Charmed scalar mesons masses within the QCD sum rules framework

Abstract

In this work, we evaluate the D + sJ (2317), D 0 0 (2308), D 0 0 (2407) and D + 0 (2403) masses. These are scalar mesons recently discovered in the BABAR, BELLE and FOCUS Collaborations. The nature of these particles is intensely discussed nowadays. We treat them as a diquark-antidiquark configuration and treat the problem using the QCD sum rules (QCDSR) approach.Keywords: Charmed scalar mesons; QCD Sum RulesThe detailed study of charmed scalar meson spectroscopy has provided many informations about the properties of qc systems. However, our knowledge is still not enough to understand all the meson states known nowadays.In 1977, R. L. Jaffe proposed a diquark (qq) antidiquark (qq) bound state structure and he explained the light scalar meson spectroscopy with J P = 0 + quantum numbers [1] using the MIT bag model. Surprisingly, Jaffe has shown that this description (qqqq) was able to accomodate the experimental masses of these mesons. In a recent work, [2] a QCDSR study of these light scalar mesons was carried out, in which they were treated as qqqq states. In that work the decay constants of these mesons were found and the result was consistent with the existing experimental data.The discovery of the D Because of the discrepancies between theoretical models and the experimental data, we propose that D Our group worked with QCDSR several times before [19][20][21][22][23][24] and there are many others references about this subject. The QCDSR formalism is based on writing the 2-point correlation functionand perform an operator product expansion (OPE). The operators are quark and gluon condensates that appear in this expansion due to the non-trivial nature of the QCD vacuum. We can write the correlation function as a dispersion relation. In the OPE side, this correlation function is given by:where the spectral density ρ OPE (s) contains both perturbative and non-perturbative contribuitions to the QCDSR.In the phenomenological side, the spectral density (a pole state plus resonances) is given by the imaginary part of the correlation function:where N depends on the decay constant f Γ and on the mass m Γ . Thus, we have the phenomenological side of QCDSR given by:We can identify (2) and (4) and apply on both sides a Borel transformation defined as:where the ratio Q 2 /n = M 2 is kept finite when Q 2 , n → ∞. The parameter M is called Borel mass. Applying this transformation to the correlation functions above we have:

Mass spectra and decay properties ofDsmeson in a relativistic Dirac formalism

“…The understanding of the weak transition form factors of heavy mesons is important for a proper extraction of the quark mixing parameters, for the analysis of non-leptonic decays and CP violating effects. QCD sum rule (QSR) [14][15][16][17][18] is non-perturbative approach to evaluate hadron properties by using the correlator of the quark currents over the physical vacuum and it is implemented with the operator product expansion (OPE). Lattice QCD (LQCD) [19][20][21] is also non-perturbative approach to use a discrete set of spacetime points (lattice) to reduce the analytically intractable path integrals of the continuum theory to a very difficult numerical computation.…”

D meson spectroscopy and their decay properties using Martin potential in a relativistic Dirac formalism

“…The understanding of the weak transition form factors of heavy mesons is important for a proper extraction of the quark mixing parameters, for the analysis of nonleptonic decays and CP-violating effects. The QCD sum rule (QSR) [15][16][17][18][19] is a non-perturbative approach to evaluate the hadron properties by using the correlator of the quark currents over the physical vacuum and it is implemented with the operator product expansion (OPE). Lattice QCD (LQCD) [20][21][22] is also a non-perturbative approach to use a discrete set of spacetime points (lattice) to reduce the analytically intractable path integrals of the continuum theory to a very difficult numerical computation.…”

Systematics of oscillatory behavior in hadronic masses and widths

“…Mesons with all quantum numbers are kept, otherwise the number of data is too small for given quantum numbers, to get well defined distributions. In insert (a) the mass difference between successive charmed meson masses, plotted versus both corresponding mean masses are shown; Pdg [2] data are in blue, LHCB data [5] are in red and Babar data [6] are in sky blue. Many data are overlaided by data from other origin.…”