Evidence for 6ΛH
M. Agnello, L. Benussi, M. Bertani, H.C. Bhang, G. Bonomi, E. Botta, M. Bregant, T. Bressani, S. Bufalino, L. Busso, D. Calvo, P. Camerini, B. Dalena, F. De Mori, G. D'Erasmo, F. L. Fabbri, A. Feliciello, A. Filippi, E. M. Fiore, A. Fontana, H. Fujioka, P. Genova, P. Gianotti, N. Grion, V. Lucherini, S. Marcello, N. Mirfakhrai, F. Moia, O. Morra, T. Nagae, H. Outa, A. Pantaleo, V. Paticchio, S. Piano, R. Rui, G. Simonetti, R. Wheadon, A. Zenoni, A. Gal
EEvidence for H M. Agnello,
1, 2
L. Benussi, M. Bertani, H.C. Bhang, G. Bonomi,
5, 6
E. Botta,
7, 2, ∗ M. Bregant, T. Bressani,
7, 2
S. Bufalino, L. Busso,
9, 2
D. Calvo, P. Camerini,
10, 11
B. Dalena, F. De Mori,
7, 2
G. D’Erasmo,
13, 14
F.L. Fabbri, A. Feliciello, A. Filippi, E.M. Fiore,
13, 14
A. Fontana, H. Fujioka, P. Genova, P. Gianotti, N. Grion, V. Lucherini, S. Marcello,
7, 2
N. Mirfakhrai, F. Moia,
18, 6
O. Morra,
19, 2
T. Nagae, H. Outa, A. Pantaleo, † V. Paticchio, S. Piano, R. Rui,
10, 11
G. Simonetti,
13, 14
R. Wheadon, and A. Zenoni
18, 6 (The FINUDA Collaboration)A. Gal Dipartimento di Fisica, Politecnico di Torino, Corso Duca degli Abruzzi 24, Torino, Italy INFN Sezione di Torino, via P. Giuria 1, Torino, Italy Laboratori Nazionali di Frascati dell’INFN, via E. Fermi 40, Frascati, Italy Department of Physics, Seoul National University, 151-742 Seoul, South Korea Dip. di Ingegneria Meccanica e Industriale, Universit`a di Brescia, via Valotti 9, Brescia, Italy INFN Sezione di Pavia, via Bassi 6, Pavia, Italy Dipartimento di Fisica Sperimentale, Universit`a di Torino, Via P. Giuria 1, Torino, Italy SUBATECH, ´Ecole des Mines de Nantes, Universit´e de Nantes, CNRS-IN2P3, Nantes, France Dipartimento di Fisica Generale, Universit`a di Torino, Via P. Giuria 1, Torino, Italy INFN Sezione di Trieste, via Valerio 2, Trieste, Italy Dipartimento di Fisica, Universit`a di Trieste, via Valerio 2, Trieste, Italy CEA, Irfu/SACM, Gif-sur-Yvette, France Dipartimento di Fisica Universit`a di Bari, via Amendola 173, Bari, Italy INFN Sezione di Bari, via Amendola 173, Bari, Italy Laboratori Nazionali di Frascati dell’INFN, via E. Fermi, 40, Frascati, Italy Department of Physics, Kyoto University, Sakyo-ku, Kyoto, Japan Department of Physics, Shahid Behesty University, 19834 Teheran, Iran Dipartimento di Meccanica, Universit`a di Brescia, via Valotti 9, Brescia, Italy INAF-IFSI, Sezione di Torino, Corso Fiume 4, Torino, Italy RIKEN, Wako, Saitama 351-0198, Japan Racah Institute of Physics, The Hebrew University, Jerusalem 91904, Israel (Dated: November 6, 2018)Evidence for the neutron-rich hypernucleus H is presented from the FINUDA experiment atDAΦNE, Frascati, studying ( π + , π − ) pairs in coincidence from the K − stop + Li → H+ π + productionreaction followed by H → He + π − weak decay. The production rate of H undergoing this two-body π − decay is determined to be (2 . ± . · − /K − stop . Its binding energy, evaluated jointly fromproduction and decay, is B Λ ( H) = (4 . ± .
1) MeV with respect to H + Λ. A systematic differenceof (0 . ± .
