High-precision atomic mass measurements for a CKM unitarity test

International Journal of Mass Spectrometry 349–350 (2013) 69–73

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High-precision atomic mass measurements for a CKM unitarity test Tommi Eronen a,b,∗ , Ari Jokinen b a b

Max-Planck-Institute for Nuclear Physics, Saupfercheckweg 1, 69117 Heidelberg, Germany Department of Physics, P.O. Box 35 (YFL), FI-40014 University of Jyväskylä, Finland

a r t i c l e

i n f o

Article history: Received 18 February 2013 Accepted 1 March 2013 Available online 26 March 2013 Keywords: CKM unitarity Penning trap mass spectrometry QEC value

a b s t r a c t The Cabibbo–Kobayashi–Maskawa (CKM) quark-mixing matrix describes the transformation of quarks from weak-force eigenstates to mass eigenstates. The most contributing element in this matrix is the up-down matrix element Vud , derived in most precise way from the nuclear beta decays and in particular, from decays having superallowed 0+ → 0+ decay branch. What high-precision mass spectrometry community can offer are decay energies of such decays derived from parent–daughter mass differences, which are ideally, and in almost all cases, determined with Penning trap mass spectrometry directly from parent–daughter cyclotron frequency ratio. Typically frequency (and thus mass) ratios are determined with 10−9 relative precision, which allows decay energies to be determined within 100 eV-level. © 2013 Elsevier B.V. All rights reserved.

1. Introduction In the Standard Model of particle physics, the Cabibbo– Kobayashi–Maskawa (CKM) matrix is a unitary matrix that describes transformation of the three generations of quarks between weak interaction eigenstates and mass eigenstates [1,2]. This 3 × 3 matrix should be unitary and deviations from it would implicate existence of physics beyond the Standard Model. The most stringent test for the unitarity of the CKM matrix is the sumsquare of the top-row elements which should equal to unity: 2 2 2 Vud + Vus + Vub = 1.

(1)

The first element, the up-down matrix element Vud , is by far the most precisely determined element of the CKM matrix with a value of 0.97425(22) [3,4]. The square of Vud is 0.94916(43) and thus it has about a 95% contribution to the unitarity test shown in Eq. (1). The second element of the test, Vus , has so far been determined either from kaon, hyperon or tau decays. Currently adopted value for it is 0.2252(9) [5] corresponding to about 5% contribution to the unitarity test but surprisingly, a similar impact to the uncer2 . The third element, V , is very small (<10−2 ) and tainty than Vud ub has negligible contribution to the top-row unitarity test. Currently 2 + V 2 + V 2 = 0.9999(6) is in perfect the top-row square-sum Vud us ub agreement with the expectation and thus excludes physics beyond the Standard Model.

∗ Corresponding author at: Max-Planck-Institute for Nuclear Physics, Saupfercheckweg 1, 69117 Heidelberg, Germany. Tel.: +49 6221 516 683. E-mail addresses: [email protected], tommi.eronen@jyu.fi (T. Eronen), ari.s.a.jokinen@jyu.fi (A. Jokinen). URL: http://www.jyu.fi/fysiikka/en/research/accelerator/igisol (A. Jokinen). 1387-3806/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.ijms.2013.03.003

There are several ways to derive Vud but by far, the most precise value of Vud comes from the superallowed beta decays. These are nuclear decays of spin-parity 0+ to 0+ transitions between isospin T = 1 triplet states either from Tz = −1 to Tz = 0 states or from Tz = 0 states to Tz = +1 states. Several such transitions exist and currently some 13 of them are known with comparable precision and contribute to the world average value. Vud can also be determined from neutron decay [6]. Although neutron decay is free of nuclear structure corrections, an additional correlation term (ratio between vector and axial-vector couplings) is needed to derive Vud from a decay of a neutron. As of now, Vud from neutron decay is inferior in precision to the Vud derived from superallowed beta decays. Also pion beta decay offers a way to obtain Vud from the decay rate [7]. Although the pion beta decay is a clean observable, there’s one major experimental difficulty which is the very small ˇ decay branch on the order of 10−8 . Recently, Vud has also been derived from ˇ decays of mirror nuclei [8]. While the superallowed beta emitters have T = 1, the mirror nuclei are isospin T = 1/2 doublets having both vector and axial-vector currents. Since the axial-vector current is not conserverd in nuclear beta decay, an additional parameter is needed to extract the mixing ratio between the Gamow–Teller and Fermi contributions. Currently only few transitions are known with moderate precision and the derived Vud has only modest precision compared to superallowed transitions but compares to that of neutron decay. For determining Vud from any of the aforementioned decay modes requires both experimental and theoretical effort. In case of nuclear superallowed beta decays one needs to measure halflife, branching ratio and the decay energy and on theoretical side, nuclear structure and radiative corrections are needed. This contribution concentrates on nuclear superallowed beta decays and especially on their decay energy measurements with

