compared sensitivities of next generation dbd experiments idea - zaragoza meeting – 7-8 november...

Compared sensitivities of next Compared sensitivities of next generation DBD experimentsgeneration DBD experiments

IDEA - Zaragoza meeting – 7-8 November 2005IDEA - Zaragoza meeting – 7-8 November 2005

C. Augier presented by X. SarazinC. Augier presented by X. Sarazin

LAL – Orsay – CNRS/IN2P3 and Université Paris-Sud XI

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)

Presentation of this workPresentation of this work

Main goals of this work:

For GERDA and CUORE sensitivities, use of their published expected sensitivities for the period. Concerning SuperNEMO sensitivity, use of the preliminary calculations to give the two extremal values for the expected T1/2(0) period. The SuperNEMO period limit obtained from actual Monte-Carlo simulations is just below the best value used in 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 process

2) obtain a useful method to directly compare the different NME calculations in terms of period sensitivity.

3) compare the predicted sensitivities on the effective neutrino mass for GERDA, CUORE and SuperNEMO projects, using both their predicted limits of periods and this study of NME range.

where G is the 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 »).


In case of light massive Majorana neutrino exchange in , period of the process is related to the effective neutrino mass by the relation

[ T ] = G|M| m

It is difficult to compare directly the NME values from the different publications. In fact, one can find in these publications

the NME value |M|, or the product of |M| by the phase space factor G Cmm,

orthe 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…


Using the values obtained in different publications, the results are presented in a Table which contains the T values, where T is defined as

T (y) = T(y)m(e

V)

From this table containing the T values, it is useful to recalculate the effective neutrino mass (in eV) associated to any given period (in y), using the relation

In fact, the T value corresponds to an effective neutrino mass m eV.

T (y)m(eV) =

T /

Two NME calculation techniquesShell modelQuasi Random Phase Approximation (QRPA) and

extensions

Choice of the NME publications and studied isotopesChoice of the NME publications and studied isotopes

Criteria used for the publication choice- reproduction of relevant nuclear properties (, ,

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.

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 »

QRPA and extensions’ calculations


1) Ref. [155] = V.A. Rodin, A.Faessler, F. Simkovic, P. Vogel, « Systematic analysis of the uncertainty in the 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 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 A1/3They 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 et) gA = 1 and RFSV 05 – QRPA (avec gpp de et) gA = 1.25



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

QRPA and extensions’ calculationsChoice of the NME publications and studied isotopesChoice of the NME publications and studied isotopes

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 experimental transition, but only for J = 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 T 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)



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 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 T extracted from these two publications are plotted and refered as AS98 – AS03 – min and AS98 – AS03 – max

Results : TResults : T00 values obtained from the studied publications values obtained from the studied publications

Minimal and maximal values of T0 used for the comparison plots

Most favored valueLess favored value

Model T0(76Ge) T0(82Se) T0(96Zr) T0(100Mo) T0(116Cd) T0(130Te) T0(136Xe)

76Ge : T0 = 1.77 x 1025 y

82Se : T0 = 2.40 x 1024 y

130Te : T0 = 9.0 x 1023 y

136Xe : T0 = 1.3 x 1024 y

Most favored isotope

Less favored isotope

m (eV) = T1/2(0) (yr) /T0

(eV)(Caurier, Nowacki, publication 1996 + « beyond NEMO3 2003)

S.M.S.M.

76Ge : T0 = 4.60 x 1024 y

82Se : T0 = 1.33 x 1024 y

130Te : T0 = 1.96 x 1024 y

136Xe : T0 = 4.17 x 1024 y

96Zr : T0 = 2.18 x 1027 y

100Mo : T0 = 2.79 x 1024 y

116Cd : T0 = 1.72 x 1024 y

m (eV) = T1/2(0) (yr) /T0

(eV)(Rodin, Faessler, Simkovic, Vogel, 2005)



RFSV 2005RFSV 2005

76Ge : T0 = 6.24 x 1024 y

82Se : T0 = 2.03 x 1024 y

130Te : T0 = 2.87 x 1024 y

136Xe : T0 = 5.46 x 1024 y

96Zr : T0 = 1.88 x 1025 y

100Mo : T0 = 3.65 x 1024 y

116Cd : T0 = 2.82 x 1024 y

m (eV) = T1/2(0) (yr) /T0

(eV)(Rodin, Faessler, Simkovic, Vogel, 2005)



RFSV 2005RFSV 2005

76Ge : T0 = 4.23 x 1024 y

82Se : T0 = 1.08 x 1024 y

130Te : T0 = 1.46 x 1024 y

136Xe : T0 = 1.04 x 1025 y

96Zr : T0 = 1.61 x 1024 y

100Mo : T0 = 4.6 x 1023 y

116Cd : T0 = 9.99 x 1023 y

m (eV) = T1/2(0) (yr) /T0

(eV)

(Simkovic, Pantis, Vogel, Faessler, 1999)



SPVF 1999SPVF 1999

The T0 value, which corresponds to an effective mass m = 1 eV, has to be as low as possible to favor the possibility of signal observationFor 76Ge : - the best sensitivity corresponds to the QRPA method with 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 adjustment and gA =1, with T0 = 3.60 x 1024 y (Rodin, Faessler, Simkovic, Vogel, 2005)

