Feasibility of an experimental search for a resonance of a pion and a light nucleus
PProg. Theor. Exp. Phys. , 00000 (6 pages)DOI: 10.1093 / ptep/0000000000 Possibility of a resonance of a pion and a lightnucleus
Hiroyuki Fujioka
Department of Physics, Tokyo Institute of Technology, Meguro, Tokyo 152-8551,Japan ∗ E-mail: [email protected] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
A hypothesis is proposed herein, suggesting that a pion-nuclear resonance maybe observed in the α + d → Li(3 . π reaction. The resonance has a πN N α structure, containing αN N and πN N subsystems. The former corresponds to the A = 6 isotriplet ( He g.s. , Li(3 . Be g.s. ), whereas the latter is a hypothetical N N -decoupled dibaryon. This resonance may be populated using the Li( p, d ) reaction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .Subject Index D01, D15, D22, D25 Introduction
Numerous investigations of the meson–nucleus bound states have beenperformed to elucidate the meson–nucleus and meson–nucleon interactions [1]. In particular,systems with a pseudoscalar meson and a few nucleons have attracted considerable attention.An example of such a system is the bound state of an antikaon ( K ) and two nucleons( N ), KN N . Two recent experiments at J-PARC independently reported observations ofthe
KN N bound state in the d ( π + , K + ) reaction [2] and the He( K − , n ) reaction [3]. Thepossible existence of a bound or virtual state of the η - He system was inferred from thesharp increase in the cross sections just above the threshold observed in the γ He → He η reaction [4] and the pd → He η reaction [5], whereas no η - He bound state was observed inthe excitation function of the dp → pdπ reaction [6]. In addition, the existence of an η (cid:48) d bound state is theoretically predicted in connection with the U A (1) anomaly in quantumchromodynamics, and it may be investigated by using the γd → ηd reaction [7].A pionic system such as πN N has been insufficiently examined in the past few decades.Instead, a non-strange dibaryon, which is defined as a system with a baryon number of 2, hasbeen extensively investigated [8]. Recently, the existence of d ∗ (2380) has been establishedusing neutron–proton scattering [9] as well as double pionic fusion such as pn → dπ π [10].The isospin and spin-parity were determined to be I ( J P ) = 0(3 + ), and d ∗ (2380) is also calleda ∆∆ dibaryon. A candidate of an N ∆ dibaryon with I ( J P ) = 1(2 + ) was also obtainedthrough a partial-wave analysis [11]. These dibaryons involve p -wave πN interaction in ahadronic picture [13].In this letter, we revisit a πN N system in which any two constituents are in a relative s -wave. In addition, we consider a six-nucleon system of a πN N α , which may be regarded asthe resonance of a pion { π + , π , π − } and the A = 6 isotriplet { He g.s. , Li(3 . Be g.s. } with a total charge of +3. A hypothesis is proposed, suggesting that a sharp structure © The Author(s) 2012. Published by Oxford University Press on behalf of the Physical Society of Japan.This is an Open Access article distributed under the terms of the Creative Commons Attribution License(http://creativecommons.org/licenses/by-nc/3.0), which permits unrestricted use,distribution, and reproduction in any medium, provided the original work is properly cited. a r X i v : . [ nu c l - t h ] J a n bserved in the excitation function of a pionic fusion reaction [12] may be accounted for bythe formation of a πN N α resonance.The rest of this letter is organised as follows. In Section 2, we briefly review some of theprevious studies on the πN N system. Section 3 introduces the six-nucleon system πN N α . InSection 4, we discuss the pionic fusion experiment conducted at the CELSIUS storage ringfacility in Uppsala, Sweden and propose a novel interpretation of the experimental result. Anidea on the experimental methods to test the existence of the πN N α resonance is discussedin Section 5. Finally, Section 6 concludes the letter. πN N System With I ( J P ) = 0(0 − ) We consider a πN N system with I ( J P ) = 0(0 − )in which any two particles are in a relative s -wave. Then, the total isospin of a πN subsystemmust be 1/2. It is well known that the s -wave πN interaction is attractive in the isospin 1/2channel and repulsive in the isospin 3/2 channel [14]. Moreover, the two nucleons are in thespin-singlet state; hence, the interaction between them is also attractive.A possible existence of such a three-body system is supported by two different theoreticalcalculations. Garcilazo solved the Faddeev equations and obtained a resonance at 2018 MeV(42 keV above the πN N threshold) with a width of 1 .
