Solar neutrino interactions with the double beta decay nuclei of 82 Se, 100 Mo and 150 Nd
SSolar neutrino interactions with the double beta decay nuclei of Se,
Mo and Nd H. Ejiri and S.R. Elliott Research Center for Nuclear Physics, Osaka University, Ibaraki, Osaka 567-0047, Japan Los Alamos National Laboratory, Los Alamos, NM, USA
Solar neutrinos interact within double-beta decay ( ββ ) detectors and contribute to backgroundsfor ββ experiments. Background contributions due to solar neutrino interactions with ββ nuclei of Se,
Mo, and
Nd are evaluated. They are shown to be significant for future high-sensitivity ββ experiments that may search for Majorana neutrino masses in the inverted-hierarchy massregion. The impact of solar neutrino backgrounds and their reduction are discussed for future ββ experiments.Key words: solar- ν interaction, double beta decay, solar- ν backgrounds, neutrino mass sensitivity. PACS numbers: 23.40.-s, 26.65.+t
I. INTRODUCTION
Neutrino-less double beta decay ( ββ (0 ν ) ) is a uniqueand realistic probe for studies of neutrino ( ν ) proper-ties and especially the Majorana mass character of theneutrino and the absolute mass scale. ββ studies and ν masses are discussed in recent reviews and their refer-ences [1–4].The rate of ββ (0 ν ) , if it exists, would be extremelysmall because ββ is a second-order weak process thatrequires lepton number conservation violation and Ma-jorana fermions. There are numerous possible mecha-nisms that can give rise to ββ (0 ν ) as is discussed in thereviews[1–4]. It is known, however, that light neutri-nos exist and therefore it is convenient to consider light-neutrino exchange as the default process by which tobenchmark ββ (0 ν ) rates. For light-neutrino exchange,the rate depends on the effective Majorana mass squaredand the typical mass regions to be explored are about 45-15 meV and 4-1.5 meV in cases of the inverted-hierarchy(IH) and normal-hierarchy (NH) mass regions, respec-tively. The ββ (0 ν ) half-lives expected for these regionsare near or greater than years, depending signifi-cantly on the nuclear matrix element (NME), includingthe effective axial weak coupling g A . As a result, the ββ (0 ν ) signal rate ( S ββ ) is near or less than a few countsper ton of ββ isotope per year (t y). Accordingly thebackground rate necessarily has to be around or less thanone count per t y.Solar- ν s are omnipresent and cannot be shielded, andthus their charged current (CC) and neutral current (NC)interactions are potential background sources for highsensitivity ββ experiments as discussed in [5, 6] and refer-ences therein. In fact, it has been shown that solar- ν CCinteractions with ββ isotopes like Mo [7],
Cd [8]and
Nd [9] can be used for real-time studies of thelow-energy solar- ν s.The ββ isotopes most often used or considered for high-sensitivity experiments are Ge, Se,
Mo,
Te,
Xe and
Nd. Here, we classify them into two groups.Group A consisting of Se,
Mo and
Nd have a large solar- ν CC rate, whereas Group B consisting of Ge,
Te and
Xe have a rather small solar- ν CC rate.In the previous paper [5], background contributions fromCC solar- ν interactions were discussed for the 3 ββ nucleiin Group B. Solar- ν interactions with atomic electrons in ββ isotopes and liquid scintillators used for ββ experi-ments were considered in Refs. [1, 6, 10, 11].The present paper aims to evaluate the backgroundcontributions for the 3 nuclei in Group A and discuss theimpact on high sensitivity ββ experiments using them.The mechanics of these calculations are identical to thosein Ref. [5], and we do not repeat all the details here. II. SOLAR NEUTRINO BACKGROUNDS
