

Transcription

1 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 and DOE/SciDAC grants DE-SC000859/SC is acknowledged

2 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, 48 Ca: v and 0v shell-model matrix elements Beyond closure approximation 76 Ge, 8 Se, 130 Te, and 136 Xe results

3 Classical Double Beta Decay Problem A.S. Barabash, PRC 81 (010) T 1/ -neutrino double beta decay [ ] 1 (ν) = G ν (Q ββ ) M v GT (0 + ) 136 Xe neutrinoless double beta decay Q ββ T 1 1/ (0v) = G 0ν (Q ββ ) M 0v (0 + ) < m [ ] ββ > ' % & m e ( * ) Adapted from Avignone, Elliot, Engel, Rev. Mod. Phys. 80, 481 (008) -> RMP08 m ββ = m k U ek k

4 Neutrino Masses PMNS matrix - Tritium decay: - Cosmology: CMB power spectrum, BAO, etc, i c 1 cosθ 1, s 1 = sinθ 1, etc Δm ev (solar) Δm 3 3 H 3 He + e +ν δ CP =? e Unitarity of U m ν e = PMNS? U ei m i <.ev (Mainz exp.) Are there m ~ 1eV sterile neutrinos? KATRIN (to take data): goal m ν e 3 i=1 m i < 0.3eV Goal : 0.01eV (5 10 y) Neutrino oscillations : NH or IH? < 0.3eV Dirac or Majorana? Majorana CPV α i =? Leptogenesis? Baryogenesis m 0 =? ev (atmospheric) Two neutrino mass hierarchies

5 Neutrino ββ effective mass m ββ = m k U ek 3 k =1 76 Ge Klapdor claim 006 = c 1 c 13 m 1 + c 13 s 1 m e iφ + s 13m 3 e iφ 3 φ = α α 1 φ 3 = α 1 δ T 1 1/ (0v) = G 0ν (Q ββ ) M 0v (0 + ) [ ] < m ββ > ' % & m e ( * ) Cosmology constraint

6 The Minimal Standard Model? φ m SM ν l = 0 l = e, µ, τ lepton flavor conserved SU() L doublet SM fermion masses : ψ il Y ij ψ jr φ Y ij < φ >ψ il ψ jr = ( m D ) ij ψ il ψ jr Local Gauge invariance of Lagrangian density L : D µ = I µ iga µ a (x)t a SU() L doublet SU() L singlet neutrino is sterile: D µ = I µ T a GA SM group : SU(3) c SU() L U(1) Y

7 Too Small Yukawa Couplings? Standard Model fermion masses arxiv: Y ν Y t -L 1 ψ Y il ijψ jr φ 1 m Dijψ il ψ jr ( m Dij = Y ij v) -L 1 m LR # ν R c c ν # L Majorana

8 -L 1 ν " L " ν m LL ( ) $ & % c ( ν R ) = m ν LR < φ > The origin of Majorana neutrino masses 0 m LR ' $ c ν " L ' T )& ) + h.c. M0 RR ( % ν " R ( m LR M 1 ν RR m LR < φ > $ & % & '& ν m LL ν m LL Type I see-saw (100 GeV ) GeV = 0.1eV (300 kev ) 1 TeV = 0.1eV A ββ T 1 1/ (0v) A ββ i U eim i q S ej j M j m i <1eV <<1 GeV << M i φ φ - ΣU ei m i term dominates in most cases - TeV collider Majorana tests not relevant arxiv: v3 m i, M 1 <1eV <<1 GeV << M i

9 -L 1 ν " L " ( ) $ & % c ( ν R ) The origin of Majorana neutrino masses 0 m LR ' $ c ν " L ' T )& ) + h.c. M0 RR ( % ν " R ( m LR See-saw mechanisms 1 $ c ( ν " L ν " R ) m LL m LR ' $ c ν " L ' & T )& ) + h.c. % m LR M RR (% ν " R ( ν m LL = m ν LR M 1 ν RR m LR $ & % & '& ν m LL ν m LL (100 GeV ) GeV = 0.1eV (300 kev ) 1 TeV = 0.1eV < φ > φ < φ > φ < φ > φ < φ > φ Left-Right Symmetric model SU() L SU() R U(1) B L W R arxiv: v3 W R search at CMS arxiv:

