Matrix elements for processes that could compete in double beta decay

Transcription

1 Matrix elements for processes that could compete in double beta decay Mihai Horoi Department of Physics, Central Michigan University, Mount Pleasant, Michigan 48859, USA Ø Support from NSF grant PHY and DOE/SciDAC grant DE-SC is acknowledged

2 Plan of the talk Short overview of standard (light neutrino exchange) DBD mechanism Other mechanisms: right-handed currents, heavy neutrinos, R-parity SUSY, etc, 48 Ca: v and 0v nuclear matrix elements The right-handed currents contribution The effect of larger model spaces Beyond closure approximation 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 Adapted from Avignone, Elliot, Engel, Rev. Mod. Phys. 80, 481 (008) -> RMP08 T 1 1/ (0v) = G 0ν (Q ββ ) M 0v (0 + ) [ ] < m ββ > ' m ββ = m k U ek k % & m e ( * )

4 Neutrino Masses - Tritium decay: PMNS matrix Δm ev (solar) Δm 3 c 1 cosθ 1, s 1 = sinθ 1, etc tan θ , sin θ 3 > 0.9, sin θ ev (atmospheric) 3 H 3 He + e +ν e m ν e = U ei i m i <.ev (Mainz exp.) Katrin exp. (in progress): goal m ν e < 0.3eV - Cosmic Microwave Background (CMB) power spectrum: m 1 + m + m 3 < 0.6eV m 0 =? Two neutrino mass hierarchies

5 Neutrino ββ effective mass m ββ = m k U ek 3 k =1 = 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 ( * ) CMB constraint m ν e = U ei i m i

6 Neutrino effective mass: the sterile neutrinos effects T 1 1/ (0v) = G 0v (Q ββ ) M 0v (0 + ) Vergados, Ejiri, Simkovic, Rep. Prog. Phys. 75, (01) 4,5 m ββ = m k U ek k =1 [ ] < m > ββ & $ % m e ' ) (

7 L The origin of (Majorana) neutrino masses +h.c. +h.c. See-saw mechanisms GUT/SUSY R-parity v. mechanism

8 Possible contributions of other mechanisms C mm = G 0ν M 0ν, [T 1/ 0ν ] 1 = C mm m ββ m e + C λλ λ + C ηη η + C mλ m ββ m e λ cosφ 1 +C mη m ββ m e η cosφ ( )] +C λη λ η cos φ 1 φ η = ζ λ = light k M WL M WR U ek V ek light U ek V ek W R ζw 1 +W k

9 Phase Space Factors All calculated with: g A = 1.54 Iachello (KI): PRC 85, (01) (see also: Stoica & Mirea arxiv: ) Suhonen (SC): Phys. Rep 300, 13 (1998) Vogel (Elliott): J. Phys. G 34, 667 (007) Cowell: PRC 73, (006)

10 Possible contributions of other mechanisms arxiv: β0ν rhc(η)

11 Possible contributions from other mechanisms + PRD 83, (011) light heavy ν e L = P L U ek ν k + U ek N k k k light heavy ν ʹ e R = P R V ek ν k + V ek N k k k η ν L = m heavy ββ η NL = U m $ p ek η NR = M ' WL & ) m e % ( k M k M WR 4 heavy k V ek m p M k < λ >,< η > mass independent : < λ >, < η > << η ν L, η N 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 + 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

12 Matrix Elements: Light Neutrinos PRL 109, (01) PRD 83, (011) NPA 818, 139 (009) η ν L = m ββ m e 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

13 Matrix Elements: Heavy Neutrinos PRL 109, (01) PRD 83, (011) # η NR = % $ M WL M WR & ( ' 4 heavy k V ek m p M k 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

14 Two Non-Interfering Mechanisms η ν = m ββ 10 6 η NR = M WL m M WR e 4 heavy k V ek m p M k 10 8 G 0ν 0ν [ i T 1/ i ] 1 (0ν ) = M (0 N ) i η ν + M i η NR i =1, η ν > 0 and η NR > 0 T 1/ ( 76 Ge)=.3x10 4 y

