RT Journal Article
T1 Comments on the dispersion relation method to vector–vector interaction
A1 Molina, R. A.
A1 Geng, L S
A1 Oset, E
AB We study in detail the method proposed recently to study the vector–vector interaction using the N/D method and dispersion relations, which concludes that, while, for J = 0, one finds bound states, in the case of J = 2, where the interaction is also attractive and much stronger, no bound state is found. In that work, approximations are done for N and D and a subtracted dispersion relation for D is used, with subtractions made up to a polynomial of second degree in s − sth, matching the expression to 1 − VG at threshold. We study this in detail for the ρρ interaction and to see the convergence of the method we make an extra subtraction matching 1 − VG at threshold up to (s−sth)3.We show that the method cannot be used to extrapolate the results down to 1270 MeV where the f2(1270) resonance appears, due to the artificial singularity stemming from the “on-shell” factorization of the ρ exchange potential. In addition, we explore the same method but folding this interaction with the mass distribution of the ρ, and we show that the singularity disappears and the method allows one to extrapolate to low energies, where both the (s − sth)2 and (s − sth)3 expansions lead to a zero of Re D(s), at about the same energy where a realistic approach produces a bound state. Even then, the method generates a large Im D(s) that we discuss is unphysical.
PB PTEP
SN 2050-3911
YR 2019
FD 2019-10-21
LK https://hdl.handle.net/20.500.14352/12879
UL https://hdl.handle.net/20.500.14352/12879
LA eng
NO Unión Europea. FP7
NO Ministerio de Ciencia e Innovación (MICINN)/FEDER
NO Comunidad de Madrid
NO Generalitat Valenciana
DS Docta Complutense
RD 6 abr 2025