The process of ββ decay from Z − A to Z +1 A via theintermediate nucleus Z A is shown in Eqn. 1. Solar ν scan produce background to this signal primarily throughCC interactions with ββ nuclei. The CC interaction pro-duces background in two ways. First the CC interactionitself can produce a signal ( B CC ) given by the promptlyemitted e − and, if the resulting nucleus is in an excitedstate, a number of γ rays may be emitted as the nucleusrelaxes to its ground state. Second, the resulting nucleus Z A can then β − decay to Z +1 A by emitting a single β − ray and possibly also γ ray(s) if the residual state is anexcited state ( B SB ). The interaction and decay schemesare shown in Fig. 1. The 3 processes are expressed as, ββ : Z − A → Z +1 A + β − + β − + Q ββ CC : Z − A + ν → Z A + e − + γ ( s ) + Q ν SB : Z A → Z +1 A + β − + γ ( s ) + Q β , (1)where ββ , CC, and SB denote the double beta decay,the solar- ν CC interaction, and the single beta decayprocesses, respectively. The Q values for each are givenas Q ββ , Q ν , and Q β respectively, as shown in Fig. 1.We consider ββ detectors where the sum energy of the β and γ rays is measured. The ββ (0 ν ) signature is apeak within the region of interest (ROI) at the ββ Qvalue ( E = Q ββ ). In contrast, the sum of the electron a r X i v : . [ nu c l - e x ] M a r FIG. 1: Schematic diagrams of the ββ of Z − A to Z +1 A, thesolar- ν CC interaction on Z − A and the electron ( γ ) decay to Z A, and the single β / γ decays of Z A to Z +1 A. Q ββ , Q β , Q ν ,and Q e are the Q values for ββ , β , ν CC and electron capture(EC), respectively.
Z-1 A Z A Z+1 AQ Q e E e Q E E i B pp ee B n Q + energy ( E e ) and any successive γ ray energy ( E γ ) is acontinuum spectrum for both the CC and SB processes.The backgrounds of interest are estimated by their yieldswithin the ROI and therefore are sensitive to the detec-tor’s energy resolution. The energy width of the ROI isgiven by the FWHM resolution ( ∆ E ) at the energy ofthe Q value. This ratio, defined as δ , is the fractionalenergy resolution at E = Q ββ . Certainly the kinematicsand event topologies for the backgrounds discussed heremay permit experimental techniques for rejection that gobeyond just a sum energy cut. We cannot anticipate allpossible rejection techniques, but instead estimate ratesso that future efforts may better assess these backgroundsfor a given experimental configuration. In fact, methodsto reduce the solar- ν backgrounds do depend on the de-tector configuration and the β − and γ decay scheme ofthe nucleus. We briefly discuss these later for individualnuclei. A. The ββ (0 ν ) Rate
We first evaluate the ββ (0 ν ) signal rate S ββ for thelight ν -mass process and then compare to estimated CCand SB background rates. Although there are numerousother potential ββ (0 ν ) mechanisms, providing this rateestimate enables a comparison to the background rates. The ββ (0 ν ) signal rate for the light Majorana- ν exchangeis written as [2, 4] S ββ = ln G ν ( m eff ) [ M ν ] (cid:15) ββ × A / t y , (2)where S ββ is the signal rate per ton per year (t y) of the ββ isotope, G ν is the phase space volume, m eff is theeffective Majorana ν -mass in units of the electron mass, (cid:15) ββ is the ββ (0 ν ) peak detection efficiency, and M ν isthe nuclear matrix element (NME) for the light ν -massprocess. Here G ν includes conventionally the axial weakcoupling g A = 1 . g V with g V being the vector couplingconstant, and M ν is given by the sum of the axial-vectorand the vector NMEs.The NMEs are expressed as M A = ( g effA /g A ) M mA and M V = ( g effV /g V ) M mV , where M mA and M mV are modelNMEs and ( g eff /g ) are the renormalization (quenching)factors due to such non-nucleonic (isobar, exchange cur-rent etc) and nuclear medium effects that are not explic-itly included in the model NMEs [2, 4, 12]. In a typ-ical case of G ν = 5 × − /y, m eff = 20 meV/ m e , M ν =2, A =100, and (cid:15) ββ =0.6, the ββ (0 ν ) signal rate is S ββ ≈ /t y. B. The β Decay of Z A Next, we evaluate the background rate for the SBcase. For SB, all solar- ν sources exciting the interme-diate states below the neutron threshold energy B n in Z A contribute to the production of the ground state of Z A via γ decay. Hence the production rate for Z A isgiven by the total solar- ν capture rate in units of SNU( S t ). The background rate per ton year for SB ( B SB ) isexpressed as B SB = 3 . × − n ββ S t (cid:15) SB , (3)where n ββ is the number of ββ isotope nuclei per ton,and (cid:15) SB is the effective efficiency for the SB signal beinglocated at the ROI after