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Compared sensitivities of next generation DBD experiments

Compared sensitivities of next generation DBD experiments. C. Augier presented by X. Sarazin LAL – Orsay – CNRS/IN2P3 and Université Paris-Sud XI. IDEA - Zaragoza meeting – 7-8 November 2005. Presentation of this work.

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Compared sensitivities of next generation DBD experiments

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  1. Compared sensitivities of next generation DBD experiments C. Augier presented by X. Sarazin LAL – Orsay – CNRS/IN2P3 and Université Paris-Sud XI IDEA - Zaragoza meeting – 7-8 November 2005

  2. Presentation of this work This work was realised and included in my HDR report in June 2005 (Section 4.3.7 « L’effet  des éléments de matrice nucléaire », p.332-343) Main goals of this work: 1) study the effect of the large nuclear matrix element (NME) range on the experimental sensitivities for different isotopes, in case of the exchange of a light massive Majorana neutrino in bb0n process 2) obtain a useful method to directly compare the different NME calculations in terms of bb0n period sensitivity. 3) compare the predicted sensitivities on the effective neutrino mass for GERDA, CUORE and SuperNEMO projects, using both their predicted limits of bb0n periods and this study of NME range.  For GERDA and CUORE sensitivities, use of their published expected sensitivities for the bb0n period.  Concerning SuperNEMO sensitivity, use of the preliminary calculations to give the two extremal values for the expected T1/2(0n) period. The SuperNEMO period limit obtained from actual Monte-Carlo simulations is just below the best value used in this work.

  3. 0n [ T1/2 ]-1 = G0n|M0n|2< mn >2 Presentation of this work In case of light massive Majorana neutrino exchange in bb0n, period of the process is related to the effective neutrino mass by the relation where G0n is the bb0n phase space factor calculated for all nuclei by Doi, and then Vogel (see « F. Boehm and P. Vogel, Physics of massive neutrinos, Cambridge University Press, second edition, 1992 »). It is difficult to compare directly the NME values from the different publications. In fact, one can find in these publications the NME value |M0n|, or the product of |M0n| by the phase space factor G0n Cmm, or the effective mass corresponding to a given period value… Morevoer, some of the authors use their own calculations of the phase space factor. Others omit the electron mass in their calculation and one have to reintroduce it before the comparison… 0

  4. 0n T1/2(y) = T0 (y) < mn >2 (eV) Presentation of this work Using the values obtained in different publications, the results are presented in a Table which contains the T0 values, where T0 is defined as In fact, the T0 value corresponds to an effective neutrino mass <mn> = 1eV. From this table containing the T0 values, it is useful to recalculate the effective neutrino mass (in eV) associated to any given bb0n period (in y), using the relation 0n T0 < mn >(eV) =  T1/2(y) /

  5. Choice of the NME publications and studied isotopes Two NME calculation techniques Shell model Quasi Random Phase Approximation (QRPA) and extensions Criteria used for the publication choice - reproduction of relevant nuclear properties (bb2n, b, nuclear states, ...) - publications with comparison of different isotopes - recent publications if authors explain why their new calculations are more credible Important note - ref [173] Staudt, Kuo, Klapdor-Kleingrothaus, Phys. Rev. C46 (1992) is NOT USED : it gives results only for 76Ge, 130Te and 136Xe, with the most favored NME values for 76Ge and 130Te, which provide period sensitivities around one order most favored than for other calculations.

  6. Choice of the NME publications and studied isotopes Shell model calculations Few publications, I decided to use Ref. [154] = E. Caurier, A. Gniady, F. Nowacki, « Beyond NEMO3 », Orsay, Dec. 2003,(NEMO meeting) in association with published results from the same authors + Ref. [163] =E. Caurier, G. Martinez-Pinedo, F. Nowacki, A. Poves and P. Zuber, Rev. Mod. Phys. 77 (2005) 427-488, also nucl-th/0402046 (2004) + Ref. [164] =E. Caurier, F. Nowacki, A. Poves and J. Retamosa, nucl-th/ 9601016 (1996) They give the NME values for 6 nuclei : 48Ca, 76Ge, 82Se, 124Sn, 130Te and 136Xe Arbitrary choice based on the fact that these authors calculate all parameters for a given nucleus, which are used to reproduce experimental nuclear levels with a good precision. Results are presented in the 1st line of the Table and in plots, refered as « Shell Model  »

