The weak decays of light hypernuclei

NUCLEAR PHYSICS A Nuclear Physics A639 (1998) 261c-268~

ELSEVIER

The weak decays of light hypernuclei V.J.

Zepsa

aUniversity

for

the E788 Collaboration’

of Kentucky,

Lexington,

KY 40506 USA

There has been recent progress on both theoretical and experimental frontiers to constrain models of weak interactions between baryons. The status of the analysis of YHe decay rates is discussed, comparing new results with other recent and old measurements. In addition to total decay widths, kinetic energy distributions and some preliminary coincidence spectra are presented. These coincidences have proven to be essential to the interpretation of the weak-decay processes. In light of these new results, there is now consensus that complementary measurement of the decays of :H is essential to address some basic questions, such as the validity of the AI = f rule for nucleon-stimulated weak decay (l-51. Prospects for such a measurement are also discussed. 1. INTRODUCTION In free space, the A-hyperon decays predominantly via the two mesonic decay channels: A --+ n7r” (35.8%) and A + p7r- (63.9%). A s with the decay of other hyperons, the decay ratio is the result of an empirical (with no universal explanation [6-81) AI = a rule. Our knowledge of the weak ANT vertex is owed to the precise determination of these decay widths, which are known to be dominated by this empirical rule. Once embedded in a nucleus, the mesonic decays are now subject to nuclear phase-space distortions, among other effects. In heavy hypernuclear systems, in fact, the pionic decay widths are reduced by several orders of magnitude due to the small momentum transfer to the decay nucleon and the high Fermi energy of the nuclear surface to which this nucleon must escape. At the same time, however, an alternative AS = 1 process becomes increasingly important; namely nucleon-stimulated weak decay, AN + NN. This process is readily distinguishable from the mesonic decay modes because of the large available energy (MA - MN = 176 MeV) for the final state nucleons. In meson-exchange models [9], these non-mesonic decay mechanisms are governed not only by the long-range one-pionexchange process, but by short-range weak interaction vertices involving heavier mesons, such as ANp or NNK; these vertices are not probed by the free hyperon decays. Predictions for these coupling strengths are usually calculated based on W(3) symmetry ideas and known hyperon free-decay widths [9]. However, there are models that suggest that the short-range AN + NN amplitudes are dominated by the direct-quark processes [lO,ll], in which no intermediate meson is present in the interaction. Such direct processes are not expected to adhere to the AI = i rule. ‘An E788 collaboration

list can be found in Ref. [5].

0375-9474/98/$19.00 0 1998 Elsevler Science B.V. All rights reserved PI1 SO37S-9474(98)00282-6

Kl Zeps/Nuclear

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Physics A639 (1998) 261c-268~

There is no one hypernucleus that probes the richness of the weak baryon-baryon interaction. A systematic study of the isospin and A dependence of the hypernuclear decay modes is the only means by which to effectively probe these weak interaction processes (see Ref. [12] for a recent review). 2.

S-SHELL

HYPERNUCLEAR

DECAY

The total decay width of a hypernucleus non-mesonic decay modes, r total =

I- mesonic

+

can be defined in terms of its mesonic and

rnon-mesonic (1)

=‘r,-+r,,+r,;+w.

