Comment on "Comparison of optical potential for nucleons and Δ resonances" by Arie Bodek and Tejin Cai
aa r X i v : . [ nu c l - t h ] J u l Comment on ”Comparison of optical potential for nucleons and ∆ resonances” byArie Bodek and Tejin Cai U. Mosel ∗ Institut f¨ur Theoretische Physik, Universit¨at Giessen, Giessen, Germany
In [1] Bodek and Cai have tried to extract the potentials for nucleons and ∆ resonances fromelectron-nucleus inclusive scattering data. They find that the ∆ potential is considerably moreattractive than that of the nucleons. This result is at variance with the results of a multitude ofanalyses of (e,A) and ( γA ) interactions, performed about 35 years ago. In a recent publication Bodek and Cai [1] have pre-sented potentials for nucleons and ∆ resonances in nu-clei [1] obtained from a phenomenological analysis of in-clusive electron-nucleus scattering data . These poten-tials are an essential input into event generators for elec-tron and in particular neutrino generators. The nucleonpotentials extracted by Bodek and Cai are roughly inline with earlier data obtained from proton-nucleus col-lisions the potentials. The ∆ potentials that these au-thors find are always more attractive than the averagepotential for nucleons. For example, for C they find U ∆ ≈ . U nucleon . The purpose of this comment is topoint out that this result is in stark contrast to all formeranalyses of electro-nuclear reactions.Potentials for the ∆ resonance in nuclei have been de-termined in a multitude of theoretical analyses of ( γA )and (eA) reactions about 30 - 40 years ago. One of theearliest studies was that of Hirata et al [2] where a poten-tial depth for the ∆ of - 30 MeV was obtained. Freedmanet al. [3] also obtained a value for the ∆ potential of - 30 MeV. Later, more refined studies of ( γ, A ) and ( e, A )reactions by Garcia-Reco et al [4] obtained a ∆ poten-tial V ∆ = − ρ/ρ MeV where ρ is the r -dependent ra-dial coordinate and ρ the central density. This is closeto the potential obtained in the study of the Delta self-energy in nuclear matter performed in [5] where a valueof V ∆ = − ± ρ/ρ MeV was obtained (all poten-tials given at zero momentum). A good summary of theprogress achieved both experimentally and theoreticallycan be found in the book by Ericson and Weise [6] whichcontains detailed theory and reviews of many analysesuntil then. These authors give a value of -30 MeV forthe depth of the ∆ potential in C and O . Essentialfor all these results is a careful evaluation of the non-resonant background terms.All of these ∆ potentials are clearly less binding thanthe nucleon potentials of about 40 - 50 MeV depth andestablish an approximate relation of U ∆ ≈ / U nucleon between the two. The result obtained by Bodek and Caiis thus in gross contradiction to all these findings. [1] A. Bodek and T. Cai, [arXiv:2004.00087 [hep-ph]].[2] M. Hirata, J. H. Koch, E. J. Moniz and F. Lenz,Annals Phys. , 205-248 (1979) doi:10.1016/0003-4916(79)90287-2[3] R. A. Freedman, G. A. Miller and E. M. Henley,Phys. Lett. B , 397-400 (1981) doi:10.1016/0370-2693(81)90068-X [4] C. Garcia-Recio, E. Oset, L. L. Salcedo, D. Strottmanand M. J. Lopez, Nucl. Phys. A , 685-702 (1991)doi:10.1016/0375-9474(91)90438-C[5] E. Oset and L. L. Salcedo, Nucl. Phys. A , 631-652(1987) doi:10.1016/0375-9474(87)90185-0[6] T. E. O. Ericson and W. Weise, “Pions and Nuclei,” Int.Ser. Monogr. Phys. , Clarendon Press, Oxford (1988) ∗ Contact e-mail: [email protected]