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Penning traps. During the past ≈10 years, the decay energy measurements have been dominated by measurements with Penning trap mass spectrometers that can provide decay energies by measuring the masses of the decay parent and daughter. 2. Superallowed beta decays Due to their simplicity and symmetry properties, superallowed beta decays have been intensively studied for more than five decades and contribute to many fundamental physics tests. The superallowed decays occur between nuclear 0+ states, which renders the process rather easy to describe. The transition matrix element is simple and consists only of vector current. Any beta decay, including the superallowed one, can be described with a comparative half-life or an ft value. For ordinary beta decays, these ft values expand several orders of magnitude but for superallowed decays it should be, according to the conserved vector current (CVC) hypothesis, the same. The ft values for superallowed beta emitters are given by ft =

K GV2 |MF |2

= constant,

(2)

where K is a constant, GV the vector coupling constant for semileptonic weak interactions and MF the Fermi matrix element. In reality, small corrections are needed, for example, due to the fact that isospin is not an exact symmetry in nuclei. The corrected ft values, denoted Ft, are usually written as [4] Ft = ft(1 + ıR )(1ıNS − ıC ) =

K 2GV2 (1VR )

,

(3)

where VR is the common transition-independent radiative correction while the rest of the correction terms are different to each superallowed transition. ıR and ıNS are radiative corrections and ıC isospin-symmetry-breaking correction. The corrections modify the ft value approximately 1%. 2.1. ft-values The ft values values depend on three experimental quantities, as illustrated in Fig. 1. These are the total transition energy, QEC , the half-life t1/2 of the parent state and the branching ratio R to the daughter 0+ , T = 1 state. While the partial half-life t depends on the t

parent state half-life t1/2 and the branching ratio R, i.e., t = 1/2 , the R 5 . Constatistical rate function f depends strongly on the QEC , f ∝ QEC sequently, relative precision requirement for the QEC value is thus five times larger than for the other two experimental quantities. 2.2. Current status Although the superallowed beta decays have been extensively studied for some six decades already, the field is still going strong both experimentally and theoretically. The improvement in precision has been tremendous, not least in the recent decade. Currently, Ft values of the ten most precise superallowed transitions are now known to precision of about 0.1% and three more to better than 0.3%. These sets are the often quoted “best 10” or “best 13” superallowed emitters. Several more cases are around the corner and are expected to be included to the set(s) in the near future. The last decade has shown that precision of all necessary quantities can still be improved. Most notably the introduction of Penning trap mass spectrometry for determining decay Q-values from masses [9], halflife and branching ratio measurements from pure and high-yield facilities (see e.g., [10–12]) has pushed the ft value precision to such precision that theoretical corrections are now the limiting factor in the corresponding Ft values.

Fig. 1. A typical T = 1 isospin triplet, here for A = 26 ions. The isobaric analog states m (26 Si and 26 Mg ground states and the isomeric state 26 Al ) are marked. The decay of Tz = −1 ground state of 26 Si has non-negligible branch to the non-analog states m while the Tz = 0 nucleus, 26 Al , decays solely to the ground state of 26 Mg.

The most recent compilation of experimental and theoretical work related to superallowed beta emitters is by J.C. Hardy and I.S. Towner from 2009 [3]. Since then, several new and more precise measurements have emerged. On one hand, already well known cases (such as 26 Alm ) have been improved even more. And on the other, new cases where precision of one or more quantities have been poor so that that emitter could be added to the set of wellknown superallowed beta emitters. One good example is the Tz = −1 emitter 38 Ca. Recently, both half-life [10] and Q-value [13–15] have been measured to better than 0.1% precision and thus only the branching ratio is needed with sufficient precision in order to add 38 Ca to the set of well known superallowed beta emitters. 3. Superallowed QEC values As already noted in the previous section, QEC values need to have relative precision five times the precision of the other experimental quantitities in order to have similar error contribution to the ft value. Before the turn of the millenia, QEC were determined with nuclear reactions such as (3 He, t), (p, n), (p, t), (3 He, n) or combination of (p, ) and (n, ) reactions (see Ref. [3] and references therein). Also, a series of QEC value difference measurements [16] with rather high precision linked several QEC values together. This kind of difference method did not produce absolute QEC values but rather precise links of QEC values. The precision of reaction measurements prevailed until 2004 when first QEC values were determined from Penning trap mass spectrometry [17,18]. Although the new Penning trap results were only of comparable precision to the older reaction-based result, the Penning traps offer very unique capability of measuring QEC value of any nuclei. Cases like 74 Rb [17], which is already three beta decays away from the valley of beta stability, are impossible to measure with reactions but given enough production yield and sufficient contamination supression a breeze for Penning traps.