  7. Choice of the NME publications and studied isotopes QRPA and extensions’ calculations • Ref. [155] = V.A. Rodin, A.Faessler, F. Simkovic, P. Vogel, « Systematic analysis of the uncertainty in the 0nbb decay nuclear matrix elements », nucl-th/0503063 • - recent paper (2005) from authors issued from different theoretical groups • - they give some arguments to explain their calculations ; • - they use QRPA and RQRPA (renormalized) approach, both with two different values of the vector-axial coupling constant gA = 1.0 and 1.25, that means 4 results per isotope • - they adjust the particle-particle coupling constant (gpp) value to bb2n experimental half-lives (which allow to have a slight dependance on the size of model space), with gph = 1 (particle-hole interaction fixed to Gamow-Teller resonance), using « higher-order » terms of nucleon currents • - they use their own phase space factor value, calculated with R = 1.1 A1/3 They give the NME values for 9 nuclei : 76Ge, 82Se, 96Zr, 100Mo, 116Cd, 128Te, 130Te, 136Xe and 150Nd (I do not present 128Te results) Results are presented in lines 2 to 5 of the Table QRPA 1, QRPA 1.25, RQRPA 1., RQRPA 1.25, and the two extremal values are plotted, refered as RFSV 05 – RQRPA (avec gpp de bb2n et) gA = 1 and RFSV 05 – QRPA (avec gpp de bb2n et) gA = 1.25

  8. Choice of the NME publications and studied isotopes QRPA and extensions’ calculations 2) Ref. [165] = F. Simkovic, G. Pantis, J.D. Vergados and A. Faessler, « Additional nucleon current contributions to neutrinoless double beta decay », Phys. Rev. C60 (1999) 055502 - paper with common authors than in the previous one, chosen for comparison with line 5 of the Table, - they use RQRPA (renormalized) approach, the vector-axial coupling constant gA = 1.25, - they use their own phase space factor value, calculated with R = 1.1 A1/3 - the only difference is that they fix the particle-particle coupling constant (gpp) value to 1, with gph = 0.8 (particle-hole interaction) and using « higher-order » terms of nucleon currents They give the NME values for 9 nuclei : 76Ge, 82Se, 96Zr, 100Mo, 116Cd, 128Te, 130Te, 136Xe and 150Nd (I do not present 128Te results) Results are presented in line 6 of the Table, RQRPA 1.25, and plotted for all isotopes comparison, refered as SPVF 99 – RQRPA avec gpp = 1 et gA = 1.25

  9. Choice of the NME publications and studied isotopes QRPA and extensions’ calculations 3) Ref. [166] = S. Stoica, H.V. Klapdor-Kleingrothaus, Nucl. Phys. A694 (2001) 269-294 - they use QRPA and 3 different extensions (RQRPA, f-RQRPA for fully renormalized, and SK-RQRPA for Stoica-Klapdor…) - For these 4 calculations, they use both small s and large l sizes of model space. , with RQRPA approach, and the vector-axial coupling constant gA = 1.25, - they fix the particle-particle coupling constant (gpp) value to the probability of bb2n experimental transition, but only for Jp = 1+ relevant state, and leave the strenght unrenormalized for the other states. They give the NME values for 8 nuclei : 76Ge, 82Se, 96Zr, 100Mo, 116Cd, 128Te, 130Te, 136Xe (I do not present 128Te results) Results are presented in lines 7 to 14 of the Table (refered from QRPA s to SK-RQRPA l). Also minimal and maximal values of T0 from this publication are plotted and refered as SK 01 – min and SK 01 – max In this paper, NME values are different from one approximation to other, and one can find the most favored values of NME for numerous isotopes Also the needed phase space factor were corrected (for example for 100Mo)