10 Majorana neutrino masses -L 1 $ c ( ν " L ν " R ) m LL m LR ' $ c ν " L ' & T )& ) + h.c. % m LR M RR (% ν " R ( ν! L active flavor neutrinos ν! c R = ν sl! sterile neutrino combinations ν, N mass eigenstates W + diag( m 1,m,m 3, M 1,M, )W ν Lʹ ν R c = W ν L N R c U S ν L T V N R c WW + =1 UU + 1 VV + 1 S, T <<1 U U PMNS

11 Low-energy contributions to 0vββ decay Low-energy effective Hamiltonian H W = G F j µ L J + Lµ + h.c. µ j L / R = e γ µ ( 1 γ 5 )ν e λ η [ ( ) + j µ R ( ηj + Lµ + λj + Rµ )] + h.c. H W = G F j µ L J + Lµ +κj + Rµ Left right symmetric model -L 1 h T αβ ( ν βl e α L ) Δ Δ 0 Δ Δ e c R ν R c + hc No neutrino exchange

12 Contributions to 0vββ decay: no neutrinos See-saw type III GUT/SUSY R-parity violation Gluino exchange Hadronization /w R-parity v. Squark exchange

13 The Black Box Theorem J. Schechter and J.W.F Valle, PRD 5, 951 (198) E. Takasugi, PLB 149, 37 (1984) J.F. Nieves, PLB 145, 375 (1984) M. Hirsch, S. Kovalenko, I. Schmidt, PLB 646, 106 (006) (i) Neutrinos are Majorana fermions. ó 0νββ observed at some level (ii) Lepton number conservation is violated by units 3 (iii) mββ = m U k ek = c1c13 m1 + c13 s1 me iφ + s13 m3e iφ 3 > 0 k =1 Regardless of the dominant 0νββ mechanism!

14 DBD signals from different mechanisms arxiv: < λ > β0ν rhc(η) t = ε e1 ε e1

15 PRD 83, (011) The 0vDBD half-life ν jl + λ η % light heavy ν " e L = U ek ν kl + S ek N kl ' k k & light heavy ' ' ν " e R = T * ek ν kr + V * ek N kr ( k k η ν L = m heavy ββ η m NL = S m # p ek η NR = M & WL % ( e $ ' # λ = % $ M WL M WR & ( ' light * * U ek T ek η = ζ U ek T ek W R ζw 1 +W k k M k light k M WR 4 heavy k V ek m p M k 0ν [ T 1/ ] 1 = G 0ν M j η j j = G 0ν M (0ν ) η νl + M (0 N ) ( η NL +η NR ) + X λ < λ > + X η < η > +M (0 λ ' ) η λ ' + M (0q ) η q + (i) η NL neglijible in most models; (ii) η & λ ruled in /out by energy or angular distributions 0ν [ T 1/ ] 1 G 0ν M (0ν ) η νl + M (0 N ) η NR G 0ν [ M (0ν ) η νl + M (0 N ) η ] NR No interference terms!

16 Two Non-Interfering Mechanisms η ν, η NR & ( ' ( ) G 0ν T 0ν [ Ge ] 1 (0ν ) = M 1/ Ge Ge η ν G 0ν T 0ν [ Xe ] 1 (0ν ) = M 1/ Xe Xe η ν (0 N ) + M Ge η NR (0 N ) + M Xe η NR η ν # η NR = % $ = m ββ m e M WL M WR & ( ' heavy k V ek m p M k 10 8 Assume T 1/ ( 76 Ge)=.3x10 4 y

17 Is there a more general description? G 0ν 01, G 0ν 0ν 06, G 09 Doi, Kotani, Takasugi 1983 Long-range terms: (a) - (c ) Short-range terms: (d) + + A ββ T[L (t 1 )L (t )] ( j V A J V A )( j α J β ) α, β : V A, V + A, S + P, S P, T L, T R A ββ L J µν = u i [ γ µ,γ ν ]( 1± γ 5 )d

18 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.