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Fig. 2. A chart of most superallowed beta emitters up to A = 74. Nuclei having its Q-value measured with a Penning trap mass spectrometer have been indicated. The nuclei marked with bold label belong to the set of “13 best known transitions” which have a significance in the current world-average Ft value.

By the end of 2012, most of the nuclei that have been measured with reaction-based techniques had also been measured with online Penning traps. As of the beginning of year 2013, only the QEC value of 14 O remains to be measured with a Penning trap from the set of “13 most precisely measured QEC values” ranging from 10 C to 74 Rb. Many heavy T = −1 above 42 Ti will remain out of reasonable z reach, at least for the near future. Fig. 2 shows most of the superallowed ˇ emitters up to A = 74. Most of them are already known to such a precision that they contribute to the world average Ft value; some of them are potential candidates which can contribute to the world average value in the future once also half-life and superallowed branching ratio are measured to high precision. 4. Q value measurements with Penning traps The most recent and currently the most precise atomic mass measurements for CKM unitarity tests have been performed with Penning traps. A comprehensive description of Penning trap mass spectrometry is given elsewhere within this special issue in an article by J. Kluge and references therein. As any Penning trap mass spectrometry experiment, the mass of the ion is determined via the cyclotron frequency c of the ion of interest. In case of short-living radionuclei such as superallowed beta emitters, the c frequency is determined from the sideband frequency [19,20]. + + − = c =

1 q B, 2 m

(4)

where + and − are the trap-modified cyclotron and magnetron frequencies, respectively, and q/m the charge-over-mass ratio of the ion of interest and B the magnetic field. By measuring the frequencies for both the beta decay parent and daughter ions, the Q can be determined (for singly charged ions) to be Q = (r − 1)(md − me ) + p,d , where r =

c,d c,p

(5)

is the cyclotron frequency ratio of the superallowed

daughter and parent ions, md the mass of the decay-daughter atom, me the mass of an electron and the term p,d accounts for

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the atomic electron binding energy differences of the parent and daughter atoms. Due to the fact that decay parent and daughter are mass doublets having the same atomic mass number, the cyclotron frequency ratio deviates from unity by less than 10−3 . This effectively cancels out any mass dependent frequency shifts in the measured frequency ratio and finally in the obtained Q value. Such a doublet technique has allowed boosting the precision (Q/m) to the level of few ×10−9 [21] while “ordinary” on-line Penning trap mass spectroscopy typically reach only 10−8 level precision [22,23]. A mass measurement with a Penning trap requires a clean sample (or even only a single) of ions. Impurities cause frequency shifts and deterioration of the measured signal [24]. At worst, signal from the ion of interest can be totally swamped by the signal from the impurities. Many of the isospin T = 0 nuclei have long-living highspin isomeric states, which are produced simultaneously with the superallowed 0+ states. Like in 26m Al case shown in Fig. 1 when 26m Al is produced, also the ground state of 26 Al is present. In cases like 54 Co and 50 Mn, where contaminant isomers (at about 200 keV) are close by, new cleaning methods were called [25] to remove the unwanted isomers. Also, the short half-lives of the superallowed beta emitters bring additional challenges. Observation times can typically be only few half-lives without excessive loss of ions. Already 38 K has a half-lives less than one second (which is a typical observation time in on-line Penning trap mass spectrometry) and 74 Rb is already below 100 ms. Some years ago, with the introduction of Ramsey’s method of timeseparated oscillatory fields to the Penning trap mass spectrometry [26,27], precision was significantly boosted in the time-limited Q value measurements. Since the introduction and the availability of the fit function lineshape, the Ramsey’s method of time separated oscillatory fields has been routinely used in almost all Penning trap measurements where high precision is required. Recently, precision Q/M of 10−9 has been reached which typically corresponds to Q/Q of better than 1 × 10−5 . It should be noted, though, that not all Q values have been measured with the doublet technique that is ideal for Q value measurements. Especially ISOL facilities, at least in this respect, suffer from chemical selectivity. For instance at 74 Rb Q value measurement at ISOLTRAP [17], different ion source was needed for the decay-parent and decay-daughter and thus the masses of the parent and daughter were measured in two different beam time periods. Before the Penning traps became the main tool for superallowed beta Q value measurements, the Q values were measured with nuclear reaction based methods. Typical reactions include (p,n) threshold measurements, (3 He,t) reactions and pairs of (n,) and (p,) measurements (see e.g., [3] for a comprehensive list). The most recent reaction-based measurements, e.g., 14 N(p,n)14 O [28] reported Q-value precisions Q/Q on the level of 4×10−5 . Currently four Penning trap facilities have contributed to the QEC value measurements: ISOLTRAP at CERN [23], Canadian Penning trap (CPT) at Argonne National Laboratory at Argonne [29], JYFLTRAP at the University of Jyväskylä [30], LEBIT at Michigan State University [31] and TITAN at TRIUMF [32].