various cuts.The solar- ν capture rates for individual neutrinosources are evaluated by using the neutrino responses( B ( GT ) , B ( F ) ) given by recent charge exchange reac-tions [13–15] and the neutrino fluxes from BP05(OP) [16].The CC neutrino responses, B ( GT ) , have been studiedby using high energy-resolution experiments at RCNPOsaka. The calculations were done as in Ref. [5] includ-ing the treatment of ν oscillations. The ββ , solar- ν in-teraction, and single β Q values and the solar- ν capturerates for Group A nuclei are shown together with thosefor Group B nuclei [5] in Table I. S t for Group A and B nuclei are plotted against theneutrino CC Q ν value in Fig. 2. The Group A nucleiof Se,
Mo and
Nd with small negative Q ν val-ues around -170 keV, have large solar- ν capture rates be-cause they are strongly excited by the pp neutrinos. Onthe other hand Group B nuclei of Ge,
Te and Xe TABLE I: ββ , CC, and SB Q values in units of MeV and solar- ν capture rates in units of SNU for selected ββ nuclei includingthe effect of oscillations. Column 8 gives S t for no oscillations. Q ββ is the ββ Q value, Q ν is the ν -CC Q value for the lowest1 + state, Q β is the single β Q value, S B is the B- ν capture rate, and S t is the total solar- ν capture rate. The background ratesfor β decay ( B SB ) and ββ (2 ν ) ( B ν ) are calculated for δ = 0 . . The small differences in solar- ν capture rates in this tablecompared those reported in Ref. [5] are due to a small arithmetic error in the Be flux calculations in that previous paper.Isotope ββ (2 ν ) τ / Q ββ Q ν Q β S pp S B S t no osc. S t B SB B ν years MeV MeV MeV (SNU) (SNU) (SNU) (SNU) events/ t y events /t y Se . × [17] 2.992 -0.172 3.093 257 10.0 672 368 4.42 0.15 Mo . × [17] 3.034 -0.168 3.202 391 6.0 975 539 0.11 1.56 Nd . × [17] 3.368 -0.197 3.454 352 15.5 961 524 0.12 1.00 Ge . × [18] 2.039 -1.010 2.962 0 5.0 15.7 6.3 0.03 0.005 Te . × [17] 2.528 -0.463 2.949 0 6.1 67.7 33.7 0.48 0.01 Xe . × [17] 2.468 -0.671 2.548 0 9.8 136 68.8 0.55 0.003 have rather small solar- ν CC rates because the thresholdenergy (- Q ν ) is large enough that the pp neutrinos cannot excite them. The pp neutrino contributions to thetotal capture rates for the Group A nuclei are around60% of the total, while the Be and B neutrino capturerate are around 30% and 3%, respectively.
FIG. 2: Solar- ν capture rates in units of SNU for current ββ nuclei are plotted against the neutrino CC Q ν value for thelowest 1 + state. S t is the total capture rate. Group A nucleihave a large S t . Group B nuclei have a small S t . . S t ( S N U ) -Q V (MeV) Mo-100Nd-150Se-82 Te-130 Xe-136 Ge-76
Group A Group B (cid:15) SB is evaluated as a function of δ for simple calorimet-ric detectors. The background rates are approximatelyproportional to the resolution, i.e. the width of the ROI. B SB for a fractional resolution of δ = 0 . are given inTable I.For the cases of Mo and
Nd, the ROI is locatednear the end-point energy at the tail of the single β -rayspectrum because Q ββ is very close to Q β . As a result, (cid:15) SB is much reduced and B SB is small for these nuclei. Inthe case of Se, however, the intermediate nucleus Brdecays primarily to the highly excited state at 2.648 MeV. Thus the ROI is located at the middle of the single β -rayenergy spectrum resulting in (cid:15) SB being relatively large,and a correspondingly large B SB . B SB for the Group Anuclei are also given in Table I. Se The oscillated solar ν capture rate on Se is calculatedto be 368 SNU. Br decays with a 98.5% branching ratioto the 2.648-MeV state in Kr and this was the onlystate considered in our calculations. The (cid:15) SB for decayof the Br product to populate the ROI was calculatedto be 2.6%, 5.2% and 15.7% for resolutions of δ = 0.01,0.02 and 0.05 respectively. The resulting SB spectrum isshown in Fig. 3. FIG. 3: The sum spectrum of β and γ -ray energies for thedecay of Br. The hatched region shows the ROI fraction fora δ = 0 . . . -3 F r a c t i o n o f E v e n t s ( a r b . un i t s ) Energy (keV) Mo The oscillated solar ν capture rate on Mo is calcu-lated to be 539 SNU.