  10. Choice of the NME publications and studied isotopes QRPA and extensions’ calculations 4) Ref. [167] = M. Aunola, J. Suhonen « Mean-field effects on neutrinoless double beta decay », Nucl. Phys. A643 (1998),and [168]J. Suhonen, M. Aunola, « Systematic study of neutrinoless double beta decay to excited 0+ states », Nucl. Phys. A723 (2003) - two review papers, with QRPA calculations. - the first one with AS1 (and AS2) for the use of standard (and adjusted) Woods-Saxon potential, the adjusted one used to obtain more realistic mean field ; the second paper refered AS3, is a compilation of different calculations of these authors. - for all the calculations, they use the vector-axial coupling constant gA = 1. - they adjust the particle-particle and particle-hole coupling constants (gpp and gph) values to the probability of b experimental transitions, They give the NME values for 8 nuclei : 76Ge, 82Se, 96Zr, 124Sn, 130Te, 136Xe, 100Mo, 116Cd Results are presented in lines 15 to 17 of the Table (refered from QRPA AS1 to QRPA AS3). With agreement of J. Suhonen, also minimal and maximal values of T0 extracted from these two publications are plotted and refered as AS98 – AS03 – min and AS98 – AS03 – max

  11. Results : T0 values obtained from the studied publications Minimal and maximal values of T0 used for the comparison plots Less favored value Most favored value Model T0(76Ge) T0(82Se) T0(96Zr) T0(100Mo) T0(116Cd) T0(130Te) T0(136Xe)

  12. S.M. mn (eV) =  T1/2(0n) (yr) /T0 Most favored isotope 130Te : T0 = 9.0 x 1023 y 136Xe : T0 = 1.3 x 1024 y 82Se : T0 = 2.40 x 1024 y 76Ge : T0 = 1.77 x 1025 y Less favored isotope (eV) (Caurier, Nowacki, publication 1996 + « beyond NEMO3 2003)

  13. RFSV 2005 mn (eV) =  T1/2(0n) (yr) /T0 Most favored isotope 82Se : T0 = 1.33 x 1024 y 116Cd : T0 = 1.72 x 1024 y 130Te : T0 = 1.96 x 1024 y 100Mo : T0 = 2.79 x 1024 y 136Xe : T0 = 4.17 x 1024 y 76Ge : T0 = 4.60 x 1024 y 96Zr : T0 = 2.18 x 1027 y Less favored isotope (eV) (Rodin, Faessler, Simkovic, Vogel, 2005)

  14. RFSV 2005 mn (eV) =  T1/2(0n) (yr) /T0 Most favored isotope 82Se : T0 = 2.03 x 1024 y 116Cd : T0 = 2.82 x 1024 y 130Te : T0 = 2.87 x 1024 y 100Mo : T0 = 3.65 x 1024 y 136Xe : T0 = 5.46 x 1024 y 76Ge : T0 = 6.24 x 1024 y 96Zr : T0 = 1.88 x 1025 y (eV) Less favored isotope (Rodin, Faessler, Simkovic, Vogel, 2005)

  15. SPVF 1999 mn (eV) =  T1/2(0n) (yr) /T0 Most favored isotope 100Mo : T0 = 4.6 x 1023 y 116Cd : T0 = 9.99 x 1023 y 82Se : T0 = 1.08 x 1024 y 130Te : T0 = 1.46 x 1024 y 96Zr : T0 = 1.61 x 1024 y 76Ge : T0 = 4.23 x 1024 y 136Xe : T0 = 1.04 x 1025 y (eV) Less favored isotope (Simkovic, Pantis, Vogel, Faessler, 1999)