74) MeV between B Λ values derived separately from decay and from production istentatively assigned to the H 0 +g . s . → + excitation. PACS numbers: 21.80.+a, 25.80.Nv, 21.10.Gv
Introduction.
The existence and observability ofneutron-rich Λ hypernuclei was discussed back in 1963by Dalitz and Levi-Setti [1] who predicted the stabilityof H consisting of four neutrons, one proton and oneΛ hyperon. Accordingly, the Λ hyperon stabilizes thecore nucleus H which is a broad resonance 1.7 MeVabove H + 2 n [2]. To be stable, H must lie also be-low H + 2 n which provides the lowest particle stabilitythreshold. This motivates a H + 2 n two-neutron halocluster structure for H, with binding energy and excita-tion spectrum that might deviate substantially from theextrapolation practised in Ref. [1]. Specifically, the studyof H and of heavier neutron-rich hypernuclei that goappreciably beyond the neutron stability drip line in nu-clear systems could place valuable constraints on the size of coherent Λ N − Σ N mixing in dense strange neutron-rich matter [3]. This mixing provides a robust mechanismfor generating three-body Λ N N interactions, with imme-diate impact on the stiffness/softness of the equation ofstate for hyperons in neutron-star matter, as reviewedrecently in Ref. [4].In this Letter we report on a study of H in the doublecharge exchange reaction at rest K − stop + Li → H + π + ( p π + ∼
252 MeV / c) (1)based on analyzing the total data sample of the FIN-UDA experiment during 2003–2007 and correspondingto a total integrated luminosity of 1156 pb − . A firstanalysis of partial data, corresponding to an integratedluminosity 190 pb − , gave only an upper limit for (1): a r X i v : . [ nu c l - e x ] D ec (2 . ± . stat +0 . − . ) · − /K − stop [5]. Although thestatistics collected on Li targets is improved by a factorfive with respect to the run of the earlier search, the inclu-sive π + spectra do not show any clear peak attributableto H near p π + ∼
252 MeV/c. Exploiting the increasedstatistics, the essential idea of the present analysis was toreduce the overwhelming background events in reaction(1) by requiring coincidence with π − mesons from thetwo-body weak decay H → He + π − ( p π − ∼
134 MeV / c) , (2)with a branching ratio of about 50% considering the valuemeasured for H → He + π − [6]. The analysis describedbelow yielded three distinct H candidate events whichgive evidence for a particle-stable H with some indica-tion of its excitation spectrum. The deduced H bindingenergy does not confirm the large effects conjectured inRef. [3].
Data analysis.
We first recall the experimental fea-tures relevant to the present analysis. For π + with mo-mentum ∼
250 MeV/c the resolution of the tracker wasdetermined by means of the peak due to monochromatic(236.5 MeV/c) µ + from K µ decay and is σ p = (1 . ± . Li targets,which corresponds to a systematic deviation on the ki-netic energy σ T syst ( π + ) = 0 . π − with momen-tum ∼
130 MeV/c the resolution and absolute calibra-tion were evaluated from the peak due to monochromatic(132.8 MeV/c) π − coming from the two-body weak de-cay of H, produced as hyperfragment with a formationprobability about 10 − − − per stopped K − [6]. Aresolution σ p = (1 . ± .
1) MeV/c and precision of 0.2MeV/c were found, corresponding to a systematic devi-ation of the kinetic energy σ T syst ( π − ) = 0 .
14 MeV.Since the stopping time of H in metallic Li is shorterthan its lifetime, both production (1) and decay (2) oc-cur at rest, and a straightforward algebra leads to thefollowing expression for T sum ≡ T ( π + ) + T ( π − ): T sum = M ( K − ) + M ( p ) − M ( n ) − M ( π ) − B ( Li) + B ( He) − T ( He) − T ( H) , (3)in which M stands for known masses, B for known nu-clear binding energies, and T for kinetic energies. Theevaluation of T ( H) using momentum and energy conser-vation depends explicitly on the knowledge of B Λ ( H),whereas T ( He) depends only implicitly on B Λ ( H)through the momentum p π − .We assume B Λ ( H) = 5 MeV, the average of 4.2 and5.8 MeV predicted in Refs. [1, 3], respectively, with re-spect to H + Λ. This choice is not critical, since T sum varies merely by 50 keV upon varying B Λ ( H) by 1 MeV,negligibly low with respect to the experimental energyresolutions σ T ( π + ) = 0 .
