In "Landau equation and QCD sum rules for the tetraquark molecular states", I list out six reasons to refute the assertion of Lucha, Melikhov and Sazdjian. In "Comment on "Landau equation and QCD sum rules for the tetraquark molecular states"", they refute my viewpoint. If they want to the refute my viewpoint robustly, they should refute the six reasons one by one, and provide at least one example to illustrate that they have obtained reliable QCD sum rules for the tetraquark states and free two-meson states, respectively.
Recently, a QCD sum-rule analysis of tetraquark molecular states has been published, having the objective of demonstrating that our previously formulated tetraquark-adequate QCD sum rules are not correct. This comment brings to the attention of the reader inconsistencies in that article and explains some subtle details of QCD sum rules for exotic states.
Without excluding the contributions of factorizable Feynman diagrams in the color space to the QCD sum rules by hand, we cannot obtain the conclusion that the factorizable parts of the operator product expansion series cannot have any relationship to the possible tetraquark bound states. The tetraquark couplings $f_T$ are of the order $\mathcal{O}(N_c)$ rather than of the order $\mathcal{O}(N^0_c)$ in the large $N_c$ limit, the conclusion "a possible exotic tetraquark state may appear only in $N_c$-subleading contributions to the QCD Green functions" is a paradox.
Comment on "Tetraquarks as diquark-antidiquark bound systems"
本文认为，在M. Monemzadeh等人，Phys. Lett. B { \bf 741}，124（2015）不正确。我们重新检查了所有已发表的结果，我们认为不仅报告的总角动量为零的四夸克态的质量不正确，而且报告的总角动量非零的状态的质量也具有相当的误导性，因为这些状态无法通过自旋独立形式主义来预测。
The quarks and gluons are confined objects, they cannot be put on the mass-shell, it is questionable to apply the Landau equation to study the Feynman diagrams in the QCD sum rules. Furthermore, we carry out the operator product expansion in the deep Euclidean region $p^2\to -\infty$, where the Landau singularities cannot exist. The Landau equation servers as a kinematical equation in the momentum space, and is independent on the factorizable and nonfactorizable properties of the Feynman diagrams in the color space. The meson-meson scattering state and tetraquark molecular state both have four…
The properties of possibly existing tetraquarks are studied in the large-$N_{\mathrm{c}}^{}$ limit of QCD by means of four-point correlation functions of meson currents.The necessity of a detailed analysis of the singularities of Feynman diagrams, by means of the Landau equations, to recognize those diagrams that might contribute to the formation of tetraquark states, is emphasized. It is found, in general, that tetraquarks, if they exist, should have narrow widths of the order of $N_{\mathrm{c}}^{-2}$.
In Phys. Rev. {\bf D103} (2021) 074015 (arXiv:2101.07281), huge (or largest) mass gaps between the ground states and first radial excited states for the tetraquark molecular states are obtained, $Δ=1.70\sim 2.35\,\rm{GeV}$. We explore the problems in the operator product expansion, Borel windows, etc, in details.
In a recent paper by N. Santowsky et al. [Phys. Rev. D 102, 056014 (2020)], covariant coupled equations were derived to describe a tetraquark in terms of a mix of four-quark states $2q 2\bar{q}$ and two-quark states $q\bar{q}$. These equations were expressed in terms of vertices describing the disintegration of a tetraquark into identical two-meson states, into a diquark-antidiquark pair, and into a quark-antiquark pair. We show that these equations are inconsistent as they imply a $q\bar{q}$ Bethe-Salpeter kernel that is $q\bar{q}$-reducible.
We briefly report the modern status of heavy quark sum rules (HQSR) based on stability criteria by emphasizing the recent progresses for determining the QCD parameters (alpha_s, m_{c,b} and gluon condensates)where their correlations have been taken into account. The results: alpha_s(M_Z)=0.1181(16)(3), m_c(m_c)=1286(16) MeV, m_b(m_b)=4202(7) MeV,<alpha_s G^2> = (6.49+-0.35)10^-2 GeV^4, < g^3 G^3 >= (8.2+-1.0) GeV^2 <alpha_s G^2> and the ones from recent light quark sum rules are summarized in Table 2. One can notice that the SVZ value of <alpha_s G^2> has been underestimated by a factor 1.6, <…