Tc decays with a 93% branchingratio of to the ground state of
Ru and 5.7% to 1130-keV state. These were the only states considered in ourcalculations. The (cid:15) SB for decay of the Tc product topopulate the ROI was calculated to be 0.06%, 0.1% and0.3% for resolutions of δ = 0.01, 0.02 and 0.05 respec-tively. The resulting SB spectrum is shown in Fig. 4. FIG. 4: The sum spectrum of β and γ -ray energies for thedecay of Tc. The hatched region shows the ROI fractionfor a δ = 0 . . . -6 F r a c t i o n o f E v e n t s ( a r b . un i t s ) Energy (keV) Nd The oscillated solar ν capture rate on Nd is calcu-lated to be 524 SNU.
Pm decays to numerous excitedstates in
Sm. We included all states to a branchingratio of 1% for a total branching ratio of 99.7%. How-ever, the branching ratio to the ground state is uncertainand we took its value to be the upper limit value of 10%.There were 12 states included in our calculations. The (cid:15) SB for decay of the Pm product to populate the ROIwas calculated to be 0.08%, 0.2% and 0.7% for resolutionsof δ = 0.01, 0.02 and 0.05 respectively. The resulting SB spectrum is shown in Fig. 5. C. The Solar Neutrino CC Interaction
The B ν spectrum extends to energies higher than Q ββ . Therefore energy deposits from B solar- ν CC in-teractions at the ROI are possible. Hence, we considerCC reactions to the i th GT state in Z A at energy E i abovethe ground state with e − emission followed by γ decaysto the ground state in Z A. For simple calorimetric detec-tors, the sum energy of the CC produced e − energy ( E e ) FIG. 5: The sum spectrum of β and γ -ray energies for thedecay of Pm. The hatched region shows the ROI fractionfor a δ = 0 . . . -6 F r a c t i o n o f E v e n t s ( a r b . un i t s ) Energy (keV) and any emitted γ -ray energy ( E γ ) is measured. If thesum of these energies lies within the ROI at Q ββ , it willbe a background to ββ (0 ν ) . The resulting values for E ν and E e are obtained from the condition, E e + E i = Q ββ ,as; E ν = Q ββ + Q e , E e = Q ββ − E i , (4)where Q e is the electron capture Q value for the groundstate of Z A. Note for Se, Q e = 171.7 keV is the Q valuefor ν capture to the 75.1 keV meta-stable state in Br,not the ground state as for the other nuclei under consid-eration here and correspondingly for this case, E i is theenergy from the meta stable state. The 5 − spin-parityassignment of the Br ground state results in a negligi-ble contribution to the CC interaction. The backgroundrate due to B- ν capture is obtained as B CC = φ ( B, E ν )∆ E (cid:88) i σ ( E i ) , (5)where φ ( B, E ν ) is the B- ν flux per MeV at E ν and σ ( E i ) is the neutrino CC cross section [5] to excite the i th GT state at E i , and the sum extends over all GT stateswith E i ≥ Q ββ . B CC is proportional to the fractionalresolution δ = ∆ E/Q ββ because the fraction of the B- ν flux contributing to the ROI is proportional to the widthof the energy window.These B CC rates are smaller by 2-3 orders of mag-nitude than B SB rates as given in Table I. Thus onemay ignore the background contribution of B CC for thepresent nuclei of the Group A as was done for the solar- ν backgrounds for the nuclei in the Group B [5]. III. SUMMARY AND DISCUSSION
The evaluated background rates for simple calorimet-ric detectors given in Table I are approximately 220 δ /ty for Se, 5.5 δ /t y for Mo and 6.0 δ /t y for Nd.In case of δ = 0 . , they are, respectively, 4.42/t y, 0.11/t y and 0.12/t y. For the case of δ =0.05, they are, re-spectively, 11/t y, 0.28/t y and 0.30/t y. Thus solar- ν backgrounds are serious for Se experiments proposingto study the IH ν mass region unless the fractional reso-lution is reduced below 10 − .For experiments with modest resolution, ββ (2 ν ) mayalso be a background at the ROI. Since this background( B ν ) and that of B SB both depend on resolution, wecompare the two. Using an approximation [21] for thenumber of ββ (2 ν ) events that populate in the ROI, thenumber of background events for 2% fractional resolu-tion is also given in Table I. Because the ββ (2 ν ) halflives vary by a factor of ≈