  16. Study of the sensitivity range for 76Ge, 82Se and 130Te The T0 value, which corresponds to an effective mass mn = 1 eV, has to be as low as possible to favor the possibility of bb0n signal observation For 76Ge : - the best sensitivity corresponds to the QRPA method with b adjustment, with T0 = 1.96 x 1024 y (Aunola, Suhonen, 1998), - the worst one corresponds to the QRPA- l method, with T0 = 1.40 x 1025 y (Stoica, Klapdor, 2001) For 82Se : - the best sensitivity corresponds to the QRPA- s method, with T0 = 2.96 x 1023 y(Stoica, Klapdor, 2001), - the worst one corresponds to the Shell-Model calculations, with T0 = 2.40 x 1024 y (Caurier, Nowacki, 1996 and 2003) For 130Te : - the best sensitivity corresponds to the QRPA- s method, with T0 = 2.63 x 1023 y(Stoica, Klapdor, 2001), - the worst one corresponds to the RQRPA method with bb2n adjustment and gA =1, with T0 = 3.60 x 1024 y (Rodin, Faessler, Simkovic, Vogel, 2005)

  17. 76Ge (Past experiments) mn (eV) =  T1/2(0n) (y) /T0 - HM best limit, T < 1.9 x 1025 yr, 0.32 < <mn> < 0.97 eV - IGEX best limit, T < 1.57 x 1025 yr, 0.34 < <mn> < 1.05 eV - Klapdor (best fit), T = 1.2 x 1025 yr, 0.40 < <mn> < 1.21 eV (eV)

  18. 76Ge (GERDA sensitivities) mn (eV) =  T1/2(0n) (y) /T0 - GERDA phase III, T < 3 x 1027 yr, 25 < <mn> < 77 meV - GERDA phase II, T < 2 x 1026 yr, 96 < <mn> < 293meV - GERDA phase I, T < 3 x 1025 yr, 247 < <mn> < 774 meV (eV)

  19. 82Se (SuperNEMO sensitivities) mn (eV) =  T1/2(0n) (y) /T0 • SuperNEMO, • « high » resolution • T < 2.2 x 1026 yr, • 36 < <mn> < 105 meV • SuperNEMO, • « low » resolution • T < 1 x 1026 yr, • 54 < <mn> <155 meV - NEMO 3, T < 8 x 1023 yr, 0.61 < <mn> < 1.72 eV (eV)

  20. 130Te (CUORE sensitivities) mn (eV) =  T1/2(0n) (y) /T0 • CUORE bkg = 0.001 • with 130TeO2 • T < 1.9 x 1027 yr, • 12 < <mn> < 39 meV • CUORE bkg = 0.001 • with natTeO2 • T < 6.6 x 1026 yr, • 20 < <mn> < 65 meV • CUORE bkg = 0.01 • with natTeO2 • T < 2.1 x 1026 yr, • 36 < <mn> < 117 meV - CUORICINO T < 4 x 1024 yr, 0.26 < <mn> < 0.84 eV (eV)

  21. T0 values corresponding to an effective mass of 50 meV T range T range <mn>= 50 meV <mn>= 50 meV T range <mn>= 50 meV

  22. For82Se : - bb0nperiod between 1.2 x 1026 y and 9.6 x 1027 y  No problem for SuperNEMO with minimal value, but it could be very difficult to measure if the NME value corresponds to the maximal period. T0 values corresponding to an effective mass of 50 meV For76Ge : - bb0nperiod between 7.8 x 1026 y and 5.6 x 1027 y  Possible with GERDA phase III (T1/2 > 3 x 1027 y) with 1000 kg.y and bkg = 0.001 cts.keV-1.kg-1.y-1 (same conclusions for MAJORANA) For 130Te : -bb0n period between 1.1 x 1026 y and 1.4 x 1027 y  No problem for CUORE with minimal value ; the maximal period could be reached for bkg = 0.001 cts.keV-1.kg-1.y-1 (T1/2> 6.6 x 1026 y) or with enriched crystals (T1/2> 1.0 x 1027 y)

  23. In conclusion T1/2(bb0n) for mn =50 meV Theoretical calculations of the NME Shell Model: Caurier (2003) RQRPA Simkovic et al. (1999) Stoica et al. (2001) Suhonen et al. (1998 and 2003) Rodin, Simkovic (2005) Big theoretical uncertainties  Thus choice of the nucleus depends on: 1) detector technique 2) • enrichment possibility • high Qbb value • high bb2n period: T1/2≥ 1020 y Goal  measure the highest possible experimental value of the bb0n period ... And wait for the good calculation