15 Neutrinoless Double Beta Decay Requires a Massive Majorana Neutrino J. Schechter and J.W.F Valle, PRD 5, 951 (198) 0νββ obs consequences: - Neutrinos are Majorana fermions (with m > 0). - Lepton numbers conservation is violated by units

16 Some mechanisms tested at LHC PRD 86, (01) +

17 T 1/ 1 = G v (Q ββ ) M GT v Double Beta Decay (DBD) of 48 Ca [ v (0 + )] E 0 = 1 Q ββ + ΔM( A Z +1 T 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 στ $ $ $ 0.77στ Horoi, Stoica, Brown, PRC 75, (007)

18 Double Beta Decay NME for 48 Ca M. Horoi, PRC 87, (013) ν ( T 1/ ) exp = [ +0.6 (stat) ± 0.4(syst) ] yr

19 Possible contributions from right-handed currents 0ν dw ν [ T 1/ ] 1 = 1 ln a 0ν = [ A(ε ( m e R) 1 ) + B(ε 1 )cosθ 1 ]w 0ν (ε 1 ) dε 1 d cosθ 1 0ν dw 0 = a 0ν ln m e R ( ) A(ε ( ) 1 )dε 1 d( cosθ 1 ) < m ββ > λ Δt e 1 e η νl = λ η νl < m > ββ = 1 light U m e m ek e η = ζ λ = light k U ek V ek ζ M WL M WR light k k m ν m k M N R 10 U ek V ek M WL M WR m ν M N R 10 9 η νl = 3 λ W R ζw 1 +W [T 1/ 0ν ] 1 = C mm m ββ m e + C λλ λ + C ηη η + η νl = 0.5 λ C mλ m ββ m e λ cosφ 1 +C mη m ββ m e η cosφ ( )] +C λη λ η cos φ 1 φ

20 The effect of larger model spaces for 48 Ca M(0v) SDPFU SDPFMUP 0 ω ω 1.18 (6%) (61%) M(0v) 0 ω / GXPF1A ω + nd ord./gxpf1a (77%) SDPFU: PRC 79, (009) SDPFMUP: PRC 86, (R) (01) arxiv: PRC 87, (013) N = 3 N = sd pf p 1/ f 5 / p 3 / f 7 / d 3 / s 1/ d 5 /

21 T 1 1/ (0v) = G 0v (Q ββ ) M 0v (0 + ) M 0v 0v = M GT # ( ) g V % $ Closure approximation for the M 0v g A [ ] < m > ββ & & ( ' $ % M F 0v + M T 0v m e ' ) ( - Closure approximation PRC 81, 0431 (010) - Includes higher order corrections in the nucleon currents M S 0v = p< p ʹ n< n ʹ p< n + ( Γ) 0 f ( a + p a + p ʹ ) J ( ) J a n ʹ a n i p p ʹ ;J q dq S ˆ h(q) j κ (qr)g FS f SRC τ q( q+ < E > ) 1 τ n n ʹ ;J as closure 0 + T = 4 48 Ca 0 + T = 4 ( ) J 0 + " f T = a + + i a # $ j 0 + T = 48 Ti ( a k a m ) J % &' 0 0 i + T = 4 Ti - Old and new short range correlations included - No quenching - New technique to calculate the many body part of M

22 Renormalization methods: Effective Hamiltonians for Large N ω Excitation Model Spaces - G-matrix: Physics Reports 61, 15 (1995) - Lee-Suzuki (NCSM): PRC 61, (000) - V low k : PRC 65, (R) (00) - Unitary Correlation Operator: PRC 7, (004) - Similarity Renormalization Group (SRG): PRL 103, (009) H PP QP = 0 PQ = 0 QQ H Bare Nucleon-Nucleon Potentials: - Argonne V18: PRC 56, 170 (1997) - CD-Bonn 000: PRC 63, (000) - N 3 LO: PRC 68, (003) - INOY: PRC 69, (004)