In this representation, ~~~ represents the pionic decay mode for charges & = 0, &1, characterized by the emission of the particular pion. r, represents the proton-stimulated decay width and is characterized by the emission of energetic protons above the Fermi energy. Likewise, the neutron-stimulated decay width r, is characterized by the emission of energetic neutrons. In this case, however, one must recognize that both the neutron- and proton-stimulated decays produce neutrons with multiplicities two and one respectively. In the simplest analysis, rJTp = i(N,/NI, - l), where N,@) are the efficiency corrected numbers of energetic neutrons (protons) observed. l?,,,b refers to the possible many-body decay mechanisms in which multiple nucleons participate in the decay process. rrnb and r,+ have traditionally been ignored in the analysis and assumed negligible. We discuss some of the implications later. The remaining two-body decay modes are generally how the hypernuclear decays are classified. From an experimental point of view, delineation between nucleon-stimulation and multi-body processes is not trivial. To detach the experimental results from theoretical interpretation, it is necessary to provide the results in complete kinematic detail. We also note that 7r+ emission is inherently a multi-body decay mode (often referred to as nucleon-stimulated pionic emission), which must have isospin counterparts in the rTT-and no channels. For accurate interpretation of these decays, it is clear that kinetic energy distributions are needed. In the end, a major goal of the study of hypernuclear decay is to determine properties of the underlying AN -+ NN interaction. To do so, one must know the relative initial and final states of the weakly interacting baryons. In nuclei the A hyperon is not Pauli blocked, thus hypernuclei decay with the A hyperon initially in the lowest 1s state. Since all nucleons can participate in the nucleon-stimulated decay, then, in order to achieve the stated goal, it is best to consider systems that confine the nucleons to only a few orbitals. Further complications arise as one increases A, because the high probability of final-state interactions dilutes the correlation between nucleons observed and nucleons responsible for the decay. Given these constraints, the lightest hypernuclei (A 5 5), in which all nucleons are predominantly in 1s orbits, should be studied in kinematic detail, while only the lifetimes for the heavier systems (A > 16) are likely to be interpretable. In the intermediate p-shell regime, the kinematic details are essential, if one wishes to seperate neutron- from proton-stimulation. In the case of s-shell systems, Fig. 1 shows the spin-isospin character of the initial (AN) and final (nN) states. The I = 1 final states are accessible to both proton- and neutron-

VJ Zeps/Nuclear

AN Initial

263~

Physics A639 (1998) 261c-268~

States: is”

nN Final States:

r-i&

/;“\\ 3Pc

3Pi, I”S,

3Di

I=0

I=1

Figure 1. Spin-isospin

‘PI

selection rules for the AN -+ nN process in Is-shell hypernuclei.

Table 1 Allowed initial states for Is-shell hypernuclei. Hypernucleus An AP :He

3s1,

4,He

lSCl 3S1, ‘So 3S1, l&l

:H 1H

‘sl

3s1,

l&l

3S1, lSll ‘SO 3% l&l

stimulated decays, while the I = 0 final states are available only for proton-stimulated decay. Table 1 shows the allowed initial state for s-shell hypernuclei. By comparison of the specific decay channels between these hypernuclei, one can establish the strengths of the decays from specific AN initial states. When coupled with detailed finite-nucleus calculations that take into account the differences in the initial- and final-state phase spaces, one can determine the strength of the fundamental AN -+ nN weak interaction processes. Few such finite nucleus calculations have been performed to date [13-171, owing in part to the lack of high-quality data. 3. E788:

MEASUREMENT

OF THE

DECAY

WIDTHS

OF 4,He AND

6,He

As part of a program to measure detailed properties of s-shell hypernuclei, the decay branches for :He and :He have been remeasured using the LESB-II kaon beamline of the AGS at Brookhaven National Laboratory. Incident 750 MeV/c kaons were used on both 4He and 6Li targets to produce :He and aLi, resp ectively in the *Z(K-, 7r-)iZ reaction. The ground state of :Li is proton unstable. Thus, decay particles measured from this reaction result from the subsequent decay of iHe. Pions from the production reaction are detected near 0” (iHe) and 10” (!Li) in the Moby Dick spectrometer, with an excitation energy resolution of the produced hypernuclear system of about 4.5 MeV FWHM. Fig. 2 shows the experimental arrangement used to detect the decay particles. The PID and energy of the decay protons and charged pions are determined by combining the crude range information from all out-of-beam detectors with the measured rate of energy loss (dE/ds) and the measured time-of-flight (TOF) between the Decay-Timing and TOF scintillators. The high-quality timing scintillators near the target determine the lifetime of the hypernucleus as well. Unlike bubble-chamber and emulsion experiments, large volume (z 1.42 m3) neutron detector arrays are placed near the target to directly

264~

Figure 2. Experimental

FL Zeps/Nuclear

Physics A439 (1998) 261c-268~

setup for the ;He experiment.