75 MeV [15]. Ueda calculated theamplitude for this system and found a strong structure at 4–5 MeV above the πN N thresholdamplitude, with a width of 4–5 MeV [16].A notable feature of this three-body system is that it does not couple with a
N N systembecause the quantum numbers I ( J P ) = 0(0 − ) cannot be realised owing to the Pauli principle.This means that a partial-wave analysis for nucleon-nucleon scattering will not provideany signature, unlike in the case of the N ∆ and ∆∆ dibaryons. As the resonance willdecay into π pn , an experimental search is highly difficult. To date, no experiment has beenconducted to search for the πN N resonance in the vicinity of the πN N threshold, predictedin Refs. [15, 16]. However, it should be noted that the production of narrow dibaryons below2100 MeV with the γd → Xπ reaction was investigated, which resulted in an upper limitof the cross section of 2–5 µ b [17], although the sensitivity may not be sufficient to rule outthe existence of such a narrow resonance. πN N α System With I ( J P ) = 0(0 − ) When the πN N system described in the pre-vious section and a He nucleus (an α particle) are in a relative s -wave, the entire systemof πN N α will also have I ( J P ) = 0(0 − ). To satisfy these quantum numbers, the subsystem αN N must have I ( J P ) = 1(0 + ) if this subsystem and the pion are in a relative s -wave. Asthis subsystem has a mass number of 6 and an isospin of 1, it corresponds to the A = 6isotriplet ( He g.s. , Li(3 . Be g.s. ). Li(3 . + state of Li and is anisobaric analogue state of He g.s. and Be g.s. .Owing to the mass difference in the A = 6 triplet and that between the charged and neutralpions, the relevant threshold energies for the He g.s. + π + , Li(3 . π , and Be g.s. + π − channels are different, as illustrated in Fig. 1. Since the lowest threshold is that of the Li(3 . π channel, the πN N α resonance will decay into Li(3 . π .To the best of the author’s knowledge, this six-nucleon system has never been proposedin the literature. As in the πN N system, pion absorption into the I = 1 di-nucleon N N inthe s -wave is forbidden in a strong interaction. This means that the decay of the πN N α resonance into a non-pionic final state is suppressed. Although a quantitative evaluation is .0003.5634.016 3.777(5) Li He Be Li(3 . π He g.s. + π + Be g.s. + π − + π + + π + π − Fig. 1
Energy levels of the A = 6 isotriplet (solid lines) and relevant thresholds (dashedlines). The energy relative to the ground state of Li is given in units of megaelectron volt.needed, the decay width of the πN N α resonance may be narrow, which is a remarkablefeature from an experimental perspective.In contrast to a deeply bound pionic state in a heavy nucleus [18, 19], of which the narrowabsorption width is due to the repulsion in the strong interaction between a π − and anucleus, the strong interaction between the pion and the A = 6 nucleus in the πN N α systemis attractive owing to the pion–nucleon attraction in the I = 1 / Hint of a Resonance Near the Li(3 . π Threshold
The pionic fusion,i.e. nuclear fusion resulting in coherent pion production, of a deuteron and an alpha particlewas investigated at the CELSIUS storage ring facility in Uppsala, Sweden [12, 20]. The totalcross section and the forward–backward asymmetry were supposed to be sensitive to thecluster structure of He g.s. and its isobaric analogue state of Li(3 . I = 1 and J = 0. For this purpose, a 2 s harmonic oscillator wavefunction was used to describe the relative motion of the alpha core and two-nucleon halo inthe momentum space, with the aim of determining the harmonic oscillator constant, whichcan be converted into the point-proton charge radius of He g.s. and Li(3 . α + d → Li(3 . π and α + d → He g.s. + π + , are illustrated in Fig. 2. For the latter reaction, the cross sections were cor-rected for the Coulomb interaction in the final state. By fitting the experimental results for