23 Shell Model Effective Hamiltonians empty valence frozen core quenched στ $ $ $ 0.77στ H valence Ψ = E n Ψ core polarization: Phys.Rep. 61, 15 (1995) H valence = H body can describe most correlations around the Fermi surface! pf sd pf PQ = excited states RMS: sd, N3LO H PRC 74, (006), 78, (008) 3.5 ME RMS 1.5 QP = 0 QQ 1 H st order nd order nd + A-dep nd + d3s1 USDA USDB

24 Beyond Closure in Shell Model M S 0v = p< p ʹ n< n ʹ p< n + ( Γ) 0 f ( a + p a + p ʹ ) J ( ) J a n ʹ a n i p p ʹ ;J q dq S ˆ h(q) j κ (qr)g FS f SRC τ q( q+ < E > ) 1 τ n n ʹ ;J as closure M S 0v = pp ʹ nn ʹ J k J ( Γ + ) 0 f ( a p+ a n ) J J k J k a p+ ( a n ) J + 0 i p p ʹ ;J q dq S ˆ h(q) j (qr)g κ FS J q( q + E k ) f SRC τ 1 τ n n ʹ ;J exact 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 : 6,146, Te :,437, Ge : 89,47,767

25 Shell model: only f 7/ K. Muto, NPA (1994) QRPA

26 M S 0v = pp ʹ nn ʹ J k J + ( Γ) 0 f p p ʹ ;J Beyond Closure in Shell Model ( a p+ a n ) J J k J k a p+ q dq S ˆ h(q) j (qr)g κ FS J q( q + E k ) ( a n ) J + 0 i f SRC τ 1 τ Challenge: there are about 100,000 J k states in the sum for 48Ca!!! n n ʹ ;J - About 300 intermediate states for each spin are (more than) enough - GT dominates and experience the largest change - A 8-1% increase from closure was found

27 136 Xe ββ Experimental Results M ν exp = MeV 1 Publication Experiment T ν 1/ T 0ν 1/ T 0ν 1/(Maj) PRL 110, 0650 KamLAND-Zen > 1.9x10 5 y PRL 107, 1501 EXO-00 (.11 ± 0.04 ± 0.1)x10 1 y PRL 109, EXO-00 (.3 ± ± 0.)x10 1 y >1.6x10 5 y PRC 85, KamLAND-Zen (.38 ± 0.0 ± 0.14)x10 1 y >5.7x10 4 y PRC 86, KamLAND-Zen >6.x10 4 y >.6x10 4 y GERDA arxiv:

28 Other Shell Model Results στ quenched $ $ $ qστ 0g 7/ 1d 5/ 1d 3/ s 5/ 0h 11/ valence space

29 136 Xe νββ Results M ν exp = MeV Xe(0 + ) 136 Cs(1 + ) New effective interaction, στ 0.74στ quenching 136 Ba(0 + ) 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

30 136 Xe 0νββ Results 134 Te 134 Xe M. Horoi and B.A. Brown, Phys. Rev. Lett. 110, 50 (013) n(0+) n(1+) M(v) M(0v) η NR = M WL M WR heavy 4 k V ek m p M k =10 8

31 Comparisons of M 0ν 0νββ Results T. Rodriguez, G. Martinez-Pinedo, Phys. Rev. Lett. 105, 5503 (010) M. Horoi and B.A. Brown, Phys. Rev. Lett. 110, 50 (013) Sn isotopes T. Rodriguez, G. Martinez-Pinedo, Phys. Lett. B 719, 174 (013) Large jump down for magic no of neutrons!!!

32 Summary and Outlook Observation of neutrinoless double beta decay would signal physics beyond the Standard Model: massive Majorana neutrinos, right-handed currents, SUSY LNV, etc 48 Ca case suggests that ν double-beta decay can be described reasonably within the shell model with standard quenching, provided that all spin-orbit partners are included. Higher order effects for 0ν ΝΜΕ included: range Reliable 0νββ nuclear matrix elements could be used to identify the dominant mechanism if energy/angular correlations and data for several isotopes become available. The effects of the quenching and the missing spin-orbit partners are important (see the 136 Xe case), and they need to be further investigated for 76 Ge, 8 Se and 130 Te.