Tetraquark-adequate QCD sum rules for quark-exchange processes

Abstract

1 A caveat about subtleties in the application of the SVZ sum rules to exotic states has been raised in [9], where it was noticed that, depending on the way one treats the contributions of twohadron states on the phenomenological side of the QCD sum rule, one arrives at different assignments of the pentaquark quantum numbers. The origin of this problem, however, was not clarified.

Analysis of the hidden-charm tetraquark mass spectrum with the QCD sum rules

“…The contributions at the order Oðα k s Þ with k ≤ 1, which are factorizable in the color space, are exactly canceled out by the two-meson scattering states at the hadron side. The nonfactorizable diagrams, if they have a Landau singularity, begin to make contributions to the (1 c 1 c -type) tetraquark states and the (1 c 1 c -type) tetraquark states begin to receive contributions at the order Oðα 2 s Þ [36]. In Ref.…”

Triply-charmed dibaryon states or two-baryon scattering states from QCD sum rules

“…From the quark-gluon operators qg s Gqqg s Gq, we can obtain the vacuum condensate hqg s σGqi 2 , the g 2 s ¼ 4πα s is absorbed into the vacuum condensate, so the diagrams in Fig. 2 [24,25]. While from other diagrams in Fig.…”

“…In the similar systems, the four-quark systems, Lucha, Melikhov, and Sazdjian assert that the contributions at the order Oðα k s Þ with k ≤ 1 in the operator product expansion, which are factorizable (or disconnected) in the color space, are exactly canceled out by the two-meson scattering states at the hadron side, the connected (or nonfactorizable) Feynman diagrams appear at the order Oðα 2 s Þ, if have a Landau singularity, begin to make contributions to the tetraquark state or tetraquark molecular state [24,25].…”

“…If we insist on applying the Landau equation to study the tetraquark molecular states [24,25], we should choose the pole mass to warrant that there exists a pole which corresponds to the mass-shell in pure perturbative calculations. In the case of the c-quark, the pole massm c ¼ 1.67 AE 0.07 GeV from the Particle Data Group [30], 2m c ¼ 3.34 AE 0.14 GeV > m η c and m J=ψ .…”

“…The QCD sum rules approach is a powerful nonperturbative tool in studying the ground state tetraquark states, tetraquark molecular states, pentaquark states, pentaquark molecular states, and has given many successful descriptions of the hadronic parameters, such as the masses and decay widths [16][17][18][19][20][21][22][23]. However, a different voice arises, Lucha, Melikhov, and Sazdjian assert that the QCD sum rules are misused to study the tetraquark or molecule masses, all the four-quark currents can be rearranged into the color-singlet-color-singlet type currents, the contributions at the order Oðα k s Þ with k ≤ 1 in the operator product expansion, which are factorizable in the color space, are exactly canceled out by the two-meson scattering states at the hadron side, the tetraquark molecular states begin to receive contributions at the order Oðα 2 s Þ [24,25]. The tetraquark molecular states are two-meson bound states or resonant states in contrast to the two-meson scattering states.…”