Line-shape and poles of the ψ(3770)

Abstract

We study the non-Breit-Wigner line-shape of the ψ(3770) resonance, predominantly a 1 3 D 1c c state, using an unitarized effective Lagrangian approach, including the one-loop effects of the nearby thresholds D + D − and D 0D0 . A fit of the theoretical result to the total cross-section e + e − → DD is performed, leading to a good description of data (χ 2 /d.o.f. ∼ 1.03). The partial cross sections e + e − → D 0D0 and e + e − → D + D − turn out to be separately in good agreement with the experiment. We find a pole at 3777−i12 MeV, that is within the Particle Data Group (PDG) mass and width estimation for this state. Quite remarkably, we find an additional, dynamically generated, companion pole at 3741 − i19 MeV, which is responsible for the deformation on the lower energy side of the line-shape. The width for the leptonic decay ψ(3770) → e + e − is 112 eV, hence smaller than the PDG fit of 262 ± 18 eV, yet in agreement with a recent experimental study. 45 monium seed state, which gets dressed by "clouds" of D + D − and D 0D0 mesons.Our aim is to study the deformation seen on the left side of the resonance in Ref.[9] with mesonic loops combined with the nearby thresholds. To this end, we use an effective relativistic Lagrangian approach in which a single vector state ψ ≡ ψ(3770) is coupled to channels D + D − and D 0D0 , as well as to lepton 50 pairs. The propagator of ψ is calculated at the resummed one-loop level and fulfills unitarization requirements. Then, we perform a fit of the four parameters of our approach, i.e. the effective couplings of ψ to DD and of ψ to leptons, the mass of ψ, and a cutoff responsible for the finite dimension of the ψ meson, to the experimental cross-section of the reaction e + e − → DD in Refs. [7] and 55[5], in the energy region up to 100 MeV above the D 0D0 threshold. We assume that the ψ(3770) resonance dominates in this energy range. We obtain a very good description of the data, which in turn allows us to determine in a novel and independent way the mass, width, and branching ratios of the ψ(3770).Moreover, we study in detail, to our knowledge for the first time, the poles of 60 this state. In fact, a pole was found in Ref. [16], using Fano resonances, at about 3778 − i14 MeV, though in lesser detail. Quite remarkably, we find two poles for this resonance, one which roughly corresponds to the peak of the resonance, the seed pole, and one additional dynamically generated pole, responsible for the enhancement left from the peak, which emerges due to the strong coupling function, turns out to be rather small, possibly due to the fact that the ψ(3770)

Line shape and D(*)D¯(*Yu1, Wu2, Bayar3 et al. 2019Phys. Rev. D81400View full textAdd to dashboardCite

“…In order to interpret the line shape of the ψ(3770) we follow the steps of Ref. [15]. We consider the propagator of the vector meson R ≡ ψ(3770)…”

“…One can keep the covariant form of Π, but as shown in Ref. [15] only the transverse part of the propagator is relevant for the discussion here. We argue in a different way, with the same conclusion.…”

“…The asymmetry of the ψ(3770) peak observed in the e + e − → DD reactions [12][13][14] has been the subject of the intense discussion (see Ref. [15] for a recent review). In Ref.…”

X(3872) as virtual companion pole of the charm–anticharm state χc1(2P)

“…In order to avoid misunderstanding, we recall that, in the I RS, the function Π(z 2 → ∞) is an utterly different complex function than e −z 2 /Λ 2 , see Ref. [43] for a detailed discussion of this point. In fact, in the I RS, besides the cut along the real axis, Π(z 2 ) is regular and well defined everywhere and does not contain any singular point, contrary to e −z 2 /Λ 2 , which contains an essential singularity at ∞.…”

“…[37][38][39][40][41][42] for the light sector and Refs. [43,44] for the charmonium sector), we follow a different and quite simple idea: instead of working with quark degrees of freedom, a Lagrangian in which a single axial-vector field χ µ c1 , which we identify -in the non-interacting limit-as acc seed state χ c1 ≡ χ c1 (2P ) with a bare mass between 3.90 and 3.95 GeV, is considered. This field couples strongly to the D 0 D * 0 and D + D * − meson pairs.…”