96 MeV and σ T ( π − ) = 0 .
84 MeV for p π + ≈
250 MeV/c and p π − ≈
130 MeV/c. There-fore, the FINUDA energy resolution for a π ± pair in co-incidence is σ T = 1 .
28 MeV. Evaluating the r.h.s. ofEq. (3) one obtains T sum = 203 ± . H can-didate events. In practice we have focused on eventsin the interval T sum = 203 ± ∼
77% of the FINUDA total energy resolution; thisvalue was chosen as a compromise between seeking to re-duce contamination from background reactions discussedin more detail below, and maintaining reasonable statis-tics, which resulted in a somewhat narrower interval thanthe experimental resolution. The raw spectrum of T sum for π ± pair coincidence events is shown in Fig. 1, whereevents satisfying T sum = 203 ± ) (MeV) - p ) + T( + p T(
120 140 160 180 200 220 240 c oun t s / M e V FIG. 1. (color online). Distribution of raw total kinetic energy T sum ≡ T ( π + ) + T ( π − ) for π ± pair coincidence events from Li targets. The vertical (red) bar represents the cut T sum =202 −
204 MeV. The dashed (blue) histogram is a quasi-freesimulation of K − stop + Li → Σ + + He + n + π − ; Σ + → n + π + background and the dotted (violet) histogram is a four-bodyphase space simulation of the same background, their best fitto the data is shown by the solid (black) histogram, see text. Figure 2 (left) shows a 2-d plot in the p π ± plane ofcoincidence events selected in the band T sum = 202 − p π + (cid:39)
245 MeV/cand higher, and at p π − (cid:39)
145 MeV/c and lower. This isclose to where H events are expected. Thus, to searchfor particle-stable H events below its ( H + 2 n ) lowestthreshold, using the two-body kinematics of Eqs. (1) and(2), a further requirement of p π + > . p π − < . p π + = (250 − p π − = (130 − H mass range from the (Λ + H + 2 n ) threshold, about 2 MeV in the H continuum,down to a H bound somewhat stronger than predictedby Akaishi et al. [3]. This does not completely excludeeventual contributions from the production and decay of( H + 2 n ) as discussed below. Results.
Out of a total number of ∼ . · K − detected at stop in the Li targets, we found three events momentum (MeV/c) - p
120 130 140 150 160 170 180 190 200 210 m o m e n t u m ( M e V / c ) + p momentum (MeV/c) - p
120 130 140 150 160 170 180 190 200 210 m o m e n t u m ( M e V / c ) + p FIG. 2. (color online). π + momentum vs π − momentum for Li target events with T sum = 202 −
204 MeV (l.h.s.) and with T sum = 200 −
206 MeV (r.h.s.). The shaded (red) rectangle on each side consists of a subset of events with p π + = 250 − p π − = 130 −
137 MeV/c. that satisfy the final requirements: T sum = 202 − p π + = 250 −
255 MeV/c and p π − = 130 − T sum interval widths (2 − −
204 MeV), and of p π ± interval widths (5 −
10 and 8 −
15 MeV/c respectively)with fixed limits at 250 and 137 MeV/c respectively toexclude the unbound region, do not affect the populationof this selected rectangle. For example, no new candidateevents appear in the shaded rectangle upon extending thecut T sum = 202 −
204 MeV in the l.h.s. of Fig. 2 to T sum =200 −
206 MeV in the r.h.s. of the figure. A similarstability is not observed in the opposite corner of Fig. 2where, on top of the events already there on the l.h.s., sixadditional events appear on the r.h.s. upon extending the T sum cut of the l.h.s. Quantitatively, fitting the projected π ± distributions of Fig. 2 left by gaussians, an excessof three events in both p π ± distributions is invariablyfound, corresponding to the shaded (red) rectangle. Theprobability for the three events to belong to the fittedgaussian distribution is less than 0 .