5. Discussion The early Penning trap measurement in the beginning of the 00’s concentrated on nuclei that could be later included to the set of well known emitter once also the other quantities would be measured to comparable precision. These were 18 Ne [33], 22 Mg [18,34] and 74 Rb [17] and consequently 22 Mg and 74 Rb could be included to the set of “13 best known emitters”. Of those, 18 Ne is still missing a high-precision branching ratio measurement. Similarly, Q values of

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Butler (1961) Barden (1962) Roush (1970) White (1977) Tolich (2003) -2.0

14

O

-1.0

0.0

1.0

2.0

Deviation from Hardy2009 (keV) Fig. 3. The most precise Q values o the 14 O ground-state-to-ground-state decay. The three top ones are from 12 C(3 Hen, )14 O measurements and the two others are from 14 N(p,n)14 O threshold measurements. The vertical line denotes the average adopted by Hardy and Towner [3], with the grey band giving the 1 scaled-up uncertainty (±0.23 keV), which accounts for the evident discrepancies among the measurements. Table 1 New Q values published after the compilation of Hardy and Towner in 2009 [3]. The nuclei marked with a bullet (•) are already included to the set of 13 best known superallowed emitters that contribute to the world average Ft value. Parent nucleus

QEC (keV)

Ref.

10

3648.12(8) 4840.85(10), 4841.6(29) 5491.662(47) 6061.83(8) 6044.223(41) 6612.12(7) 7016.83(25) 7052.44(10) 10416.8(39)

[14] [38,39] [40] [14] [38] [14] [41] [14] [42]

C 26 Si 34 Cl 34 Ar 38 m K 38 Ca 42 Ti 46 V 74 Rb

• • • •

• •

26 Si, 30 S, 38 Ca, 42 Ti, and 66 As are now well known but either half-life

or branching ratio is still missing [3]. Another set of measurements concentrated on improving Q values that were already rather precisely known with reactionbased measurements. The most controversial case was 46 V, for which Penning trap measurements deviated for more than 2 from the reaction based measurements [29,35,36]. Later, similar deviations were found also in 42 Sc, 50 Mn and 54 Co [21,35] which finally resulted in rejection of the results reported in [36]. Later, a remeasurement of 46 V Q value was done using partly the same equipment than in [36], which gave a value that was much closer to the Penning trap measurements [37]. Other Penning trap measurements were in agreement with older reaction-based values; also agreement between the different experiments have been rather good like in the case of 38 Ca, which was measured with three different trap facilities and the results agree perfectly [14,15,27]. What still remains to be measured with a Penning trap from the set of “13 best known superallowed emitters” is 14 O. Its Q value is measured with reactions down to Q/Q = 3 ×10−5 or 170 eV and could potentially be improved by a factor of five using mass doublet-technique Penning trap mass spectrometry. What is striking here is that the precision of the adopted QEC value has only 230 eV precision. This is due to mutually disagreeing experimental values as shown in Fig. 3. Since the publication of the most recent compilation of superallowed input data by Hardy and Towner [3], there have been several new Q value measurements, summarized in Table 1. This development already shows that the field of superallowed beta decays is still very active.

but some other quantity. What still remains to be measured with Penning traps is 14 O and new cases like Tz = −1 emitters above 42 Ti and heavy Tz = 0 emitters like 70 Br, 78 Y and above. Even though Q values of these new emitters could be measured, it will take years or even decades until reasonable precision in half-life and branching ratio is achived - let alone of theoretical corrections which are already known to be large for 62 Ga and heavier. Future Q value measurements could well utilize advanced techniques such as charge breeding, which was already demonstrated in the case of 74 Rb at TITAN [42]. This helps to either increase the precision or decrease the measurement time, which is of the essence with exotic superallowed emitters as the half-lives on the heavy nuclei are approaching 10 ms. What was also recently demonstrated was nuclear mirror transitions for contributing to the CKM unitarity test [8]. While the precision in the superallowed beta decays is limited by the theoretical corrections, in mirror decay the precision is still predominantly limited by the experimental data. Although it is the Fermi/Gamow–Teller ratio that is the least known in these decay, also improvements in Q values are called for. Acknowledgments This work has been supported by the Academy of Finland under the Finnish Centre of Excellence Programme 2006–2011 (Nuclear and Accelerator Based Physics Programme at JYFL). References [1] [2] [3] [4] [5]

[6] [7]

6. Summary and outlook In the past decade, Penning trap mass spectrometry has helped to further decrease the uncertainties in the Q values of superallowed beta emitters. In all measured cases the obtained precision is in such a level that contribution of the particular transitition to the CKM unitarity test is not limited by the precision in the Q value

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