38 140 142 144 146 148 150 [MeV] c ) g.s. Li ( m - E c r o ss s ec ti on [ nb ] t h r e s ho l d p + L i ( . ) t h r e s ho l d + p + g . s . H e t h r e s ho l d -p + g . s . B e p+ Li(3.563) fi d +a + p+ g.s. He fi d +a Fig. 2
Cross sections for the α + d → Li(3 . π reaction (red) and the α + d → He g.s. + π + reaction (black) as a function of the excitation energy, i.e. the centre-of-massenergy minus the rest energy of the ground state of Li. The systematic error for a multi-plicative factor in each reaction is not indicated. The bands are drawn as a visual guide. Thedata are taken from Ref. [12].the Coulomb-corrected cross section and the asymmetry for the α + d → He g.s. + π + reac-tion, the harmonic oscillator constant was obtained, corresponding to a point-proton chargeradius of 1 . He g.s. . However, their model could not reproduce the behaviour inthe α + d → Li(3 . π reaction; the exceptionally large cross section, together with asmall asymmetry, at 1 . Li ions with (or mimicking) a more symmetric distribu-tion in the c.m. frame” was pointed out. Nevertheless, any candidate reactions could not beidentified.Now, we suppose that some resonance, which can decay into Li(3 . π , exists nearthe Li(3 . π threshold. If the decay width of the resonance is sufficiently narrow,the formation of the resonance may explain the sharp increase and decrease in the crosssection of the α + d → Li(3 . π reaction. The small asymmetry may be qualitativelyaccounted for. Herein, the πN N α system described in Section 3 is proposed as a promisingcandidate for it, while the theoretical calculations for the structure of this system and itsformation cross section in deuteron-alpha fusion are called for. Pion-Transfer Reaction to Populate the πN N α
Resonance
Currently, we cannotdraw any strong conclusion from Fig. 2; however, the intriguing result is worth considering. straightforward approach to validate the sharp structure of the excitation function shownin Fig. 2 is to repeat the measurement of the pionic fusion reaction with finer steps in thebeam energy.Alternatively, we propose the ( p, d ) reaction on a Li target to populate the πN N α res-onance. Although the spectroscopy using the ( d, He) reaction to transfer a π − to a targetnucleus is well established in the study of deeply bound pionic states in heavy nuclei [18, 19],a similar pion-transfer reaction ( pn → dπ ) is desirable to populate the πN N α resonance viathe Li- π doorway from Li. Although the recoilless condition is satisfied when the kineticenergy of the incident proton is approximately 330 MeV, a higher kinetic energy as well asscattering at finite angles, both of which contribute to increasing the momentum transfer,are preferred for two reasons. First, an angular momentum transfer of | ∆ (cid:96) | = 1 is necessarybecause a neutron in the (0 p ) / shell is picked up and a pion in the s state is transferredto the neutron-hole state corresponding to Li(3 . . ◦ from the unreacted beam, which is guided to adump located in a shield wall around 25 m downstream of the target. In these kinemati-cal conditions, the momentum transfer is less than 100 MeV /c . Owing to the Grand Raidenhigh-resolution magnetic spectrometer, a missing-mass spectrum for the Li( p, d ) reactionnear the Li(3 . π threshold can be investigated precisely. Conclusion
For the first time, it is pointed out that the possibility that the sharpincrease and decrease in the cross section of a pionic-fusion reaction, α + d → Li(3 . π , observed in an experiment at CELSIUS, may be due to the formation of a πN N α resonance. As a subsystem of πN N is expected to have a resonance slightly above thethreshold, a four-body calculation of the structure of the πN N α system is worthwhile inelucidating the origin of the peculiar excitation function. We also discussed a future plan toinvestigate the resonance using the Li( p, d ) reaction at RCNP.
Acknowledgements
We would like to thank S. Hirenzaki, E. Hiyama, A. Hosaka and K. Itahashi for the helpful discussions.
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