300 for these 6 isotopes, thisbackground varies greatly also. For
Mo and
Nd,and to a lesser extent Se, this is a significant issue forexperiments approaching the ton scale and B ν dominatesover B SB . Therefore, the resolution of Mo and
Nddetectors should be around 0.01 or less to avoid seriousbackground from ββ (2 ν ) to study the inverted hierarchy ν mass region. For Ge,
Te, and Xe B ν is small.It is noted that fractional resolution of around 2% orless is required for the Te and
Xe experiments toreduce B SB in order to study the inverted hierarchy massregion.So far, we have discussed selection of the true ββ (0 ν ) signal and rejection of the background by only energyselection at the ROI in simple calorimetric detectors.Improvement of the energy resolution reduces the back-ground rates by reducing the width ∆ E of the ROI en-ergy window. There are also several techniques to reduce (cid:15) SB and hence B SB . Each technique depends on specificdetector configurations and thus we do not discuss suchdetails in the present paper, but briefly describe possiblereductions in general.For solar- ν interactions on Se and
Nd, the inter-mediate nuclei of Br and
Pr decay primarily by emit-ting β and γ rays. One can reduce B SB by measuringthe spacial distribution of the energy deposits, since γ rays will interact in a much larger volume of the detectorthan the ββ (0 ν ) signal. If detector segments are small,the γ rays detected outside the segment can be used toreject B SB and B CC . Signal selection by time correlation (SSTC) can beused to reduce solar- ν background rates [2]. Since thehalf-life of the intermediate nucleus of Tc is only 16sec, B SB in Mo ββ experiments can be rejected bydelayed anti-coincidence with the preceding CC e − . Thistechnique, however, is not useful for Se and
Nd be-cause of the long half-lives (35.3 hr and 2.68 hr, respec-tively) for the intermediate nuclei. In other wards,
Mocan be used to study pp solar- ν CC e − by a delayed co-incidence with the successive SB β rays [7], but Se and
Nd would be less effective as solar ν experiments.Tracking detectors as used for real-time Se and Mo ββ experiments can be used to select ββ signals by mea-suring the individual two β rays [19, 20], and to reject B SB with only one β ray. However, development of largetracking chambers with multi-ton scale enriched ββ iso-topes is a real challenge for future.Finally, it should be remarked that the ν -mass sen-sitivity for ββ experiments with N T t y of ββ isotopeexposure is given by [2, 4, 21]; m ν < . meV M ν (cid:114) AG(cid:15) (cid:18)
BN T (cid:19) / (6)with constant G , A , M ν , (cid:15) , B being the phase space inunits of − /y, mass number, nuclear matrix element,detector efficiency, and background rate per year inthe ROI per ton of ββ nuclei. Therefore one needs tooptimize a number of key elements when planning future ββ experiments with the background being critical.The solar- ν background discussed here is just one ofmany components of the background, that needs tobe considered for high-sensitivity ββ (0 ν ) experimentshoping to cover the IH ν -mass region. Acknowledgments
We acknowledge support from the Office of NuclearPhysics in the Department of Energy, Office of Science.We gratefully acknowledge the support of the U.S. De-partment of Energy through the LANL/LDRD Program. [1] S. Elliott S and J. Engel 2004
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