Comment on "Search for η ′ Bound Nuclei in the 12 C(γ,p) Reaction with Simultaneous Detection of Decay Products"
aa r X i v : . [ nu c l - e x ] J un Comment on “Search for η ′ Bound Nuclei in the C( γ, p ) Reaction withSimultaneous Detection of Decay Products” H. Fujioka, ∗ K. Itahashi, † V. Metag, M. Nanova, and Y. K. Tanaka Department of Physics, Tokyo Institute of Technology,2-12-1 Ookayama, Meguro, 152-8551 Tokyo, Japan RIKEN Cluster for Pioneering Research, RIKEN, Wako, Saitama 351-0198, Japan II. Physikalisches Institut, Universit¨at Gießen, Heinrich-Buff-Ring 16, 35392 Gießen, Germany (Dated: June 5, 2020)
In Ref. [1], N. Tomida et al. report the first result of amissing mass measurement of the C( γ, p ) reactions nearthe η ′ emission threshold. They conducted a simultane-ous analysis of the η ′ escape channel and the η ′ absorp-tion by a B nucleus followed by emission of an η anda proton ( p s ), making use of the large-acceptance elec-tromagnetic calorimeter, BGOegg. An upper limit wasdeduced for the formation cross section of an η ′ boundstate with subsequent ( η + p s ) decay. Its comparison tothe theoretical cross section leads to a relation betweenthe real part ( V ) of the η ′ - B optical potential and thebranching fraction of the η ′ N → ηN process in η ′ boundnuclei.The theoretical signal cross section is defined as: (cid:18) dσd Ω (cid:19) η + p s theory = F (1) × (cid:18) dσd Ω (cid:19) η ′ abstheory × Br η ′ N → ηN × P ηp s srv , (1)where the “normalization factor” F (1) is assumed to bethe same as F (2) defined as: F (2) = (cid:18) dσd Ω (cid:19) η ′ escexp ,(cid:18) dσd Ω (cid:19) η ′ esctheory . (2)They fitted ( dσ/d Ω) η ′ escexp , measured as a function of inci-dent photon energies, with theoretical cross sections mul-tiplied by F (2) . Here, for the sake of clarity, we explic-itly distinguish the two normalization factors as F (1) and F (2) , whereas the common normalization factor F is in-troduced in Ref. [1]. While we are not convinced of thevalidity of the conjecture of F (1) = F (2) , we hereby raisequestions with regard to the evaluation of F (2) , whichmay affect the interpretation of the upper limit of thesignal cross section.First, we are concerned with the impact of the imagi-nary part of the η ′ -nucleus potential ( W ) on the decom-posed cross sections in Eqs. (1) and (2). The contribu-tions of the two competing processes, i.e. absorption andescape, in the η ′ unbound region ( E ex − E η ′ >
0) areof comparable magnitudes, reflecting the moderate ab-sorption width of η ′ [2, 3], as shown in Fig. 2 of Ref. [4].The accuracy of W , which is responsible for the absorp-tion process, is essentially important for the estimationof both ( dσ/d Ω) η ′ abstheory and ( dσ/d Ω) η ′ esctheory , which appearexplicitly in Eqs. (1) and (2). While W was fixed at −
12 MeV in accordance with the CBELSA/TAPS result( − ± ± W shouldbe taken into account, so as to evaluate the uncertaintyof the l.h.s. of Eq. (1), owing to systematic uncertaintiesof F (2) and ( dσ/d Ω) η ′ abstheory .Secondly, we would like to point out a wide range of themomentum transfer, due to the polar angle ( θ p ) coverageof the ejectile protons as well as the range of the inci-dent photon energy ( E γ ) between 1.3 and 2 . E ex − E η ′ = 0) is 0 . .
49 GeV /c at E γ = 1 . . .
36 GeV /c at E γ = 2 . θ p coverage of0 . ◦ –6 . ◦ . Note that the strengths of subcomponents ofthe η ′ -nuclear system with different orbital angular mo-menta behave differently as a function of the momentumtransfer (see, e.g., Fig. 1 of Ref. [4], exhibiting scattering-angle dependence of the formation spectrum). Therefore,it requires justification to apply a common F (2) factor tothe whole kinematical region. It would be more appropri-ate to evaluate F (2) as a function of E γ and θ p . Indeed,Fig. 3 in Ref. [1] implies a possible E γ -dependence of F (2) .In summary, the “suppressed normalization ambigu-ity”, stated in the abstract of Ref. [1], may stem fromthese simplifications, and, consequently, the real part ofthe η ′ -nucleus interaction as well as the branching frac-tion of the η ′ N → ηN process may be overconstrained.We emphasize that the two aforementioned aspects aremuch less significant in the inclusive measurement of the C( p, d ) reaction by the η -PRiME/Super-FRS collabo-ration [5, 6] with a fixed beam energy of 2 . . .
49 GeV /c ) at the threshold energy. While theauthors of Ref. [5, 6] have not evaluated F in a similarway, the µ parameter defined in Ref. [5, 6] is nothingbut the normalization factor, which must be differenti-ated from the F (2) factor in Ref. [1], obtained for thedifferent kinematical conditions including the reaction it-self. The boundaries of the allowed ( V , W ) regions forvarious µ parameters are explicitly depicted in Fig. 4of Ref. [5] and Fig. 11 of Ref. [6]. ∗ [email protected] † [email protected][1] N. Tomida et al. (LEPS2/BGOegg Collaboration), Searchfor η ′ bound nuclei in the C( γ, p ) reaction with simulta-neous detection of decay products, Phys. Rev. Lett ,202501 (2020).[2] M. Nanova et al. (CBELSA/TAPS Collaboration), vTransparency ratio in γA → η ′ A ′ and the in-medium η ′ width, Physics Letters B , 600 (2012).[3] S. Friedrich et al. (CBELSA/TAPS Collaboration), Mo- mentum dependence of the imaginary part of the ω - and η ′ -nucleus optical potential, Eur. Phys. J. A , 297(2016).[4] H. Nagahiro, Formation of Possible η ′ (958)-NucleusBound States and η ′ N Interaction, JPS Conf. Proc. ,010010 (2017).[5] Y. K. Tanaka et al. ( η -PRiME/Super-FRS Collaboration),Measurement of Excitation Spectra in the C( p, d ) Reac-tion near the η ′ Emission Threshold, Phys. Rev. Lett. ,202501 (2016).[6] Y. K. Tanaka et al. ( η -PRiME/Super-FRS Collaboration),Missing-mass spectroscopy of the C( p, d ) reaction nearthe η ′ -meson production threshold, Phys. Rev. C97