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Register a new userFinite-width effects on Delta baryons in QCD Sum Rules
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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.
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We study the triply heavy baryons $Omega_{QQQ}$ $(Q=c, b)$ in the QCD sum rules by performing the first calculation of the next-to-leading order (NLO) contribution to the perturbative QCD part of the correlation functions. Compared with the leading order (LO) result, the NLO contribution is found to be very important to the $Omega_{QQQ}$. This is because the NLO not only results in a large correction, but also reduces the parameter dependence, making the Borel platform more distinct, especially for the $Omega_{bbb}$ in the $overline{rm{MS}}$ scheme, where the platform appears only at NLO but not at LO. Particularly, owing to the inclusion of the NLO contribution, the renormalization schemes ($bar {MS}$ and On-Shell) dependence and the scale dependence are significantly reduced. Consequently, after including the NLO contribution to the perturbative part in the QCD sum rules, the masses are estimated to be $4.53^{+0.26}_{-0.11}$ GeV for $Omega_{ccc}$ and $14.27^{+0.33}_{-0.32}$ GeV for $Omega_{bbb}$, where the results are obtained at $mu=M_B$ with errors including those from the variation of the renormalization scale $mu$ in the range $(0.8-1.2) M_B$. A careful study of the $mu$ dependence in a wide range is further performed, which shows that the LO results are very sensitive to the choice of $mu$ whereas the NLO results are considerably better. In addition to the $mu=M_B$ result, a more stable value, (4.75-4.80) GeV, for the $Omega_{ccc}$ mass is found in the range of $mu=(1.2-2.0) M_B$, which should be viewed as a more relevant prediction in our NLO approach because of $mu$ dependence.
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.
The method of QCD sum rules at finite temperature is reviewed, with emphasis on recent results. These include predictions for the survival of charmonium and bottonium states, at and beyond the critical temperature for de-confinement, as later confirmed by lattice QCD simulations. Also included are determinations in the light-quark vector and axial-vector channels, allowing to analyse the Weinberg sum rules, and predict the dimuon spectrum in heavy ion collisions in the region of the rho-meson. Also in this sector, the determination of the temperature behaviour of the up-down quark mass, together with the pion decay constant, will be described. Finally, an extension of the QCD sum rule method to incorporate finite baryon chemical potential is reviewed.
One of the advantages of the finite energy sum rules is the fact that every operator in the operator product expansion series can be selected individually by the use of an appropriate kernel function which removes other operator poles. This characteristic is maintained by QCD systems in the presence of external homogeneous magnetic field, providing interesting information about the magnetic evolution of QCD and hadronic parameters. In this work finite energy sum rules are applied on QCD in the light quark sector, combining axial and pseudoscalar channels in the presence of an external homogeneous magnetic field, obtaining the magnetic evolution of the light quark masses, pion mass, the pion decay constant, the gluon condensate and the continuum hadronic threshold.
Using general baryon interpolating fields $J_B$ for $B= N, Xi, Sigma, $ without derivative, we study QCD sum rules for meson-baryon couplings and their dependence on Dirac structures for the two-point correlation function with a meson $iint d^4x e^{iqx} bra 0|{rm T}[J_B(x)bar{J}_B(0)] |{cal M}(p)ket$. Three distinct Dirac structures are compared: $igamma_5$, $igamma_5fslash{p}$, and $gamma_5sigma_{mu u}q^mu p^ u$ structures. From the dependence of the OPE on general baryon interpolating fields, we propose criteria for choosing an appropriate Dirac structure for the coupling sum rules. The $gamma_5sigma_{mu u}q^mu p^ u$ sum rules satisfy the criteria while the $igamma_5$ sum rules beyond the chiral limit do not. For the $igamma_5fslash{p}$ sum rules, the large continuum contributions prohibit reliable prediction for the couplings. Thus, the $gamma_5sigma_{mu u}q^mu p^ u$ structure seems pertinent for realistic predictions. In the SU(3) limit, we identify the OPE terms responsible for the $F/D$ ratio. We then study the dependence of the ratio on the baryon interpolating fields. We conclude the ratio $F/D sim 0.6-0.8$ for appropriate choice of the interpolating fields.
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