  24. Results : T0 values obtained from the studied publications Model T0(76Ge) T0(82Se) T0(96Zr) T0(100Mo) T0(116Cd) T0(130Te) T0(136Xe) Used in the comparison plots

  25. Study for other isotopes (48Ca, 124Sn, 150Nd) Results for 48Ca Ref. [163] = E. Caurier, G. Martinez-Pinedo, F. Nowacki, A. Poves and P. Zuber, Rev. Mod. Phys. 77 (2005) 427-488, for Shell Model calculation T0 = 8.84 x 1024 y Ref. [169] = C. Barbera et al., Nucl. Phys. A650 (1999) for QRPA calculations T0 = 2.31 x 1024 y Ref. [170] = Pantis, Simkovic,Vergados and Faessler, Phys. Rev C53 (1996), for QRPA calculations T0 = 2.44 x 1024 y 48Ca  (Z and N are magic numbers) 24 20  QRPA values are nearly the same, and three times more favorable than the value obtained from SM calculation

  26. Study for other isotopes (48Ca, 150Nd, 124Sn) Results for 124Sn (Qbb = 2.29 MeV, magic proton number Z = 50) Ref [167] Aunola, Suhonen, Nucl. Phys. A643 (1998) adjustment on b-decay transition AS1 : T0 = 4.58 x 1023 y (standard WS potential) AS2 : T0 = 1.14 x 1024 y (adjusted WS potential) Ref. [154] = E. Caurier, A. Gniady, F. Nowacki, « Beyond NEMO3 », Orsay, Dec. 2003,(NEMO meeting) This nucleus is treated as a « core of 100Sn  » + 24 neutrons  50 50 (stable) T0 = 1.60 x 1024 y • 1) There is a factor 2.3 between the two QRPA calculations, 2) AS2-QRPA and SM calculations give nearly the same value

  27. Examples of isotope comparison for different publications Publications used Caurier, Nowacki, 1996 + « beyond NEMO3 » 2003 → Shell Model Rodin, Faessler, Simkovic, Vogel, 2005 QRPA gpp from bb2n and gA = 1.25 → RFSV 05 – QRPA gA = 1.25 RQRPA gpp from bb2n and gA = 1 → RFSV 05 – RQRPA gA = 1. Simkovic, Pantis, Vergados, Faessler, 1999, gpp =1 and gA = 1.25 →SPVF 99 – RQRPA gA = 1.25  See the 4 comparison plots

  28. Study for other isotopes (48Ca, 150Nd, 124Sn) Results for 150Nd (deformed nucleus, difficult to calculate) Ref. [155] = V.A. Rodin, A.Faessler, F. Simkovic, P. Vogel, « Systematic analysis of the uncertainty in the 0nbb decay nuclear matrix elements », nucl-th/0503063 from T0 = 1.92 x 1023 y (QRPA gA = 1.25) to T0 = 3.03 x 1023 y (RQRPA, gA = 1.0) Ref. [165] = F. Simkovic, G. Pantis, J.D. Vergados and A. Faessler, « Additional nucleon current contributions to neutrinoless double beta decay », Phys. Rev. C60 (1999) 055502 T0 = 8.84 x 1022 y (this value was more favorable)  All these QRPA values are nearly the same, even if the value from 1999 was more favorable.

  29. Choice of the NME publications and studied isotopes QRPA and extensions’ calculations Other publications found as reference in previous papers. Results are put in the Table but not used in the plots because their T0 values are included in the range obtained from previous publications (except for 100Mo, where the T0 value in QRPA (4) is only 6% higher than the maximal value used in the plots) Ref. [171] = Simkovic, Novak, Kaminski, Raduta, Faessler, Phys. Rev. C64 (2001) Ref. [172] = Muto, Bender and Klapdor-Kleingrothaus, Z. Phys. A334 (1989) Ref. [169] = C. Barbera et al., Nucl. Phys. A650 (1999) Ref. [170] = Pantis, Simkovic,Vergados and Faessler, Phys. Rev C53 (1996) Results are presented in lines 18 to 21 of the Table (refered from QRPA (1) to QRPA (4)).

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