Study of the sensitivity range for Study of the sensitivity range for 7676Ge, Ge, 8282Se and Se and 130130TeTe

- Klapdor (best fit), T = 1.2 x 1025 yr, 0.40 < <m> < 1.21 eV

m (eV) = T1/2(0) (y) /T0

(eV)

- IGEX best limit, T < 1.57 x 1025 yr, 0.34 < <m> < 1.05 eV

- HM best limit, T < 1.9 x 1025 yr, 0.32 < <m> < 0.97 eV

76Ge (Past experiments)

m (eV) = T1/2(0) (y) /T0

(eV)

- GERDA phase I, T < 3 x 1025 yr, 247 < <m> < 774 meV

- GERDA phase II, T < 2 x 1026 yr, 96 < <m> < 293meV

- GERDA phase III, T < 3 x 1027 yr, 25 < <m> < 77 meV

76Ge (GERDA sensitivities)

m (eV) = T1/2(0) (y) /T0

- NEMO 3, T < 8 x 1023 yr, 0.61 < <m> < 1.72 eV

-SuperNEMO, « low » resolution T < 1 x 1026 yr, 54 < <m> <155 meV

-SuperNEMO, « high » resolution T < 2.2 x 1026 yr, 36 < <m> < 105 meV

(eV)

82Se (SuperNEMO sensitivities)

m (eV) = T1/2(0) (y) /T0

- CUORICINO T < 4 x 1024 yr, 0.26 < <m> < 0.84 eV

- CUORE bkg = 0.001 with 130TeO2

T < 1.9 x 1027 yr, 12 < <m> < 39 meV

(eV)

- CUORE bkg = 0.001 with natTeO2

T < 6.6 x 1026 yr, 20 < <m> < 65 meV

- CUORE bkg = 0.01 with natTeO2

T < 2.1 x 1026 yr, 36 < <m> < 117 meV

130Te (CUORE sensitivities)

TT00 values corresponding to an effective mass of 50 meV values corresponding to an effective mass of 50 meV

T range

T range

T range

<m>= 50 meV <m>= 50 meV

<m>= 50 meV

TT00 values corresponding to an effective mass of 50 meV values corresponding to an effective mass of 50 meV

For 76Ge : - period between 7.8 x 1026 y and 5.6 x 1027 y

Possible with GERDA phase III (T1/23 x 1027 y) with 1000 kg.y and bkg = 0.001 cts.keV-1.kg-1.y-1 (same conclusions for MAJORANA)

For 130Te : - 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)

For 82Se : - period 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.

Shell Model: Caurier (2003)

RQRPA Simkovic et al. (1999)

Stoica et al. (2001)

Suhonen et al. (1998 and 2003)

Rodin, Simkovic (2005)

Theoretical calculations of the NME

Big theoretical uncertainties Thus choice of the nucleus depends on:

1) detector technique2)

T1/2() for m =50 meV

In conclusionIn conclusion

enrichment possibility high Q value high period: T≥ 10 y

Goal measure the highest possible experimental value of the period ... And wait for the good calculation

Use

d in

th

e co

mp

aris

on

plo

ts

Results : TResults : T00 values obtained from the studied publications values obtained from the studied publications

Model T0(76Ge) T0(82Se) T0(96Zr) T0(100Mo) T0(116Cd) T0(130Te) T0(136Xe)

Study for other isotopes (Study for other isotopes (4848Ca, Ca, 124124Sn, Sn, 150150Nd)Nd)

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

QRPA values are nearly the same, and three times more favorable than the value obtained from SM calculation

48Ca (Z and N are magic numbers)20

24

Study for other isotopes (Study for other isotopes (4848Ca, Ca, 150150Nd, Nd, 124124Sn)Sn)

Results for 124Sn (Q = 2.29 MeV, magic proton number Z = 50)

Ref [167] Aunola, Suhonen, Nucl. Phys. A643 (1998) adjustment on -decay transition

AS1 : T0 = 4.58 x 1023 y (standard WS potential)

AS2 : T0 = 1.14 x 1024 y (adjusted WS potential)

1) There is a factor 2.3 between the two QRPA calculations,

2) AS2-QRPA and SM calculations give nearly the same value

Ref. [154] = E. Caurier, A. Gniady, F. Nowacki, « Beyond NEMO3 », Orsay, Dec. 2003, (NEMO meeting)

T0 = 1.60 x 1024 y

This nucleus is treated as a « core of 100Sn » + 24 neutrons

(stable)

5050

Caurier, Nowacki, 1996 + « beyond NEMO3 » 2003 → Shell Model

Rodin, Faessler, Simkovic, Vogel, 2005 QRPA gpp from and gA = 1.25 → RFSV 05 – QRPA gA =

1.25RQRPA gpp from 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

Examples of isotope comparison for different publicationsExamples of isotope comparison for different publications

Publications used

See the 4 comparison plots

Study for other isotopes (Study for other isotopes (4848Ca, Ca, 150150Nd, Nd, 124124Sn)Sn)

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 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.



Other publications found as reference in previous papers. Results are put in the Table but not used in the plots because their T values are included in the range obtained from previous publications (except for 100Mo, where the T 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)).

compared sensitivities of next generation dbd experiments idea - zaragoza meeting – 7-8 november...

Documents