19 T 1/ 1 = G v (Q ββ ) M GT v Double Beta Decay (DBD) of 48 Ca [ v (0 + )] E 0 = 1 Q + ΔM ββ ( A Z +1T A Z X) 48 Ca Ikeda satisfied in pf! p 1/ f 5 / p 3 / G v ββ # # f 7 / 48 Ti The choice of valence space is important! B(GT) = ISR 48Ca 48Ti pf f7 p f σ τ i (J i +1) Ikeda sum rule(isr) = B(GT;Z Z +1) B(GT;Z Z 1) = 3(N Z) quenched g A στ $ $ $ 0.77g A στ Horoi, Stoica, Brown, PRC 75, (007)

20 Double Beta Decay NME for 48 Ca M. Horoi, PRC 87, (013) ν ( T 1/ ) exp = [ +0.6 (stat) ± 0.4(syst) ] yr G p 1/ f 5 / p 3 / f 7 /

21 Closure Approximation and Beyond in Shell Model!##### many #" # body ###### $!############ two # " body ############# $ M S 0v = J, p< p # n< n # p< n + ( Γ) 0 f $ ( a + p a + p # ) J %& ( ) J a n # a n 0 ' + () 0 i p p #;J $ q dq S ˆ h(q) j κ (qr)g FS f ' & SRC τ q( q+ < E > ) 1 τ ) n n #;J % ( as closure M S 0v = ( ) J J k J k ( a # ) J + 0 i ( Γ + ) 0 f a p+ a + a n p n p p #;J # p p # n n # J k J ( q dq S ˆ h(q) j κ (qr)g FS f + * SRC τ J q( q + E k ) 1 τ - n n #;J )*,- beyond M 0v = M 0v GT ( g V /g A ) M 0v 0v F + M T σ 1 τ 1 σ τ Gamow Teller (GT) S ˆ = τ 1 τ Fermi (F) [ 3(! σ 1 n ˆ )(! σ n ˆ ) (! σ 1! σ )]τ 1 τ Tensor (T) Challenge: there are about 100,000 J k states in the sum for 48Ca Much more intermediate states for heavier nuclei, such as 76 Ge!!! No-closure may need states out of the model space (not considered). Minimal model spaces 8 Se : 10M states 130 Te : M states 76 Ge : 150M states

22 mixed, <E>=1 MeV mixed, <E>=3.4 MeV mixed, <E>=7 MeV mixed, <E>=10 MeV pure closure, CD-Bonn SRC mixed, CD-Bonn SRC pure closure, AV18 SRC mixed, AV18 SRC Error [%] error in mixed NME N, number-of-states cutoff parameter 8 Se: PRC 89, (014) Closure energy <E> [MeV] M mixed (N) = M no closure (N) + [ M closure (N = ) M closure (N)] GT, positive GT, negative FM, positive FM, negative J=0 J=1 J= J=3 J=4 J=5 J=6 J=7 J=8 J=9 Spin of the intermediate states Optimal closure energy [MeV] Ca 46 Ca 44 Ca 76 Ge 8 Se GXPF1A FPD6 KB3G JUN45

23 New Approach to calculate NME: New Tests of Nuclear Structure Brown, Horoi, Senkov arxiv: , GT, positive GT, negative FM, positive FM, negative I=0 I=1 I= I=3 I=4 I=5 I=6 I=7 I=8 I=9 Spin of the neutron-neutron (proton-proton) pairs

24 136 Xe ββ Experimental Results Publication Experiment T ν 1/ T 0ν 1/(lim) T 0ν 1/(Sens) PRL 110, 0650 KamLAND-Zen > 1.9x10 5 y 1.1x10 5 y PRC 89, EXO-00 (.11 ± 0.04 ± 0.1)x10 1 y Nature 510, 9 EXO-00 >1.1x10 5 y 1.9x10 5 y PRC 85, KamLAND-Zen (.38 ± 0.0 ± 0.14)x10 1 y M ν exp = MeV 1 EXO-00 arxiv: , Nature 510, 9

25 136 Xe νββ Results M ν exp = MeV Xe(0 + ) 136 Cs(1 + ) 136 Ba(0 + ) New effective interaction, στ 0.74στ quenching 0g 7/ 1d 5/ 1d 3/ s 5/ 0h 11/ model space 0h 9/ B(GT;Z Z +1) B(GT;Z Z 1) = 5 Ikeda: 3(N Z) = 84 0h 9/ 0h 11/ 0h 11/ s 5/ 0h 9/ M ν = MeV 1 s 5/ 1d 3/ 1d 5/ 0g 7/ 0g 9/ 1d 3/ 1d 5/ 0g 7/ 0g 9/ 0h 11/ s 5/ 1d 3/ 1d 5/ 0g 7/ 0g 9/ 0g 7/ 1d 5/ 1d 3/ s 5/ 0h 11/ 0h 9/ B(GT;Z Z +1) B(GT;Z Z 1) = 84 Ikeda: 3(N Z) = 84 n (0+) n (1+) M(v) 0g 9/ np - nh

