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Register a new user$Z_c^+(3900)$ decay width in QCD sum rules
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We identify the recently observed charmonium-like structure $Z_c^pm(3900)$ as the charged partner of the X(3872) state. Using standard techniques of QCD sum rules, we evaluate the three-point function and extract the coupling constants of the $Z_c , J/psi , pi^+$ and $Z_c , eta_c , rho^+$ vertices and the corresponding decay widths in these channels. The good agreement with the experimental data gives support to the tetraquark picture of this state.
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We present a global analysis of the observed Z_c, Z_cs and future Z_css-like spectra using the inverse Laplace transform (LSR) version of QCD spectral sum rules (QSSR) within stability criteria. Integrated compact QCD expressions of the LO spectral functions up to dimension-six condensates are given. Next-to-Leading Order (NLO) factorized perturbative contributions are included. We re-emphasize the importance to include PT radiative corrections (though numerically small) for heavy quark sum rules in order to justify the (ad hoc) definition and value of the heavy quark mass used frequently at LO in the literature. We also demonstrate that, contrary to a naive qualitative 1/N_c counting, the two-meson scattering contributions to the four-quark spectral functions are numerically negligible confirming the reliability of the LSR predictions. Our results are summarized in Tables III to VI. The Z_c(3900) and Z_cs(3983) spectra are well reproduced by the T_c(3900) and T_cs(3973) tetramoles (superposition of quasi-degenerated molecules and tetraquark states having the same quantum numbers and with almost equal couplings to the currents). The Z_c(4025) or Z_c(4040) state can be fitted with the D*_0D_1 molecule having a mass 4023(130) MeV while the Z_cs bump around 4.1 GeV can be likely due to the (D^*_s0D_1+ D^*_0D_s1) molecules. The Z_c(4430) can be a radial excitation of the Z_c(3900) weakly coupled to the current, while all strongly coupled ones are in the region (5634-6527) MeV. The double strange tetramole state T_css which one may identify with the future Z_css is predicted to be at 4064(46) MeV. It is remarkable to notice the regular mass-spliitings of the tetramoles due to SU(3) breakings M_{T_cs}-M_{T_c}= M_{T_css}-M_{T_cs= (73- 91) MeV.
Assuming the newly observed $Z_c(3900)$ to be a molecular state of $Dbar D^*(D^{*} bar D)$, we calculate the partial widths of $Z_c(3900)to J/psi+pi;; psi+pi;; eta_c+rho$ and $Dbar D^*$ within the light front model (LFM). $Z_c(3900)to J/psi+pi$ is the channel by which $Z_c(3900)$ was observed, our calculation indicates that it is indeed one of the dominant modes whose width can be in the range of a few MeV depending on the model parameters. Similar to $Z_b$ and $Z_b$, Voloshin suggested that there should be a resonance $Z_c$ at 4030 MeV which can be a molecular state of $D^*bar D^*$. Then we go on calculating its decay rates to all the aforementioned final states and as well the $D^*bar D^*$. It is found that if $Z_c(3900)$ is a molecular state of ${1oversqrt 2}(Dbar D^*+D^*bar D)$, the partial width of $Z_c(3900)to Dbar D^*$ is rather small, but the rate of $Z_c(3900)topsi(2s)pi$ is even larger than $Z_c(3900)to J/psipi$. The implications are discussed and it is indicated that with the luminosity of BES and BELLE, the experiments may finally determine if $Z_c(3900)$ is a molecular state or a tetraquark.
The quantum chromodynamics (QCD) sum rules for the Delta baryons are analyzed by taking into account the finite-width effects, through explicit utilization of the Breit-Wigner shape. We apply a Monte-Carlo based analysis to the traditional and the parity-projected sum rules. The first Delta excitation state is also considered as a sub-continuum resonance and the widths are calculated using the mass values as input.
Using the QCD sum rules we test if the charmonium-like structure Y(4260), observed in the $J/psipipi$ invariant mass spectrum, can be described with a $J/psi f_0(980)$ molecular current with $J^{PC}=1^{--}$. We consider the contributions of condensates up to dimension six and we work at leading order in $alpha_s$. We keep terms which are linear in the strange quark mass $m_s$. The mass obtained for such state is $m_{Y}=(4.67pm 0.09)$ GeV, when the vector and scalar mesons are in color singlet configurations. We conclude that the proposed current can better describe the Y(4660) state that could be interpreted as a $Psi(2S) f_0(980)$ molecular state. We also use different $J^{PC}=1^{--}$ currents to study the recently observed $Y_b(10890)$ state. Our findings indicate that the $Y_b(10890)$ can be well described by a scalar-vector tetraquark current.
The saturation of QCD chiral sum rules of the Weinberg-type is analyzed using ALEPH and OPAL experimental data on the difference between vector and axial-vector correlators (V-A). The sum rules exhibit poor saturation up to current energies below the tau-lepton mass. A remarkable improvement is achieved by introducing integral kernels that vanish at the upper limit of integration. The method is used to determine the value of the finite remainder of the (V-A) correlator, and its first derivative, at zero momentum: $bar{Pi}(0) = - 4 bar{L}_{10} = 0.0257 pm 0.0003 ,$ and $bar{Pi}^{prime}(0) = 0.065 pm 0.007 {GeV}^{-2}$. The dimension $d=6$ and $d=8$ vacuum condensates in the Operator Product Expansion are also determined: $<{cal {O}}_{6}> = -(0.004 pm 0.001) {GeV}^6,$ and $<{cal {O}}_{8}> = -(0.001 pm 0.006) {GeV}^8.$
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