5% in both cases. Thisrules out systematic errors associated with the presentanalysis selection.The three H candidate events are listed in Table I to-gether with nuclear mass values derived separately fromproduction (1) and from decay (2). These mass valuesyield a mean value M ( H) = 5801 . ± . σ from the mean mass value, TABLE I. Summed kinetic energy T sum = T ( π + ) + T ( π − ),pion momenta p π ± , and mass values inferred for the three H candidate events from production (1) and decay (2). Themean mass value is M ( H) = 5801 . ± . T sum p π + p π − M ( H) prod . M ( H) decay (MeV) (MeV/c) (MeV/c) (MeV) (MeV)202.6 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± an observation that could indicate some irregularity inthe reconstruction of the third event. To regain confi-dence, each one of the three events was checked visuallyfor irregularities, but none was found.Furthermore, we note from Table I that the mass val-ues associated with production are systematically higherthan those associated with decay, by 0 . ± .
74 MeVrecalling the 1.28 MeV uncertainty for T sum from whicheach of these mass differences is directly determined. Un-like the mean H mass value, the spread of the produc-tion vs decay mass differences is well within 1 σ . Thesemass differences are likely to be connected to the excita-tion spectrum of H as discussed below.
Background estimate and production rate
Acomplete simulation was performed of K − stop absorptionreactions on single nucleons, as well as on correlated few-nucleon clusters, that lead to the formation and decay ofΛ and Σ hyperons. Full details will be given elsewhere,here it is sufficient to focus on two chains of reactionslikely to produce π ± coincidences overlapping with thoseselected to satisfy H production (1) and decay (2).(i) Σ + production K − stop + Li → Σ + + He + n + π − , (4)where p π − ≤
190 MeV/c, followed by Σ + decay in flightΣ + → n + π + [ p π + ≤
282 MeV / c] . (5)The Σ + production was treated in the quasi–free ap-proach, following the analysis of the FINUDA experi-ment observing Σ ± π ∓ pairs [8]. This simulation is shownin Fig. 1, normalized to the experimental distributionarea. It provides too sharp a decrease in the 200-210MeV region. To have a satisfactory description a contri-bution ( ∼ χ = 40 /
39) in the 180-220 MeV range. The simulatedbackground spectra reproduce reasonably the projecteddistributions of π ± momentum too, showing in particularonly a small contribution to the signal region, evaluatedto be 0 . ± .
07 expected events (BGD1).(ii) H production K − stop + Li → H + 2 n + π + , (6)where p π + ≤
252 MeV/c, with H decay at rest H → He + π − [ p π − ∼ . / c] . (7)The π − momentum in this H decay is close to p π − ∼
134 MeV/c from the two-body decay of H, evaluatedassuming B Λ ( H) = 5 MeV as discussed above. A valueof 0 . ± .
01 expected events for the (6)-(7) reactionchain, negligible when compared to BGD1, was obtainedunder most pessimistic assumptions for the various termsof the calculation.All other reaction chains that could produce π ± coin-cidences within the described selection ranges were ruledout by the selections applied. Turning to potential instru-mental backgrounds, we note that these could result fromfake tracks, misidentified as true events by the track re-construction algorithms. To this end we considered, withthe same cuts, events coming from different nuclear tar-gets used in the same runs ( Li, Be, C, O). We foundone event coming from Be. Furthermore, we consideredevents relative to the Li targets, selected with a value of T sum = 193 −
199 MeV, so as to search for neutron-richhypernuclei produced on the other targets. No event wasfound. We evaluate 0 . ± .
27 expected fake events from Li, due to instrumental background (BGD2).To recap, the estimated number of events due to phys-ical and instrumental backgrounds feeding through theselection criteria are 0 . ± .
07 (BGD1) and 0 . ± . . ± .
28 ex-pected events. Thus, using Poisson distribution, thethree H-assigned events do not arise from backgroundto a confidence level of 99%. The statistical significance of the result is S=7.1 considering only the physical back-ground, S=3.9 considering both physical and instrumen-tal backgrounds.Given the above background estimates, plus efficiency,target purity and cut estimates, it is possible to evaluatethe product R ( π + ) · BR( π − ), where R ( π + ) is the Hproduction rate per K − stop in reaction (1) and BR( π − )the branching ratio for the two-body π − decay (2): R ( π + ) · BR( π − ) = (2 . ± . · − /K − stop . (8)Details will be given in a separate report. AssumingBR( π − ) = 49%, as for the analogous H → He + π − decay [6], we find R ( π + ) = (5 . ± . · − /K − stop , fullyconsistent with the previous FINUDA upper limit [5]. Discussion and Conclusion.