26 S. Vigdor talk at LRP Town Meeting, Chicago, Sep 8-9, 014 Goals (DNP14 DBD workshop) : T 1/ > y, after? years T 1/ > y, after 3 years T 1/ > y, after 5 years! (nexo) T 1/ > y, after 5 years T 1/ > 10 6 y, after? years T 1/ > y, after 5 years

27 IBA- J. Barea, J. Kotila, and F. Iachello, Phys. Rev. C 87, (013). QRPA-En M. T. Mustonen and J. Engel, Phys. Rev. C 87, (013). QRPA-Jy J. Suhonen, O. Civitarese, Phys. NPA (010). QRPA-Tu A. Faessler, M. Gonzalez, S. Kovalenko, and F. Simkovic, arxiv: ISM-Men J. Menéndez, A. Poves, E. Caurier, F. Nowacki, NPA (009). SM M. Horoi et. al. PRC 88, (013), PRC 89, (014), PRC 90, PRC 89, (014), in preparation, PRL 110, 50 (013).

28 CD Bonn SRC AV18 SRC IBA- J. Barea, J. Kotila, and F. Iachello, Phys. Rev. C 87, (013). QRPA-Tu A. Faessler, M. Gonzalez, S. Kovalenko, and F. Simkovic, arxiv: SM M. Horoi et. al. PRC 88, (013), PRC 90, PRC 89, (014), in preparation, PRL 110, 50 (013).

29 Take-Away Points Observation of 0νββ will signal New Physics Beyond the Standard Model. Black box theorem (all flavors + oscillations) 0νββ observed at some level ó (i) Neutrinos are Majorana fermions. (ii) Lepton number conservation is violated by units (iii) m ββ = m k U ek = c 1 3 k =1 c 13 m 1 + c 13 s 1 Regardless of the dominant 0νββ mechanism! m e iφ + s 13m 3 e iφ 3 > 0

30 Take-Away Points The analysis and guidance of the experimental efforts need accurate Nuclear Matrix Elements. T 1 1/ (0v) = G 0ν (Q ββ ) M 0v (0 + ) [ ] < m > ββ ' % & m e ( * ) m ββ m v = c 1 c 13 m 1 + c 13 s 1 m e iφ + s 13m 3 e iφ 3 φ = α α 1 φ 3 = α 1 δ

31 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. m ββ = c 1 c 13 m 1 + c 13 s 1 m e iφ + s 13m 3 e iφ 3 Σ = m 1 + m + m 3 φ = α α 1 φ 3 = α 1 δ from cosmology

32 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. SuperNEMO; 8 Se η ν, η NR & ( ' ( ) G 0ν T 0ν [ Ge ] 1 (0ν ) = M 1/ Ge Ge η ν G 0ν T 0ν [ Xe ] 1 (0ν ) = M 1/ Xe Xe η ν (0 N ) + M Ge η NR (0 N ) + M Xe η NR 0ν [ T 1/ ] 1 = G 0ν M j η j j = G 0ν M (0ν ) η νl + M (0 N ) ( η NL +η NR ) + X λ < λ > + X η < η > +M (0 λ ' ) η λ ' + M (0q ) η q +

33 Take-Away Points Accurate shell model NME for different decay mechanisms were recently calculated. The method provides optimal closure energies for the mass mechanism pure closure, CD-Bonn SRC mixed, CD-Bonn SRC pure closure, AV18 SRC mixed, AV18 SRC Decomposition of the matrix elements can be Closure energy <E> [MeV] used for selective quenching of classes of Ge states, and for testing nuclear structure. M mixed (N) = M no closure (N) + [ M closure (N = ) M closure (N)] GT, positive GT, negative FM, positive FM, negative J=0 J=1 J= J=3 J=4 J=5 J=6 J=7 J=8 J=9 Spin of the intermediate states GT, positive GT, negative FM, positive FM, negative I=0 I=1 I= I=3 I=4 I=5 I=6 I=7 I=8 I=9 Spin of the neutron-neutron (proton-proton) pairs

34 Experimental info needed 0.15 Experimental Theoretical 1 Σ B(GT) B(GT) ,000 1,500,000,500 Energy (KeV) ,000 1,500,000,500 Energy (KeV)

35 Collaborators: Alex Brown, Roman Senkov, CMU and CUNY Andrei Neacsu, CMU Jonathan Engel, UNC Jason Holt, TRIUMF