measure the decay neutrons. The neutron energies are determined by time-of-flight. Thus, E788 measured directly Ftotd, while Fr-, r,, r, are extracted from the measured pion, proton, and neutron kinetic energy spectra for the decay particles. The r+ fraction is not distinguished from the K- distribution, but is known to be small, F,+/F,= 0.043 & 0.017% [18]; also a significant fraction are below our detection threshold. F,o is inferred by subtraction; the 7r” decay rate is thus more poorly determined, and may be systematically over-estimated due to multi-body decay modes. Along with branching width measurements, the back-to-back arrangement allows for tagging nucleon-nucleon coincidences. These coincidences provide additional insight into the decay mechanism, in particular multi-body effects, that have enjoyed much theoretical speculation as the possible source for the large observed l?,/Fp ratio seen in both IHe and fi”C [19,20]. The analysis of the :He data is nearing completion, while some :He has been published [21]. A significant amount of ;He data is still to be analyzed. Present results of our complete reanalysis of the :He data are shown in Table 2 along with other measurements of s-shell hypernuclear decay ratios. Before these results are finalized, a cross-check with the updated Monte Carlo neutron detection efficiency is needed. These updated corrections are not expected to alter significantly this analysis. 4. INTERPRETATION

OF ;He

AND

%He RESULTS

Within errors, there now appears to be reasonable agreement amongst the various weak decay measurements that have been made on :He using both counter and bubble chamber methods. We find F,/F, to be even smaller than previously thought, owing in part to the methods by which the older data sets were interpreted [23,24]. Without direct neutron measurements, energy cut-offs were placed on observed protons to determine the neutron-stimulated events; all protons observed below the cut-off were assumed to

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b!J Zeps/Nuclear Physics A639 (1998) 261c-268~

Table 2 Measured decay properties of light hypernuclei. Decay ratios This work Outa et al. [22] :H rtotlrh Ill,/I,-

Older results

References

1.36f;:f:

r(v +4He)/I’,‘1,He rtotirh I, /I,,, Ina /IA r,- /IA

1.07 0.57 0.61 0.26

f f f f

0.11 0.09 0.08 0.03

I+ /I,-

2.3 f 0.4

1.03+::,,12 0.515 Zt 0.035 0.53 f. 0.07 0.33 Zt 0.05

0.26 f 0.13 0.69t;:;;

WI 1251

1.15 & 0.48

i41*

2.49 f??0.34 2.20 0.39

ii:;

0.043 % 0.017

P81

0.51 f 0.16

0.56 * 0.09

PI*

0.06 % 0.40

0.40 f 0.13 0.29 0.15

ii:;

1.03 0.18 0.44 0.21 0.20 0.92

[211 II ,t 1, >, ,, ,,

1.59 f 0.20

r,+/I,IP/IA In/IA

0.16 rt 0.02 0.04 f 0.02

0.16 f 0.02 0.01 f 0.05

I,,/I,-

0.77 f 0.15

rap

0.25 < 0.40 f 0.13

;He rtot /IA rxo /IA I=- /IA IP/IA In/IA I,,/I,-

r4-k * reanalysis

i f i f. f f

0.08 0.20 0.11 0.07 0.11 0.31

0.93 f 0.55 of many older measurements.

be spectator protons. If properly fit, some of these protons could likely be ascribed to proton-stimulation as the low-end tail of the Fermi distribution. Furthermore, these older data sets have clearly underestimated uncertainties, as the neutron and proton numbers were taken as uncorrelated and the errors were not increased when subtracting out contamination estimates. Thus, care must be taken in interpreting these old results or combining them with newer results, since many assumptions have gone into those numbers. These older numbers must be reanalyzed in a consistent fashion to be reliably accumulated with the newer data sets. r,(4,He) is indeed small, as predicted by most weak interaction models. This would indicate that the potentially large neutron-stimulated decay fraction seen in the decay of :He would result predominantly from the parity-violating 3Sr+3Pr transition. Analysis of the remaining :He data should constrain the neutron-stimulated fraction at a comparable level to the :He data set, and set the neutron-stimulated decay fraction unambiguously. Should the large effect persist, it would be most important to compare the neutron-

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Physics A639 (1998) 261c-268~