Table I yields a meanvalue B Λ ( H) = 4 . ± . H + Λ, asshown in Fig. 3, in good agreement with the estimate 4.2MeV [1] and close to B Λ ( He) = 4 . ± .
10 MeV (withrespect to He + Λ) for the other known A = 6 hypernu-cleus [9], but considerably short of Akaishi’s prediction B thΛ ( H) = 5 . N − Σ N mixing in the s -shell hypernucleus H [10] be-comes rather ineffective for the excess p shell neutrons in H. Indeed, recent shell-model calculations by Millenerindicate that Λ N − Σ N mixing contributions to B Λ andto doublet spin splittings in the p shell are rather small,about (10 ± H [11]. [3] 5799.64[1] 5801.24H + n + n L L H + 2n + L H + L FIG. 3. (color online). H mass (r.h.s.) from three H candi-date events, as related to several particle stability thresholdsand theoretical predictions (l.h.s.).
Next, we ask whether the three events that give evi-dence for a particle-stable H provide additional infor-mation on its excitation spectrum which is expected toconsist of a 0 + g.s. and 1 + excited state as in H (1.04MeV), and a 2 + excited state as for the p -shell dineutronsystem in He (1.80 MeV). In fact, it is H(1 + ) that islikely to be produced in reaction (1) simply because Paulispin is conserved in production at rest, and the Pauli spinof Li is S = 1 to better than 98% [11]. The weak decay(2), however, occurs from H(0 + ) g.s. since the (unseen) γ transition 1 + → + is about three orders of magnitudefaster than weak decay. Indeed, the production vs decaymass difference 0 . ± .
74 MeV extracted from the three H events listed in Table I is comparable to the under-lying 1.04 MeV 1 + excitation in H but, again, smallerthan the 2.4 MeV predicted by Akaishi et al. [3]. If thisis the case, then the B Λ value for the g.s. would be largerby 0.5 MeV than that determined above, amounting to B Λ ( H g . s . ) = 4 . ± . H, based on detecting threeevents shown to be clear of instrumental and/or physicalbackgrounds. The derived binding energy of H limitsthe strength of the coherent Λ N − Σ N mixing effect pre-dicted in neutron-rich strange matter [3] and togetherwith the conjectured 0 + − + doublet splitting it placesa limit on this mixing that could orient further explo-rations of other neutron-rich hypernuclei. A search of H and
Li in the ( π − , K + ) reaction at 1.2 GeV/c on Li and B, respectively, is scheduled in the near futureat J-PARC. ∗ Corresponding author: Elena Botta, [email protected] † deceased[1] R.H. Dalitz and R. Levi-Setti, Nuovo Cimento , 489(1963); L. Majling, Nucl. Phys. A , 211c (1995).[2] A.A. Korsheninnikov et al. , Phys. Rev. Lett. , 092501(2001).[3] Y. Akaishi and T. Yamazaki, in Frascati Physics Series
XVI , 59 (1999); S. Shinmura, K.S. Myint, T. Harada,and Y. Akaishi, J. Phys. G , L1 (2002); For a recentreview, see Y. Akaishi and K.S. Myint, AIP Conf. Proc. , 277 (2008), Y. Akaishi, Prog. Theor. Phys. Suppl. , 378 (2010), and references therein.[4] J. Schaffner-Bielich, Nucl. Phys. A , 309 (2008), Nucl.Phys. A , 279 (2010).[5] M. Agnello et al. , Phys. Lett. B , 145 (2006), includ-ing a detailed description of the FINUDA experiment, inparticular for the ( K − stop , π + ) production reaction.[6] H. Tamura et al. , Phys. Rev. C , R479 (1989).[7] M. Agnello et al. , Phys. Lett. B , 219 (2011).[8] M. Agnello et al. , Phys. Lett. B , 474 (2011).[9] D.H. Davis, Nucl. Phys. A , 3 (2005).[10] Y. Akaishi, T. Harada, S. Shinmura, and K.S. Myint,Phys. Rev. Lett. , 3539 (2000).[11] D.J. Millener, Lect. Notes Phys.724