0

Figure 3. Opening angle (77) distibution for all neutron-proton coincidences. The dashed line indicates the geometrical acceptance for neutrons and protons that have no angular correlation. stimulated decay from XHe to that from ,,4H, as both have the same neutron-lambda initial-state correlations. Excluding final-state and multi-body effects, the nucleon pairs appear within a narrow back-to-back cone smeared only by the Fermi momentum of the initial state. However, if there are significant final-state or multi-body effects, then a large fraction of the events will be distributed according to three-body phase space kinematics, which do not favor high energies or back-to-back angles. Fig. 3 shows the distribution of all neutron-proton coincidences. As can be seen, there is a strong enhancement of events peaking at cos n = -1. We identify these as twobody (Ap + np) decay coincidences. If we further evaluate the sum kinetic energy of the two nucleons (Fig. 4), these back-to-back events roughly follow what one expects from intranuclear motion of the interacting nucleons. Additional modeling is needed to

Figure 4. Sum energy for all neutron-proton events with cosn < -0.8 (> -0.8).

coincidences.

The solid (dashed)

line is for

U Zeps/Nuclear Physics A639 (1998) 261c-268~

26lc

fully support this assertion. It is clear, however, that the events away from cosv = -1 have much lower sum energies for the pair. These events appear to be consistent with spectator neutrons in coincidence with participant protons. Since the total number of observed protons is N, = 592, we expect the number of neutron-proton coincidences to be N, = en . R, . N, = 78, where E, z 0.22 is the intrinsic neutron detection efficiency of each neutron detector array, Q, M 0.6 is the effective neutron solid angle for tagged proton events. For the latter number, we use the observed angular spread of the backto-back peak folded with the calculated geometrical coincidence solid angle. We observe N, = 66flO. From this analysis, we conclude that any significant final-state interactions or multi-body effects are at a level of 15 f 15% of the two-body decay width. A similar neutron-neutron coincidence spectrum has been analyzed. In this case, the number of true coincidences is expected to be extremely low, owing to the smallness of both Pn and en. A crude upper limit of five back-to-back events were seen with sufficient sum energy. From this, a strict upper limit on I,/I’, = (Nnn/Nnp)/en < 0.40 is set. Another factor of two neutron-neutron coincidence data exist, but need to be calibrated and analyzed before they can be added to these results. We note that a similar coincidence analysis with the ;He should prove most convincingly the evidence for neutron stimulation, which up to now has been marginal. 5. USING

THE

NMS

TO STUDY

iH

The analysis of existing data has indicated the need for non-mesonic decay measurements from :H. The recent transfer of the NMS (neutral meson spectrometer) to Brookhaven has afforded a unique opportunity to study :H via the isospin analog 4He(K&,ti,rr0)~H reaction. The NMS is used to measure the hypernuclear production by precision measurement of the decay photons resulting from rr” + yy. Talks by others at this conference have demonstrated the utility of exploiting this device for hypernuclear studies [26]. The NMS acceptance matches well with the out-of-beam detection and count-rate requirements. A similar geometry to that of E788 can be employed, in which the Moby Dick spectrometer at 0” is replaced with the NMS set in a fore-aft arrangement (opening angle of around 55”) centered around 90” below the beam. Table 3 indicates the estimates for the number of events that can be accumulated with 600 hours of production running at the AGS C8 beamline. The important non-mesonic events are calculated as-

Table 3 Expected counts for decay of :H assuming duction is 4 x 104. Decay mode rj x R/4lr 7rs ? ?rProtons pn Coincidences Neutrons nn Coincidences

600 hours of production.

The total :H pro-

Branching fraction 0.14

Counts -

0.25 0.27

0.69 0.02

0.06

0.15 -

6900 215 37 770 61

26%

V.J Zeps/Nuclear

Physics A639 (1998) 261c-268~

suming the AI = i rule. Should that rule be substantially protons should increase markedly.

violated,

the number of tagged

6. SUMMARY

The decays of :He are well in hand. Comparable quality data for :He decays await analysis. With the prospects for a counter-based IH measurement, we have an opportunity to have a complete set observables from the three key s-shell hypernuclei using similar decay geometry for all. These relatively high-statistics experiments should provide the cornerstone for improving our understanding of the weak baryon-baryon interaction, including the role of the AI = f rule. REFERENCES 1. 2.

3. 4. 5. 6. 7. 8. 9. 10. 11.

12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26.

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